the advantages which will manifestly accrue to this kingdom by abatement of interest from six to four per. cent culpeper, thomas, sir, 1626-1697. 1668 approx. 3 kb of xml-encoded text transcribed from 2 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2003-11 (eebo-tcp phase 1). a35404 wing c7554 estc r215465 99827330 99827330 31748 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a35404) transcribed from: (early english books online ; image set 31748) images scanned from microfilm: (early english books, 1641-1700 ; 1864:7) the advantages which will manifestly accrue to this kingdom by abatement of interest from six to four per. cent culpeper, thomas, sir, 1626-1697. 1 sheet ([1] p.) printed by t.l. for christopher wilkinson, at the black-boy over against st. dunstans church in fleetstreet, london : 1668. signed at end: t. c. (i.e. sir thomas culpeper). reproduction of the original in the goldsmiths' library, university of london. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng usury -england -early works to 1800. interest -england -early works to 1800. 2003-07 tcp assigned for keying and markup 2003-07 aptara keyed and coded from proquest page images 2003-08 sara gothard sampled and proofread 2003-08 sara gothard text and markup reviewed and edited 2003-10 pfs batch review (qc) and xml conversion the advantages which will manifestly accrue to this kingdom by abatement of interest from six to four per. cent. 1. it will inviolably establish the crown of england , by the advancement of his majesties customs the ease of his majesties subjects . the making of lands w ch are in safe hands the over-ballancing scale of wealth and power . 2 it will accommodate his majesty in his present wants even by a land tax if better expedients be not offered ▪ ) which the owner may well afford to admit of ( at least pro hâc vice ) being eased another way ; the slie usurer ( who could never yet be met with ) in effect contributing as much as he . 3. it willl in short time pay the debts of the whole gentry , by timely sales , and yet leave them ( one with another ) richer than they are . 4. it will make money so easie to be borrowed , that even the lender will shortlie pay the broker and coveyancer , by diminishing the number enlarging the securitie of borrowers . 5. it will speedilie double , if not treable , the yearly fruit , and product of our lands , ( the only solid basis of our wealth and trade ) by enabling , encouraging , and even forcing improvements of all kinds , whereby we may afford to under-sell our neighbours , who now under-sell us . 6. it will revive our dying manufacture , 〈◊〉 making the stock of it cheap , and the market quick . 7. it will plentifully relieve the poor , by setting all our heads and hands to work , in the countrie , for improvement of lands ; in cities and towns by way of manufacture . 8. it only can preserve the utter destruction of our timber . 9. it only can re-build london speedily , as to the publick , profitably as to the builder . all which assertions i am ready to prove to any man , that will discourse it with me fairly , closely , and methodically . t. c. london printed by t. l. for christopher wilkinson , at the black-boy over against st. dunstans church in fleetstreet . 1668. a short appendix to a late treatise concerning abatement of usury by the same author. culpeper, thomas, sir, 1626-1697. 1668 approx. 7 kb of xml-encoded text transcribed from 4 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2003-11 (eebo-tcp phase 1). a35411 wing c7563 estc r31353 11929498 ocm 11929498 51082 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a35411) transcribed from: (early english books online ; image set 51082) images scanned from microfilm: (early english books, 1641-1700 ; 1001:18) a short appendix to a late treatise concerning abatement of usury by the same author. culpeper, thomas, sir, 1626-1697. 7 p. printed by tho. leach for christopher wilkinson ..., london : 1668. attributed to thomas culpeper the younger by wing and nuc pre-1956 imprints. imperfect: pages stained and torn. reproduction of original in the university of illinois (urbana-champaign campus). library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng usury -england. interest -england. 2003-07 tcp assigned for keying and markup 2003-07 apex covantage keyed and coded from proquest page images 2003-08 mona logarbo sampled and proofread 2003-08 mona logarbo text and markup reviewed and edited 2003-10 pfs batch review (qc) and xml conversion a short appendix to a late treatise concerning abatement of usury . by the same author . london , printed by tho. leach , for christoper wilkinson , at the black-boy over against st. dunstans church in fleetstreet . 1668. a short appendix to a late treatise &c. since the publishing of my late treatise concerning usury , i have met with some objections , commonly urged with great vehemency , which ( though in themselves frivolous enough , yet that nothing may remain unanswered ) i shall briefly examine . 1. we are all charged with ingratitude to god , and murmuring at his goodness , in sending us such cheapness as we now enjoy ; 2. the people of england in general are taxed of incorrigible sloath : 3. the gentry in particular are branded for dissoluteness : betwixt these three , the usurer endeavours to shift all blame from himself , by laying it upon other shoulders . for the first of these , viz. our ingatitude to god , &c. surely we cannot thankfully enough acknowledge gods compassion towards us , in affording us cheapness at this season , it being the only hopeful sign we have left , that , he intends not , now , our destruction ; for if , to the calamities of war , pestilence , and fire , his justice had likewise added that of extreme dearth , how could we have supported it ? nevertheless it may concern us to enquire out the natural cause of our present cheapness ; for , if upon serious scrutiny it appear , we cannot impute it to the greatness of our late crops , but rather to the deadness of forein markets , being cloyed by others who had greater crops than we , and there ore undersel us ; we may have cause to apprehend ▪ that our present cheapness is almost a certain presage of future dearth : for surely , that our crops begin to fail , it is only because we cannot afford our lands their ordinary improvements , being discouraged both by unprofitable vent , and the high rate of our stock , which likewise forces us to sell at any price : now the progress of this decay will soon disable even our ordinary tillage : and meeting with the disasters incident to husbandry , may unawares expose us to extreme scarcity , when money , perhaps , will be as scarce as bread. the prices of grain and fodder , one year with another , are certainly better now , then they were thirty or forty years since ; yet our titheries , ( the model of our yearly growth ) generally decline in value ; and whence can this come , but from the impoverishment of our farms and farmours ? who , it seems are not able to manure their land , nor yet forbear the market ; since neither will answer interest , with the inconveniencys attending it , which are such ; that many farmours already can scarce afford to kill the moles and level the mole-hills in our best meadows . for the second , viz. the incorigible sloath of our people , i should unwillingly grant , that englishmen are not naturally more active and fit for labour than hollanders ; i suppose they have formerly given better proof of themselves in most occasions : but , alas , their encouragements are not equal ; the one sure , that he works for himself , the other almost as sure , that he works for his creditor : the labourer in the netherlands by steady employment , still hoping to grow rich , however forced to work and fare hard , because provisions are always dear ; in england ( betwixt dispair of thriving , and easiness of subsisting ) for the present wastful , careless of the future . for the third , viz. the dissoluteness of our gentry : methinks , it argues smal ingenuity in 〈…〉 first to oppress , and then reproach g 〈…〉 doth : let me therefore make their apology . of gentlemen , some have considerable estates , others have little : for such as have little , it will not i doubt , be easy , now a days , to find any employments , but derogatory in peace , or mercenary in war. object . but should they not betake themselves to one of the three faculties ? answ. 1. their friends , many of them are not able ; 2. themselves , some are not capable : 3. our professions , i fear are already full , even to overflowing : and if all must be divines , lawyers , or physitians , where are the patients , clyants , and cures ? of such as have estates , some are free from debt , others incumbred ; for the latter , i dare boldly say , that in many of their extravagancies , frailty is only accessory , usury is the principal . for the former , i would ask any sober man , how gentlemen , not naturally studious , ( as many sure are not ) shall spend their time : if they fall to husbandry , they are by many upbraided with rusticity , by more with imprudence , and perhaps both not altogether without cause ; for why should gentlemen usurp the farmours calling , or hope to thrive themselves , where tenants cannot . object . but might they not turn merchants ? answ. alas ! therein is our cheifest bane ; our trade is now most hazardous , and with all intricate ; for our own growth is certainly become a drugg , and little to be gotten by the sale of it , being undersold by three per cent ; even superfluity , though of better vent , will oft-times scarce answer charges , without stealing the duties , which are considerable in the price : so as gentlemen of estate being , in effect , excluded from all hope of profiting themselves by their industry , ( if they be not bookish ) sleep is , for ought i see , their cheapest employment , and company their manliest diversion . but were our estates by low interest rendred improvable , to the advantage both of our selves and the common-wealth , truly , he deserved not land , that wanted convenient businesse ; nor could he be excused from lachesse , that found not out , at worst , a comfortable provision . again , were trade , by abateing the rate of its stock , made generally gainfull , it would likewise soon grow transparent , so as we needed not dispair , without long apprentiship to comprehend it ; since , in holland , women , nay children now trade securely and profitably ; and then what should hinder ; but that all might be either principals or factors ? till improving of land be cheaper than purchasing , industry more beneficial than usury : till merchandising cease to be mysterious , and become familiar to us . we must never look to flourish . finis . a short addition to the observations concerning trade and interest of money by the same hand. child, josiah, sir, 1630-1699. 1668 approx. 19 kb of xml-encoded text transcribed from 7 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2004-05 (eebo-tcp phase 1). a32837 wing c3864 estc r23516 12071868 ocm 12071868 53494 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a32837) transcribed from: (early english books online ; image set 53494) images scanned from microfilm: (early english books, 1641-1700 ; 864:7) a short addition to the observations concerning trade and interest of money by the same hand. child, josiah, sir, 1630-1699. 3-14 p. printed for henry mortlock ..., london : 1668. reproduction of original in huntington library. attributed to sir josiah child. cf. nuc pre-1956. a continuation of his brief observations concerning trade, and interest of money. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng interest -early works to 1800. 2004-01 tcp assigned for keying and markup 2004-02 spi global keyed and coded from proquest page images 2004-03 mona logarbo sampled and proofread 2004-03 mona logarbo text and markup reviewed and edited 2004-04 pfs batch review (qc) and xml conversion a short addition to the observations concerning trade and interest of money . by the same hand . london , printed for henry mortlock , and are to be sold at the sign of the white heart in westminster hall 1668. a short addition to the observations concerning trade , and interest of money . objection i. as to that objection , that the low interest in holland , proceeds from their abundance of money , and not the force of laws : i think i have sufficently answered it already in my printed treatise : but this further may be said , which i knew not then : laws have done it here , as hath been proved ; and laws did do it there : for the very next year after intrest was brought from ten to eight per cent . in england , the dutch brought it by a placart or law to six per cent . in holland ; and the same year that the long parliament were about to bring it to six , they brought it to five per cent . this i have from an unerring hand : and i presume they have since brought it by a law to four per cent . but of that i know not . however of this i am certain , let the law bring it to five or four at this time , & the people of themselves , by encreasing the riches of the kingdom , will bring it to a lower ra●e ▪ which is manifest in all the progressions of nature . as for example : a poor man that by his labour can but just maintain his family , with much care and diligence ; if he have the good hap to light on a small stock of 50 or 100 l. or have so much given him ; upon that small foundation he may arrive to an estate of 1000 l. it may be 10000 l. and so i● often falls out : whereas without such an opportunity , he might have laboured all his days for bread onely . so it is in diseases in the body natural ; remove but the cause , take but away the shackles of nature , and she will soon recover strength and flesh : so take off the burthen from trade ( whereof none is so heavy as that of interest ) and the people will work out the rest to the prodigious increase of their riches , as the dutch have done . objection ii. another objection i have lately met with , is , that holland is but a small tract of land , and consequently land is dear there not because interest of money is low . i answer , this is a gross mistake : for land and interest of money are , all over the universe , like two buckets ; if one go up , the other must go down , and the contrary , whether it be a great or small territory ; as is evident in our own plantations , as well as in all other places of the world mentioned in the former treatise . ( viz. ) barbadoes is a small te●ritory , & the richest in the world , ordinary land being worth there 10 l. per ann . the acre ; use of mony by law is 15 l. per annum , and their plantations sell but at seven years purchase at most . new england is a country where the legal interest is eight per cent . and i am told they are now about bringing of it down to six per cent . there the plantations will sell at fourteen to fifteen years purchase , though it be a vast continent . in virginia interest is at fifteen per cent . and plantations sell not at above seven years purchase at most , and , which is more observable , all those places are not rich or poor according to the goodness of their soil , but exactly according to the rate of interest . barbadoes the richest land , hath the poorest people ; virginia the next best land , but a much poorer people than the new-english . new england incomparably is the worst land of the three , and yet the richest people of them all , and increasing dayly to a miracle , unto those that know not that by their laws about interest of money , they must necessarily suck the blood of the other two places , with whom they have a constant intercourse in trade ; which in effect is the same as if they lent them money . and the consequences of this to that island of barbadoes , are so visible and fatal , that if all the planters or owners of the territory of that island should now make up their accompts with the city of london , they would be found so much indebted to this city , that the sale of all their lands and goods to their very shirts , would not pay one half of what they owe. this i have reason to know , having as much experience of the trade of that place , and the condition of that people , as most merchants in london : and this i have asserted in the company of many of the most considerable barbadoes planters now in london , who have ingeniously confess'd it to be true : although most certain it is ▪ that the late sir iames drax , sir thomas muddiford , collonel birch now of giddy-hall in essex , and some few other planters , have arrived there to very great estates , after they could bring their affairs to such a consistency as to stem the desperate current of that interest , and row with the stream , by ceasing to borrow , and becoming lenders : it being the necessary and never-fayling consequence of a high interest all the world over , to inrich a very few , and impoverish all the rest of the nation : which was the true reason that we had in former times about half a dozen such as gresham , sutton , craven , and spencer ; but besides them , not one man of 10000 l. estate , for a hundred which we have now . objection iii. to that objection , that vsurers will call in their money if it be now brought to four per cent . whereas if it be brought but to five per cent . it is hoped ( by some gentleman ) that the vsurers will be more favourable . i think that objection is likewise fully answered in the printed treatise . but to inlarge a little further upon it , i premise the common usurers qualifications ; for of such only i speak in this place ( viz. ) he is always a sly , subtile , wary , covetous , timerous thrifty ( alias , miserable ) person , and commonly well striken in years ; and if this character be true , which i submit to the judgment of those that are better acquainted with them ; then i say it is impossible for the generality of usurers to call in their money , though it be brought to four per cent : to demonstrate this , i suppose the usurers to be of two sorts ( viz. ) the country vsurer , and the city vsurer . suppose likewise the law were past to reduce interest to four per cent , and see what the country vsurer will do ? very angry doubtless he will be ; but what then ? no question but he will threaten and talk of calling in his money , but being no fool but a subtile person ( as hath been said ) his prudence will prompt him to consider how to mend himself , by being possest of his money , and what to do with it when he hath it . trade , or run it by exchange he cannot , being too old to learn ; and too wise to be cheated ; as he must be sure to be ; if he precipitate himself into business he understands not : let it lie dead by him he dares not ; being possest already with several qualifications that will inhibit him ; insomuch , that if he should doe it , he must never after think of sleeping quietly ; his natural timerousness being such , that every noise he hears will put him into a panick fear of thieves come to rob him ; and his covetousness is such , that upon the very thoughts of having no use-money coming in , it will almost , if not altogether , break his heart ; and then his miserableness is such , that upon the frightful apparition of no income , or more properly the disappearance of all his incomes at once , it may be feared he will go near to starve himself . what other course then can he take ? i say there are but two left him in the world , viz. either to purchase lands , or improve those he hath . all lands after such a law will certainly advance six years purchase : so that new purchasers shall never , by buying lands , make 3 per cent . of their money , and in consequence , the usurers great subtilty that now directs him to t●ke 6 per cent . for his money , rather then buy lands at eighteen and ninteen years purchase , will then advise him to continue his money at four per cent , rather then buy lands at twenty six years purchase , which he must give after the making of this law. for improvement of his own lands , if he take to that , i will not offer a word to hinder him ; he may certainly make the best profit that way , after this law : but what shall be called in to that purpose , i know , cannot much affect gentlemen in debt , because the use-money the usurers receive , will be sufficient to carry on that work , being a gradual expence without calling in the principal . the city vsurer differs from the country vsurer only in this , that he hath formerly had some experience of trade , and hath now the opportunity of laying out his money by building , which the country usurer hath not . for the first ( viz. ) trade , they have been so long out of it , that very few of them will now settle to it again themselves , but they will bring up their children to it , which otherwise they would not have done . for building , i know many of them will be doing in that , but that likewise is a gradual expence , somewhat like improvement of lands , and the great usurers may build annually as much as it is convenient for one man to have in hand at one time , upon the receipt of their growing interest only , that is let out upon personal security . further , i do affirm catigorically , that in all parts of the world where-●ver interest of money is lowest ; securities are safest to the lenders , and easiest to the borrowers , and were-ever interest of money runs high , they are more dangerous to the lenders , and difficult to the borrowers . whither this be true or no universally , i appeal to the experience and observation of all travelers and merchants , so far as the teder of my conversation hath suffered me to range , i am sure it never failed . for instance ; in barbadoes , it is a more difficult thing to take up 100 l. vallew in sugar ( which is the money of that country ) at 15 per cent . then it is to take up 1000 l. at 6 per cent . in england ; the like is in tobacco in virginia . in ireland the like , at the rate of that country ; with this also that whoever can be credited for 1000 l. there must give 4000 l. worth of land for security ; whereas 2000 l. worth of land is esteemed in england a good security for 1000 l. money at 6 per cent . in holland , likewise any man that is a competent good husband , prudent and careful in his business , may take up 500 l. or 1000 l. at 3 per cent . upon his own note only , whereas in england where the present rate is double , the usurers require three good mens bonds at the least , for 500 l. at 6 per cent . which safety to the usurer and ease of giving security by the borrower , must needs proceed from the lowness of the rate , because the usurer being a crafty fox , knows that 6 per cent , will certainly impovrish the gentlemen ; and weaken the merchant and tradesman , if they take up much at interest , and the rather , because he knows the merchant must beyond the seas meet with a dutch competitor , that hath his money at 3 per cent . and therefore is so wise as to have two or three securities , that if one be undone , he may have time enough to force in his money from the rest before they be all ruined : whereas when money is here at four per cent , the usurer that hath his money out at present upon mortgages , will find his security he already hath bettered , and therefore it will be his wisdom to continue it , that land being then worth 2600 l. which is now worth but 2000 l. and the merchant or tradesmen tha● he knew six per cent . would ruine , may subsist under four per cent . and consequently the usurer will not be so jealous of his standing , as it appears they are not in holland , because that at a low rate they may live comfortably , that must break at a high . objection 4. there is another objection , which i may properly call the vsurers objection , for i commonly meet with it from them ( viz. ) they say all the money in the nation is imployed ; and although they imploy it not themselves , they lend to others that do , and more cannot be imployed then we have , though interest were at three or two per cent . i answer , that no money is imployed to the advantage of any kingdom ; but that only which is imployed in forreign trade , or by artificers , and in manufacture , or improvement of land. and that no money is or can be imployed in those profitable ways , but so much only as we can make above six per cent . of , as for example : a merchant in london that hath an estate of 30000 l. or 40000 l. can hardly imploy with all his art and skil above one fourth , or half at most of his said stock in forreign trade to make above six per cent . because all other trades that afford a less profit ( all hazards considered ) are supplied by the dutch , and must necessarily be so till interest of money be abated . whereas , were interest of money here at four per cent . merchants own wisdom would induce them to trade with all their stocks ; or at least so much as they could make a greater gain of then four per cent . which would be just one third more then is now imployed in forreign trade , or those other profitable imployments to the kingdom . objection , 5. another objection i frequently meet with , which i may not improperly call the merchants obiection , because it generally comes from them ( and their language and designs i may pretend in part to understand , if i understand any thing at all . ) the said obiection is , that we have already so many traders , and so much stock imployed in trade , that we can scarce live by what we do ; and if we should bring a greater stock into trade , which the sequel of this law will do ; and multiply traders , no trade will be worth the following . before i answer this objection , i must do right to my fellow citizens and merchants , in confessing that although at the first starting of this controversie in publick discourses ; above ninetenths of all those i conversed with were against it ; yet that since , upon reading and hearing what hath been said and printed for it , above three fourth parts of all those i have had communication with , are come over to acknowledge . that the abatement of interest from six to four per cent . will be a real advantage to the kingdom in general . but further , to satisfie such as are yet in doubt , i say , those merchants that have great stocks , and would have interest continued at six per cent . if they prefer their own private gain to the common good , they are in the right as to themselves ; for the abatement of interest will certainly and necessarily increase industry and good husbandry ; it will as certainly multiply traders and stock in trade , and in consequence the gain of the present merchant who employs his own stock , and lends to others , will be the less . but he must be wilfully blind that cannot see the advantage of the king and kingdom will be the more , by the multiplication of merchants , and increase of stock in trade , the effect & success whereof in this particular ( as already it hath been ) will be mathematically the same as in the advance of land , viz. all the land of this kingdom will be advanced one third in value ; and the very same properties will the gain of the kingdom be advanced by the increase of trade and traders : onely with this difference : every individual gentleman now possest of lands will receive his proportional benefit thereby presently ; whereas the benefit by trade will redound to the king and kingdom in general , and not to the particular advantage of any of the present merchants , except such onely as pay interest for all or part of their stock in trade . but the rest of merchants who receive not a present benefit , will partake of the future advantage thereof to themselves and children in common with their country : which when well weighed and meditated upon , i am perswaded will convince those worthy merchants that are yet unreconciled to this principle . query . but here it may be said , how shall we increase our trade , when we cannot get by what we have already ? if it be seriously considered , this question is answered in what i have before said . but further to explain it : the dutch drive a great trade in salt from rochel , st. vvals , and other places , to the baltick seas ; by which , if they can get eight or nine per cent . they are very well content : we , while money is at six per cent . cannot live on so small a profit as is the surplusage of that above the interest and in consequence we look not after it , but rather choose to put out our money at six per cent . whereas were money with us at four per cent . we should then be content with the surplusage of that profit , and follow it closely . but if it be here objected , from what i formerly published , that we have no such bulky ships to sail with little charge as the dutch have : i answer , we are composed of the same elements as they are , and have hands and heads as well as they ; and that a low interest is the cause of these and many other profi●able engines , which they work withal . and that he hath not half considered this point , who doth not know infallibly , that a low interest is a spur to invention as well as industry and good husbandry : nay further , that it multiplies men , as well as increaseth trade in any nation , the latter naturally generating the former . finis . several objections against the reducement of interest propounded in a letter with the answer thereunto. culpeper, thomas, sir, 1626-1697. 1671 approx. 19 kb of xml-encoded text transcribed from 5 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2004-03 (eebo-tcp phase 1). a35410 wing c7562 estc r24113 07952008 ocm 07952008 40688 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a35410) transcribed from: (early english books online ; image set 40688) images scanned from microfilm: (early english books, 1641-1700 ; 1205:3) several objections against the reducement of interest propounded in a letter with the answer thereunto. culpeper, thomas, sir, 1626-1697. brown, ignatius, 1630-1679. r. w. 6 p. [s.n.], london : printed in the year, 1671. consists of two letters signed, i.s., and r.w., respectively. attributed by wing to t. culpeper. reproduction of original in the huntington library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng interest -great britain. 2003-07 tcp assigned for keying and markup 2003-07 aptara keyed and coded from proquest page images 2004-01 emma (leeson) huber sampled and proofread 2004-01 emma (leeson) huber text and markup reviewed and edited 2004-02 pfs batch review (qc) and xml conversion several objections against the reducement of interest propounded in a letter , with the answer thereunto . london , printed in the year , mdclxxi . several objections against the reducement of interest ; propounded in a letter , with the answer thereunto . sir , by divers persons whom i have spoken with upon your late argument ▪ i find , that the main of your discourse is either granted or faintly controverted , very few directly denying the rise of land by the fall of interest , but rather , as it were , confessing and avoiding it : they say , it holds in the notion , but fayles in the practise ; being clogged with divers appendant inconveniencies , which either wholly frustrate its good success , or overballance it with other and worse effects , the grand objections are these ; some affirm , it will have no influence at all ; whatsoever is defalked from interest will be more then supplied in gratuities ; brokage , new devices for security , &c. according to the old saying , necessity hath no law : some alledge , that since it is now so hard to borrow at six per cent. it will be almost impossible at four , because men will rather keep their monies in their ch●sts , then run so great a hazard , ( as lenders they say now do , ) for so small a profit , by others , it is offered by way of grave and friendly advice to borrowers , that they take heed what they do , for most will be driven upon purchasing and other dealings , and so their debts generally and ruinously called in , i desire to be clear in this argument , that so i may be able to maintain it , and therefore your resolution herein will much oblige sir , your most humble servant , i s. sir , i am glad to find , that the maintainers of our present rate of interest , being driven from their main defences , betake themselves to such shifts and colours ; it shews . they would only seem to say somewhat , which in popular causes , they think may p●ss for reason : in the first place , they tell us the legal restraint of interest at this time will prove abortive , law being subordinate to necessity ; but if not now , say i , when may it take effect ? surely never , since when borrowers are few it needs not , when many , belike it boots not . might not this exception be equally taken against most of our coercive laws ? and were it not reasonably answered by demanding the experiment ? especially since the benefits promised by its success are so many and great , and the evils threatned from its miscarriage so few and flender . yet in regard of the stress it bears , i shall further examine its strength and substance : first , methinks these objectours do a little prevaricate , for if they believed themselves , they might spare their opposition , and as persons unconcerned , ●eely give it their passport . secondly , let them reflect , whether the same argument , having been as confidently urged against eight per cent. be not sufficiently soyled ; and whether though some necessitous borrowers have been shrewdly bitten by extortion , ( as some ever were and will be ) yet thousands , who otherwise had certainly paid higher rates , have not borrowed at six per cent. and reaped such benefit by those reducements , as without other unequal payments , would alone have enriched , or at least fairly relieved them . thirdly , my errour , if such , is however charitable , in judging better of creditours , then it seems they do of themselves ; for whereas they are h●reby represented as contemners of authority , i rather admit them to be persons of strict obedience and great caution , presuming they will now , ( as formerly most of them have done ) observe that law , from which they challenge their only protection and warrant fourthly , paenal laws are like large nets ; chiefly designed to catch the great fish ; some frie will escape , and it matters not greatly here though they do , for single extortions weigh little in this ballance , it is the steady rate of interest , which coming clear into the lenders own purse , and in ease and certainty far surpassing other courses , quite turns the scale on that side , so as the abatement thereof must even naturally buoy up our lands . lastly , it seems more then morally certain , that the same land which is now accepted for the loan of a thousand pounds at six pawnes ipso facto for fifteen hundred at four per cent. ( there being no other imaginable standard for mortgages and consequently for sales ) then the computing of rent with interest ) whereby security will be restored ; and vastly enlarged , and the land ( acquiring as it were a new fund ) will lightly carry that burthen , which it now hardly bears , soon shake of its fetters , and in time turn extortion quite out of doors . the second objection , namely , that if interest be abated , men will hoard up their monies , seems only considerable from the quality of those that urge it ; who are some of them wise men , and too wise i doubt , too mean as they speak : i might again refer them to former experience , since this likewise within our memorie hath been once disproved ; not one that ever i heard of having kept any considerable stock dead for the smallness of that revenue , but too many being even charmed with the sweetness of it insomuch as i have lately known divers , who upon the overture of a convenient purchase , consulting their pillows , and perceiving , ( as needs they must if they do no● wink ) the present disparity betwixt interest and rent , have parted abruptly ; neither indeed have i observed any such treaty which this estimate did not govern , sometime● to the utter disappointment , alwayes to the notable pre●●dice of the seller . surel● the greater danger is . that too many will still continue t● lend at four per cent. with improved security , rather then otherwise get less with trouble and hazard : but tha● any should ruinously keep in their stock● to no account , seems too panick a fear , if either we consider the reason of the thing , or temper of the persons : the owner of land in this fall and casualty of rents , being generally a looser accomptant of his advantage , were likelier to incur this prejudice ; and better he might in prudence justifie his preferring some present want of revenue before the disparagement of his land : he might with good colour pretend , it hath been overtilled and wants resting ; that a low rent will scarce countervail the spoil commonly committed by tenants at will , and short termours : however he knows the worst , and that he cannot be robbed of his land : yet how few farms do we see vacant , where the owner is not either by misfortunes distant of abode , or other more pressing occasions disabled or diverted from the best managery ? might we not judge him worthier of a guardian then a freehold , who having land , and not wanting other requisites , should for any considerable time , both perversely refuse to let , and carelesly neglect to stock it ? much more absurd were it for monied men ( no way obstructed ) neither to lend nor employ their stocks ; and therefore to be presumed , that persons so wise in their generation , will not starve for lack of a feast , and ruine themselves to incommode some body . nothing is so like to interrupt the free course of lending ( or at least dealing ) as the unsoundness of credit , and scarceness of security , which are evidently improved by law , but undermined by high interest : for that which we call money lent being upon the matter nothing else , but credit from the lender to the borrower , and security from the borrower to the lender , ( as i have occasion often to repeat , and as appears not only by that e●cellent law and practice of transferring debts in holland , but even by daily proof among our selves , where a small note , nay a promise , frequently serves to represent the payment of a considerable sum ) plenty or scarcity of current security and credit , ( the manifest effect of high or low interest , ) must needs cause plenty or scarcity of current money . besides the loan of money corresponds in good measure with letting of land : now the landlord that lets good penny worths seldome wants substantial tenants , who , commonly thriveing , pay their rents punctually , and challenging a kind of tenant right , securely repair and improve as upon their own free-hold : whereas hard landlord's are generally and justly met with by hinderly and troublesome farmers , and have their estates often and ruinously turned into , and lying on their hands . upon the same grounds of reason , may we not observe , that even in this low ebb of credit , such as are known to have sound estates , and noted to be current paymasters , shall oftimes be trusted , upon much easier then the common terms of lending ; as on the other side , those that accept low interest , pick and chuse their security . and is it not most pregnant but withal most evident , that wheresoever trade is clogged with high interest , there is no end of pledges and extreme cautions ▪ where the rate is tolerable there appears little use or need of them , fame it self in effect serving as the common surety for borrowers , and few that have a name of honesty wanting convenient credit ? admit then for arguments sake , the land of this kingdom most of it to be vastly over-letten , so as no usual husbandry could raise near the rent of it ▪ ( and whether this be not now too like ●●e case of borrowing at six per cent. i appeal to the sad experience of all those , either l●ndlords or tenants , whose misfortune it hath been of late considerably to borrow , ) what could thence ens●e , but such a decay of farmers , failer of payments ▪ and dearth of fair dealing on all sides , as must needs speedily tend to publick ruine ? wherefore i ●onclude , that sober creditours , who propound not to themselves the lucre of meer extortion , though for their ease and benefit they chuse interest money as their livelihood , yet ( if they will give themselves leave and leisure to think , ) cannot but prefer four and even three freely payd and fully secured , before six nay eight per cent. ventured upon the stretch of security and credit , torne piecemeal from their debtours , with such breach of friendship and charity , such ill natured arrests , seisures , entries , shifts , hazard● , charges , and delayes , as now do , and must every day more and more attend those contracts ; and consequently that the moderating of interest to a rate , which the land may comfortably bear , is the only means now left for men to lend safely , borrow easily , and pay duely , costly experience , will some say , may in time rectifie all , when most that borrow do not pay , , and few that pay borrow : when our great and numerous incumbrances expiring and discharging themselves in the ruine of most borrowers and too many lenders , credit and security shall sink together , as they fairly begin to do , and our disease abate for want of humour to feed it : but truly i cannot fancy this remedy , which too much resembles the decay of nature , and in stead of real comfort faintly bids us hope , that when things are at the worst they may mend . their last argument importing the danger of calling in sums unseasonably by such as being abridged of their former income will endeavour otherwise to repair their loss , to the great inconvenience of borrowers , presents more shrewdly to those at least , who spie not its fallacy and self-contradiction : for quitting all publick considerations ; and yielding , as it were the main dispute , it craftily insinuates it self , and whispers singly to every borrower this seemingly pertinent question , what then will become of you , when all your debts shall be called in together ? now this meeting with the natural ●w of borrowers , frights many of them into a palsie ; and the more unreasonable it is , perhaps the more unanswerable , since for a groundless and extravagant fear , no humane wisdom can provide : thus are the maintainers of this policy furnished with arguments of all kinds and colours , accommodated to every purpose ; to the sender they suggest , that they visibly loose one third of their revenue , without any hope of recompence , for that all the improvements from thence expected are silly projects ; to the borrower , that however , in the end it may fare with the publick , yet they , to be sure will in the mean time be undone , by a general calling in of sums to purchase land ; to persons more indifferent , as not greatly or immediately concerned in either condition , that abatement of interest by law wil never in any degree answer what is expected from it ; for such as have power will use it as they list , and no man be induced to purchase or trade one whit the sooner ; to vulgar capacities , that our rich men will hoard , our best stocks lie dead , and there will scarce be any lending . to reconcile these were indeed a masterpiece of wit : but in the mean time , such shifting of scenes and shuffling of notions ( so inconsistent , ) notably serves to amuse the unwary and embroyle discourse which in popular causes , as i said before , proves oftimes a dextrous way of arguing ▪ the only way therefore to deal with such a proteus is to confront his several arguments , and hold him strictly to the point , which an unsound thesis will scarce abide for instance , how comes the note to be so changed say i ? it was once alledged that lenders would still use their own discretion , and take no notice of any law for restraint ; the● in another vein , most men would be so sullen , as neither to purchase nor lend ; now in full career , and , as it were in some grand conspiracy ( for plots must be all along presumed ) all will call in their sums together and be dealing : what a sure bow is this that hath so many and so able strings ! but is there no medium betwixt these extreams ? are there not in the world persons of different condition , genius , nay humour ? are there not many by their education or present capacity qualified only to live upon interest ? are there not others , who being either affected with thrifty retirement , or enured to the ease and immunity of good towns , nay , addicted to special fraternities and cabales , are so wedded to it , that a sentence of the spiritual court would scarce divorce them ? are there not yet others , who being engaged in callings and employments scarce consistent with countrey affairs or forrain traffick , may prudently enough continue to lend at a lower rate , rather then entangle them with such variety of concernments ? and may there still be good store of those , who meerly guided by their natural arithmetick , do now betake themselves to interest for its many present advantages , but were the tide and stream of profit turned , would certainly row and sayle with it ? he that was sent to discover the strength of the french-army at agencourt , ●eturned with this auspicious verdict , that there were enough to kill , to take , and to ●scape by flight . so were the gain of lending now reduced to a nearer correspondence with that of other dealings , by the same good omen , it might soon appear , that among our legions of creditours , there would be enough greatly to raise the value of our lands ●y purchasing ; enough , vastly to agument the bulk of our commerce by trading , and ●et enough , if not too many to lend at interest : however our comfort is , they would ●en , live , and let live , this being the principal end herein aimed at , and indeed most ●●portant to the commonwealth , that such as will not use their own stock , may , ( if not ●or private conscience , yet for publick good , ) afford a pennyworth to those that manage for them , of whom it is certain , that now ( in husbandry at least , ) not one of twenty ●oth , or can , with his best condu●● , thrive , but in truth this objection of prejudicing ●ebtours , by the sudden and general calling in of sums for better employment , answers it ●elf by granting all that is required : for who sees not , that such a summons necessarily im●orts great store of purchasing whereby the market of our lands would be exceeding ●ickned , all that have estates to more in value then their debts , abundantly gratified for ●eir trouble , if any they should receive , and enabled to relieve themselves by ●onvenient sale ; and the gentry being this in good measure disenthralled ; bor●●wing would soon become more easie and tolerable to tradesmen , who now ●●stly complain , that credit is almost engrossed by land : certainly the notion of rui●●ng borrowers by abatement of interest , ( if the parties concerned would vouchsafe to ●●nsider it , ) is not much unlike that of undoing tenants by letting them good penny●orths , and punishing landlords with ease of their taxes . it were not unreasonable to suppose , that well-advised creditours , finding they can●●t mend their rate , liking their security , and naturally both fearing hazard and loath●●g trouble , ( perhaps the most of any , ) would be as backward to demand their princi●● , as borrowers to provide it , since the difficulty of well placing a sum proves commonly ●ow a dayes equal in effect with that of procuring it ( so generally do credit and secu●y go hand in hand , being , as was said before , perfect relatives : ) yet to leave nothing considered , but even , if possible , prevent the doubts of all such as do not either affectedly ●take scruple for wisdom , or are naturally afraid of their own shadows , whom miracles ●ly can convince , i refer the unsatisfied to the wise provision and president of former ●tutes for abatement of interest , whereby the reducement takes place only in new and succeeding contracts , the former rate being still permitted , where the security is no● altered ; upon which account much credit in this kingdome is yet legally continued ● eight per cent . if not to the profit , yet to the presumed ease of borrowers , in whose option it rests ; thus would the wise lender be further bribed so compliance as it were with the yearly brokage of two per cent. debtours that have , or can procure credit would be forthwith considerably relieved in their constant payments , others equally 〈◊〉 their trouble , and necessary charges , and the suffering , in comparison of the gaining bo●rowers , must needs be , ( if any ) not one to a hundred . having thus , as briefly 〈◊〉 i could , delivered you my sense , i remain . sir , your faithfull servant . r. w. finis . a tract against vsurie. presented to the high court of parliament. culpeper, thomas, sir, 1578-1662. 1621 approx. 25 kb of xml-encoded text transcribed from 11 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2003-11 (eebo-tcp phase 1). a19689 stc 6108 estc s109127 99844777 99844777 9619 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books, 1475-1640 ; 830:12. (eebo-tcp ; phase 1, no. a19689) transcribed from: (early english books online ; image set 9619) images scanned from microfilm: (early english books, 1475-1640; 830:12). a tract against vsurie. presented to the high court of parliament. culpeper, thomas, sir, 1578-1662. 21, [3] p. printed by w[illiam] i[aggard] for walter burre, and are to be sold at his shop in paules church-yard, at the signe of the crane, london : 1621. anonymous. by sir thomas culpeper. printer's name from stc. the last leaf is blank. in this edition the page numbering commences 3,6,7,6; second line of imprint ends: are. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng interest rates -great britain -early works to 1800. 2003-07 tcp assigned for keying and markup 2003-07 apex covantage keyed and coded from proquest page images 2003-08 mona logarbo sampled and proofread 2003-08 mona logarbo text and markup reviewed and edited 2003-10 pfs batch review (qc) and xml conversion a tract against vsvrie . presented to the high court of parliament . heb ddiev heb ddim printer's or publisher's device london , printed by w. i. for walter burre , and are to be sold at his shop in paules church-yard , at the signe of the crane . 1621. to leaue the proofes of the vnlawfulnesse of vsurie to diuines , wherein a number , as well protestants as papists haue learnedly written ; heere is onely set downe some arguments to shew how great the hurt is it doth to this kingdome which hath no gold nor siluer mines , but plenty of commodities , and many and great aduantages of trade to which the high rate of vsury is a great preiudice and decay . for proofe , how much the high rate of vsury decayes trade ; we see that generally all merchants when they haue gotten any great wealth , leaue trading and fall to vsury , the gaine thereof being so easie , certain , and great : whereas in other countries , where vsury is at a lower rate , and thereby lands deerer to purchase , they continue merchants from generation to generation to enrich themselues and the state. neyther are they rich trades-men onely that giue ouer trading , but a number of beginners are vndone or discouraged by the high rate of vsury , their industry seruing but to inrich others , and begger themselues . wee also see many trades themselues much decayed , because they will not afford so great a gaine as ten in the hundred ; whereas if the rate of vsurie were not higher here then in other countries , they had still subsisted and flourished , and perhaps with as much aduantage to the publique , as those that doe bring more to the priuate aduenturers . yet are not those the greatest hinderances the high rate of money brings to trade ; our greatest disaduantage is , that other nations , especially our industrious neighbours the dutch , are therein wiser then we : for with them , and so in most countries with whom we hold commerce , there is not any vse for money tolerated , aboue the rate of sixe in the hundred : whereby it must of necessitie come to passe , though they haue no other aduantages of industry and frugality that they must out-trade vs ; for if they make returne of tenne per centum , they almost double the vse allowed , and so make a very gainefull trade . but with vs , where ten in the hundred is so currant , it is otherwise ; for if we make not aboue ten , we are losers , and consequently the same trade beeing with them and vs equally good for the publique , is to the priuate aduenturers losse-full with vs , with them very gainefull . and where the good of the publique and priuate mens goe not together , the publique is seldome greatly aduanced . and as they out-trade , so they may afford to vnder-sell vs in the fruits of the earth , which are equally naturall to our and their lands , as to our great shame wee see our neighbours the dutch doe , euen in our owne countrey : for in most commodities the earth brings forth , the stocke imployed in planting and managing of them , makes a great ( in many the greatest ) part of their price ; and consequently , their stocke with them being rated at sixe in the hundred , they may with great gaine vnder-sell vs , our stocke with vs being rated at ten . and as they may out-trade vs and vnder-sell vs , so are all contributions to the warre , workes of pietie , and glory of the state , cheaper to them then to vs : for the vse for money going with vs neere double the rate it doth in other countries , the giuing the same sum must needs be double the charge to vs , it is to them . amongst other things which the king with so much wisdome deliuered to the house of parliament , he committed to their consideration the ballancing of trade and commerce , wherein there is nothing of greater consequence , then the rate of vsury , which holds no proportion with vs and other nations , to our disaduantage , as by experience we see and feele . neyther is the high rate of vsurie lesse hurtfull to commerce within the land , the gaine by vsurie being so easie , certaine , and extreame great , as they are not onely marchants and trades-men , but landed-men , farmers , and men of profession that grow lazie in their professions , and become vsurers ; for the rate of vsury is the measure by which all men trade , purchase , build , plant , or any other waies bargaine . it hath beene the wisedome and care of former parliaments to prouide for the preseruation of wood and timber ; for which there is nothing more auaileable then the calling downe of the high rate of vsury ; for as the rate of mony now goeth , no man can let his timber stand , nor his wood grow to such yeeres growth as is best for the common-wealth , but it will be very lost-full to him : the stocke of the woods after they are worth forty or fifty shillings the acre , growing faster at ten in the hundred then the woods themselues doe . and for shipping , which is the strength and safety of this land ; i haue heard diuers marchants of good credit say , that if they would build a shippe , and let it to any other to imploy , they cannot make of their money that way , counting all charges , teare and weare , aboue tenne or twelue in the hundred , which can be no gainefull trade , money it selfe going at ten in the hundred . but in the low-countries , where money goeth at sixe , the building of ships , and hiring them to others in a gainefull trade ; and so the stocke of rich men and the industry of beginners , are well ioyned for the publike . and yet that which is aboue all the rest , the greatest sinne against the land is , that it makes the land it selfe of small value , neerer the rate of new-found lands , than of any other countrie ▪ where lawes , gouernement , and peace , haue so long flourished ; for the high rate of vsury makes land sell so cheape ; and the cheape sale of land is the cause men seeke no more by industry and cost to improue them : and this is plaine both by example , and demonstration ; for we see in other countries , where the vse of money is of a low rate , lands are generally sold for 30. 40. in some for 50. yeeres purchase : and wee know by the rule of bargaining , that if the rate of vse were not greater here , then in other countries ; lands were then as good a penniworth , at twenty yeeres purchase , as they are now at sixeteene : for lands being the best assurance and securest inheritance , will still beare a rate aboue money : now if lands were at thirty yeeres purchase , or neere it , there were no so cheape purchase as the amendment of our owne lands ; for it would be much cheaper to make one acre of land , now worth fiue shillings by the yeere , to be worth ten shillings , or being worth ten to be worth twenty shillings : and so in proportion , then to purchase an other acre worth fiue or ten shillings . and in euery acre thus purchased to the owner , by the amendment of his owne , there were another purchased to the common-wealth . and it is the blessing of god to this land , that there are few places of it to which he hath not giuen meanes by reasonable cost and industry , greatly to amend it , in many to double the value , so as in time , if for their owne good , mens industry were compelled that way , the riches and commodities of this land would neere be doubled : then would all the wet lands in this kingdome soone be drained , the barren lands mended by marle , sleech , lime , chalke , sea-sand , and other meanes , which for their profit , mens industry would finde out . we see with how great industry and charge our neighbours , the dutch , doe draine and maintaine their lands against the sea which floweth higher aboue them , then it doth aboue the lowest parts of our drownd lands . i will admit a great deale to their industry , but i should very vnwillingly grant , that they are so much more ingenuous and industrious then wee , as that all the oddes were therein : certainely , the maine cause of it is , that with vs money is deere , and land cheape , with them lands deere , and money cheape ; and consequently the improuement of their lands at so great a charge with them , is gainefull to the owners , which with vs would be loss-full ; for vsury going at ten in the hundred , if a man borrow fiue pounds , and bestow it on an acre of ground , the amendment stands him in ten shillings the yeere ; and being amended , the land is not worth aboue fifteene yeeres purchase : but if the vse of money went at no more with vs , then in other places , then fiue pound bestowed vpon an acre of ground , would stand a man but in fiue or sixe shillings a yeere , and the acre of land so amended , would be worth , as hath beene shewed , sixe and twenty or thirty yeeres purchase . whereby it appeareth that as the rate of vse now goeth , no man ( but where the land lieth extraordinarily happily for it ) can amend his land , but to his own losse ; whereas if money were let as it is in other countries , he might bestow more then double so much as now hee may , and yet be a great gainer thereby ; and consequently , as was before remembred , should to his owne benefit purchase land to the common-wealth . neither would such purchase of land to the common-wealth , be the benefit to the landed men onely , the benefit would be as much to the poore labourers of the land ; for now when come and other fruits of the land which grow by labour , are cheape , the plowe and mattocke are cast into the hedge , there is little worke for poore men , and that at a low rate , whereas if the mendment of their owne lands were the cheapest purchase to the owner ; if there were many more people then there are , they should readily set a worke , at better rates then they now are , and none that had their health and lims could be poore , but by their extreamest lazinesse . and as the high rate of vsury doth imbase land , so it is as great a hindrance to discoueries , plantations , and all good vnder-takings , making it neere double as chargeable to the aduenturers , ( mony being at ten in the hundred ) as it is in other countries , where the vse of money is so much lower . now let vs see by the contrary , and conceiue if vsury were tolerated at fifteene or twenty in the hundred ( and i feare many borrowers , all things considered , pay aboue ten ) what the condition of things would then be , and if it appeare how desperate the hurt would be which that would bring ; it may ( at least vpon good reason ) perswade vs how great the good would be of calling it downe . certainely , it must of necessity come to passe , that all trades would in a short time decay ; for few or none ( and reckon the hazard at nothing , yeelde so great againe , as twenty in the hundred ) & all other nations might with so great gaine out-trade and vnder-sel vs that more then the earth would of her selfe bring forth , we should scarce raise any thing from it , euen for our owne vse within the land ; and land would be so much imbased , as men might affoord , without losse to themselues , to carry the composte out of their closes , vpon their next adioyning lands to mend them : so far should we be from marling , liming , draining , planting , & any other workes of cost or industry , by which , lands are purchased to the common-wealth . so farre from building , making of hauens , discoueries , new plantations , or any other actions of vertue and glory to the state ; for priuate gaine is the compasse men generally saile by : and since we cannot without extraordinary diligence plant , build , draine , or any other way amend our lands but it will be deerer to vs , then the purchase of others , money being at ten in the hundred ; if mony then should goe at twenty in the 100. the charge of mending our land would be doubled , and the land abased to seuen or eight yeres purchase ; and consequently all workes of industry and charge , for improuing of lands would be quite neglected and giuen ouer : wee should onely care vpon one another with vsury , haue our commodities from other nations , let the land grow barren and vnmanured , and the whole state in short time , come to beggery . against this ( perhaps ) may be obiected , that before the 37. of h 8. there was no limitation of vsury , and how did we then ? to this , may bee answered , that in those times there was a stricter band in that point vpon mens consciences ; so far forth as vsurers were in the same case as excommunicate persons , they could make no wills , nor were allowed christian buriall . th●refore let vs for our forefathers sake , hope , that the rye vpon their consciences then , was a greater restraint of vsury then the statute of ten in the hundred is now ; i fear fornication is too frequent among vs , yet thanks bee to god not so much vsed as where there is allowance of curtizans and stewes . the obiections likely to bee made against the calling downe of money , are first , that generall obiection of ignorance against all changes , bee they neuer so necessary and apparantly good , that it hath beene so a long time , and beene well enough ; what will become of the alteration , wee cannot tell , why then should wee make any change ? secondly , that as in bodies naturall , so in politicke , great and suddaine changes are most commonly dangerous . thirdly , that money wil be suddenly called in , and so all borrowers greatly preiudiced . fourthly , that money will bee harder to come by , and thereby commerce greatly hindred . lastly , that much money of forreiners , by reason of the high rate of vsury , is brought ouer here to bee managed at interest , which would be carried away againe , if the rate of vsury should bee called downe . to the first , that money hath long gone at ten , and things bin well enough . it is answered , that it is not long that the practise of vsury hath beene so generally vsed , without any sence or scruple of the vnlawfulnesse of it : for mens consciences were hardned to it , with example and custome , by degrees , and not vpon the suddaine . and as the beginning of many dangerous diseases in healthfull bodies , so the beginning of many incōueniences in a state , are not presently felt . with vs , after that with long ciuill warres the land was halfe vnpeopled , so as till of late yeeres , it came not to his full stocke of people againe , there being the same quantity of land to halfe the number of people , the surplusage of our in land commodities must needs be so great , that though trade were not equally ballanced with vs and other nations , we could not but grow rich : beside , france & the low countries were for many yeeres halfe laid waste with warres , and so did trade but little , nor manage their owne lands to their best aduantage , whereby they did not onely not take the trade and market from vs , which now they doe , but they themselues were fed and cloathed by vs , and tooke our commodities from vs at great high rates : whereas now wee see the dutch doe euery where out-trade vs , & the french feede vs with their corne , euen in plentifull yeeres ; so as now our land being full stocked with people , our neighbours industrious and subtle in trade , if we do not more equally ballance trade and bring to passe , that we may afford the fruits of our land as cheape as other countries affoord the same of the same kinde ; we must ( though we leaue a number of our superfluities ) as ( god forbid but wee should ) in a short time grow poore and beggerly . and in this condition tenne in the hundred in a little more time will as well serue to doe it , as if mony were at twenty : for ( as was before remembred ) in most of the commodities the earth bringeth forth , the stocke imployed in planting and managing of them , makes a great part of their price , and consequently they make with great gaine to themselues , vnder-sell vs , our stocke with vs going at double the rate that theirs goes with them . and this wee see and feele too well by experience at this present ; for hauing a great surplisage of corne , we can finde no vent for it ; the french with their owne , the dutch with the corne of poland , euery where supplying the markets at cheaper rates then wee can afford it : and euen our cloathes which haue hitherto beene the golden mine in england , i haue heard many marchants say , that ( except it be in some few of the finest sort of them , which is a riches peculiar to this nation ) other countries begin to make them of their owne wooll , and by affording them cheaper then wee may , so to take our markets from vs. and this i hope may in part serue for answere to the next obiection ; that all great and sudden changes are commonly dangerous ; for that rule holds true , where the body naturall or politicke is in perfect state of health , but where there is a declining ( as i haue some cause to feare there is or may soone be with vs ) there to make no alteration is a certaine way to ruine . to the third : that money will be suddenly ●alled in , and so all borrowers greatly preiudiced ; for that there may be a clause in the end of the statute whensoeuer it shall be made : that it shall be lawfull for all that haue lent money at ten in the hundred , which is now forborne , and owing , to take for such money so lent and owing , during two yeeres after this session of parliament , such vse as they might haue done if this acte had not beene made : whereby borrowers shall be in lesse danger of sudden calling in of their money then now they are ; for where the lenders vpon continuance of their olde securitie , may take tenne in the hundred ; vpon new securitie they must be content with lesse , so the calling in of their money will be to their owne preiudice . and if there be any borrower to whom this giueth not sufficient satisfaction , if such borrower haue lands of value to pay his debt , the worst condition hee can feare , is to haue at the least twenty yeeres purchase for his land , wherewith to cleere his debts ; for as i said before , land being the best securitie , and securest inheritance , will still beare a rate aboue money . and so there being no vse allowed for money aboue the rate tolerated in other countries , land will as readily sell at twenty yeeres purchase , as it doth now at twelue . and i thinke there is no borrower that hath land of valew to pay his debts , doth doubt if he will now sell his land at ten yeers purchase , he might soone be out of debt . to the fourth obiection , that money will bee hard to be borrowed , and so commerce hindred : i answer , that it were true , if the high rate of vsurie did increase money within this land ; but the high rate of vsury doth inrich onely the vsurer , and impouerish the kingdome , as hath beene shewed ; and it is the plenty of money within the land that maketh money easie to bee borrowed , as wee see by the examples of other countries , where money is easier to bee borrowed then it is with vs , and yet the rate tollerated ; for vse is little more then halfe so much . it is the high rate of vse that vndoeth so many of the gentry of the land , which maketh the number of borrowers so great , and the number of borrowers must of necessity make money the harder to bee borrowed , whereas if vse for money were at a lower rate , land as hath been shewed , would be much quicker to bee sould , and at deerer rates , and so the nobility and gentry would soone be out of debt , and consequently the fewer borrowers , and so to trades-men and marchants money easie to bee had . further , let vs consider if money were called downe , what vsurers would do with their mony ; they would not i suppose long be sullen , & keepe it a dead stocke by them ; for that were not so much as the safest way of keeping it : they must then eyther imploy it in trade , purchase land , or lend for vse at such rate as the law will tolerate , if it quicken trade , that is the thing to bee desired ; for that will inrich the kingdome , and so make money plentifull . and yet need not any borrower feare that money will so bee imployed in trade , as that there will not be sufficient of money to purchase land , where the purchaser may haue as much , or neere so much rent by the purchase of land , as he can by putting his money to vse : for a great number of gentlemen and other in the countrie , know not how to imploy any stocke in trade , but with great vncertainty , and lesse satisfaction to themselues , then the letting of their money at a lower rate , or purchasing land at twenty yeeres purchase or vpwards . no doubt for the present there would be great buying and selling of land , till men had cleered themselues , and payed their debts : but in short time land , as it is shewed before , would sell at so deere a rate , as money let at a lower rate of vse , would bring in proportion as great a rate aboue the rent that would be made then by the purchase of land , as the rate of money now is aboue the rent of land , purchased at fourteene or fifteene yeeres purchase , and so by consequence money would then as easily bee borrowed as it is now , and so much easier , as it would bee more plentifull , and fewer borrowers . to the last and weakest of obiections ; that there is now much money of forreiners in the land to be managed at tenne in the hundred , which if money should be called downe , would be carried out of the land ; there is no doubt it is true : but i desire to know , whether any man thinke it better for the state , that they should now carry out one hundred pounds , or seauen yeeres hence , two ; or foureteene yeeres hence , foure ▪ or one and twenty yeeres hence eight : for so in effect vpon the multiplying of interest , they doe . it will seeme incredible to such as haue not considered it , but to any that will but cast it vp , it is plainely manifest ; that a hundred pounds managed at ten in the hundred , in seauenty yeeres multiplies it selfe to a hundred thousand pounds . so if there should bee an hundred thousand pounds of forreiners money now managed here at tenne in the hundred , ( and that doth seeme no great matter ) that an hundred thousand pound in threescore and ten yeeres , which is but the age of a man , would carry out ten millions , which i beleeue is more then all the coyne at this present in the land. i know we cannot conceiue how any such summe should be managed at interest , yet this is sufficient to make vs little to ioy in forreiners money . besides , wee must not conceiue that the money of forreiners , which is here managed at vsury , is brought into the land in readie coine or bullion : the course is , that marchants send ouer bils of exchange to their factors , for which they receiue our money here ; and this is the money they mannage at interest , and so they eate vs out with our owne monies . the old comparison , which compares vsury to the butlers boxe , deserues to be remembred ; whilest men are at play , they feele not what they giue to the boxe , but at the end of christmas it makes all or neere all gamesters loosers : and i feare the comparison holds thus much farther , that there is as few escape , that continue in vsury , as that continue gamesters , a man may play once or twice and leaue a winner , but the vse of it is seldome without ruine . now because i know mens priuate interests doth many times blinde their iudgements , and least any may be tempted for their owne , against the publique good , i will desire them to remember , that if they haue lands as well as money , that what they loose in their money they shall get it in their land ; for land and money are euer in ballance one against the other , and where money is deere , land is cheape ; and where money is cheape , land is deere . and if there be any yet so harty a well-wisher to tenne in the hundred , as that hee still thinke it fit to be continued , my wish is ; that hee and his posteritie may haue the priuiledge to borrow , but not to lend at that rate . in the beginning of this treatise , i did disclaime the proofes of the vnlawfulnesse of vsury , leauing them to diuines , this one onely ( rising from the premises ) which may serue for all , i thinke fit to set downe . it is agreed by all the diuines that euer were , without exception of any , yea and by the vsurers themselues , that biting vsury is vnlawfull : now since it hath beene prooued that tenne in the hundred doth bite the landed men , doth bite the poore , doth bite trade , doth bite the king in his customes , doth bite the fruites of the land , and most of all , the land it selfe ; doth bite all workes of pietie , of vertue , and glory to the state ; no man can deny but ten in the hundred is absolutely vnlawfull , howsoeuer happily a lesser rate may be otherwise . to the king increase of his customes . to the kingdome increase of land , by inriching of this . to the nobility and gentry deliuerance from bondage and debt . to marchants continuance and flourishing in their trades . to yong beginners in trade and commerse , the fruits of their owne labours . to laborers quicke imployment . to vsurers land for their money . finis . a discourse of the nature, use and advantages of trade proposing some considerations for the promotion and advancement thereof, by a registry of lands. preventing the exportation of coyn. lowering the interest of money. inviting foreign families into england. child, josiah, sir, 1630-1699. 1694 approx. 36 kb of xml-encoded text transcribed from 19 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2004-05 (eebo-tcp phase 1). a32828 wing c3855 estc r214188 99826396 99826396 30799 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a32828) transcribed from: (early english books online ; image set 30799) images scanned from microfilm: (early english books, 1641-1700 ; 1827:5) a discourse of the nature, use and advantages of trade proposing some considerations for the promotion and advancement thereof, by a registry of lands. preventing the exportation of coyn. lowering the interest of money. inviting foreign families into england. child, josiah, sir, 1630-1699. [2], 31, [1] p. printed, and are to be sold by randal taylor, near stationers-hall, london : 1694. by sir josiah child. the words "a registry .. into england." are bracketed together on title page. reproduction of the original in the british library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng interest -early works to 1800. land titles -registration and transfer -england -early works to 1800. great britain -commerce -early works to 1800. 2004-01 tcp assigned for keying and markup 2004-02 aptara keyed and coded from proquest page images 2004-03 mona logarbo sampled and proofread 2004-03 mona logarbo text and markup reviewed and edited 2004-04 pfs batch review (qc) and xml conversion a discourse of the nature , use and advantages of trade . proposing some considerations for the promotion and advancement thereof , by a registry of lands . preventing the exportation of coyn. lowering the interest of money . inviting foreign families into england . from slender hints , men serious and discerning , may gain experience that is worth the learning . london : printed , and are to be sold by randal taylor , near stationers-hall , 1694. a discourse of the nature , use and advantages of trade . when fallen man was driven out of paradice , the heavy charge imposed on him was , that in the sweat of his face he should eat his bread : and he who first was made of clay , must receive his nourishment and sustenance from the earth . his body must be daily coveting the necessaries of life ; and his mind as earnestly pursuing the vanities and superfluities thereof . thus thro' the whole course of humane life is mankind destined to labour and trouble , as the sparks fly upward ; and all his industrious efforts after the good things of this world , determined in vanity and vexation of spirit . 't is true , in the infancy of the world , men contented themselves with the natural produce of the earth ; and it sufficed them to injoy such fruits and benefits thereof , as that portion of land where their lot fell did properly afford them . but when the inhabitants of the earth began to increase and multiply ; those who had first gained the possession thereof , and assumed to themselves a distinct propriety and right therein , had excluded the succeeding race of men , from all other livelihood and subsistance , but what was subordinate to , and dependant on such proprietors , who having power and means to support them , did thereby claim a right of dominion over them . then men began to build cities , and constitute societies , and propose to themselves establish'd laws , and rules of government and commerce . and as men were more and more dispersed over the face of the earth , they discovered , that the productions thereof were various in some places and countries , from those of others . that some countries abounded in corn , cattel and woods : some in drugs , spices and balsoms : some in minerals , gems and precious stones ; and severally produced things of different kinds and natures . and hence man's restless mind became transported , with a fond desire of possessing and trying all things . and tho' an easie portion of natures bounties did suffice to answer the ends of life ; yet the treasures of the universe were not sufficient to satisfie the pride of life , or give content to the unaccountable desires of boundless imagination . what men could readily possess and injoy , were of little esteem , and soon became indifferent ; but things novel and of difficulty to be acquired , were accounted valuable ; even apes and peacocks , if but far fetch'd and dear bought , were thought creatures of ornament and diversion . and those commodities which one country did most readily part with , were as earnestly coveted and sought for by another . mens curiosities increased with their discoveries , and their inventions were wrackt , to find out arts and ways of building ships , wherewith to plow the ocean , and descry the remotest parts of the earth , and searching after the hidden treasures thereof . the use and nature of all those secrets , were industriously inquired into , and mens contrivances were set on work , to make those things desirable for ornament or luxury , which were no way needful for common use. kings and princes had their crowns and scepters beset with gold and precious stones ; their palaces and thrones supported and adorned with marble , ivory and cedar ; their chambers beautified with the choicest paintings and carvings ; their beds and furnitures inriched with the costliest tapestries and imbroideries , and their cloaths and linnen sweetned with the noblest perfumes ; their tables replenished with all those delicacies , that art and nature could contribute , to indulge and gratifie the nicest appetites . every subordinate degree of men in proportion to their abilities studied to imitate , if not outvie each other in profuseness : and those of the meanest condition , were only deficient in power , not in good will , to be as vain glorious and extravagant as the greatest . nevertheless , there are excellent ends in all the instances of natures varieties and productions thereof , differing in so many several countries , from each other ; and the indefatigable labour of men , in their anxious endeavours , to possess and injoy them . and all those excellent arts and inventions that have been studied , to improve and apply them , to the several purposes of curiosity and delight ; have created most infinite and profitable occasions of traffick and commerce : and the various measures and methods of making all things subservient to man's use or pleasure , are so many providential circumstances of susteining those millions of people , that might starve for want , had they not opportunities of ministring to those that abound in plenty . there is much of innocency and ingenuity in many arts and sciences ; in the various manufactures and painful imployments , whereby the greatest part of mankind support themselves , in the exercise of their several faculties ; their business keeps them free from passions ; they are generally sedate and composed in their minds ; and in their recesses from their labour , they eat their bread with chearfulness . since therefore man is placed in a sphere of activity , and either of choice or necessity , will always be contriving and acting something , more or less significant , to busie or profit himself withal . i hope it may not be improper , to offer some short reflections upon a subject matter , wherein the greatest part of mankind are so industriously concerned and imployed . now the great ends and use of trade and commerce , are for our mutual accommodation , whereby such occasional interchanges of one thing for another , become a just measure of property , betwixt man and man ; the chief inducements and motives thereto , being created from a desire of pleasure or profit . thus , when men are possessed of some things , wherewith they are satiated ; they either sell them for money , or exchange them for some other thing , without regard to any gain thereby , or any other end , but that of pleasing their own fancy . sometimes men part with such things as they can well spare , for what they have a greater need of , for their present accommodation ; but without any design of enriching themselves thereby ; but the principal part of trade , consists in such sort of commerce , in the disposal whereof , men propose to themselves some gainful advantage . and from the various opportunities of men's ministring to each others pleasures or necessities , is the great concern of trade , supported and maintained . and the principal advantage and foundation of trade in england , is raised from that wealth which is gained out of the produce of the earth . the proprietors whereof having a greater proportion of lands , then they alone can manage to advantage , are thereby induced to let out the same to tenants , who by contracts and stipulation with their landlord , do render some certain rent for what they hold and injoy . hence the painful husbandman becomes interested and concerned to imploy his utmost labour in the cultivation of the earth , and improving every species that may be gained thereout , and turning the same to profit . the surplus and benefit whereof beyond the rent reserved to be paid , being properly his own , and becomes a competent livelyhood to himself and family . and from this labour of the husbandman , are derived many other improvements of trade , in the disposal of those treasures which he hath raised out of the earth by his industry and pains . his corn gives trade and imployment to the miller , the baker , the maulster and the brewer ; besides his several other grains , and seeds , and fruits , and herbs , which imploy and support as many several callings : by his grass he increases and nourishes all sorts of cattle , and they support the butcher , the tanner , and many other trades ; his wooll gives trade to the clothiers ; his milk , and cheese , and butter supply the markets with necessary food ; his timber is imployed in building ; his clay in making brick and tile ; his mines of iron , lead , tin and coals , besides many other particulars , too tedious to be enumerated , give maintenance to an infinite variety of trades and manufactures , that in a wonderful manner depend upon , and are subordinate to each other ; all which are to be accounted as so many flourishing branches , derived out of this principal stock of good husbandry . thus we see how great a part of the people of this nation , who have no propriety in the soil thereof , yet by cultivating and improving the same to the best advantage , and applying the produce thereof , to be imployed in manufactures , and transferring the same from one to another in a way of traffick and commerce , obtain a distinct and peculiar interest in the general wealth of the nation , by the several benefits accruing to themselves , and greatly contribute to the weale-publick . as land therefore is so principal a fund of trade , it may not be improper to consider , whether it be not the interest of england , that the lands of ireland should be improved as much as may be , that out of the produce thereof , the great advantages of trade and commerce may be equally incouraged , and promoted there 〈◊〉 here . and that england and ireland should have one joynt interest , and by uniting the strength of both , they should become thereby considerably more powerful . for this is certain , that england has sustained no prejudice by uniting the dominions of wales to it ; nor is london the poorer , because several towns in england have fall'n into a great way of trade , and thereby grown rich ; for in the one case , the wealth and trade of england is greatly increased and advanced , by the addition of so much more land to it , and of so much more traffick and commerce that is gained out of the produce of it ; and so many more hands and purses are thereby rendred contributary on all emergent occasions , to the assistance and support of the publick government . and in the other case , london , as it is the metropolis , and the principal seat of majesty and government , of the administration of justice , and directing the laws and methods of trade , it is sure to partake in a plentiful measure of all the benefits and advantages that may arise from the increase of trade in any other places under the same dominion and government : but time and experience only can be able to remove and over-rule the mistaken prejudices , and private interests , that too unhappily obstruct at present so just an undertaking . another foundation of trade is created from the fishery of the seas , the particular advantages whereof , having been truly represented in several discourses set forth on that subject ; i shall only make mention of it in this place , and could wish that so certain and continual imployment for seamen , and so great an occasion of trade and commerce , may receive a publick and lasting establishment . and from these two fundamentals of trade , is derived the great opportunity of traffick from mutual commerce , where merchants buy commodities purely to sell again , or exchange the commodities of one nation , for those of another , for no other end , but that of their own private benefit and profit . by which medium of mutual commerce , the riches of our own country are not only communicated to infinite numbers of families at home , through whose hands our native productions and manufactures do pass , before they are finally disposed of , but the surplus , which is transported to the remotest parts of the habitable known world , does not only maintain a correspondence with mankind , and tends to the civilizing the unsociable tempers of many barbarous people , but accommodates our own nation with much of their treasures , and very much helps to support our navigation , wherein consists our greatest safety , strength and honor. from hence it is observable , how unprofitable the institution heretofore was of lazy monks and fryars in this nation ; how little of religion , and less of charity there was in such endowments , where the fat of the land was devoured by a generation of people , that were no way serviceable , or instrumental towards the publick good , whereof every man's experience cannot but be a self-conviction and whoever compares the state and condition of england , holland and france , since they have applyed themselves to trade and navigation with that of spain , or any other nation that is less conversant in merchandize , cannot but acquiesce in this truth , that nothing can so effectually maintain and support the power and glory of a nation , as traffick and commerce . the intent therefore of this discourse is not to instruct men in their particular way of trade , how to manage the same to the best advantage ; for every man 's own experience , is the best director for such purposes ; and every man 's private interest is the strongest persuasive to the promotion of his own concerns . i shall only propose three general considerations wherein foreign trade may be beneficial , or injurious to the nation . the chief design of this treatise being to represent several instances , whereby the great advantages of trade in this nation are obstructed and prevented , for want of such provisions in the law , as may be reasonably wished for , and endeavoured towards the promotion of so great a concern . and first , it must be allowed , that all sorts of commerce that incourages the manufacture , or at least , the disposal abroad of such commodities as are of our native growth , and are not necessary to be consumed at home , are of general benefit , and ought to be promoted secondly , all such commerce as brings in no more than is carried out , tho' it do not enrich the nation , yet it is beneficial , in respect to those families that gain a profitable livelihood by transferring so many commodities from one hand to another . thirdly , such commerce as in it self is unprofitable to the nation , yet if it procure to us collateral advantages that are profitable , it may be allowed ; but such commerce as serves purely to the support of luxury , and tends in all other respects to the impoverishment of the nation , is as much as may be to be restrained by law. trade , therefore having such peculiar excellencies , that it is a just and certain measure of acquiring a property in any thing , and is communicable to all , in proportion to their qualifications of industry and ingenuity . that it is a an universal method of transferring wealth from hand to hand , whereby millions of people are imployed and susteined ; and men's necessary occasions are thereby mutually supplyed , without the violent and inhumane contrivances of rapine and force ; and that it is the greatest security and preservation of our publick honour and welfare . it may not be improper to reflect on such impediments as have obstructed trade , and propose some considerations , whereby the same may more effectually be advanced . now as the produce of land is a principal foundation of trade ; and the good management of land gives the greater life and vigor to trade : so it must be consider'd , that money is the common standard and valuation of most commodities in traffick and commerce ; and if such money be wanting when commodities are exposed to sale , a great part of trade is prevented thereby ; the command of ready money giving more easie and quick dispatches and returns in trade , then can possibly be effected without it , wherefore it is our publick interest , that coin should be continually passing from one to another ; in the disposal whereof , there is always something of gain to both parties , having their ends in traffick , tho' in different respects . and since all men cannot imploy their money in trade , but that the impediments of birth in some that are above it ; of age in some that are past it ; of sex in others ; and in some that of sloth and idleness render them uncapable of disposing their money in a way of commerce ; it follows of consequence , that unless some proper incouragement be contrived for such to lend their money to others , that can and will trade therewith ; so much trade will be wanting in the nation , by how much money lies hoarded up in chests from those impediments . so that , notwithstanding the great advantages of trade , whereby all persons are under a possibility of improving their fortunes , in proportion to their parts and industry ; yet there will be a great deficiency in trade , where land cannot be safely transferred from one to another ; and money cannot as freely be laid out , or lent , without mens apprehensions of being cheated and defrauded . thus , a person being indebted , but not being able to sell or mortgage his land for payment of such debt , may under such circumstances , be compared to one of the wheels of a clock that is rusty , and thereby impedes the whole motion . as where a gentleman may owe 1000 l. to several tradesmen ? to pay which , he would gladly sell , or mortgage his estate ; and a third person , who has a 1000 l. lying by him dead , would readily lay it out in a purchase or mortgage , could he do it safely . in this case here are three evils : the person indebted would gladly pay , could he be able to raise the money ; but by reason of the disparagement and distrust that is upon him and his estate , he is forced to fence with his creditors for two or three years ; in the mean while , his creditors prosecute him with chargeable suits ; and having extended the gentleman's estate , he is forced to break up his house and abscond , his family ruined , his estate wasted and untenanted by mismanagement ; and so much trade as would have arisen from the produce thereof , wholly lost , and that estate which was worth 2000 l. at first , will not perhaps suffice at last , to pay the creditors their debts and charges . the creditors are likewise injured , for want of their present money ; which in two or three years time , in a course and circulation of trade , might have passed to some advantage , more or less , through the hands of a thousand persons . the monied man is no less injured , having so much money lie dead so long , without making any benefit thereby . so that , unless some provision in the law may be found out , to make men safe and easie in their purchases ; so much trade will be lost in the nation , as shall from time to time be obstructed ; where men cannot readily dispose of their estates to answer their conveniences ; since all sales and mortgages imply a necessary occasion of laying out so much money ; no man ever parting with land for money , on purpose to hoard it up ; tho' many hoard up money , for want of an opportunity to dispose of it . and here it may be considered , for promoting the credit , and securing those priviledges which land is justly intitled to ; whether publick taxes that are laid on land , might not much better be laid on the produce thereof , by way of excise , and by easing those few that are the proprietors of land , to lay it on those many that raise their estates out of the produce of land , since every burthen that is supported by few hands , feels much heavier than what is susteined by a land tax ; being like the digging and cutting up the roots of trees for fuel , which might more safely and conveniently be gained from the branches . for , suppose a tax were laid on iron , lead , tin , salt , wool , leather , tallow , corn , hay , and on plate , glass , brick , earthen ware , paper ; and many manufactures in this nation , which pay no customs or taxes . [ the burthen of such an excise would be susteined by so many persons , that it would be insensible ; and the price and credit of land being hereby supported , men would more readily bestow their money in the purchase , as well as their labour and pains in the improvement of it . another consideration may be concerning money , which is not only the just valuation of all commodities , but it is also valuable in it self , upon its certain and constant intrinsick worth ; and is to be accounted a part of the wealth of the nation . every occasion therefore , of exporting it in specie , without bringing in as profitable a return of money in a circulation of trade , tends to the impoverishment of the nation , and brings a manifest decay on trade ; money being as necessary for the carrying on of trade , as nerves and sinews are for the motion of the natural body . for , if there be a scarcity of money , there will be a deadness of trade ; even amidst the greatest plenty of commodities ; as may be seen in those countries , that have no other accommodation for disposing their commodities , but by exchanging and bartering one merchandize for another ; wherein there is much of difficulty and trouble , with little profit ; and is mostly undertaken for necessity sake . and it is an unhappy mischief , where the intrinsick value of our money , by exceeding of other countries , gives an incouragement to such exportations ; as if our money being three pence in the crown better than in other countries . a foreign merchant should export a thousand pounds of our coyn into france , and by new coyning it there , get five per cent. and then bring over a thousand pounds worth of wine , and having sold it here , he then exports another thousand pounds , and by new coyning it there , should get five per cent. more ; hereby two thousand pounds are exported , never to be retrieved ; and one hundred pounds are gained thereby , besides the profits in the commodity sold here ; so that , unless some provision may be made to prevent such advantages in exporting our coyn , a great part thereof , will inevitably be drawn into foreign parts . from whence it may be questioned , whether it be not of publick concern ; when a proper opportunity presents to new coyn all our money ; with such regard had to the allay of other countries , that it shall not be the interest of any to export it , for the sake of new coyning it elsewhere . it may likewise be considered , whether the advancement of trade is not greatly prevented , by the unaccountable humour of having so much plate in every family ; which if turned into coyn , would infinitely promote the general trade ; but while it remains in plate , is of no more publick benefit , then if it were buried in the bowels of the earth ; while so many other manufactures are neglected , that would otherwise be imployed to supply the use and ornament of plate . another consideration may be concerning the interest of money ; which with great reason and justice , ought to be limited to such a rate , as may be consistent with the circumstances of borrowers ; whereby they may be inabled to answer their own ends in borrowing , as well as the others gain in lending . as if it be , a country gentleman that borrows on a mortgage ; his end is , chiefly to prevent the present sale of his land , in hopes of some favourable opportunity , to pay the debt some other way ; and having occasion to borrow one thousand pounds , sets out threescore pounds per annum ; which he could have sold for so much money , and lays by the profits every year , to pay the interest . now , if he pays but four per cent. for interest ; perhaps , he may raise forty pounds per annum , clear of all charges , out of the sixty pounds per annum , wherewith to pay the interest ; but more than that , he cannot hope to clear out of threescore pounds per annum : nor if the lender had purchased the same estate , could he have made clear of all charges , more than forty pounds per annum ; so that , it is plain , that four per cent. is the full value of the increase of money , with respect to purchases and mortgages ; and consequently , if he pays two per cent. more than he can raise by the benefit of the money borrowed , he must run insensibly in debt ; and the cankered excess of usury shall devour the gentleman's estate in a competent time , at two thirds of the real value , be the gentleman never so painful and industrious to prevent it . it is therefore most clear , that no man can with a good conscience take more interest on any security by mortgage , then the profits of land will answer on a purchase . or if one thousand pounds were lent to a trader , unless he can have it at 4 l. per cent. as it is lent in other countries , he can neither afford to buy so dear by 1 l. per cent. nor sell so cheap as forreign merchants if he pays 2 l. per cent. more for his money , and consequently , must either be beat out of his trade , or forgoe so much of his reasonable profits , as upon any contingent losses , may hazard his undoing , while the lender secures a certain exorbitant gain out of the unprofitable returns of the unsuccessful merchant : or if the trader by purchasing his money at too high an interest , do therefore inhance the price of his commodity , the generality of the people become the sufferers thereby . such a dead weight , and of so pernicious consequence , is the payment of 2 l. per cent. more than the common interest in foreign countries ; that in bearing too hard upon the merchant , it overwhelms his trade , and destroys all that traffick in his ruine , which might have been carried on by him , and by his means , derived with good advantage to many others , or else inforces him to inhance the price of his commodities , to the oppression of the subject , which is a publick grievance , and ought in no sort to be indulged for the particular benefit of the selfish lender . nor will there be any severity or injustice in restraining the interest of money to 4 l. per cent. since foreign nations that cannot pretend to have more plenty of money than england , do constantly lend at 4 l. per cent. or under , as being convinced , that it is an adaequate interest for the use of money , where a proportionable share of the profit of such money , is as justly due to the borrower , imploying the same in trade , as to the lender for the usu-fruit thereof . live and let live , is an honest and usual saying in trade ; and if the unconscionable usurers , insatiable thirst after ungodly gain , will not permit him to say so . the law may with great justice compel him to do so ; for wherever common convenience or necessity requires any thing to be done for the publick welfare , every man owes a conformity thereto , and many be restrained by law from doing otherwise . upon this reason is grounded , the statute directing the price of bread and beer , to be limited from time to time according to the price of corn. and all ingrossers , regraters and forestallers are prohibited to trade in a way so injurious to the publick ; and one weight and one measure is required to be observed in buying and selling , to prevent the crying evils of extortion and oppression , whereby men are inhibited from making any private gain to themselves , that is inconsistent with the common convenience of the publick . there are many arguments that may be brought against the cursed vice of extortion , whereof excessive usury may be accounted a principal species ; but such as will not be convinced by these two plain instances of lending upon mortgages , or in trade , will be very deaf to any other perswasions with , but the compulsory obligation of law , which is well known to have had a good effect in reducing interest from eight to six per cent. for which benefit the nation might have waited long enough , if the usurer's conscience had still remained a law to himself . and since the general use of trade was never intended to be an occasion of inriching one man by the impoverishment of another , but to be a universal support to mankind , by a medium of traffick and commerce , to communicate and impart to each other , the conveniences of life , the law has frequently interposed to oblige perverse and refractory men to comply with such rules and measures in trade , as have been thought most conducing to the general good of a nation . nor will it excuse to say , men are not compelled to take up money at interest , and if they find they cannot afford to give 6 l. per cent. for money , they may forbear to carry on a greater trade then their own money will enable them to undertake ; for the government having an interest in the promotion of trade , is consequently interested in the welfare of every person that may be instrumental thereto ; and is concerned to see them , not only accommodated , but as much as may be , incouraged in all things tending to the advancement of traffick and commerce . thus the law requires inn-keepers to accommodate travellers at a reasonable price ; and the like constraint is by law on butchers , brewers , bakers , and others , to sell their victuals at a reasonable price ; and yet these persons have as much , and as good a propriety in their respective commodities , as any man has in his money ; and it might as well be said , that men are not under a necessity to buy of the butcher , for that they may kill their own victuals , if they please : but money being as essential to trade as victuals are , to the support of life ; and the publick interest , being alike concerned in the circumstances of both cases ; they both fall under the same reason in the law , and are equally subjected to the same considerations and measures of justice . a further consideration for the improvement of trade , may be by a reasonable endeavour , to multiply our people ; for as land cannot yield its utmost increase , but through men's labour and pains ; nor can such increase be improved to the best advantage , but by the application of many hands : and since there are many parts of england uncultivated , that would maintain thousands of families in way of farming ; and ten times as many thousand families would be maintained in subserviency , out of the trade and manufacture that would necessarily arise from the produce of such farms . it follows then of consequence , that the nation is deficient in the want of so much wealth and plenty , as might be gained by the increase and assistance of so many thousand people . to effect which great advantages , the gentry of england may please to bethink themselves , how much it is there interest to reside in those countries where their estates lye ; and may , if they please , consider how much it is their duty by a tacite condition annexed to that estate , that is descended on them from their ancestors , by their example : authority , incouragement and assistance , to preserve good government and good husbandry among the many inferior people in their neighbourhood , by which means , and by repealing such rigorous laws , as drive our people beyond the seas ; and by putting the laws in execution against those many that live idly in and about london , and elsewhere , who subsist mostly by stealing , or cheating , or such like indirect courses , many such persons would be glad to forsake their present habitations , and wicked course of life , and returning to their own countries , betake themselves to a way of husbandry . another defect , is the imprisonment of men's persons for debt , which seldom or never procures the payment of what is owing , and yet many an unfortunate man , who by reason of his poverty , could no longer continue a master , might , if he had his liberty , become a useful servant , and thereby contribute something to the publick ; but while he continues in prison , he is not only unserviceable to himself and his creditors , but unprofitable and buthensome to his country , in respect of that charity that is thereby diverted from the sick and infirm , in relieving these walking ghosts , or men halfe buried alive , while the nation is deprived of the service and benefit of those thousands of people that labour under such hard circumstances , to which they are subjected by a barbarous inhumanity , indulging revenge , purely for revenge sake . but i rely not on either of these expedients , for i fear there is too much infatuation in the world , to expect any such conduct in the one case , and too little charity to expect so much good nature in the other . the most effectual remedy therefore may probably be this . to grant one general freedom and priviledge for all persons and their families , to come into this kingdom , and enjoy the benefit of our laws , equally with all other our native subjects , upon some solemn declaration to be by them subscribed , and to be inrolled , whereby they shall promise an entire submission and subjection to this government , and take the oath of allegiance , which would be a sufficient caution and ceremony to introduce them amongst us , without imposing any other test upon them ; that being principally intended and provided to secure us against those that were to be admitted to offices of trust , wherein they might have some influence on the government : but as to the trading part of the nation , it was never apprehended necessary to apply a caution so extraordinary towards such ; nor can it be prudential to create difficulties , that may obstruct the trade and welfare of the nation , where there is more of humour than necessity requiring it ; and perhaps it is not without great offence , that so mysterious and religious a duty should be made subservient to secular ends and purposes . from what has been thus represented , in as short a discourse as the subject matter could be well comprehended ; may be drawn these observations . that trade does contribute in a very great measure , to the honour , strength , wealth and preservation of our government . that the principal foundation of our trade , is derived out of the land and the sea. that the produce of the land and of the sea is improved by manufacture and merchandize . that the multiplicity of people increase manufacture and merchandize . that money is the principal medium , whereby people promote trade . that land which is a substantial valuable and lasting fund ; being made a safe and ready security , whereon money may be borrowed at a reasonable interest : a great part of the coyn that lies dead , would more freely be dispersed , in a circulation of traffick and commerce . finis . plain english in a familiar conference betwixt three friends, rusticus, civis, and veridicus, concerning the deadness of our markets : offer'd as an expedient to serious consideration, and for the general good of gentry and commons. culpeper, thomas, sir, 1626-1697. 1673 approx. 52 kb of xml-encoded text transcribed from 13 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2003-11 (eebo-tcp phase 1). a35409 wing c7561 estc r24899 08647984 ocm 08647984 41527 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a35409) transcribed from: (early english books online ; image set 41527) images scanned from microfilm: (early english books, 1641-1700 ; 1254:13) plain english in a familiar conference betwixt three friends, rusticus, civis, and veridicus, concerning the deadness of our markets : offer'd as an expedient to serious consideration, and for the general good of gentry and commons. culpeper, thomas, sir, 1626-1697. 24 p. printed by t.j. and are to be sold by henry million, london : 1673. attribured to thomas culpeper--nuc pre-1956 imprints. errata: p. 24. reproduction of original in the huntington library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng interest -great britain. great britain -economic conditions. 2003-07 tcp assigned for keying and markup 2003-07 apex covantage keyed and coded from proquest page images 2003-08 mona logarbo sampled and proofread 2003-08 mona logarbo text and markup reviewed and edited 2003-10 pfs batch review (qc) and xml conversion plain english , in a familiar conference betwixt three friends , rusticus , civis , and veridicus , concerning the deadness of our markets . offer'd as an expedient to serious consideration , and for the general good of gentry and commons . london , printed by t. i. and are to be sold by henry million at the bible in fleet street , 1673. plain english , in a familiar conference , &c. c. vvelcome gentlemen , in troath i have long'd for another meeting in pursuance of our late discourse , it hath so run in my mind ever since , i mean the reducing of interest : upon my life , ' twilll send all our widows and orphans a begging together , r. must our policy then be wholly squar'd to the advantage of those whom you please to call widows and orphans ? or admitting onely such concern'd , would you not have them buy and sell by the same measure that others do ? v. indeed you might with the same reason propose ▪ that widows lands should be lett for double it 's worth ; all necessaries sold to orphans at half the market-price ; and that they might be liable to no publick charges . c. you make a jest of it , but 't is a case that deserves rather your pity . v. we read of depopulations by sheep more savage than wolves , and which devour whole hamlets : are not some of your widows and orphans akin to those innocent creatures ? c. how uncharitably you talk ! v. but consider it seriously ; are there veryer drones , nay cankers , in the common-wealth , than most of those that pass under that character ? they possess goodly revenues , clog'd with no publick ch●●ge or service , and brought to their hands without trouble , or so much as thought ; which they commonly spend in forraign superfluity ; and so become the ring-leaders of that excess and sloath , now so much complained of . c. you do not , i hope , take all our widows and orphans for such as you here describe . v. god forbid : there are , i grant , many of them exemplary for their sobriety and vertue : but , as rusticus said , t will not follow that the common-wealth it self must truckle to such a handful in comparison . c. surely that tribe is not so small as you fancy : and you will allow them very deserving , at least of publick compassion . v. if you would look upon usury with both your eyes at once , and count , as well the real widows and orphans that now groan under it , you would find , that perhaps it makes three holes for one it mends : in plain english , to swell the superfluous in-come of a few , many orphans are daily cast up to the wide world ; such inequality on all sides attending an inconvenient rate of interest . c. i perceive all your cry is against usury , as if that were now our onely grievance : but you may remember , at our last meeting i offered to name divers common abuses , which have possibly hurt us more than usury , and would therefore be principally reoress'd . v. well , i must lay odds before-hand , they are but of the same nature with those i then mentioned , viz. effects and symptoms , mistaken for causes . c. to me there 's nothing clearer , than that the lazyness of our poor , insolence of servants , and excessive wages , are now our principal grievances . r. our gentry then , it seems , may hope at length to be quiet : but to say the truth , 't is high time ; for they are in a fair way to reform themselves , as tradesmen may shortly feel . v. for my part , i ever took it , that the noyse of our excess was but like my ladies laying all the blame upon poor button . c. nay i must still condemn many of our gentry for squandring their estates , and running in debt as they do . r. i protest i can look ten miles round , and scarce spy a prodigal amongst them : but it seems , t is the art of scolding to cry whore first . v. in our most thriving times , to my knowledge , we had twice as may real unthrifts as now , and not half the good husbands ; t is not with us then , to be sure , that luxury now keeps its court. and therefore our censors may do well , if they please , to reflect a little homewards . c. but divers may formerly have transgrest in that kind , who would now redeem their errour , by making a vertue of necessity , when for them perhaps , it s too late . v. to whom do we owe that soveraign thrift of one meal a day , but to persons of the highest quality , especially compounders ? r. what you call luxury , mr. civis , i know not : sure i am , most of our gentry have long done , and still do their utmost , in the fall of their rents , to preserve their ranks ; but find , that even their thrift tends to their undoing . c. how , in gods name should that be ? r. marry , in endeavouring to preserve themselves , they destroy their tenants . c. t is great pity indeed , they will not live hospitably in the countrey , as their ancestours did . v. you would do them a singular favour , if you would please to teach them your knack of living in the same fashion with lesse then half the revenue . r. most of them , no question , might againe bouy up , if you of the city could be perswaded to give them credit at conscionable rates , for the stocking of their farmes , tax fairely with them , and purchase part of their estates at tolerable prices . c. however , would to god , they were sensible , how they ruine their families and the countrey , by sculking here , as too many of them do : what they get in the hundred , i am confident , they loose in the shire . r. troth , they are even too sensible of it , but it seems can find no better fence for your flayls . v. soft , mr. civis , do not at one breath condemn our gentry for spending , and sparing too . c. what think you of the lazyness of our poor ? is 't not a national infelicity ? v. find us steady employment , say they , and then spare us not : but till then , pardon us for driving our bargains as we can afford it , or at least for not working without hire . c. i look you should urge the reducing of money upon this occasion . v. you have reason , for in effect , the poor of all nations under heaven are more or less idle or industrious , according to the current rate of their interest : and there 's no such antidote to expel that venom of sloath , either in poor or rich. c. if laws be not executed , what can we hope for ? v. coercive laws , i must tell you , without suitable policies and encouragements , are but like the contrivance of strict discipline for unpaid armies : but in earnest , 't is pity you are not a justice your self to try . c. you would fain palliate it ; but certainly , our greatest plagues at this time are , the incorrigible ideness of our poor , and excessive rate of wages . v. was the stinting of wages ever successfully attempted in any trading-countrey ? c. i marvel it should not , being of such importance to trade . v. surely , their varying every where , as they do , argues them to be of a boundless nature . c. you still affect singularity . v. how can you herein tax me with it ? there being as well a personal , as a local difference in the case : for as one horse of the same size , will sooner bring ten pounds , than an●ther five ; one farmers corn is better worth five shillings , than his neighbours four : so one servant , labourer , or artificer , may well deserve double the wages that another doth in the same place . c. somewhat , i 'm confident , might and would be done in 't . v. truly , nothing at all , but regulate interest , and let nature work : for let us reflect on our former laws of this nature , what have they signified ? : and consider our late act for the militia , which assigns twelve pence a day , as a general and standing hire for those that serve with other mens arms : how hath it been observ'd ? c. the greater fault somewhere . v. 't is in the very nature of wages , which are so variable , that perhaps the same rate , being but half pay in countreys near london , proves double hire in the remoter parts of england . c. if there be no other redress for wages ▪ a fig for all other expedients . v. wages are money ▪ and therefore in abating money , you vertually abate wages : you reduce six , to four pounds a year of real value ; and consequently , eighteen pence to twelve pence a day : but this is not all , it hath a double edge , for in raising the price of land , it ipsa facto quickens and raises all other markets ; and so subdues idleness of course , without noise : servants and workmen being ever noted to be tractable enough , when provisions bear a price . c. nay , if you have no better way to curb their insolence and exaction , we must bid adieu to trade . v. the corrupting of the people is a certain and genuine effect of embasing the land ; for 't is one and the same mischief which oppresses masters , and debauches servants , viz cheapness without plenty . c. cheapness without plenty ! troath i ever took them for the same thing . v. 't was a plain mistake ; for i assure you , they are vastly different . c. do you not take our present plenty for a singular blessing ? v. such plenty is nothing else throughout , but the pampering of sloath , by starving of industry . c. well , 't were a strange abuse , if cheapness should highten wages . v. 't were a miracle , if it should not here : for why should we suppose that any subsisting with ease , and no way depending , will work or serve but on their own terms ? c. but how can wages rise , or indeed , hold in the countrey , tillage so much declining ? r. 't were indeed as broad as 't is long , could our charges be apportioned to our prices : if you artisans and men of profession could but comply with our rents , we should never complain : no , 't is their encroachment , concurrent with the failing of our markets , which mortally wounds us . v. to say the truth , 't is the growth and grandeur of london , which thus imposes on our drooping tillage and manufacture , to their undoing . c. are you bound to imitate our follies ? v. the contagion is unavoidable : for how should those , at least in the adjacent countreys , expect to regulate their wages , whilst you in the city are continually raising yours , as you must , and indeed may well afford , though we cannot without ruine . c. cheapness without plenty , with your pardon , founds odly ; whence , i pray , should it proceed ? v. from this capital inconvenience . that in a necessitous time , the measure of selling is not the worth or cost of the commodity sold , but the sellers exigence . c. a special maxime ! for how is the value of any thing known but in the sale ? v. have you never observed , how one that is clouded sells a fair jewel , or a goodly lordship ? c. you will not , i hope , frame a general rule from a particular case . v. but by private distresses , we may much more judge of publick necessities : borrowers and sellers , i assure you , now live under one unkind planet , the seller being no less a servant to the buyer , than the borrower is to the lender . r. indeed , 't is generally noted , that most men now adays , either borrow to shun the precipice of selling , or sell , to avoid the gulf of borrowing ; so that all things follow the measures of land , and dance with it to the usurers pipe , onely the fate of borrowing commonly lights heavier on the landlords ; that of selling , lights on poor tenants and artisans most . v. to speak freely , what can we judge of our present trafique ( manag'd at such an uneasie rate of interest ) but that much of it is excessive usury turn'd the wrong side outwards ? nay , the trading extortion , perhaps , bites hardest of any : for creditors seem confin'd by . law , whilst chapmen , methinks , know no bounds : and sellers , having generally less command of credit than borrowers , are therefore more expos'd to extremities . c. to me you talk hebrew . v. there is certainly an evil ( though secret ) ferment in the oppressive rate of usury , which in effect poysons all our commerce , one vein or exigence and extortion running through out . c. do you take all sellers to be bankrupts ? v. the greatet part to be sure are now necessitous : and that 's enough to marr the market . c. to what cause will you impute this state of necessity ? v. alas , the ground-work was laid in the impoverishment of our gentry by the late war , though since notoriously amplified by a double grievance obvious enough , viz. the unequal rate of our interest in respect of forraign trade , and that of taxes among our selves , which , methinks , have fairly built upon that foundation . v. 't would make a sick man smile to hear some fore-handed gentlemen , as we call them , how scornfully they defie borrowing , when already most of them pay interest and brokage too with a vengeance . c. can they pay interest then without borrowing ? v. whoever now hath rents to receive , lands to let ▪ corn or stock to vend , must look to drink deep of that cup ▪ whilst interest runs higher with us than with our trading neighbours and land alone , undergoes in effect , all publick burthens . c. it 's a payment , god be thanked , they feel not . r. just thus , for all the world , do many of our wise landlords slight our rates for the poor , and other duties charged on land , because forsooth , they immediately light on the tenant . v. faith , this is a melancholy subject : for as matters now goe , i see not , how any thing but extream scarcity can yield the farmer a tolerable and saving price for his grain : and where , do you think , that must end ? r. in all likelihood , such a discouragement and disabling of our tillage , must produce a dangerous dearth , whenever it pleases god to send ill seasons or harvests , which after so many kindly years , we may now of course expect . c. i wish that were our greatest danger . v. flatter not your self : cheapness and dearth are nearer akin than you dream ; the cheapness of commodity proceeding mostly from the dearth of current money , as that , again , doth from the mean value of land : our chronicle tells us , that in queen maries reign , wheat the same year was sold for a noble and six pence the bushel : a vast disproportion , parallel perhaps to four nobles and two shillings of ours . c. that story , i suppose , will hardly concern our times . v. god forbid it should ; though 't is a clear case , our cheapness now proceeds from nothing less than plenty of commodity : for i 'm confident , there hath scarce ever been less in the granary : and surely the prospect of our next harvest is not over-hopeful : besides , we are told of great dearths in forraign parts ; so as , for ought appears , had we grain , we might have vent enough : thus all things , one would think , should conspire to give corn a considerable price at this time : and yet , he that would now sell any quantity of wheat , can scarce get four nobles the quarter : neither stores , crops not prices : ghess , mr. civis , at the reason . c. 't is quite out of my element . v. you must be blind not to see , how our markets are enthral'd by necessity , and the benefit thereof wholly ravished from the poor farmer , who as to avoid a wretched bartering and retailing trade with his indigent neighbours , that now live but from hand to mouth , falls a prey to some usurious interloper . c. i should rather wish him to keep his grain for better prices , which time and patience no doubt would bring him . v. have you not heard , that the steed may starve whilst the grass grows ? who , i beseech you , in the mean time shall pay his two rents and make good his seasons ? you would do him a courtesie either to bayl him for the present , or secure him from loss in the upshot : his fruits being perishable , and our markets now adays seldom mending : for indeed , the first , how low soever , are generally noted to be the best . c. i never heard that to be observed before , nor can i devise any good reason for it . v. can it be , but forbearance of sale must still further aggrevate the sellers necessity ? r. pox on 't , i 'm sure 't was not wont to be so : we had once a kind of market in every parish , and could utter most of our commodities at home : we were not then forc'd to carry our corn god knows whither , deal with god knows whom , sell for god knows what , to be paid god knows when : but are we to marvel at this want of vent , when so many good seats and farms , every where , stand empty , the crows being tenants , and the rooks landlords ? v. never look to see things mend , but still further decline , whilst the land it self is so cheap , and the revenues of money and land at so wide a distance ; for if the spring-head be brackish , how can the streams be wholsome ? r. carry your compost still from the soyl , say we in the countrey , and see what your farmes will come to . c. belike , you imagine low interest will quicken your vent , and mend your prices . v. it glories in nothing more than the due balancing and fixing of markets : for want of which in languishing countries they float , and are bandyed from one extreme to another , always either choaked or pin'd ; now shivering , as it were , with treacherous cheapness , anon burning with grievous dearth . c. quickness of markets , no doubt , were a great felicity to us at this time ▪ but will low interest , think you , produce it ? r. will you put us to prove ▪ that by the fall of money , all things bought with money must rise ? v. 't is a plain case , land , like a primum mobile of commerce , swayes the lesser orbs : so as by a natural sympathy and symmetry as it were of parts with the whole : wheresoever land is cheap or dear , all the native commodities are cheap or dear with it ; and whatsoever depresses or exalts the fund it self , accordingly embases or ennobles it's fruits , either affecting them with a mean and contingent price , as in colonies , or with a considerable and constant value , as in flourishing countries . r. indeed 't is remarkable , that the prices of our corn and cattel have all along ebb'd and flow'd with that of land : the same deadly exigence , which hath driven the free-holder to part with his estate at half the value , constraining likewise the farmer to expose his fruits at a rate , even beneath what they cost him . c. i perceive yoa are all for land. v. so would you be too , did you but consider , that land is eminently all things else : i have heard it notably aver'd , that two years purchase gain'd or lost in the price of land , doth ipso facto augment or impair the capital of this kingdome more than the value of all our cash , and other goods together , ( stock upon the land excepted . ) c. sure you expect a fee from the landlords . v. some others , perhaps , may soon be as sensible as the landlords themselves , what an immediate character of decay the fall of land stamps on the commonwealth , what a fatal and contagious cheapness and penury always attends it ! r. methinks 't is of prime importance to this argument . that the whole burthens of excise or impost , however design'd , now certainly light on the part already grieved , viz. the land , as humors resort to a bruise . c i ever took it , that excises and imposts fell on the consumer , i 'm sure it hath been generally so receiv'd . v. 't is then a vulgar error , for the merchant informs us , that high duties are an embasement to any commodity , amounting to a kind , of prohibition . c. yet i have heard able merchants wish , the customs were taken off from forraign trade , either in whole , or at least in part , and a recompence otherwise charg'd , viz. by an easie pound rate upon land , or moderate excise . r. the same notion have i met with from traders , and once from a worthy gentleman . v. were interest roundly reduced , and money brought into the tax , it might do rarely well , but what , indeed , almost could then miscarry ? r. so i answer them , yet still they affirm , that even as things now stand , the countrey would chiefly reap the benefit of it . v. beshrow their partiality : but in earnest , can they think us such fools to be so impos'd on ? let them go preach at barbadoes , and virginia , what a lift it would give to their trade , if additional duties were laid on sugars and tobacco's , certainly land-taxes ( besides the ruinous clog of our inheritances , where continued ) are dangerous imposts upon all growth at the first hand , and no way now to be born , without the regulating of interest . r. nay , i ever disrelisht the proposal , for indeed , common sence dictates , that publick burthens are far more comfortably laid upon forraign superfluities , viz. wine , silk , spice , &c. than upon our native commodities , viz , corn , wool , flesh , &c. all which are evidently taxed in the land : and therefore so to transfer the customs , what were it but like the rash cure of a sore leg , by driving back the humour , to the hazard of life ? v. besides , 't is suppos'd , the very maintenance of our poor , alone considered , is already , in point of charge at least double to all the burthens of forraign trade : that of the church , by tithes and other duties , more than treble : and yet , perhaps , these are not half the incumbrances of land. c. well , 't is thought by knowing men to be a wholsome expedient . v. it may prove so in time , but never till usury be tam'd , without publick ruine : for consider of what consequence it must be for poor farmers still to encounter with bad markets ; alas , 't is nothing but over-charging the land hath already brought us to this pass . c. i ever took you to be a zealous advocate for trade , but find you rather its adversary . v. a fair and well-grounded trade advances land , and therefore cannot be enough honored and encouraged : whereas our present traders can subsist with no less profit than must undo the countrey . r. 't is too manifest indeed , that without grinding the farmer and artificer , our merchant could scarce abide any forraign market , but being , as he oftimes is , sorely bitten , he licks himself whole with a witness at their cost , easily trampling where the hedge is low ▪ so that there all our miseries center , as heavy things natuaally sink to the bottom ▪ v. this take for an infallible rule : the immoderate benefit of traders hath an evil aspect , and is inconsistent with good trade ; for light gains , we say , makes the purse heavy , which rule holds more currently in the national , than in the personal concernment . c. do you grudge the merchants gains , or would you have them limited ? v. i onely wish them more regular , and doubtless had we a just rate of interest , they would need no other limits ; but now , to be sure , where the traders benefit is vast , the poor countrey pays the reckoning ; since the market abroad affords it not , as our good neighbours the dutch will inform us . c. these are but notions . v. nay , there 's nothing in proof more familiar , for to instance in our vent of corn ; suppose good english wheat now carry eight shillings the bushel in the mediterranean , where we read of so much scarcity in our weekly gazettes : if the merchant here give five , his profit is very competent , yet consistent with a livelihood to the farmer : but if he lade , as i doubt he doth , at three , nay , oftimes under , he , indeed , may soon thrive , if his stock be his own , but our tillage must certainly droop ; the same reason holds in our manufactures . c. where all this while doth the sho●e wring ? r. as to the sale either of our lands or goods , there is now one general complaint , viz. that of many sellers to a few chapmen ; not to be redrest with such a retrenchment of interest , as shall oblige our usurers to purchase or trade in good earnest . v. in holland , we know ▪ money being cheap and land dear , mighty stocks , even the whole estates of wealthy and wise men are generally pour'd into commerce , with profit suitable to low interest , and great thrift necessarily attending it , but with certain and prodigious vent : whereas here the able merchant dallies with trade , contenting himself with the credit and outside of his profession , and dealing onely with a small stock to his private ease and advantage , but to publick decay : as for the bulk of his estate , 't is manag'd at interest , or at best laid out on some easie purchase of land : wer 't not for these helps at maw , to be sure , our traders would long since have swallowed low interest , perhaps more greedily , than the very farmer or landlord . r : we find it , indeed , to our cost , scarce any traffique comes amiss to the fleming ; he under-sells his neighbours , even in their own commodities : whilst we , on the other side , are confin'd to a few trades , being forc'd to take his leavings , and quit divers of the greatest bulk and advantage to the publick ; for such are commonly those that yield small benefit to traders . v. nay , for a clear demonstration , what the cheapness of money effects , he can afford to furnish us with our own corn hoarded divers years ; the sale whereof , few of our farmers can at all forbear : to see such a spot of ground undergo such burthens , equip such fleets , maintain such wars , repair such losses , one would think it should make their neighbours enamoured of low interest . c. 't is suppos'd , the dutch have a world of other arts and advantages for trade beyond us . v. some they had need to have to carry it as they do , but this is their mother-policy , which gives them so much the start of us , nay , which gives life to all the rest . this , no doubt , is the very hinge upon which they all move : they subsist by endeavour , we thrive by sloath ; their merchants are merchants indeed , ours onely in countenance . c. will you blame men for playing the best of their game ? v. 't is pity , i 'm sure , it should be so ; yet i must neeeds partly acquit them ; for in countreys , where interest runs higher than with their trading neighbours , small dealings are commonly gainful , whereas vast stocks are scarce to be imploy'd in trade without ruinous hazard ; it being , indeed , in the nature of high interest , to make the gains of merchandise great , but altogether contingent ; in that of low , to render them moderate , but withal , certain . r. what a par-boyl'd traffique do we drive in the mean time ! such a sickly and languishing trade may well prove hectick to the commonwealth . c. you your self have often noted from the advancement of the customs , and other the like measures , that our trade hath long been , and still is upon encrease : how doth this suit with the languishing trade you complain of ? v ▪ the late encrease of customs and of our trade in bulk , we owe partly to the growth of our plantations , but principally , i doubt , to the fatal cheapness of our land ▪ and it's fruits , it being in effect but a web spun from our own bowels , and a pyramide erected on the farmers decay ; though therewith 't is slow and scarce discernable , like the growth of dwarfs and stunted trees ▪ whereas the low rate of interest in holland , and the late notable abatement of it in sweden , renders their advancement in trade and shipping as conspicuous as the sun in it's noon-day brightness : now if we stand still whilst our neighbours thus advance , the old rule , non progredi est regredi , may ( all things considered ) prove our case . c. is 't possible , the odds of a little interest money should be of such moment ? v. is 't possible a tradesman should ask that question , who daily sees how a grane turns the scales ? and therefore cannot be to learn , wh●t a change must ensue from the difference of a third part in our r●te of interest , since by it all contracts are weighed , measured , and finally governed : surely high interest must dangerously affect all our dealings , and especially the minds of men , who acting rationally , and not being troubled with squeamishness of conscience , cannot but prefer ease and certainty before pains and hazards , though the benefit were equal , which generally , i presume , it is not . r. nay , but in the matter if self , ( as you said before ) betwixt trading at a rate above or beneath the market ; be the difference never so little , the general disproportion is vast . the one rowing , as it were , with wind and tide ; the other , against both ; the one being sure of current vent for the greatest fraughts ; the other running manifest hazard of bad market for the smallest . c. i 'm sure , we celebrate those for flourishing and happy times , when less than half the trade serv'd us that now we drive . v. to advance in a small estate , is far more hopeful and cheerful , than to decline in a great . c. remember interest was at 10 per cent. in that which we reckon our golden age. v. and , forget not , if you please , how the case is since alter'd with us , by the late war athome , and the general peace abroad , by the excessive growth of holland , and by the necessity of several impositions for the support of the government . c. it was once your judgement , that land and trade could have no divided interest . v ▪ land and trade , to be sure , cannot : but land and traders ▪ methinks , may . c. what would you be at ? all never did , nor could thrive ; and if some now do , what matter to the publick , who the parties be ? v. with your favour , if a few , and those idle persons onely swagger , whilst the many , and the industrious droop , where must it end ? let 's however stick to our ancient motto , god speed the plough . c. have you never heard the proposal of a different interest upon real and personal contracts ; methinks , it might now be seasonable . v. it was of old , my lord bacons : and truly , if you will warrant it practicable , i dare pronounce it equitable , in respect of hazard and gain ▪ for visibly most trades-men might yet better afford to borrow at eight , then gentlemen at three per cent. c. upon the whole matter ; there 's much i see to be said for low interest : but you 'l ne're convince me , that 't is such an elyxir , as you fancy . v. assure your self , want of good vent in an island , blest with so many advantages as this above all , with liberty , safety , and peace , doth even naturally guide us to that expedient : neither is bloud letting a more specifick cure for the pleurisie , as may appear by the preamble of the statute 21 iacob l , which you will find instar omnium to my sense , if you please to consult it . c. i hope , you do not , mean the art , which first brought money from ten to eight in the hundred : for how can that serve your present purpose ? v. believe me , 't is a fair and perpetuall looking-glass , clearly representing , how the price of all our native commodities waits on that of land ; how all things then were , and must ever be embased , nay even prostituted to an inconvenient rate of interest : for thereunto it imputes a very great abatement in the value of land , and other the merchandises , wares , and commodities of this kingdom , the disabling men to pay their debts , and continue the maintenance of trade ; the enforcing them to sell their lands and stocks at very low rates , to forsake the use of merchandise and trade , and to give over their farms , and so become unprofitable members of the common-wealth . c. i trust , you will not draw arguments for four per cent. from the authority which permitted eight . v. by the resemblance of symptoms , i leave you to judge of the disease , and consequently it's cure : for is not our condition here describ'd to the life ? doth it not speak our very idiom ? and if the same reason , why not the same law ? r. you may swear , it hath long been our very case : our farmes have proved meet plantations , our freeholds sorry cattels ; and consequently all the fruits of the land as errand drugs , as any stale mackerel cry'd about london-streets in iunc . c. i could almost afford to wish , that money were for a while abated by way of probation . v. your proposal , indeed , is back'd with the authority of former precedents ; though temporary laws are seldom through paced : but what a change would it make , if money were but cheap with us , and land dear , 't would be a salve for every sore , and of such general advantage , as if our very climate were altered , and our countrey carried ten degrees southward : all ranks from the prince to the swain would soon feel the warmth of it . c. if 't would ascertain the payment of rents , that we might have current security again , 't were somewhat like ; but for raising the purchase of land , i reckon , 't is onely robbing peter to pay paul. v. are you deaf , or asleep ? would not our rents be current , if our markets were quick and steady ? and what hath been all this while the drift of our argument , but to shew , how all things rise and fall with the land ? c. nay , i am not yet your proselyte . v. but do you not apprehend of what importance 't is to raise the purchase of land ; how it enlarges both the publick fund , and every individual estate ; what an indies 't were to us , if our lands were currently sold for thirty or forty years purchase ; and what magnificent improvements of revenue must of course ensue ! c. you are still vnpouring with your improvements , when 't is the opinion of our wisest men , we have already improv'd our selves out of doors , and nothing else hath undone us . v. nothing hath indeed undone us , but the discouragement of it : for most of our land without it , is no better than a waste to the commonwealth , and de-quoy to the farmer ; whereas solid improvements are to the owner more valuable than any purchase to the state , more considerable than conquest . c. well , you differ herein from all i converse with . v. then you converse with none but money-mongers : for rusticus knows , there 's not half the improvement now stirring , he and i remembred , which is , and must be the ruine of our farmers ; since without regular cost bestowed on most lands , it is easily ghessed , what the tillage of them will come to . r. i would not be bound to plough the better half of our farms rent — free , without constant and chargeable manuring them . but alas , where are the tenants , or indeed owners , that are able , as things now go , considerably to mend their land without borrowing ? which are like the chymists vanity , to make gold without loss . v. nay , though they never borrowed , could they afford it at our present rate of interest , and the now current prices of land and stock , unless they challenged the priviledge of doing what they list with their own : would not they raise double the ret venue by lending , or purchase cheaper at least by half ? r. that likewise would be well advis'd on . v. as i am grieved to see such tracts of arable lye untill'd upon these accounts ; so am i scandaliz'd to observe thousands of acres yearly ploughed to great loss for want of good husbandry , which ▪ with our familiar amendments ( not discourag'd ) might have yielded crops equally profitable to the owner and the publick . r. did but our sages and criticks mark the different product of the same lands , according as they are well or ill husbanded , and withal consider , that however the crop proves , the charge of tillage is the same , they would not so deride improvement , but wise men are apt to abound in their own sence . v. nay surely , if the farmer , who now hath twelve or fourteen bushels of wheat on an acre , and sells by the medium of three shillings , could ( as formerly ) have eighteen or twenty , and sell by that of five , 't would soon make all things smile : 't is doubtless from the same decay , that both our crops and prices falls , and as they fell , so they must rise together . c. imarvel , you should still rove on improving the land , when already it yields more than people we have can consume . v. are we then purely to depend on our own consumption ? c. i suppose we must , if we find no better vent abroad . v. small cause we have to complain of forrain vent , especially at this time , having more market than grain to vend . r. no 't is a fatall constellation , where half-crops , low prices , and high wages meet , as we see they here do in the embasing of the land. c. do you not then alow our deadness of vent to proceed from want of people ? v. as if there were any thriving without encrease , or decay without fayler of people . c. that want however , it seems , you admit . r. we feel it indeed shrewdly in the countrey ; but methinks , we do not meet with it in your streets at london , nor find it by your buildings in the suburbs : now surely 't were charitable in you to spare us some of your colonies . v. 't is too manifest , that both in wealth and people , ( which are plainly inseparable , ) and in effect synonomous , our cities and trading towns have of late dangerously gain'd upon our villages , though perhaps without loss in the total : in london , within forty years , there hath been an encrease of inhabitants , alone sufficient to stop all our gaps ▪ witness our weekly bills of christenings and burials : however , can we colourably complain for want of people ▪ that employ not half those we have ? use leggs , and have leggs , was the old rule . c. to me it appears , we want only mouths to eat what we cannot utter . r. where i beseech you , are those vast granaries of ours ? if we be not grosly abus'd in our intelligence , we might soon be rid of that burthen ▪ were our stores far greater , then i doubt they 'l prove . v. had you told me , mr. civis , we wanted hands to work , or stocks to employ them , you had said somewhat : but mouths without hands , introth , 't is such a complaint , as was never , i think , offer'd before : for were not that want soon supply'd , by cherishing our breed of vermine ? r. doth any large and fruitfull parish , judge you , lack a hundred poor and lazy families to maintain for vent of their corn ? if not why should you fancy the common-wealth wants creeples or beggars ? c. still i affirm , that had we twice the people , 't were much the better . r. troth , i should be of your mind , if i saw those we now have , a little more useful and profitable to us than they are : indeed the more the merrier , we say , yet withall the fewer the better cheer v what pastime 't is to hear the goodly expedients commonly propounded to quicken our vent ! one is for the raising and fixing of prices by law ; another would have sowing of corn , when cheap , prohibited ; a third gives sentence against great crops , to be half burnt ; a fourth is for the drowning of our fens and marshes , and restraint of all future improvements : a fifth is tooth and nayl for polygamy : with such bulrushes am i oft encountred by the bravest champions of six per cent. c. but what if our consumption were promoted , by generally clogging the importation of forraign growths and manufactures . r. as if trade would soar the higher for being more clog'd . v. i hate these shallow and penny-wise projects , which serve rather to proclaim us bankrupt , than prevent or cure our poverty : 't is like the tithing of mint and rue , but neglecting matters of moment : or like hard pumping in a ship without stopping the leaks : god help us , when we must have recourse to such shifts as are sometimes offered ; that were playing at small game indeed : no , i 'le for feit my senses if any thing effectually raise our markets , but the buoying up of land by the fall of ujury , and equality of assessments , not the publick only , but the parochial : in a word , be but just to the land , and all will come right of it self . r. to baffle truth , and maintain paradoxes is a sophisters task : but common sense , one would think , might soon discover , that an inconvenient rate of interest and taxes is alone sufficient to embase the land , and consequently all its fruits , though lofty wits , it should seem cannot stoop to such vulgar aphorismes . v. indeed the profound enquiries , politick lectures i daily meet with concerning the fall of rents , make me think of the butcher , that searcht narrowly for his knife , when 't was in his mouth : and most of the remedies offer'd are not unlike a plaister to the shin or toe for a hectick feaver . c. i was lately at a serious club , where this was the argument : and low interest was there resolv'd to be profitable , if seasonable : but 't was withall agreed , that matters with us are not yet ripe for 't . v. yet a little sleep , a little slumber , saith the sluggard : but surely never were matters so ripe as now ; when our farmes are half under-stocked , yet our markets clog'd ; when borrowing notoriously crushes almost wheresoever it lights ; when tillage and trade cry aloud for it , as it were one and all ; when mortgages of double or treble value daily become scarce worth redeeming ; when security as well as credit is worn thredbare , and lenders almost as much distrest as borrowers : when the business expects only the midwifery of law , being ready , ( if 't were possible ) to teem of it self . c. you are princes in conceit , but for abatement of interest , let me tell you , for your comfort , 't will not pass in our time . r. then let me tell you , for your comfort , the tayl of this comet , i doubt , hangs over your city . v. for my part , really i should despair , from the strange contradictions and evasions it meets with , if i saw any shift could be made without it : but though reason may be foyl'd , yet sence and fatal experience will not ; for who can now provide for posterity with an indifferent estate ? and what , indeed , doth a great one signifie more than the noise and trouble of it ? how casual do most of our dealings , and even our callings prove ? besides , without the rise of land , what can enliven our farmers , quicken our markets , or rescue us from the deadly fits of cheapness and scarcity ▪ but above all ; in case his majesties occasions and the publick safety should require large and frequent levies , ( as in reason they must ) what else can enable us to the comfortable payment of them ? 't were a miracle one would think , if one of these motives should at length prevail : my life for 't , this distemper of ours hath a speedy crisis . r. nay , 't is a catching disease , and will without speedy prevention , go round the house . v. i tell you mr. civis , i would scarce thank any man to secure me , that interest shall be abated within a few years : for 't will cut it's way through the rocks , and is now methinks , at our threshold ; though i wish we might step forward to meet him ; for otherwise , as near as it is , e're it do it self , we , i doubt , shall be more than half undone : and , indeed , who can be without concernment , for thousands of honest families are now languishing under the delay of it ? but you may remember , i have often upon this occasion compared my self to the man in the dark , digging for day , which with a little patience will certainly come of it's own accord . c. faith , come and welcome ▪ four per cent. say i , could we but hope for a register of titles and incumbrances ; there were some comfort yet ▪ if once they passed hand in hand . v. how many knots do you find or make in a bulrush ! alas , low interest and a register have a little mutual dependence or affinity ▪ though some would cunningly pin them together , that the heavier may clog the lighter ; a register will be an engine , which will be long in framing , and then perhaps not work in an age ; whereas abatement of interest being fully precedented to our hands , and lying ready for present use , may both pass in a trice , and operate from the very time of it's passing . besides , what i pray , would your register finally import to the due and necessary ballance of our trade ▪ and markets , or to the exciting of industry , and curbing of sloath , which are our principal aims : but i must take another evening to discourse it with you ; 't is time we were at our lodgings . errata . page 5. line 17. for ranks , read rooks. finis . the doctrine decimal arithmetick, simple interest, &c. as also of compound interest and annuities generally performed for any time of payment or rate of interest by help of a particular table of forbearance of 1l principal, with enlarged rules, formerly abridged for portability in a letter case / by john collins ; and since his death, both made publick by j.d. collins, john, 1625-1683. 1685 approx. 107 kb of xml-encoded text transcribed from 55 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2005-12 (eebo-tcp phase 1). a33998 wing c5372 estc r23930 07929253 ocm 07929253 40487 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a33998) transcribed from: (early english books online ; image set 40487) images scanned from microfilm: (early english books, 1641-1700 ; 1203:2) the doctrine decimal arithmetick, simple interest, &c. as also of compound interest and annuities generally performed for any time of payment or rate of interest by help of a particular table of forbearance of 1l principal, with enlarged rules, formerly abridged for portability in a letter case / by john collins ; and since his death, both made publick by j.d. collins, john, 1625-1683. [5], 102, [1] p. printed by r. holt for nath. ponder, london : 1685. note in manuscript: p. 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that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng interest -great britain. decimal system. 2005-07 tcp assigned for keying and markup 2005-08 apex covantage keyed and coded from proquest page images 2005-09 john latta sampled and proofread 2005-09 john latta text and markup reviewed and edited 2005-10 pfs batch review (qc) and xml conversion the doctrine of decimal arithmetick , simple interest , &c. as also of compound interest and annuities ; generally performed for any time of payment , or rate of interest , by help of a particular table of forbearance of 1 l. principal , with inlarged rules . formerly abridged for portability in a letter case . by john collins accomptant , philomath . and since his death both made publick by j. d. london , printed by r. holt for nath. ponder at the peacock in the poultry , near the stocks-market , 1685. the epistle to the reader . courteous reader , it is the accustomed way to dedicate books to some honourable person , that thereby the book might have the greater esteem . this book needs no such dedication , for the name of the author ( which will never dye , ingenious mr. john ted at the end of the book , whereby the reader may see it no ways derogates from the old copy , and thereby may see how full and plain the new rules are in comparison to the old. this book is a fit companion for all gentlemen , merchants , scriveners , and other trades-men , that deal much in lending of money upon interest , mortgages , buying of estates either in fee , copy , or lease , holding annuities , rent charges , forbearance of money , discompt , or any other way concerning interest , &c. when any person does perfectly understand the large rules , he may if he pleases lay by the book , and only use the compendium with the tables to be carried about in a letter case ; and i hope in perusing this small treatise the reader will find that which will give him satisfaction , both as to the rules and tables . yours , j. d. decimal arithmetick . a decimal fraction is such a one whose denominator is understood , and not expressed ; and is an unit with as many cyphers following it , as there are figures and cyphers in the numerator . corollary , wherefore the annexing of cyphers towards the right hand of a decimal , alters not its value . a decimal fraction of coin may be easily valued without the help of tables . for each unit in the first place is in value 2 s. 5 in the second place 1 s. and the rest farthings ; but if they exceed 25 / 48 there must be two farthings abated . example . so ,854 is in value 17 s. 1 d. ,418 8. 4½ addition and substraction in decimals is the same , as in whole numbers , keeping the place of units just under each other . multiplication in decimals is the same , as in common arithmetick , saving as many decimal parts as are in both multipliers , so many must be cut off from the product , which if it have not so many places , the defect is to be supplied with cyphers towards the left hand . division is the same as in whole numbers , without regard to decimals till the work is done , and then use the converse of the rule for multiplication ( viz. ) so many decimals as are in the dividend , so many there must be in the divisor and quote , and if there be not so many , the quotient must be supplied with cyphers towards the left hand . simple interest . prop. 1. to compute the interest for a day , 6 / 365 is the interest of 100 l. for a day the 1 / 100 , whereof is the interest of 1 l. for a day ( viz. ) 6 / 36500 ; or 6 ( with cyphers put on at pleasure ) divided by 36500 is , 000164383 the interest of 1 l. for a day . prop. 2. the decimals of days in the table at the end will serve to find the amount of 1 l. simple interest of any rate for any time under 365 days or a year . if you take the decimal for one day ( or more ) and multiply that by , 06. 7. 8. &c. per cent. or any other rate , the product will give the interest of one pound for a day , or more under 366 days at simple interest . example 1. the decimal for a day is ,002739726     ,06 the interest of 1 l. for a day ,00016438356 example 2. the decimal of 121 days is ,331506849   ,06 the interest of 1 l. for 121 days ,01989041094 ,002739726 decimal for a day ,07 per cent. ,00019178082 the interest of 1 l. for a day at 7 l. per cent. and so of any other rate of interest . prop. 2. forbearance of money at simple interest . the interest of 1 l. for any number of days , at what rate of interest you please , be first found by the first proposition , that product multiplied by the sum propounded , gives the interest thereof for the time required . example . to know the amount of 140 l. for 121 days , at 6 l. per cent. simple interest . the decimal of 1 l. for 121 days 1,019890410 multiplied by 140 which is 142 l. 15 s. 8 d. 40795616400   1,019890410   142,784657400 prop. 3. rebate , or the present worth of money due hereafter . find the interest of 1 l. for the time given , as in prop. 1. and thereto add an unit by it . divide any other sum propounded , and the quote is its present worth. example . if 142 l. 15 s. 8 d. be due at the end of 121 days , what is it worth in ready money ? worth in ready money 140 l. at 6 l. per cent. simple interest , and may be done for any other rate of interest , working by the first proportion and this former rule . prop. 4. equation of payments . by prop. 3. compute all the present worths , and then by proportion . if all those present worths amounted to the total of all those payments , what did one pound amount to in the said time ? from the result substract an unit , the remainder is the interest of 1 l. for the time sought , which divide by the interest of 1 l. for a day , the quote is the number of days sought . if you are to aequate an annuity , at simple interest . i presume a compendium may be found in mengolus his arithmetical quadratures ( a book i never saw ) who it 's probable by a compendium gets the fact of an arithmetical progression , and adds fractions that have a constant numerator , and an arithmetical progression for their denominators . so much for simple interest , my design being more for the explanation of the tables for compound interest and annuities . of compound interest . the original thereof is derived from simple interest , for if it be lawful to take interest at all , then it is as lawful to put out the interest-money to use , as the principal . for ease in calculating questions that concern compound interest , arithmeticians do usually frame tables in store , to shew what 1 l. principal forborn at any rate for any determinate time shall amount unto ; the construction whereof is by the golden rule , as followeth ; as 100 l. principal is to the amount thereof at the years end ; so is an unit. to its amount ( to wit. ) so is 1. 1 , 06. if 6 be the rate of interest , then it will hold again for the next year . as 1. 1 , 06 , so 1 , 06 , to 1 , 1236 , the principal and interest at the second year . now because an unit is in the first place , which doth not divide , it followeth , that the second years amount squares the number 1 , 06 , being the quotient of 1 , 06 divided by 100 , and that is the amount of 1 l. forborn a year , the compound interest the third year cubes it , &c. and the said number 1 , 06 is by arithmeticians called the ratio , quote or denominator of the ratio propounded , and the logarythm thereof multiplied by the time doth raise those powers agreeable to the nature of logarythms . by the former proportion was the following table for years made , or for abridgment by addition , only by help of a table of 1,06 multiplied by all the digits ; and this raising of powers is by some called involution , and as for that of months may be made by finding mean proportionals , and those of days by help of the common logarythms , or without , supplied far enough downward , by help of mean proportionals , and a decimal table for time , and three months here is understood to be the precise ¼ of a whole year , and so of the rest . that which we add concerning it , is , that it self is in effect no other than a table of logarythms , but of another kind than those in print , yet herein agreeing therewith , that in both the logarythm of an unit is o , and therefore this table may be continued for any large time by one or some few multiplications , it is here continued to each year for 50 years , then for every 10 years to 100 , whereby you may perceive that an inheritance , or a sum due after such a time is worth little more than a three hundred and fortieth part of its present worth. and in the next place it will supply the defect of all other tables ( especially those that relate to the said rate of interest ) whether of discount of money or of forbearance of and discount of annuities , or for the purchase thereof . in the tables following the number of years are the logarythms or indexes , and the amounts are the numbers to which the logary thms belong , and because this is no full table of logarythms to ten or one hundred thousand , we therefore use multiplication and division to supply those defects , wherefore the first prop. is ; prop. 1. to continue the said table . multiply the numbers together that belong to any numbers of years , that added together make the years of continuance required . example . let it be required to find the amount of 1 l. for 50 years . 20 years   3,20713 30 years   5,74349 50 years product is 18,42015 and is the number sought , omitting the five superfluous places of decimals . another example . it is required to find the amount of 1 l. forborn 20 years three quarters . 20 years is 3,20713 9 months 1,04467 the product 3,25180 and the like may be done for days , and the converse when an amount is given , the time thereto may be found by division , searching in the table what number amongst the decimals for time agrees to the divisors and last quote . see prop. 8. the first section . and here it is worth noting , that many questions may be put concerning compound interest , which are of the like difficulty , as to raise the printed logarythmetical cannon . for example such a question may be put ; one pound was put out at compound interest , and in 10 years time amounted to 10 l. in what space of time did it amount to 2 l. the answer is the logarythm of the number two ( to wit ) 3,01023 years which was not raised without much toyl , and the rate of interest in those logarythms is near 26 l. per cent. to wit 25,89292 . the uses of the said table . prop. 2. a sum forborn for any time , to find to what it shall amount to at 6 l. per cent. compound interest . find in the table , or compute by 1. prop. the amount of 1 l. for the said time , and then it holds . as 1 l. is to its amount ; so any other sum to its amounts : wherefore the amount of 1 l. must be multiplyed by the sum proposed . example . what shall 136 l. 15 s. 06 d. amount unto being forborn 20 years at 6 per centum ? the amount of 1 l. for 3,20713 20 years is which multiplied by 136,775 the product is 438,655 reduced is 438 l. 13 s. 1 d. 4● prop. 3. a sum of money due hereafter , to find what it is worth in ready money . find in the table what 1 l. forborn , the like time shall amount unto at compound interest , then it holds . as the said amount is to an unit ; so is any sum propounded , to its present worth. corollary . therefore if an unit be the sum whereof you would find the present worth , you will frame the numbers in the usual table for discount , and for all other sums : because an unit doth not multiply , it will follow they must be divided by the amount of 1 l. for the like time . discount , or the present worth of money due hereafter . example first , for making the table of discount . an unit divided by 3,20713 , the quotient is 311804 , the present worth of 1 l due 20 years hence . example second . if 400 l. be due 20 years hence , what is it worth in ready money , abating compound interest at 6 per centum per annum ? divide 400 by 3,20713 , the amount of 1 l. forborn 20 years at compound interest , and the quotient is 124 l. 722 , or 124 l. 14 s. 5 d. ¼ and how to reduce sundry payments , to an equation of time at compound interest . see first example of prop. 8. prop. 4. of forbearance of annuities . to find the arrearages of an annuity . the difference between the forbearance of an annuity , and of a principal put out to interest , is this , that every year there is a principal like the first added . the proportion holds . as , 06 the compound interest of 1. l. for a year , is to the amount less by an unit of one of one pound forborn at compound interest for the time proposed . so is any annuity or yearly payment of rent forborn the like time , and at the same rate , to the arrearages thereof due . and when the rent is payable half-yearly , quarterly , the first term in the proportion must be the compound interest of 1 l. for acordingly , &c. half a year , quarter , example . let it be required to find what one pound a year annuity forborn for 30 years at 6 per centum shall amount to . one pound forborn at compound interest so long amounts to 5 , 74349 which lessened by an unit is 4 , 74349 which divided by 06 , the quotient is 79 , 0581 and this is the number found in the vulgar tables for forbearance of annuities . second example . let it be required to find what 20 l. annuity forborn for 15 years shall amount unto at 6 per centum . 1 l. principal forborn 15 years amounts to 2 , 39655 from which subtracting an unite it holds . as , 06 to 1,39655 so 20 to 465 , 516 , that is 475 l. 10 s. 4 d. third example . a quarterly rent of 25 l. was respited 20¾ years , by the first proportion the amount of 1 l. so long forborn was 3 , 34978. and the interest of one pound for a quarter is 0 , 14675 wherefore by proportion , as , 014675 is to 2 , 34978 : so is 25 to 4003 , 032 that is 4003 l. 00 s. 7¾ d. this useful proportion i thus demonstrate which the reader may pass by . imagine the land or stock that yields an annuity to be such a principal sent out for the whole term as will bring in so much yearly interest as the annuity comes to , then at last the whole at compound interest is to be repaid , whereof so much is supposed to be repaid in the value of the land , as its first principal came to , and the rest in money ; wherefore out of the whole amount of that principal and its interest , the principal must be deducted unless to shun it by that which geometers call conversion . see commentators on 16 def. quinti euclidis &c. we say , as the first term is to the difference of the first and second ; so the third term to the difference of the third and fourth . the plain proportion grounded upon the former considerations runs thus , as 1 l. principal . is to its amount for the time forborn ; so the principal that shall bring in any annuity proposed . to the sum of the said principal and of the arrearages of the annuity . then it will hold by conversion of reason . as 1 l. forborn at compound interest is to its amount less by an unit for the time forborn ; so is the principal of an annuity , forborn the like time , to the arrearages of the annuity . and instead of the third term of this proportion , we may take in a fraction equivalent thereto , the numerator whereof is the annuity or yearly payment of rent , and the denominator the interest of 1 l. for a year ; for to find the principal of an annuity say , as 6 is to 100. or rather , 06 : 1. so is the annuity to its principal . and both these latter proportions compounded into one will be the proportion first delivered , the units in each being expunged as insignificant either in multiplication or division . prop. 5. to find the present worth of an annuity . if an annuity be forborn till the last payment be due , then for as much as the interest of each particular payment is by the former or 4th . proposition computed , if by the 3d. proportion the same , together with the rebate of each payment be destroyed ( to wit ) the present worth of the whole arrearage be computed it shall be the present worth of the annuity , the proportion in both those propositions being after the manner of the 4th . prop. composed into one it will hold for annual payments at 6 per centum . as the fact of ( ,06 ) the interest of 1 l. for a year , and of the amount of one pound compound interest for the time proposed , is to the said amount less an unit. so is the annuity or yearly rent to the present worth thereof . example . first for making the tables . to find the present worth of an annuity of 1 l. per annum , to continue 25 years at 6 per centum compound interest . the amount of 1 l. for that time is 4,29187 which multiplyed by ,06 the fact is ,257512 , whereby dividing 3,29187 the quote is 12 l. ,78335 the present worth sought . example . secondly for half-yearly payments . an annuity of 40 l. payable , 20 l. each half year is to befold for 12 years at 6 per centum . the compound interst of 1 l. for half a year is — ,029564 the amount of 1 l. forborn 12 years — 2,012196 multiply these two together , and that added together makes the fact of both ; which is — ,058487 it therefore holds , as ,058487 is to ,1,012196 . so is 20 to 346 , 166 that is 346 l. 3 s. 4 d. the present worth thereof . if this annuity were paid yearly it must be of less value because the mony is longer in coming in , and accordingly the worth of it l. s. d. would be but — 335 — 7 — 1 admit it were required to know what an addition of 8 years more is worth after 12 are expired .   the worth of the said annuity for 20 years , is — 458. 15. 11 the difference of these two is — being the present worth of the 8 years sought . 123. 8. 10 prop. 6. to find what annuity any sum of ready money shall purchase . this is but the converse of the former proposition , and it holds therefore ; as the amount of 1 l. forborn at compound interest less an unit is to the fact of , 06 and of the amount of one pound so forborn , so is any sum of ready mony to the annuity it shall purchase . in this and the two former propositions by ,06 is understood the compound interest of 1 l. for a year , and when the payment is by quarters or half years , instead thereof must be put in the interest of a quarter or half a year . and instead of the annuity or yearly payment , the quarterly or half-yearly payment accordingly . corollary . if 1 l. be the sum of ready mony then the two middle terms of the proportion are the fact above mentioned , and you will frame the other vulgar table for this purpose . example the first . to find what annuity 1 l. shall purchase to continue 30 years , it holds ; as 4,74349 to ,06 . so 5,74349 to 0,07264 . example second . let it be required to find what rent payable yearly 8 l. shall purchase at 6 per centum to continue 21 years . as 2,39956 the amount less an unit of 1 l. for 21 years is to ,20397 the fact of ,06 and the amount , so is 8 to ,68 or 13 s. 7¼ d. the annuity sought . memorandum , that by the fact is meant that you should multiply the foregoing figures by ,06 . viz. 2,39956 by ,06 , which makes 2,2039736 . now whereas the lease of a house of 1 l. per annum to continue 21 years is commonly sold for 8 l. or 8 years purchase , and your mony will purchase a certainty but of 13 s. 7 d. ● per annum , you see by this supposition you are abated 6 s. 5 d. 3 / ●nt of taxes reparations and casualties ; and verygood reason there is for great abatements , for a tenant taking a lease on a tunber house , if it be burnt down by a fire beginning at his neighbours as leases commonly run , is bound to build it up again and hath no relief either in law or equity against his landlord , as i am informed by able council , only he hath the benefit of a benevolence , his action against them where the fire began ( who perchance are ruined . ) s.   s. d.   will purchase an — 11 — 11 10 annuity to continue 21 years of — 12 — 9 10   — 14 — 5½     — 15     — 17     1 — 5 — 3½ — 1-00-0 hence it appears that the value of leases of houses cannot be estimated near the truth by the common tables for annuities at the currant rate of interest , and that if any one would use them to this purpose it were much nearer the truth first to abridge the rent as aforesaid . prop. 7. any number of years in a lease or annuity being propounded to find the present worth of any greater or lesser number of years therein . this is one of the most usual and useful propositions of this nature , and as propounded is not sufficiently limited , and the question in this cas● will be , what is the most equitable rate of interest whereby to resolve the proposition ; to find out which it is either necessary to assign how many years purchase the fee simple or inheritance is worth , or the present worth of a lease of any number of years therein . 1. if the worth of the inheritance be assigned , then thereby divide 100 the quote shews the annual interest for . example : let the fee simple or copy-hold lands be worth 16 years 8 months purchase , then dividing 100 by 16⅔ the quotient is 6 , whereof 6 pound in the 100 is an equitable rate of interest whereby to compute the present worth of a lease of any number of years therein , and so è contra if mony were at 8 per centum , the laws of arithmetick allow the worth of the inheritance of the best land that is , to be but 12½ years purchase , which some would confirm , from this reason , because otherwise their money would yield a better income at simple or compound interest , but the most proper reason is derived from the nature of a geometrical progression decreasing ad infinitum ; for instance , admit you have a tenant in the tenure or possession of 1 l. per annum , and you say to him , pay the rent now that will be due at the end of 1 years , &c. ad infinitum . 2 3 4 and you will rebate him after the rate of compound interest . i say the total of all those payments shall never exceed 12 l. 10 s. 00 d. the proportion for casting up the sum of a sinite geometrical progression runs thus , as the difference of an assumed extreme and its next inward mean is to the next inward mean ; so is the difference of the remote extremes to the sum of the progression , except the assumed extreme . the reason wherof is , that if a rank of numbers be in geometrical progression their sums and differences are likewise in the same proportion . see 35 of 9 book of euclid , or briggs his arithmetica logarithmica . example . 6 , 18 , 54 , 162 , 486 ,   3 , 9 , 27 , 81 , 243 , 729 wherefore it holds by euclid . 6 as one difference is to its consequent — 9 so is the sum of all the differences ( which is here the difference between the first and last term ) — 726 to the sum of all the consequents is 1089. wherefore the sum of the whole progression is — 1092. and supposing this progression to decrease infinitely , then will the first term be o , and the sum of all the differences 729 , and it holds . as wherefore the sum of this infinite progression is 1093½ , and can never exceed it , and the said progression continued but in part towards the left hand , would stand thus , &c. 1 / 729 1 / 243 1 / 81 1 / 27 1 / 9 ⅓ i. 2. but admit the present worth of a lease for a certain number of years be given , some third term must be further given , let that be the yearly rent , and then you cannot assign the rate ; ( and the contrary ) in this case to find the rate is one of the most difficult questions that commonly happens about annuities , because the proposition in the 5 , 6 , ( also 4th . ) prop. will not hold conversly , there are but two terms in the proposition given , which contain but a bare ratio , &c. therefore though out of tables of forbearance of money at compound interest , you can make those for annuities , yet the converse will not hold . in this case you must either by help of the 5 prop. and common logarithms , or of tables of the present worth of annuities , calculated to the best rate that shall suit the inheritance , find the present worth of the number of years proposed according to two rates assumed as near the truth as you can possible , and then if you have not lighted upon the given worth of the years assigned , use the help of this approximation . as the difference of the present worths found , is to the difference of the assumed rates of interest ; so the difference between the given worth and the truest of those tryal worths ; to the difference between the rate of interest of the tryal worth and that sought . and when the rate of interest is truly found , compute accordingly the present worth of the years sought . but this were to send away the reader , as if we could in this case give no answer to the question , by help of the table here used ; whereto i answer , that if the worth of the inheritance be assigned , repair to the following proposition . but if not , let the casualty as in the 6th . proposition be reduced to a certainty ; viz. if it concern the lease of a house which is a casualty , abridge the annual rent , and then you may by the 5th . prop. cast up the value of any number of years therein . but herein i would not be misunderstood , as if when a lease of a house of 1 l. yearly for 21 years is sold for 8 l. 10 s. the which will purchase an annuity or certainty of 14 s. 5 ½ per annum , and any number of years in this certainty shall be equivolent to as many in that casualty , that therefore tables made to both rates , and a computation to both the yearly rents must needs agree , because all tables of annuities are made for certainties not casualties . or lastly , repair to the first and last prop. and you will there find how to cast up the amount of 1 l. principal for any time , and at any rate , where the true manner of such equations is shewed . in this second case is couched two usual questions , most commoly propounded without sufficient limits : as , 1. when a lease is sunk by a fine to a certain yearly rent , for a certain term of time , what the whole lease is worth : or , 2. what any number of years to be added , after the term in lease is expired , is worth . in order to the resolution of either of these questions it must be agreed how much the sunk rent was , or at least as much given as before was required , and then as before you have a foundation whereon to raise a rate of interest , for there is now given the yearly rent sunk , its present worth , and the time , and the rate being found , you may then , according as is done in the 5th . prop. resolve both these questions . prop. 8. a table for the forbearance of money at any rate of interest being in store to extend it to serve to all other rates . it was before asserted that any such table was a table of logarithms , and if filled up with proportionable numbers ( by 1. prop. ) or otherwise suitable to such time or decimals thereof , as may come in use , might for these purposes be more convenient than those already made , because it would admit a manifold proof , as also because the differences would not be so vast near the beginning , but in some other respects inferiour thereto . and so contrarily , a number being assigned to find the logarithm thereto made , upon any kind of rate or supposition , it may easily be done out of the common logarithms , for the differences of all logarithms are either equal or directly proportional . example first . as 74108 , speidells difference of the logarithm of 13 and 14. is to 32184 d. brigs his difference of those logarithms ; so is 16000 , speidells difference of the logarithms of 62 and 63. to 69487 , the difference of those logarithms in mr. brigs , or the common tables . moreover van schooten in his miscellanies gives you an account of all numbers under 1000 , that are prime or incomposite , to wit , 1226 in number , viz. the which no other number will divide , to the which if the differences be first found by proportion , which in this case having the two fixt terms fixed , may be converted into a multiplication or division , and that multiplier or divisor being multiplied by all the digits into an addition or substraction , the logarithms of all the composite numbers will easily be made out of the rest , by the continual addition of the logarithm of 2 , or otherwise . in the table here used the time is the logarithm , and the amount the number thereto belonging , and a proportion accordingly may be applied to any kind of logarithms , to find the excess of time above a year , in which a 100 l. at 6 per centum did amount to 108 l. but it may be more easily thus done . as , 02530586 , the logarithm of the amount 1 , 06. is to 1 , viz. one year the time that 1 l. principal was forborn ; so is , 03342375 the logarithm of the amount 1 , 08. to 1 , 32079 , the time required , and that is 1 year , 3 months , and about 26 days , and thus the nearest way of resolving such a proposition , having the common logarithms in store , is by a division of the logarithms : but supposing no such tables , it may be supplied by two divisions by help of this table , which i shall explain in two cases . sect. 1. the amount of 1 l. being proposed , to find what time it must be forborn , at 6 per centum to amount unto as much . divide the given amount by some amount in the table , next lesser , and that quotient , again by the next lesser amount , reserving the quotient . if the time in the tables belonging to the two first divisors , and last quote be added together , it is the time sought . example . 1 l. in a year at 8 per centum did amount to 1 s. , 08 , in what time at 6 per centum , shall it amount to so much .         in decimals       time     dividend 108     1. divisor — 106 — 1 year 1   quote — 1,018867 second dividend   2. divisor — 1,014675 — 3 months ,25     1,0041 quote 26 days ferè ,07079         1,32079 but to save the reader this trouble we have added the equated time for these rates .   l. years 100 l. shall 105 in ,83732 at 6 per 106 1 centum 107 1,16114 amount 108 1,32079 unto 109 1,47896 and by the second proposition the present worth of sundry payments due hereafter being computed , after the manner of this example , a ●ue time may be found when the total of all those payments may equitably be paid at once . sect. 2. the rate of compound interest , and the time being given to find what 1 l. principal did amount to in that time . or rather let it be thus proposed : how long shall one pound at 6 per cent. be forborn to amount to as much as 1 l. forborn any space of time at any other rate of interest doth amount unto , and what is the said amount ? by the time proposed multiply the equated time , next before found ( in the first case ) that agrees to the rate proposed , and you have the time sought , and what it shall amount , is found by the first proposition . for instance , if 1 l. be forborn 18 years at 8 per centum , what shall it amount to ? or 〈…〉 how long shall 1 l. at 6 per centum be forborn , to amount 10 as much , as if the said 1 l. had been forborn 18 years at 8 per centum , and what is the said amount ? by the former example the equated time or logarithm of the ratio found , was ,   years   1,3207 this multiplied by 18 , the product is 23,7726 to wit the time of forbearance . and the product of the interest sums belonging to the true time is 3,99601 — or 3 l. 19 s. 11 d. the amount of 1 l. forborn 18 years at compound interest , and the amount of 1 l. being in store , you see before that thereby all other questions concerning annuities are resolved . but when the law settles a new rate of interest , it may be more speedy to frame a table thereto , or use such as the scale of interest , or other authors afford . now what i have hitherto wrote was chiefly to explain the use of the table , and to shew , that in case of necessity , with a little more pains , it takes away those multitudes of tables that are made , as well for quarterly as yearly payments , at several rates for interest and annuity questions , and by reason it , with its precepts , is contained in one quarter of a sheet of paper , which i made my constant companion in my letter case , that thou mightest reap the like benefit of it , it is also printed apart . it is not my intent to inlarge upon a multitude of particular questions , which would all be reduced unto or resolved by some of the former propositions . that i leave to the practice of the studious . advertisement . mercennus in the preface of his synopsis mathematica , speaking of certain supplements made to geometry , and amongst the rest of torricello's hyperbolical solid of an infinite length , found equal to a finite cylinder , saith , that a certain geometer found the like in a space made by a curved line drawn through the tops , all right proportional lines ( supposed ) and by a right line , on which the said proportional lines stand as perpendiculars at a like parallel distance from each other ; if it may be said to be a space which is not closed , unless perchance at an infinite distance , which proportionals , he saith , would not long after be published : he wrote it in 1644 , but as yet i cannot hear of any such treatise . now , as i said before , the time being the logarithms , and the amounts the proportional numbers thereto belonging , by the help of the curved line he mentions ( which may also be described by mean or continual proportionals in lines without the help of numbers ) the logarithmetical lines of numbers , sines , tangents , versed sines , on gunter's rule may be graduated , and the meridian line of mercator's projection , or the true sea chart ( being in the same ratio with the logarithmetical tangents ) supplied , and whereas he mentions by one curved figure , there will also arise another for the same purpose , when the equal parts increasing in arithmetical progression , are raised as perpendiculars on their proportional numbers placed in a base line , and then the tops of those perpendiculars joyned with a slexuous curved line passing through them ; but the properties of these figures as their areas or contents , centors of gravity , round solids , and their first and second segments , &c. are not as yet treated of by geometers , and perchance might be more worthy their contemplation than divers other speculations , which seem to be of less use , to which ( amongst many ) might be added the curves made by the annuity lines , and the curve in mercator's chart that represents a semicircle of the great arch , with a method of discribing it by points , or instrument ( if possible ) from its own intrinsick nature , without the help of calculations or other projections ; also how to cut a cylinder that the surface thereof unrolled shall render the curve proposed of the like nature , standing upon the stage of proposal , have troubled all france and galileus for 35 years together , and since his death received their resolution . a table of decimals of days , which may serve for any rate of simple interest , and a table of forbearance , or amount of 1 l. compound interest at 6 l. per cent. per annum , for 365 days and 11 months . days decimals of days amounts 1 ,002739726 1,000159617 2 ,005479452 1,000319336 3 ,008219178 1,000479037 4 ,010958904 1,000638768 5 ,013698630 1,000798522 6 ,016438356 1,000958305 7 ,019178082 1,001118111 8 ,021917808 1,001277942 9 ,024657534 1,001437800 10 ,027397260 1,001597683 11 ,030136986 1,001757592 12 ,032876712 1,001917526 13 ,035616438 1,002077486 14 ,038356164 1,002237471 15 041095890 1,002397482 16 ,043835616 1,002557511 17 ,046575342 1,002717580 18 ,049315068 1,002877667 19 ,052054794 1,003077802 20 ,054794520 1,003197919 21 ,057534246 1,003358083 22 ,060273972 1,003518273 23 ,063013699 1,003678488 24 ,065753425 1,003938729 25 ,068493151 1,003998995 26 ,071232877 1,004159285 27 ,073972602 1,004319605 28 ,076712329 1,004479948 29 ,079452055 1,004640310 30 ,082191781 1,004800712 31 ,084931507 1,004961132 32 ,087671233 1,005121577 33 ,090410959 1,005282467 34 ,093150685 1,005442545 35 ,095890411 1,005603068 36 ,098630137 1,005763616 37 ,101369863 1,005924190 38 ,104109589 1,006084789 39 ,106849315 1,006245414 40 ,109589041 1,006406528 41 ,112328767 1,006566741 42 ,115068493 1,006727443 43 ,117808219 1,006888171 44 ,120547945 1,007048924 45 ,123287671 1,007209703 46 ,126027397 1,007370508 47 ,128767123 1,007531338 48 ,131306849 1,007692194 49 ,134246575 1,007853076 50 ,136986301 1,008013983 51 ,139726027 1,008174916 52 ,142465753 1,008335850 53 ,145205479 1,008496859 54 ,147945205 1,008657870 55 ,150684931 1,008817905 56 ,153424657 1,008979967 57 ,156164383 1,009141054 58 ,158904109 1,009302121 59 ,161643835 1,009463306 60 ,164383561 1,009624470 61 ,167123287 1,009785661 62 ,169863014 1,009946877 63 ,172602739 1,010108118 64 ,175342466 1,010269386 65 ,178082192 1,010430680 66 ,180821918 1,010591909 67 ,183561644 1,010753343 68 ,186301369 1,010914719 69 ,189041096 1,011076110 70 ,191780822 1,011237532 71 ,194520548 1,011398513 72 ,197260274 1,011560453 73 ,200000000 1,011721952 74 ,202739726 1,011883485 75 ,205479452 1,012045028 76 ,208219178 1,012206604 77 ,210958904 1,012368207 78 ,213698630 1,012529835 79 ,216438356 1,012691489 80 ,219178082 1,012853169 81 ,221917808 1,013014874 82 ,224657534 1,013176606 83 ,227397260 1,013338368 84 ,230136986 1,013500145 85 ,232876712 1,013661955 86 ,235616418 1,013823790 87 ,238356164 1,013985650 88 ,241095891 1,014147538 89 ,243835617 1,014309449 90 ,246575342 1,014471385 91 ,249315068 1,014633352 92 ,252054794 1,014795341 93 ,254794520 1,014957357 94 ,257534246 1,015119399 95 ,260273972 1,015281466 96 ,263013698 1,015443560 97 ,265753424 1,015605678 98 ,268493150 1,015767824 99 ,271232876 1,015929992 100 ,273972602 1,016092892 101 ,276712320 1,016254415 102 ,279452055 1,016416663 103 ,282191781 1,016578938 104 ,284931517 1,016741243 105 ,287671243 1,016993540 106 ,290410960 1,017065919 107 ,293150695 1,017228295 108 ,295890411 1,017396994 109 ,298630137 1,017553130 110 ,301369863 1,017715585 111 ,304109589 1,017878065 112 ,306849315 1,018045851 113 ,309589041 1,018203108 114 ,312328767 1,018365664 115 ,315068493 1,018528254 116 ,317808219 1,018690866 117 ,320547945 1,018853504 118 ,323287671 1,019016177 119 ,326027397 1,019178857 120 ,328767123 1,019345733 121 ,331506849 1,019504313 122 ,334246575 1,019667083 123 ,336986301 1,019829875 124 ,339726027 1,019991694 125 ,342465753 1,020155541 126 ,345205479 1,020318411 127 ,347945206 1,020481309 128 ,350684942 1,020644233 129 ,353424667 1,020807182 130 ,356164393 1,020970158 131 ,358904119 1,021133159 132 ,361643845 1,021296189 133 ,364383572 1,021461593 134 ,367123298 1,021622323 135 ,369863024 1,021785425 136 ,372602749 1,021948558 137 ,375342476 1,022111715 138 ,378082202 1,022274899 139 ,380821928 1,022438109 140 ,383561654 1,022601344 141 ,386301379 1,022764607 142 ,389041106 1,022927895 143 ,391780832 1,023091208 144 ,394520558 1,023254549 145 ,397260284 1,023417914 146 ,400000000 1,023581308 147 ,402739736 1,023744727 148 ,405479462 1,023908170 149 ,408219188 1,024071642 150 ,410958914 1,024235137 151 ,413698640 1,024398660 152 ,416438366 1,024562213 153 ,419178092 1,024725785 154 ,421917818 1,024989386 155 ,425657544 1,025053613 156 ,427397270 1,025216666 157 ,430136997 1,025380346 158 ,432876722 1,025544052 159 ,435616448 1,025707783 160 ,438356174 1,025871541 161 ,441095900 1,026035316 162 ,443835626 1,026199125 163 ,446575352 1,026362972 164 ,449315078 1,026526834 165 ,452054804 1,026690723 166 ,454794531 1,026854641 167 ,457534256 1,027018579 168 ,460273982 1,027182546 169 ,463013708 1,027346543 170 ,465753434 1,027510559 171 ,468493161 1,027674605 172 ,471232887 1,027838677 173 ,473972613 1,028002774 174 ,476712339 1,028166899 175 ,479452065 1,028331053 176 ,482191791 1,028495226 177 ,484931517 1,028659434 178 ,487671243 1,028823659 179 ,490410969 1,028987914 180 ,493150695 1,029152196 181 ,495890421 1,029316503 182 ,498630147 1,029480838 183 ,501369873 1,029645199 184 ,504109599 1,029809584 185 ,506849325 1,029973997 186 ,509589051 1,030138442 187 ,512328777 1,030302901 188 ,515068503 1,030467393 189 ,517808229 1,030631911 190 ,520547955 1,030796454 191 ,523287681 1,030961026 192 ,526027407 1,031125622 193 ,528767133 1,031290244 194 ,531506859 1,031454895 195 ,534246585 1,031619570 196 ,536986311 1,0317●4●●● 197 ,539726057 1,031949●●● 198 ,542465763 1,032137521 199 ,545205489 1,032278534 200 ,547945215 1,032443342 201 ,550684941 1,0326●8174 202 ,553424667 1,032773034 203 ,556164393 1,032937920 204 ,558904119 1,033102832 205 ,561643845 1,033267771 206 ,564383571 1,033432736 207 ,567123298 1,033597703 208 ,569863024 1,033757985 209 ,572602756 1,033927789 210 ,575342478 1,034092859 211 ,578082204 1,034257956 212 ,580821929 1,034423079 213 ,583561656 1,034588204 214 ,586301382 1,034753404 215 ,589041108 1,034918606 216 ,591780834 1,035083763 217 ,594520559 1,035249089 218 ,597260286 1,035414370 219 ,600000000 1,035579678 220 ,602739727 1,035745010 221 ,605479453 1,035910371 222 ,608219179 1,036075759 223 ,610958905 1,036241173 224 ,613698631 1,036406611 225 ,616438357 1,036572078 226 ,619178083 1,036737573 227 ,621917809 1,036903089 228 ,624657535 1,037068659 229 ,627397261 1,037234207 230 ,630136987 1,037399804 231 ,632876713 1,037565430 232 ,635616439 1,037731080 233 ,638356165 1,037896757 234 ,641095891 1,038062462 235 ,643835617 1,038228192 236 ,646575343 1,038093948 237 ,649315069 1,038559733 238 ,652054795 1,038725542 239 ,654794521 1,038891378 240 ,657534247 1,039057241 241 ,660273973 1,039223106 242 ,663013699 1,039389046 243 ,665753425 1,039554988 244 ,668293152 1,039720972 245 ,671232878 1,039886952 246 ,673972604 1,040052974 247 ,676712329 1,040219022 248 ,679452056 1,040385096 249 ,682191782 1,040551198 250 ,684931508 1,040717326 251 ,687671234 1,040888480 252 ,690410959 1,041049661 253 ,693150686 1,041215868 254 ,695890412 1,041382102 255 ,698630138 1,041548363 256 ,701369864 1,041714649 257 ,704109589 1,041880960 258 ,706849316 1,042047303 259 ,709589042 1,042213669 260 ,712328768 1,042380062 261 ,715068494 1,042546482 262 ,717808219 1,042712928 263 ,720547946 1,042879401 264 ,723287672 1,043045901 265 ,726027398 1,043212426 266 ,728767124 1,043378979 267 ,731506850 1,043545559 268 ,734246576 1,043712164 269 ,736986302 1,043878797 270 ,739726028 1,044045456 271 ,742465754 1,044212141 272 ,745205480 1,044378853 273 ,747945206 1,044545592 274 ,750684932 1,044712357 275 ,753424658 1,044879150 276 ,756164384 1,045045969 277 ,758904110 1,045212813 278 ,761643836 1,045379786 279 ,764383562 1,045548585 280 ,767123288 1,045713509 281 ,769863014 1,045884074 282 ,772602740 1,046057440 283 ,775342466 1,046214445 284 ,778082192 1,046381477 285 ,780821918 1,046548530 286 ,783561644 1,046710807 287 ,786301371 1,046882733 288 ,789041097 1,047049872 289 ,791780823 1,047217036 290 ,794520548 1,047384229 291 ,797260275 1,047551448 292 ,800000000 1,047718696 293 ,802739727 1,047885989 294 ,805479453 1,048053264 295 ,808219179 1,048220589 296 ,810958905 1,048387941 297 ,813698631 1,048555320 298 ,816438357 1,048722726 299 ,819178083 1,048890158 300 ,821917809 1,049057400 301 ,824657535 1,049225103 302 ,827397261 1,049392616 303 ,830136987 1,049560107 304 ,832876713 1,049727721 305 ,835616439 1,049895336 306 ,838356165 1,050062933 307 ,841095891 1,050230335 308 ,843835617 1,050398261 309 ,846575343 1,050565953 310 ,849315069 1,050733679 311 ,852054795 1,050901432 312 ,854794521 1,051020810 313 ,857534247 1,051237020 314 ,860273973 1,051404858 315 ,863013699 1,051572714 316 ,865753425 1,051738180 317 ,868493152 1,051908515 318 ,871232877 1,052076452 319 ,873972603 1,052244425 320 ,876712329 1,052412418 321 ,879452055 1,052580440 322 ,882191782 1,052748489 323 ,884931508 1,052916563 324 ,887671234 1,053084180 325 ,890410954 1,053252794 326 ,893150686 1,053420949 327 ,895890412 1,053589108 328 ,898630138 1,053757318 329 ,901369864 1,053925553 330 ,904109589 1,054093831 331 ,906849316 1,054262131 332 ,909589042 1,054430478 333 ,912328768 1,054598766 334 ,915068494 1,054767113 335 ,917808219 1,054935559 336 ,920547946 1,055103982 337 ,923287672 1,055272407 338 ,926027398 1,055440912 339 ,928767124 1,055609416 340 ,931506850 1,055778678 341 ,934246576 1,055946508 342 ,936986302 1,056115093 343 ,939726028 1,056283706 344 ,942465754 1,056452343 345 ,945205480 1,056621012 346 ,947945206 1,056789705 347 ,950684932 1,056958443 348 ,953424658 1,057127172 349 ,956164384 1,057295946 350 ,958904110 1,057464748 351 ,961643836 1,057633576 352 ,964383562 1,057802434 353 ,967123288 1,057971313 354 ,969863014 1,058140222 355 ,972602741 1,058309157 356 ,975342467 1,058478129 357 ,978082193 1,058647110 358 ,980821919 1,058816127 359 ,983561645 1,058985178 360 ,986301371 1,059154242 361 ,989041097 1,059323339 362 ,991780823 1,059492461 363 ,994520549 1,059661616 364 ,997260275 1,059837952 365 ,100000000 1,060000000 months decimals amounts 1 ,083333 1,004867 2 ,166667 1,009659 3 ,250000 1,014675 4 ,333334 1,019613 5 ,416667 1,024576 6 ,500000 1,029564 7 ,583334 1,034574 8 ,666667 1,039610 9 ,750000 1,044671 10 ,833334 1,049756 11 ,916667 1,054865 a table of forbearance , or amount of 1 l. at compound interest , at 6 l. per cent. per annum for 50 years , and from thence continued to 100. years   1 1,06 2 1,236 3 1,191016 4 1,262477 5 1,338225 6 1,418519 7 1,503630 8 1,593848 9 1,689479 10 1,790848 11 1,898298 12 2,012196 13 2,132928 14 2,260904 15 2,396358 years   16 2,540352 17 2,692773 18 2,854339 19 3,025599 20 3,207135 21 3,399564 22 3,603537 23 3,819750 24 4,048935 25 4,291871 26 4,549383 27 4,821346 28 5,111687 29 5,418388 30 5,743491 31 6,088101 32 6,453386 33 6,840589 34 7,250025 35 7,686087 36 8,147252 37 8,636087 38 9,154252 39 9,703507 46 10,285715 41 10,902857 42 11,557032 43 12,250453 44 12,985481 45 13,764609 46 14,590486 47 15,465915 48 16,393869 49 17,377502 50 18,420152 60 32,987488 70 59,075911 80 105,795933 90 189,464433 100 339,398871 the doctrine of decimal arithmetick , simple interest , &c. as also of compound interest and annuities : generally performed for any time of payment , or rate of interest , by help of any particular table of forbearance of 1 l. principal . abridged for portability in a letter case . by john collins accomptant , philomath . a decimal fraction is such a one whose denominator is understood and not expressed ; and is an unit with as many cyphers following it , as there are figures and cyphers in the numerator . corollary . wherefore the annexing of cyphers towards the right hand of a decimal alters not its value . a decimal fraction of coin may be easily valued without the help of tables . for each unit in the first place is in value 2 s. 5 d. in the second place 1 s. and the rest farthings ; but if any exceed 15 / 48 there must be ½ farthings abated : so ,854 is in value 17 s. 1 d. ,418 8 4 ½ . addition and substraction in decimals is the same as in whole numbers , keeping the place of units under each other . multiplication in decimals ; as many decimal parts as are in both multipliers , so many must be cut off from the product ; which if it have not so many places the defect is to be supplied with cyphers towards the left hand . division in decimals is the converse annex cyphers sufficient ( if need be ) to the dividend towards the right hand , that it may have more decimal parts than the divisor , then as many decimal parts as are in the dividend , so many must be in the divisor , and quote , when the division is finished ; and in case of defect , the quote is to be supplied with cyphers towards the left hand . simple interest . prop. 1. to compute the interest of 1 l. for a day . 6 / 105 is the interest of 100 l. for a day , the 1 / 100 whereof is the interest of 1 l. for a day , viz. 6 / 16500 , or 6 divided by 36500 , namely , days interest of 1 l. 1 ,000164384 2 ,000328768 3 ,000493152 4 ,000657536 5 ,000821920 6 ,000986304 7 ,001150688 8 ,001315072 9 ,001479456 prop. 2. forbearance of money at simple interest . the interest of one pound for any number of days may be taken from this table by addition , ( instead of a multiplication , by the number of days , the trouble whereof is by the help of this table spared ) and that product multiplied by any other given sum , makes the interest thereof for the time given . prop. 3. rebate , or the present worth of money due hereafter . find the interest of one pound , for the time given , and thereto adding an unit. by it divide any other sum given , and the quote is its present worth . prop. 4. equation of payments . by prop. 3. compute all the present worths , and then by proportion . if all those present worths amounted to the total of all those payments , what did 1 l. amount to in the said time ? from the result substract an unit , the remainder is the interest of 1 l. for th● time sought , which divide by the interest of 1 l. for a day , the quote is the number of days sought . if you are to equate an annuity at simple interest , i presume a compendium may be found in mengolus his arithmetical quadratures , ( a book i never saw ) who its probable by a compendium gets the fact of an arithmetical progression , and adds fractions that have a constant numerator , and an arithmetical progression for their denominators . days decimals amount 5 years amounts 1 ,002739 1,000160 1 1,06 2 ,005479 1,000319 2 1,1236 3 ,008219 1,000479 3 1,191016 4 ,010959 1,000639 4 1,262477 5 ,013698 1,000798 5 1,338225 6 ,016438 1,000958 6 1,418519 7 ,019178 1,001118 7 1,503630 8 ,021918 1,001278 8 1,593848 9 ,024657 1,001438 9 1,689479 10 ,027397 1,001598 10 1,790848 11 ,030137 1,001757 11 1,898298 12 ,032877 1,001917 12 2,012196 13 ,035617 1,002077 13 2,132928 14 ,038357 1,002237 14 2,260904 15 ,041097 1,002397 15 2,3●6●58 16 ,043837 1,002557 16 2,540352 17 ,046577 1,002717 17 2,692773 18 ,049316 1,002878 18 2,854339 19 ,05●055 1,003038 19 3,025599 20 ,054795 1,003198 20 3,207135 21 ,057536 1,003358 21 3,399564 22 ,060274 1,003518 22 3,603537 23 ,063016 1,003678 23 3,819750 24 ,065755 1,003839 24 4,048935 25 ,068495 1,003999 25 4,291871 26 ,071233 1,004159 26 4,549383 27 ,073973 1,004319 27 4,822346 28 ,076714 1,004480 28 5,111687 29 ,079454 1,004640 29 5,418388 30 ,082193 1,004801 30 5,743491 60 ,164386 1,009625 31 6,088101 90 ,246579 1,014472 32 6,453386 120 ,328772 1,019342 33 6,840589 150 ,410965 1,024335 34 7,250025 180 ,493158 1,029153 35 7,686087 210 ,575351 1,034093 36 8,147252 240 ,657544 1,039057 37 8,636087 270 ,7●9737 1,044●45 38 9,154252 300 ,821930 1,049●●7 39 9,7●35●7 330 ,904193 1,054093 40 10,285715 360 ,986316 1 , ●59154 50 18,420152 mo. 1 ,083334 1,004867 60 32,927388 2 ,166667 1,0●9759 70 50,075911 3 ,250●●● 1,014●74 80 1●5,795933 6 ,500000 1 , ●29563 90 189,464433 9 ,750000 1,014●71 100 339,398471 the annexed table is a table of the forbearance or amount of 1 l. at compound interest at 6 per cent. per an. this table as to the years , is composed by the continual multiplication of 1,06 ( or by addition tabulating the same ) and as to the days may be supplied either by continual proportionals , or the common logarithms , which also are no other than answers to interest questions , at the rate of near 26 per cent. ( or the amount is as 1 , to 1,2589292 ) supposing 1 l. in 10 years to amount to 10 l. the logarithms ( distinguishing the first figure with a conmma ) shew the years and decimals when it amounted to 2 l. 3 l. &c. and those logarithms may be raised from the former . for the differences of all sorts of logarithms of any four numbers , are directly proportional , and may be raised from any table of forbearance of money at compound interest . prop. 1. to continue the said table , or to find the amount of 1 l. forborn for any time proposed . multiply those amounts together that belong to such time , as added together makes the time given . prop. 2. the amount of 1 l. being given , to find the time of forbearance . search the amount in the tables , and divide by the next lesser amount , and that quote again by the next lesser amount , &c. reserving the quotes , the time belonging to the divisors , and the last quote is the time sought . example , 1 l. did amount to 1,08 in 1,32079 years . prop. 3. to compute the amount of 1 l. for any time at any rate of interest . by prop. 2. compute in what time at 6 per cent. 1 l. shall amount to as much as in one year at the rate proposed , that keep in store , and multiply by the time proposed , the fact is the time in which at 6 per cent. 1 l. shall amount to as much as it should do at the other rate given ; to know which , use prop. 1. example , 100 l. did amount to 105 l. in , 83732 years .   l.     or , 1 l. did amount to 1,05 in years ,83732 1,06 1 , 1,07 1,16114 1,08 1,32079 1,09 1,47896 1,10 1,63569 admit it were required to find what 1 l. amounted to in 20 years at 8 per cent . multiply 1,32079 by 20 , the fact or product is 26,14158 , and by prop. 1. 1 l. at 6 per cent . in that time did amount to 4 6609. now if the amount of 1 l. be given , annuity problems are salved thereby . and for the advantage of this proposition the decimals of time were added . prop. 4. forbearance of monies at compound interest . as an unit is to its amount in the tables suitable to the time given : so is any other sum to its amount . prop. 5. discount of money at compound interest , the converse of the former . as the tabular number , is to an unit , its present worth : so is any other sum , to its present worth. in annuity questions the proportions are suited for yearly payments ; if the payment be half-yearly , then instead of ,06 ( or 1,06 ) and the annuity in any term , take half a years interest ,029565 , and the half yearly payment ; and for quarterly payments the quarters interest ,014674 , and the quarterly payment , &c. prop. 6. forbearance of annuities . as ,06 the annual interest of 1 l. is to the amount less an unit of 1 l. forborn any term : so is the annuity or yearly pension , to the sum for the whole arrearages thereof . prop. 7. discount of annuities , or their present worth. as the fact of ,06 and of the amount of 1 l at compound interest for the time proposed , is to the said amount less an unit : so is any annuity , to its present worth , to this proposition belongs the purchace of the fee-simple . for yearly payments divide the rent 1 l. by the interest ,06 the quotes are 16 , ⅔ half-yearly   ,5   ,0295613   16,91303 quarterly   ,25   ,01674   17,07843 and so many pounds ( or years purchace ) is the inheritance worth ( as may be proved from tacquet's arithmetick ) which sums are no other than the totals of the present worths of the infinite payments to be made . hereto also belong equation of payments at compound interest : for having computed the present worths , by proportion , you may find what 1 l. amounted to in the time sought , and by the second proposition the time it self . prop. 8. to find what annuity any sum of ready money shall purchase for any time proposed . as the amount less an unit of 1 l. forborn at compound interest , the time proposed , is to the fact of , 06 , and of the amount of 1 l. so forborn : so is any sum of ready money , to the annuity it shall purchase . from these three propositions the tables in common use may be raised , if you put an unit in the third place . prop. 9. the worth of an annuity being proposed , to find the time of its continuance . get the difference of the facts of 1,06 into the annuity , and of ,06 into the sum of the present worth and annuity , then , as the said difference , is to an unit : so is the annuity , to the amount of 1 l. for the time sought ( to be found by the second proposition . ) prop. 10. an annuity , its present worth , and time of continuance proposed , to find the rate of interest . this is the hardest of annuity problems , and not to be resolved with logarithms without position or trials ; the use is to find the value of any other number of years therein : to facilitate which , observe , that by prop. 8. for 21 years at 6 per cent. you may purchase annuity of s. d. for l. s. 11 11 7 00 12 9 7 10 13 7 8 00 14 5 8 10 15 3 9 00 17   10 00 and these are the rates for leases of houses of such a time , to wit , 1 l. a year for 21 years , is worth about 7 l. 10 s. or 8 l. as men agree , which is a certainty of 12 s. 9 d. or 13 s. 7 d. per annum , whereby you have a direction to accord an abate for casualty , and then use the 6 proposition . most of the many propositions in the learned doctor wallis his arithmetick concerning geometrical progression ; as also in mr. dary's sheet of algebra , may be easily resolved by help of the former table : but this i have handled in my supplements to accomptantship , where also somewhat of logarithm curves , derived from mean or continual proportionals , or tables of interest , and serve for making the logarithm scales of numbers , sines , tangents , ( or mercator's meridian line ) geometrically . prop. 9. more easily . as on annuity , less the fact of ,06 into its present worth , is to the annuity : so is an unit , to the amount of 1 l. for the time sought . if the payments be half yearly , for the annuity in the first and third terms , take half the annuity , and for ,06 in the first term as a multiplier , take ,02956 the half years interest . for another rate of interest as 8 per cent. take in ,08 as a multiplier , and find the time in years and decimals by 2. prop. as at 6 per cent. which divide by the fitted number of the rate in prop. 3. to wit 1,32079 , the quote is the true time sought in years and decimals , which is easily reduced into days by the decimal table of days . example . 50 l. a year at 8 per cent. is worth 490 l. 18 s. 2½ , or 490,91 , the time of continuance is 20 years . an amount is proposed for 20 years to be 4,6609 , what is the rate of interest ? 1. the time in which 1 l. came to so much at 6 per cent. is 26,4158 , found by the second proposition . 2. divide 26,4158 by 20 , the time proposed , the quote is 132079 years . 3. 1 l. at 6 per cent. in that time amounted to 1,08 , the ratio sought . a perpetual almanack , to find what day of the week the first of march shall happen upon . add to the number 2 the year of our lord , and the fourth part of that , neglecting the odd , and divide by 7 , the remainder is the day of the week ; but if none remains it is saturday , for you must account from sunday , monday , & c.. example . so that the first of march is the first day , that is , sunday . the number — 2 the year of our lord , 1685. 1685 the fourth part — 421 divisor — to find on what day of the week any day of any month in the said year hapneth . to perform this proposition , the following verse being in effect a perpetual almanack , is to be kept in memory . in this verse are twelve words relating to the number of the twelve months of the year , accounting march the first ; wherefore the word proper to that month , is an , and so in order of the alphabet , which will never exceed seven ; and the number of the said letter shews what day of the month proper to the said word shall be the same day of the week the first of march happ'ned upon , as the example above . to find the prime or golden number and epact . add to the number 1 the year of our lord , and divide by 19 , the remainder gives the prime . multiply the prime by 11 , and divide by 30 , gives the epact . a table of primes or golden numbers and epacts for ever . to find easter for ever . substract the epact ( if less than 28 or 29 ) from 47 , if the epact be 28 or 29 from 77 , the remainder is easter limits ; so the first sunday after the remainder , beginning from march , is easter sunday . to find the age of the moon . add to the epact the day of the month , and so many more as there are months from march ( accounting march one ) the sum if less than 30 is the moon 's age ( if more ) substract 30 , ( when 31 days in the month ) but if 30 days or less , substract 29 , the remainder is the moon 's age. to find the southing of the moon , and high water at london-bridge . multiply the moon 's age by 8 / 10 shews the southing , to which add 3 hours , shews high-water at london-bridge . to find it another way . multiply the moon 's age by 4 , and divide by 5 , the quotient shews it , every unit that remains is in value 12 minutes , at full moon reject 15 from it . add to this 3 hours , shews high-water at london-bridge . to find what day of the month the sun enters into any sign of the zodiack , by the following verse . aries taurus gemini cancer leo virgo ♈ ♉ ♊ ♋ ♌ ♍ evil attends its object , unva●●'d vice , libra scorpio sagittar . capricorn aquar . pisces ♎ ♏ ♐ ♑ ♒ ♓ vain villains , jest into a paradise . in which are twelve words to represent the twelve months of the year , the first march , the second april , &c. and over the respective words are the characters of the twelve signs of the zodiack , thereby denoting , that in the month to which the word belongs , the sun is in that sign over head : and if it be required to know the day of the month in which the sun enters into any of those signs ; if the first letter of the word , proper to the month , be a consonant , the sun enters into the sign thereto belonging on the eighth day of the said month , as in the word paradise , belonging to february , in that month he enters pisces the eighth day ; but if it be a vowel , as all the rest are , add so many days unto eight , as the vowel denotes ; now the vowels are but five in number . to know in what degree of the said sign he is for any other day . if the number of the day of the given month exceed the number of that day in which the sun enters into any sign , substract the lesser from the greater , and the remainder is the degree . example . on the 21 of april i would find the sun's place by the verse . it appears the sun enters into taurus on the ninth of that month , which taken from 21 , there remains 12 , shewing that the sun is in the 12 degree of taurus , the second sign . 2. but if the number of the day of the given month be less than the number of that day in which the sun enters into the beginning of any sign , the sun is not entred into the said sign , but is still in the sign belonging to the former month. in this case substract the given day from the day of his entrance into the next sign , and again substract the remainder from 30 , and the remainder shews his place in the sign of the former month. example . let it be required to know the sun's place the fifth of august on the thirteenth day of the month the sun enters into virgo , 5 from 13 rests 8 , and that taken from 30 there remains 22 , shewing that the sun is in the 22 degree of leo , the fifth sign . finis . arithmetick vulgar, decimal, & algebraical. in a most plain and facile method for common capacities. together with a treatise of simple and compound interest and rebate; with two tables for the calculation of the value of leases and annuities, payable quarterly; the one for simple, the other for compound interest, at 6. per cent. per annum; with rules for making the like for any other rate. to which is added a new, and most practical way of gauging of tunns. as also the art of cask-gauging, for the use of his majesties officers of the excise. mayne, john, fl. 1673-1675. 1675 approx. 181 kb of xml-encoded text transcribed from 114 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2003-01 (eebo-tcp phase 1). a50423 wing m1482 estc r217772 99829418 99829418 33857 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a50423) transcribed from: (early english books online ; image set 33857) images scanned from microfilm: (early english books, 1641-1700 ; 1919:7) arithmetick vulgar, decimal, & algebraical. in a most plain and facile method for common capacities. together with a treatise of simple and compound interest and rebate; with two tables for the calculation of the value of leases and annuities, payable quarterly; the one for simple, the other for compound interest, at 6. per cent. per annum; with rules for making the like for any other rate. to which is added a new, and most practical way of gauging of tunns. as also the art of cask-gauging, for the use of his majesties officers of the excise. mayne, john, fl. 1673-1675. [16], 206, [2] p., plate : ill., tables printed for j.a. and are to be sold by most book sellers, london : 1675. with an engraved frontispiece portrait of john mayne. epistle dedicatory and the preface signed: john mayne. with a table of contents. "a short treatise of simple & compound interest" and "stereometry" have separate title pages dated 1673; pagination and register are continuous. "a new way of gauging the frustum of a pyramid or conical tunn" and "some practical rules & examples for cask-gauging" have divisional titles; pagination and register are continuous. with a final leaf of errata and a notice advertising john mayne as a teacher of mathematics. the words "vulger .. algebraical." are bracketed together on the title page. reproduction of the original in the british library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng interest -early works to 1800. arithmetic -early works to 1800. 2000-00 tcp assigned for keying and markup 2001-12 apex covantage keyed and coded from proquest page images 2002-01 tcp staff (michigan) sampled and proofread 2002-01 tcp staff (michigan) text and markup reviewed and edited 2002-02 pfs batch review (qc) and xml conversion vera effigies iohannis mayne philo : accomp : arithmetick : vulgar , decimal , & algebraical . in a a most plain and facile method for common capacities . together with a treatise of simple and compound interest and rebate ; with two tables for the calculation of the value of leases and annuities , payable quarterly ; the one for simple , the other for compound interest , at 6. per cent. per annum ; with rules for making the like for any other rate . to which is added a new , and most practical way of gauging of tunns . as also the art of cask-gauging , for the use of his majesties officers of the excise . london , printed for j. a. and are to be sold by most book sellers . 1673. to his honoured friend tho. williams , m. d. physician in ordinary to his s. majesty . sir , though the happiness which i formerly enjoyed in your converse , hath been , to my great loss , for some years discontinued ; yet i easily perswade my self , that the favour of a great prince , and the best master in the world , has not wrought such a change upon your even virtue , but that you will still descend to remember him whom you were once pleased to honour with the name of friend . this confidence has embold'ned me to present you with this small trifle ; too mean indeed and trivial for your acceptance , but that i know you are wont to admit of any thing that proceeds from an honest undesigning gratitude . and though i am not at all inclin'd to vanity from the merits of the work it self , yet i am proud that it affords me an opportunity to discover the lasting impressions , which your many favours have made upon my breast . geometry , with arithmetick her woman , are beauties , that having truth written in their foreheads , dare appear in the court of the greatest monarch , and i doubt not but they will find very easie and courteous admittance into your appartment ; where if they shall afford you any divertisement when you return wearied from your ingenious elaboratory , i shall then accompt that i have written to very good purpose . however , they certainly assure you , that it is impessible the teeth of time should obliterate the honourable esteem conserved for you , in the heart of , sir , your most humble servant , john mayne . the preface . i shall not trouble thee , reader , nor my self , with a long apology for the publishing this treatise . how demurely soever i should pretend to the contrary , i fear thou wilt still be apt to imagin , that i had a tolerable good opinion of it , before i ventur'd it to the press ; and truly i my self cann't well conceive , how any man should be over ambitious of being publickly laught at . if it be in any measure suited to the general good , ( for which i intended it , ) i may at least expect thy pardon ; but if upon the perusal thou shalt find it otherwise , i ingenuously acknowledge my self to have been mistaken . my design in this work is , to render the rules of those excellent arts , which the title-page pretends to , so plain and obvious , as that they may be easily apprehended without the assistance of a living master . and if there were nothing new in the whole , but the perspicuity of the principles , and easiness of the method ( which out of civility to my self i must deny ) yet those alone are sufficient to vindicate me in this publication ; and i hope thou wilt not be angry , that i am a well-wisher to thy vnderstanding . for when i consider'd , that among the many good books of this nature , that are abroad in the world ( though written by persons of greater knowledge than i dare pretend to ) some were so learned and obscure , as not to be understood , unless by those who have already made a considerable proficiency in these things ; others , so voluminous and prolix , that they fright the endeavours of such who cannot spend their whole time this way : i was willing , according to my abilities , to obviate both these inconveniences , and accordingly applied my self to the composure of something , which for its plainness and brevity might be accommodated to those of mean capacities and small leisure ; and this book is the result of those contemplations . whether i have accomplish'd my purpose or no , i make thee the judge ; requiring only that thou censure impartially of the author and his endeavours , without being offended that he is desirous to do thee a courtesie . i shall not here expatiate in the praise of the arguments i treat of , nor give thee one line of encomium : though out of the great affection i bear to these arts , i find a strange inclination in my self to be rhetorical , yet i am resolv'd not to affront thee ; for truly their usefulness and excellency is so universally known , that to tell thee of it as a new thing , were to suppose thee a person of more than ordinary ignorance ; only ( as i said before ) i must be so civil to my self too , as to inform thee , that ( besides the introduction to arithmetick and the treatise of interest , of which i challenge no more than thou shalt find thy self very willing to give me ) that part which concerns the measuring of solids , viz. the prismoid , cylindroid , &c. is wholly new , and never before made publick . the bulk is bigger than at first by me intended ; but to gratifie the book-seller , the vulgar arithmetick was an appendix , though previous to the rest . but if one , or other , or all , prove either profitable or pleasant to thee , i am sufficiently oblig'd to subscribe , from my house at the golden-ball in shaws-court , near st. georges church , southwark ; july 29. 1673. thy friend , john mayne . to the ingenious author , concerning his decimals . sir , by your art , and pythagorean pen , i 'd prove a metempsychosis agen ; and were his soul of decimals but made , as plato's soul o' th' world of seven is said , i 'd swear 't was slunk to you ; but that you shew more skill than e're his rambling fancy knew , let roving rabbies praise their seven and four ; we 'l shew them misteries enough and more : the heav'nly orbs are ten , their motions all conspire to make a perfect decimal : this is their musick , and they shall be thus , in spight of tycho or copernicus . 't is said the muses are but nine , but who ( rather than fail ) cann't add apollo too ? thus may we range the world , and quickly find , we all to th' number of our fingers bind . thus logick all the wandring species brings , and places under tenfold heads of things . thus i , to give the author praise in all , reduce my verses to a decimal . on his gauging . your circles , sir , would make my folly ghess , you were a conjurer , though you wo'n't confess . and gauging is the rugged dev'lish name of some hobgobling imp , the very same that brought in custome ; but what e're he be , he 's a rare fellow at the rule of three : he doth just square the circle ; nay so true , that the king 's right is given to a cue . there 's none else such impossibles can do : you give the king's , i give this right to you . j. w. on his worthy friend mr. j. mayne , the author of this book . jngenious artist , whither do'st aspire ? or why t'outvye the ancients do'st desire ? have they not left enough to following ages ? no : thou their master art , they but thy pages . my feeble muse can never soar so high , as thy deserts herein extend , nor nigh . yet give me leave hereof to speak my mind : no man could better teach us in this kind , each part so useful , and so plain i find . t. w. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . to his ingenious friend the author mr. john mayne . vvho reads thy book with an impartial eye , will see how plain , and how ingeniously thy rules are fram'd ; here every child may learn arithmetick , which doth the truth discern . the judges of our realm could not dispence to all men justice , were 't not fetch'd from hence : those sons of mars that furrow neptune's brow , unto this science must their labours bow : the wealthy merchant , and all traders , hence must calculate their gain , or their expence : the greedy miser , here may plainly see his pelf's increase at compound vsurie : the purchaser of farms , may also here , value his lordships , whether cheap or deer . thy squares and cubes , methinks , so plain do seem , that i old euclid should thy father deem . all humane arts , mechanical and free , for this companion are oblig'd to thee . by lines and numbers , we our buildings bring in due proportion , framing every thing . by these our wooden walls and towers are fram'd , which guard our island , and the seas command : these fill our stores with rich and costly things , born from both indies under canvas wings : these fortifie our towns with forts , by line ; by these we learn our foes to undermine : by these th' excise and customs we do scan , without injustice to the trading man. thanks to our author then , that hath set forth these arts so plain , and of abundant worth : which do to sea and land such profit yield , in court , in city , garrison , and field . hugh handy , philomath . a table of the contents . the first book . notation or numeration . pag. 1 addition . 4 subtraction . 8 multiplication . 12 division . 17 reduction . 20 the rule of three . 22 the rule of practice . 28 notation of decimals . 34 addition of decimals . 37 subduction of decimals . 38 multiplication of decimals . ib. division of decimals . 41 reduction of decimals . 48 a table of reduction . 52 the golden rule . 54 the double golden rule . 61 of the square root . 66 a table of square roots . 71 of quadratique equations . 80 of the cube root . 91 the second book . of simple interest . pag 99 prop. 1. to find the interest of any sum , forbor● any time , at any given rate . 100 prop. 2. to find the present worth of any sum. due at any time hereafter , at any given rate of interest . 102 prop. 3. having the principal , amount , and rate of interest , to find the time of for be forbearance . 103 prop. 4. having the principal , the time , and the amount , to find the rate . 105 a table of the amounts of 1 l. from one to twelve months . 107 to find the interest or discomps of any sum of money by that table . 107 , 108 a table for equation of time. 110 a more exact way of equation . 111 , 112 , 113 a decimal table of the present worth of 1 l. per quarter for 124 quarters , at 6 per cent. per aunum , simple interest . 114 the use of the table . 117 of compound interest . 118 prop. 1. to find the increase of any given sum , for forborn any known time , at a known rate per cent. per annum . 118 prop. 2. the amount of a sum of money , the rate of interest per cent. per annum , and the time being known , to find what was the principal . 120 prop. 3. the principal , the time , and the amount of a sum of money being known , to find the rate of interest per cent. per annum . 121 prop. 4. the principal , the rate , and the amount being known , to find the time in which it hath so increased . 122 of compound interest infinite . 123 prop. 1. to find the present worth of an estate in fee simple , at any rate of interest per c. per ann. 123 prop. 2. to find what free-hold estate any sum of money will buy , at any rate of interest per c. per ann. 126 prop. 3. an estate being offered for a sum of money , the annual rent being known , to find what rate of interest the purchaser shall have for his money . 126 to find how many years purchase any free-hold estate is worth at any given rate of interest . 128 the number of years purchase being propos'd to find the rate of interest it is offered at . 129 a decimal table for the val●ation of leases or annuities , payable quarterly , at 6 per cent. per annum , interest upon interest for 31 years . 130 the way of making the table before-mentioned , for this , or any other rate of interest . 133 the use of the table . 134 six questions performed by aid of the canon of logari●hms . 137 the third book . the definition of a prismoid . pag. 151 to find its solidity . 153 prop. 1. an example in numbers . ib. prop. 2. the inversion of the former solid upon its opposite base , the rule and example . 157 prop. 3. another example . 161 prop. 4. the inversion . 163 the definition of a pyramid . 171 to find its solidity . 172 a table of divisors for reduction of the polygons , and the cone , ●o cubick inches or gallons . 173 an example of a trigon . 174 of a tetragon . 179 of a pentagon . 182 of a cone . 184 to find the fall of a conical tunn . 186 of cask-gauging . 191 to find a casks length . 192 to find the head-diameter . 193 to find the diagonal . ib. to find the content as spheroidal . 194 as parabolical . 196 as conical . 197 by a table of area's . 199 , 200 , &c. to find the ullage . 202 , 205 arithmetick in whole numbers . notation . it is necessary , that all persons that would acquaint themselves with the nature and use of numbers . do first learn to know the characters by which any quantity is expressed . these characters are in number nine , who with a cypher are the foundation of the whole art of arithmetick . their form and denomination as in this example . 0. cypher . 1. one. 2. two. 3. three . 4. four. 5. five . 6. six . 7. seven . 8. eight . 9. nine . these characters standing alone express no more than their simple value , as 1 is but one , 2 standing by it self signifies but two , and so of the rest ; but when you see more than one of those figures stand together , they have then another signification , and are valued according to the place they stand in , being dignified above their simple quality , according to the examples in this table . hundred millions .                 1 ten millions .               1 2 millions .             1 2 3 hundred thousands .           1 2 3 4 ten thousands .         1 2 3 4 5 thousands .       1 2 3 4 5 6 hundreds .     1 2 3 4 5 6 7 tens .   1 2 3 4 5 6 7 8 unites . 1 2 3 4 5 6 7 8 9 the denomination of places according to this table , must be well known , and are thus exprest ; those standing in the place of unites , signifie no more than their value before taught ; but standing in the second place toward the left hand , they are increased to ten times the value they had before , 1 or one in the unite place signifies but one ; if it stand in the second place toward the left hand , and a cypher before it thus 10 , it hath ten times its simple value , and is called ten ; if 2 stand in the place of the cypher thus 12 , it is then twelve , being ten and two unites ; 1 , 3 , or 3 , standing in third place , with figures or cyphers toward the right hand of it , doth signifie hundreds , as 100 is one hundred , 123 is one hundred twenty three , 321 is three hundred twenty one , 213 is two hundred thirteen ; and so any three of the other figures have like value , according to their stations , the first to the right hand in the unite place signifies so many unites , the second , or that in the place of tens , is increased to ten times its simple value , and in the third place , or place of hundreds , any figure there standing hath a hundred times the value it would have had were it in the unite place . the fourth place is the place of thousands , any figures standing there , with three figures or cyphers to the right hand of it , is so many thousands as simply it contains unites , so 3000 is three thousand , 9825 is nine thousand eight hundred twenty five , &c. the fifth place is ten thousands , and any five figures placed together , are to be read after this manner : example . 45326 forty five thousand three hundred twenty six . 12345 twelve thousand three hundred forty five . the sixt place hath the denomination of hundred thousands , and those six in the table that stand in a rank are to be read , one hundred twenty three thousand four hundred fifty six . the seventh is the place of millions , and the seven in the table are , one million two hundred thirty four thousand five hundred sixty seven . and the eighth rank of figures are to be read , twelve millions three hundred forty five thousand six hundred seventy eight . the ninth rank is , one hundred twenty three millions four hundred fifty six thousand seven hundred eighty nine . and so any greater number of places , every figure one place more toward the left hand , is increased ten times in value more than in the place it stood before . addition . addition , is a gathering or collecting of several numbers or quantities into one sum , by placing all numbers of like denomination under one another , carrying all above ten to the next place , as in these examples . there is likewise another kind of addition , that is not of whole quantities , wherein is necessary to be known the number of parts the integer or whole number is divided into , as pounds and shillings , every pound is divided into 20 shillings , and one shilling is divided into twelve pence , one penny into four farthings . now being to add a number of pounds and shillings together , they are thus set down with a small line or point between them . if these be added together , observe in casting up your shillings , so many times as you have 20 in the shillings , you must carry unites to the pounds , and set down the remainder , being under 20 , as in these examples . in the first example , i find in adding the shillings together , they make 21 , so i set down 1 and carry 1 pound to the pounds : in the second example , i find among the shillings 53 , which is 2 pounds 13 shillings , so i set down 13 under the shillings , and 2 to the pounds . any number of shillings and pence being to be added together , if your number of pence amount to above 12 , carry 1 to the shillings , and set down the remainder under the pence ; if they make above 24 , carry 2 shillings , and set down the remainder , as before . examples . in the first example , you carry one shilling ; in the second , two ; and in the third , three . in addition of pence and farthings , carry so many times four as you find in the number of farthings to the pence , setting down the remainder under the farthings , as in these examples . when you would know the sum of any number of pounds , shillings , pence , and farthing , they are to be placed thus : addition of weight and measure is performed after the same manner . 16 ounces averdupois , make a pound . 28 pounds , make a quarter . 112 pound , or 4 quarters , make an hundred gross . 20 hundred , make a tun. examples . where observe , that so oft as i find 16 ounces , i carry 1 to the pounds ; so often as i find 28 pounds , i carry 1 to the quarters ; and as many times as i find 4 in the quarters , so many times 1 do i carry to the hundreds . subtraction . svbtraction is the taking a lesser number from a greater , and exhibits the remainder . in subtraction the numbers are placed one under another , as in addition , thus : the first of these numbers is called the minorand , the second the subducend , and the third number , or the number sought , is the resiàuum . examples of coins . but when the number of pence or shillings , are greater than the number that stands over it in the minorand , you must borrow the next denomination , as in this example . this example i work after this manner , saying 9 d. out of 3 d. i cannot have , wherefore i borrow 1 s. from the shillings , and subduct the 9 d. from that , and there will remain 3 d. which added to the other 3 d. maketh 6 d. i place therefore 6 d. in the place of pence , and proceed saying , 1 s. that i borrowed and 19 is 20 from 1 i cannot , wherefore i borrow 1 l. from the pounds , and subduct from that the 20 s. and there remains nothing but the 1 s. which i place under the shillings , and say , 1 that i borrowed and 6 is 7. from 7 and there remains nothing , then i place a cypher under the 6 , and say , 1 from 2 and there remains 1 , which i set down , and 1 from 1 and there resteth nothing . after this manner is performed subduction of weight and measure . examples . by which examples , the learner may perceive , that where the number to be subducted is greater than the number standing over it , i then borrow one from the next greater denomination , adding the remainder , if any be , to the lesser number before-mentioned , and setting them underneath those of like denomination with them . the proof of subtraction is by adding the subducend and remainder together , and their aggregate must always be equal to the minorand , as you may see by the last example . i could here add many more examples of weight and measure , but to the ingenious practitioner i hope it will be enough , all other being wrought after the same manner , respect being had to the number of lesser denominations contained in each greater . as in troy weight , 24 grains make a penny-weight . 20 penny-weight one ounce . 12 ounces one pound . long measure . 4 nails make a quarter of a yard . 4 quarters one yard . 5 nails one quarter of an ell. 4 quarters one ell. 12 inches a foot. 3 feet a yard . 16½ a perch . 40 perches a furlong . 8 furlongs make an english mile . liquid measure . 8 pints make a gallon . 63 gallons make a graves hogshead . 4 hogsheads make a tun. 36 gallons make a beer barrel . 32 gallons make an ale barrel . dry measure . 8 gallons of corn make a bushel . 8 bushels make a quarter . multiplication . mvltiplication is a kind of addition , and resolveth questions to be performed by addition in a different manner : in order whereunto , it is necessary the learner do well acquaint himself with this table ; the having this table perfectly by heart , will make both this rule and division also very facile , otherwise they will be both troublesome and unpleasant . 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72 7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144 in the first rank of this table , you have an arithmetical progression from 1 to 12 , and also in the first column toward the left hand downwards . this table doth at first sight exhibit the sum of any number , so often repeated as you shall require , provided the numbers do neither of them exceed 12. multiplication hath three members , thus called , a multiplicand , a multiplicator , and a product : the multiplicand , is the number to be repeated ; the multiplicator , is the number of times the first is to be repeated ; and the product , is the sum of the multiplicand so often repeated . as for example . a countrey-man sold 6 bushels of wheat for 5 s. how many shillings ought he to receive ? but by multiplication it is done thus : now if you look in the table precedent , in the first column find 5 , then look in the first rank for 6 , and cast your eye down to their angle of meeting , and you will find 30 standing under 6 and against 5 , i then conclude that 5 times 6 is 30 ; that is called the product , and they will stand thus : but when you have a number to multiply , greater than any in the table , as for example : a gentleman having forborn his rent of a farm , at 157 l. per quarter , for 3 quarters , what ought he to receive ? the multiplication will stand thus : i then say , 3 times 7 is 21 , i set down 1 and carry 2 ; then , 3 times 5 is 15 and 2 is 17 , i set down 7 next the 1 , and carry 1 ; saying , 3 times 1 is 3 and 1 is 4 , as in the example before-going ; and the product is 471 l. there is yet more variety , of which take these examples following . if 65 ships do carry 536 men in every ship , how many men will there be in all ? i say 5 times 6 is 30 , set down 0 and carry 3 ; then 5 times 3 is 15 and 3 is 18 , set down 8 and carry 1 ; then 5 times 5 is 25 and 1 is 26 , which i set down : then for the next figure , i say , 6 times 6 is 36 , i set down 6 one place short of the former rank , and carry 3 ; then 6 times 3 is 18 and 3 is 21 , set down 1 and carry 2 ; again , 6 times 5 is 30 and 2 is 32 , these i set down : then draw a line , and cast them up as they are placed , and the sum is the product and answer to the question , viz. 34840 men. in multiplication , always make the lesser number the multiplicator , for it is all one whether i multiply 5 by 15 , or 15 by 5 , the product is always the same . if 128 men of war have each made 746 shot , how many shot were made in all ? begin as before with the unites place , and say , 8 times 6 is 48 , set down 8 and carry 4 ; 8 times 4 is 32 and 4 is 36 , set down 6 and carry 3 ; then 8 times 7 is 56 and 3 is 59 , which set down : then go forward with the 2 , ( but remember to place your remainder one figure short of the former ) saying , 2 times 6 is 12 , set down 2 under the 6 and carry 1 ; 3 times 4 is 8 and 1 is 9 , which set down ; twice 7 is 14 , which set down : also then , once 6 is 6 , which place under the 9 ; once 4 is 4 , which set under the 4 ; and once 7 is 7 ; which set under the 1 : then cast them up , as in addition , and the sum is the product , and answers the question , viz. 95488 shot . if any number be to be multiplied by 1 with cyphers , it is but adding so many cyphers to the multiplicand as there is in the multiplicator . as for example . if 35678 be to be multiplied by 10 , add one cypher to the multiplicand , thus , 356780 ; if by 100 , add two cyphers , thus , 3567800 ; &c. and when any number is to be multiplied by any other number , that hath cyphers annexed , always place the cyphers immediately under the line , as in these examples . division . division is also a kind of subduction , and informs the querent , how many times one number is contained in another . there is in division these three things to be observed , viz. the dividend , the divisor , and the quotient . the dividend is a number to ●e divided into parts , the divisor is the quan●ity of one of those parts which the former is ●● be divided by , the quotient is the number ●● such parts as the dividend doth contain●●●ere is also by accident a fourth number in ●●●s rule necessary to be known , which is a ●●mainder , and that happens when the divi●●● doth not contain an equal number of such ●●●ntities as it is divided by , as when 15 is to be divided by 4 , the dividend is 15 , the divisor is 4 , and there is a remainder 3. in division you may place your numbers thus . dividend . multiplication is positive , but division is performed by essays or tryals , after this manner : here i first inquire how many times 3 i can have in 14 , i find 4 times , i place 4 in the quotient , and then multiply the divisor by that 4 , placing the product underneath the dividend , as in the example ; say , 4 times 5 is 20 , set down a cypher under the 6 and carry 2 , then 4 times 3 is 12 and 2 is 14 , which i set down also , as in the example ; then subduct this product from the figures standing over them , and set down the remainder . then for a new dividend , i bring down the next figure , and postpone that to the remainder , and inquire how many times 3 in 6 , i cannot have twice , because i cannot have twice 5 from 5 , i say then once , and place 1 in the quotient , proceeding as before saying , once 5 is 5 , which i place under the first 6 toward the right hand , and once 3 is 3 , which i set down under the other 6 ; subducting these as the former , i find the remainder to be 31. after which i bring down the next figure in the dividend , and postpone it to the remainder , as in this example : then i inquire how many times 3 in 31 , i suppose 9 times , placing 9 in the quotient i multiply again ; saying 9 times 5 is 45 , 5 and carry 4 ; then 9 times 3 is 27 , and 4 is 31 ; these being set down , as before directed , and subducted , there will remain nothing . i then conclude , that the divisor is so often contained in the dividend as is expressed in the quotient , viz. 419 times . for further instructions , take these examples . reduction . reduction is twofold , viz. bringing greater denominations into smaller , and that by multiplication , as pounds into shillings , shillings into pence , &c. also lesser denominations are reduced into greater , by division , as pence into shillings , shillings into pounds , minutes into hours , hours into days , and days into years , &c. having any number of pounds to reduce into pence , multiply them by 240. example . how many pounds , shillings , and pence , are contained in 22929 farthings ? in 544542 cubique inches , how many beer barrels , firkins , and gallons ? the rule of three . this rule is so called , because herein are three numbers given to find a fourth ; of these three numbers , two are always to be multiplied together , and their product is to be divided by the third , and the quotient exhibits the fourth number , or the number sought . and here note , that of the three given numbers , if that number that asketh the question be greater than that of like denomination with it self , and require more , or if it be less , and require less , then the number of like denomination is the divisor . or , if the number that asketh the question be less than that of like denomination , and require more ; or if it be more , and require less , then the number that asketh the question is the divisor . example . if 3 yards of sarcenet cost 15 s. what shall 32 yards cost ? which 3 numbers if you please may stand thus : here you may see the term that asketh the question is greater than that of like denomination , being 3 , and the other 32 , and also requires more , viz. a greater number of shillings ; therefore , according to the rule , the first term , or the term of like denomination to that which asketh the question , is the divisor . and the answer is 160 shillings , which being divided by 20 will be found 8 l. again , if 32 ells of holland cost 160 s. what shall 3 ells cost ? in this question ( being the converse of the former ) you may see the term that asketh the question , here 3 , is lesser than that of like denomination , being 32 ells , and also requires less ; therefore the first term here also is the divisor . and the answer is 15 s. if 36 men dig a trench in 12 hours , in how many hours will 144 men dig the same ? in this question , the term that asketh the question is greater than that of like denomination , and requireth less ; wherefore the term that asketh the question is the divisor . if 144 workmen build a wall in 3 days , in how many days will 36 workmen build the same ? this question you may perceive to be the converse of the former , here the term that asketh the question is less than that of like denomination , and requires more , the term that asketh therefore is the divisor . if 125 lb. of bisket be sufficient for the ships company for 5 days , how much will victual the ship for the whole voyage , being 153 days ? this question is of the same kind with the first example ; here the two terms of like denomination are 5 days and 153 days , the term that asketh the question being more than the term of like denomination , and also requiring more ; so , according to the general rule , the term of like denomination to that which asketh the question is the divisor . it matters not therefore in what order they are placed , so you find your true divisor ; but if you will you may set them down thus : the answer is 3825 lb. weight of bisket . a ship having provision for 96 men during the voyage , being accompted for 90 days , but the master taking on boord 12 passengers , how many days provision more ought he to have ? which is no more than this : if 96 men eat a certain quantity of provision in 90 days , in how many days will 108 men eat the same quantity ? the answer is 80 , so that for 108 men he ought to have 10 days provision more . if the assize of bread be 12 ounces , corn being at 8 s. the bushel , what ought it to weigh when it is sold for 6 s. the bushel ? in this question , the term inquiring being less than the term of like denomination , and requiring more ; therefore is the term so inquiring the divisor . the answer is 16 ounces . the rule of practice . it is necessary that the learner get these two tables perfectly by heart , which are only the aliquot parts of a pound and of a shilling . the parts of a shilling . d. q.   0 1 forty eighth . 0 2 twenty fourth . 0 3 sixteenth . 1 0 twelfth . 1 2 eighth . 2 0 sixth . 3 0 fourth . 4 0 third . 6 0 half. the parts of a pound . s. d. q.   0 00 1 the nine hundred and sixtieth . 0 00 2 the four hundred and eightieth . 0 00 3 the three hundred & twentieth . 0 01 0 the two hundred and fortieth . 0 01 2 the hundred and sixtieth . 0 02 0 the hundred and twentieth . 0 03 0 the eightieth . 0 04 0 the sixtieth . 0 05 0 the forty eighth . 0 06 0 the fortieth . 0 08 0 the thirtieth . 0 10 0 the four and twentieth . 1 00 0 the twentieth . 1 03 0 the sixteenth . 1 04 0 the fifteenth . 1 08 0 the twelfth . 2 00 0 the tenth . 2 06 0 the eighth . 3 04 0 the sixth . 4 00 0 the fifth . 5 00 0 the fourth . 6 08 0 the third . 10 00 0 the half. having these tables perfectly in memory , any question propounded will be readily resolved , only by dividing the given number of yards , ells , feet , inches , gallons , quarts , pounds , or ounces . of which take some examples . having any number of shillings to reduce into pounds , cut off the last figure toward the right hand by a line , and the figures on the left hand of the line are so many angels as they express unites ; draw a line under them , and take the half of them , and you have the number of pounds . examples . any commodity , the value of 1 yard being the aliquot part of a pound , is thus cast up : take the one third part , and that is the answer in pounds : 3 in 8 twice , and carry 2 ; 3 in 23 seven times , and carry 2 ; 3 in 26 eight times , and carry 2 ; the third part of 2 l. is 13 s. 4 d. where always observe , that the remainder is always of the same denomination with the dividend . where the price is not aliquot . to cast up the amount of any commodity , sold for any number of farthings by the pound , i borrow from the dutch a coin called a guilder , whose value is 2 s. english. then if a question be proposed of the amount of an hundred weight of any commodity , by the hundred gross , viz. 112 lb. so many hundred as there be , the amount is so many guilders so many groats , as there are farthings in the price of 1 lb. as for example . a hundred weight of iron is sold for 5 farthings the pound , comes to 5 guilders , that is 10 s. and 5 groats , which together is 11 s. 8 d. again . a hundred weight of lead is sold for 2 d. farthing the pound , that is 9 guilders and 9 groats , which is 21 shillings . but if it be the subtil hundred , it is then but so many guilders so many pence : as if a hundred weight of tobacco be sold for 5 d. farthing the pound , the hundred comes to twenty one guilders and twenty one pence , that is forty three shillings and nine pence . arithmetick in decimals . notation . integers . decimals . 3 thousand millions . 9 hundred millions . 8 ten millions . 7 millions . 6 hundred thousands . 5 ten thousands . 4 thousands . 3 hundreds . 2 tens . 1 unites . 1 tenths . 2 hundredths . 3 thousandths . 4 ten thousandths . 5 hundred thousandths . 6 millioneths . 7 ten millioneths . 8 hundred millioneths . 9 thousand millioneths . as in whole numbers , the value or denomination of places do increase by tens , from the unite place toward the left hand ; so in decimals , the value or denomination of places do decrease by tens , from the unite-place toward the right hand , according to the precedent table . a fraction or broken number is always less than a unite , as pence are parts of a shilling , and shillings of a pound ; inches of a foot , and minutes of an hour , &c. fractions are of two kinds , and are thus called vulgar , & decimal . a vulgar fraction is commonly expressed by two numbers set over one another , with a small line between them , after this manner ● , the uppermost being called the numerator , and the lower the denominator . the denominator expresseth into how many parts the integer or whole number is divided , and the numerator sheweth how many of those parts is contained in the fraction . example . if the integer be a shilling ; is 8 d. if it be 1 l. or 30 shillings , it is 13 s. 4 d. if a foot , it is then 8 inches . or if an hour , it will be 40 minutes . a decimal fraction hath always a common number for a numerator , and a decimal number for its denominator . a decimal number is known by unity , with one or more cyphers standing before it , as 10 , 100 , 1000 , &c. a decimal fraction is known from a whole number by a point , or some other small mark of distinction , whether it stand alone , or be joyn'd with whole numbers ; as in these following examples . or else with a point over the head of unity , or the unite place ; as in these examples . in decimal fractions , the numerators only are set down , the denominator being known by the last figure in the numerator . example . .2 is two tenths . .25 is twenty five hundredths . .257 is thousandths . .2575 is ten thousandths , &c. as cyphers before a whole number have no value , so cyphers after a decimal fraction are of no signification : but cyphers before a decimal fraction , are of special regard ; for as cyphers after a whole number do increase that number , so before a decimal fraction they diminish the value of that fraction . example . .25 twenty five hundredths . .025 twenty five thousandths . .0025 twenty five ten thousandths . each cypher so added removing the fraction further from unity , making it ten times less than before . addition . addition in decimals , whether in pure decimals , or whole numbers mixt with decimals , differs not from addition in whole numbers , only care must be had to the seperating lines or points , that all places of like denomination stand one under another , both in the addends and in the sum ; as in these examples . subtraction . as in addition , so in subtraction care must be had to the placing each figure under that of like denomination with it self , then it is the same with subtraction in whole numbers . examples . multiplication . mvltiplication in whole numbers serveth instead of many additions , and teacheth of two numbers given to increase the greater as often as there are unites in the lesser . it likewise consists of three requisites , viz. a multiplicand , a multiplicator , and a product . the multiplicand is the number to be increased . the multiplicator is the number by which it is to be increased . and the product is the sum of the first number so often repeated as there are unites in the second . in decimal fractions , or whole numbers mixt with fractions , the two first numbers are called factors , and the last is called the fact. multiplication , whether in decimal fractions , or whole numbers mixt with fractions , differeth not ( in the operation ) from multiplication in whole numbers . the last figures in both the factors may be placed under one another , without respect to the distinction of places , or places of like denomination standing under one another , as in addition and subduction ; yet from the product must be cut off by a line or point so many places as there are figures in decimal fractions in both factors of the last figures standing toward the right hand . examples . if it happen when the multiplication is ended , that there be fewer figures in the product than there are places in decimals in both the factors , then put cyphers before the product till the number of places be equal to those in both the factors : as in these examples . where by may be observed , that the multiplication of two fractions doth not increase them as in whole numbers , but they are hereby made less , and the fact is removed further from unity than either of the factors . if a whole number be to be multiplied by a decimal number , put so many cyphers after the whole number as there are in the decimal number , and that number will be the product . if 48 be multiplied by 10 , it will be 480 ; by 100 , 4800 ; &c. in multiplying decimal fractions , or mixt numbers , by a decimal number , you need only remove the point or seperating line so many places toward the right hand as there be cyphers in the decimal number . if you multiply .2845 by 10 , the fact will be 2.845 ; by 100 , it will be 28.45 ; by 1000 , 284.5 ; &c. division . division , both in whole numbers and fractions , is by young practitioners found to be more difficult than any of the four species ; it will therefore require a little more industry in the learner : but when once had , there will appear small difference between the operation herein , as in any the precedent . division is also constituted by three requisites , and a fourth by accident , viz. a dividend , a divisor , and a quotient : the fourth is a remainder , which doth not always happen to be . the dividend is the number to be divided . the divisor is the number by which the other is to be divided . the quotient is the number found out by the division . and the remainder is that which is left of the dividend after the division is ended , and is always less than the divisor . example . if 12 be to be divided by 4 , then is 12 the dividend , 4 the divisor , and the quotient will be 3. if 13 be divided by 3 , then 13 is the dividend , 3 the divisor , 4 the quotient , and there will be a remain , which is here 1. decimal fractions , or mixt numbers , are divided after the same manner as whole numbers are divided , only care must be had in giving a true value to the quotient . to perform which , observe well this general rule . the first figure in the quotient is always of the same denomination with that figure which stands ( or is supposed to stand ) over the unity place in the divisor . as to the manner of placing your figures , and the way of dividing , there are many published by divers writers of arithmetick : the way of placing the divisor under the dividend , is the most apt for giving a value to the quotient ; but the rasing of figures , and repeating the divisor so often , is found an inconvenience ; which to avoid , observe the following examples . being to divide 2487.048 by 53.6 , i place them in this order : then i consider if the divisor were placed under the dividend , the unity place in the divisor , here 3 would stand under the 8 in the dividend , i then set a mark over the head of the 8 , and conclude the first figure in the quotient to be of the same denomination with it , which is tens , in whole numbers . having thus found the value of the first figure in the quotient , i proceed to the division , and inquire , how many times 5 in 24 ? i find 4 ; i then set 4 in the quotient , and go back , multiplying the whole divisor by that figure , and subduct the product out of the dividend , placing the remainder underneath as part of a new dividend : thus 4 times 6 is 24 , from 27 , and there remains 3 , which i place under the 7 ; again , 4 times 3 is 12 , and 2 that i borrowed is 14 , from 18 , and there remains 4 , which i place under the ● , as in the example ; then 4 times 5 is 20 , and 1 i borrowed is 21 , from 24 , and there remains 3 , which i place under the 4. for my new dividend , i bring down the next figure , here a cypher , and postpone it to the remainder , and the example will stand thus : then proceeding in my division , i ask , how many times 5 in 34 ? finding 6 times , i then place 6 in the quotient , and as before say , 6 times 6 is 36 , from 40 , and there remains 4 , which i set down under the cypher ; then 6 times 3 is 18 , and 4 i borrowed is 22 , from 23 , and there remains 1 , which i place under the 3 ; then 6 times 5 is 30 , and 2 i borrowed is 32 , from 34 , and there will remain 2 , which i place under the 4 ; then to this remainder i bring down the next figure in the dividend , postponing it as i did the cypher , and they will stand thus : i now inquire , how many times 5 in 21 ? and find 4 times , i then place 4 in the quotient , and go on as before ; there being yet a remainder , i add a cypher , and proceed as before ; and find , upon the adding one cypher , my divisor greater than the dividend , i place a cypher in the quotient : example . having placed a cypher in the quotient , i add another to the dividend , and make it 800 ; and then inquire , how many times 5 in 8 ? finding once , i put 1 in the quotient , working as before : where note , so long as there is a remainder , if you add cyphers and work after this manner , you may have as many decimals as you please . it doth often happen in division , in decimal fractions , or mixt numbers , that the unite place in the divisor will stand beyond all the significant figures in the dividend , either toward the right hand or toward the left ; in which case , that you may the better find out the value of the first figure in your quotient ( according to the precedent general rule ) add cyphers to the right or to the left hand of the dividend , till you come over the unity place in the divisor , and what value or denomination that place is of , that is the denomination of the first figure in the quote ; as in these examples . if in division in whole numbers , there happen to be a remainder , it is the numerator of a common fraction , and the divisor is the denominator , and this fraction is part of the quotient . example . if you divide 66 by 8 , the quotient will be 8 and 2 / 8 , according to the way of vulgar fractions , but in decimal fractions it will be 8.25 . if you be to divide a whole by a decimal number , cut off so many places by a mark , as there are cyphers in the decimal number : if 468 be divided by 10 , the quote is 46.8 ; by 100 , 4.68 ; and by 1000 , quotes .468 . if a decimal fraction , or a mixt number , be to be divided by a decimal number , remove your line or point so many places toward the left hand , as there are cyphers in your decimal number , supplying the vacant places with cyphers , if there be occasion : 69.5 divided by 10 , is 6.95 ; by 100 , it will be .695 ; by 1000 , .0695 ; and by 10000 , quotes .00695 ; &c. division being the converse of multiplication , as multiplying a mixt number or decimal fraction by a decimal number , you remove your mark of distinction toward the right hand ; so in dividing a decimal fraction or mixt number by a decimal number , the mark is removed toward the left hand , as in the foregoing examples . reduction . to reduce a vulgar fraction into a decimal fraction , your rule is : divide your numerator by your denominator , and the quotient will be a decimal fraction of the same value with the vulgar fraction . so 1 / 4 , if reduced into a decimal fraction , will be .25 . example . here note , that only the even parts of an integer will be exactly reduced into a decimal fraction , as 1 / 2 , 2 / 8 , 2 / 16 , &c. in all surds , there will be some remainder , but if you carry your decimal fraction to four or five places , making the last one more than it is , if the sixth figure be above 5 , or else leave them out , and your calculation will come near the truth ; but if any desire to be more exact , he may take as many as he please . examples . to reduce any decimal fraction out of a greater denomination into a lesser , multiply the fraction by those parts of the integer into which you would have it reduced ; as .65 being the parts of a pound , you would know how many shillings are contained in the fraction , multiply it by 20 : if you desire the pence therein contained , multiply it by 240 ; or if farthings , multiply by 960 , the number of farthings in a pound or 20 shillings . the decimal parts of a foot are reduced , by multiplying them by 12 ; if parts of a foot square , by 144 ; and the decimal parts of a foot solid , by 1728 , the cubick inches in a foot of solid . the decimal parts of a pound , are reduced by 16 , the ounces in a pound averdupois ; and 12 , the ounces in a pound troy. the decimal parts of a beer barrel by 36 , and by 32 reduceth the parts of an ale barrel , into gallons ; and gallons into pints , by 8 ; gallons into cubick inches , by 282 ; and for wine gallons , by 231 , the number of cubick inches in such a gallon , &c. as greater denominations are reduced to lesser , by a multiplication of the several parts of the integer ; so lesser denominations are reduced to greater , by division . any number of shillings are reduced into pounds , and the decimal parts of a pound , if you divide them by 20 ; and pence , if divided by 240. example . hours are reduced into the decimal parts of a day , if you divide them by 24 , the hours in a day natural ; and minutes into the parts of an hour , if divided by 60. perches are reduced into the decimal parts of an acre , if you divide them by 160 , the number of square poles or perches in an acre ; and any ●●mber of feet into poles , and the decimal parts of a pole , if you divide them by 16.5 the feet in a pole , or by 15.8.25 the number of square feet in a square pole ; but if wood-land measure by 18 , or if a square pole by 324 , the square feet in a pole or perch of such measure . any number of inches are reduced into the parts of a beer barrel , if divided by 10152 ; and into ale barrels and parts , by 9024 ; &c. for the ease of the reader here is made a table of english coin reduced into the decimal parts of a pound sterling . a table of reduction of english coin , the integer being one pound . shillings . decimals . pence . decimals of a pound . 19 .95 11 .0458333 18 .9 10 .0416667 > 17 .85 9 .0375 16 .8 8 .0333333 < 15 .75 7 .0291667 > 14 .7 6 .025 13 .65 5 .0208333 12 .6 4 .0166667 > 11 .55 3 .0125 10 .5 2 .0083333 < 9 .45 1 .0441667 > 8 .4     7 .35     6 .3     5 .25 farthings . decimals of a pound . 4 .2     3 .15 3 .003125 2 .1 2 .0020833 1 .05 1 .0010417 > the vse of the table . having any quest. wherein pounds , shillings & pence , are required to be under one denomination , viz. pounds , and the parts of a pound : first seek in the column of shillings for your shillings , and set down the fraction that stands against it ; then in the column of pence , seek your pence ; in the farthings , your farthings ; add all these together , and the sum is the decimal fraction desired . example . what is the decimal fraction for 17 s. 9 d. 3 / 4 ? first as the decimal parts of a pound seek for 17 s. and the fraction against it in the other column is . 85 ; which is the number required , and is the decimal fraction for 17 s. 9 d. 3 / 4 , as parts of a pound . again , having a decimal eraction in the parts of a pound , and its desired to know the value thereof in lesser denominations : let it be the fraction before found , viz. .890625 : i seek in the table of fractions for the neerest to it , and find .85 , and against it 17 s. i then set .85 down , and subduct it from the other , and there remains .040625 ; i look over the table again , and find the next neerest is .0375 , against it 9 d. i subduct that ; and find the remainder .003125 , stand against 3 farthings . so finding the value of any other decimal fraction : if any thing remain after the last subduction , being less than a farthing , i cast it away as of small regard . the golden rule . this rule is called the rule of three , because herein are three numbers given , to find a fourth . it is also called the rule of proportion , for as the first is in proportion to the second , so is the third to the fourth : and the converse . this rule is called the golden rule for its excellent use in the solution of questions of various kinds , and great advantage is made of it in almost all kind of calculations arithmetical . two of the three numbers given in every rule of proportion are of one denomination , and the third is of the same kind with the fourth sought ; and one of the two numbers that are of like species doth always ask the question . arithmeticians distinguish this rule by two denominations , one they call the direct , and the other the inverse or backer rule of three . one of the three given numbers of like denomination in any rule of proportion is a divisor , the other remaining two are multipliers . to find which of the forementioned numbers is the divisor , take these following rules . 1. if that term to which the question is annexed be more than that of like denomination , and also requires more ; or if it be less , and require less than the term of like denomination ; then that term of like denomination to that which asketh the question is the divisor , and the question is in the direct rule of three . 2. if the term which asketh the question be more than that of like species , and requires less ; or less , and requires more ; then that term which asketh the question is the divisor , and the question is in the backer or inverse rule of three . having by the precedent rules discovered the divisor , multiply the other two numbers , and divide by the divisor , your quote will be the answer to the question . note , if any of the numbers given be in several denominations , they must be reduced into one , either greater or lesser , as before directed . example . quest. 1. if 12 1 / 2 yards of taffaty cost 5 l. 7 s. 9 d. 3 q. what shall 5 1 / 2 yards cost ? in this example , of the three numbers given there are two of like denomination , and they are 12 1 / 2 and 5 1 / 2 , the latter of which is the term which asketh the question , known always by the words what or how much . and this term is less than that of like kind with it self , and also requires less , therefore according to the precedent rule , this question is in the golden rule direct . these three numbers may be placed in what order you please , provided you mistake not your divisor , but according to the general way , being reduced into decimals , and of one species , they will stand thus : then , as before directed , multiply the second and third numbers , and divide by the first , and the quotient exhibits the fourth proportional or the number sought . the answer is 2 l. 7 s. 5 d. 1 q. quest. 2. if 6 yards of broad cloth cost 4 l. what shall 32 yards cost ? here the term which asketh the question is greater than the term of like denomination , and requires more ; therefore the term of like denomination to the term that asketh the question is the divisor . the answer is 21 l. 6 s. 8 d. quest. 3. if 320 men raise a breast-work in 6 hours , in what time will 750 men do the same ? here the term that asketh the question is more than the term of like denomination , and requires less ; therefore the term that asketh the question is the divisor , and this is the backer rule of three . the answer is 2 hours , 33 minutes , and 36 seconds . quest. 4. if 756 men dig a trench in 12 hours , in how many hours will 126 dig the same ? here the term that asketh the question is less than the term of like denomination , and requires more ; then according to the rule the term demanding is the divisor , and this question is also in the inverse rule of three . the answer is 72 hours . there is sometimes four numbers given in a question , yet is it but a single rule of three , for one of the four numbers is of no signification , and might as well have been left out . example . quest. 5. if 10 workmen build a wall 40 foot long in 3 days , in what time might 50 men have done the same ? here note , there is four numbers given , and yet there is but three to be used in working the question , you must therefore find which those 3 are that are necessarily to be used : thus , first , you must take the term that asketh the question , here 50 workmen ; secondly , you must have the term of like denomination with it , which is 10 workmen ; thirdly , the term sought , being days ; you must take the term of like denomination with that also , which is here 3 days : the superfluous term then in the question is 40 , which might have been left out , and they will then stand thus : the answer is half a day or 12 hours . this question is in the rule of three inverse . quest. 6. if 100 l. gain 6 l. in 12 months , what shall 32 l. gain in the same time ? in this question the 12 months is the superfluous term , being of no use in the calculation , the terms required being 100 l. 6 l. and 32 l. note , though the terms in this question be all money , and so may seem to be of one species , yet they are not ; 100 l. and 32 l. are of one kind , being both principal , and the other term is of the same denomination with the term sought , viz. gain or interest . the answer is 1 l. 18 s. 4 d. 3 q. ferè . and this question is in the direct rule of three , the term that asked the question being less than the term of like denomination , and also requiring less , &c. the double golden rule . this rule is called the double golden rule , or double rule of three , because it requires two distinct calculations , before you can answer the question . and in this rule there are five numbers given to find a sixth sought . this differs not in the operation from the single rule , only the calculation is twice repeated . of the five numbers given , the question is sometimes annexed to two , and sometimes but to one . if the question be annexed to two of the five given numbers , then are there two of the other three of the same species with those that ask the question , and the third is proportional to the number sought . for the due regulation of these two calculations , when the question is annexed to two of the five numbers , take these directions . first , take one of the numbers demanding , and let that ask the question in the first operation ; secondly , take that of the same species , and also that of the like quality with the respondent , of these three constitute your first rule of proportion ; then find which is your divisor , according to your rule pag. 55. and proceed to find the fourth in proportion . then for your second rule of three , take the other of the two numbers to which the question is annexed , and let that ask the question ; take also the number of like kind , and the fourth number found in the first calculation ; judge which is your divisor , and work accordingly ; the last quotient will be the sixth number , or the number sought . example . if a trench be 20 perches in length , and made by 12 men in 18 days ; how long may that trench be , that shall be wrought be 48 men in 72 days ? here the question is annexed to two of the five numbers , viz. 48 men and 72 days ; now according to the foregoing direction , take one of the two numbers inquiring , 48 , and say , then take the other of the two numbers inquiring , and say , if 6 lighters bring 60 tuns of ballast in 5 tides , how many tun will 15 bring in 12 ? if a man travel 160 miles in 4 days , when the days are 10 hours long ; in how many days will he travel 195 miles , when the days are 14 hours long ? when a question is stated in the double rule of three , so that there is but one number inquiring , first , take that number , and let it ask the question in the first rule ; take also the number of like denomination , together with the number joyn'd to that of like denomination ; and of these three numbers constitute your first rule of proportion . secondly , let that number which was found in the first operation , ask the question in the second ; then take the number of like denomination to it , and also the number joyn'd with that like number ; of these three is your second compounded ; find your divisor , and proceed ; the last quote exhibits the answer . example . if 4 crowns at london make 2 ducates at venice , and 8 ducates at venice make 20 patacoons at genoa ; how many patacoons at genoa will make 120 crowns at london ? of the square root . the measure of a square is by a square , that is , when it is known how many square inches , feet or perches , is contain'd in any superficies , the content or area of the said superficies is then said to be known . and in a square , it is found by multiplying the length by the breadth , which being equal , it is called squaring of a number , and by the learned dr. pell , involution , and the product or area is the second power ; now the side of such a square is by geometricians called a root or the first power . let the side a b be 222 inches , feet , or perches , &c. now having the area of a square or square number given , and the side or root be required . this is called the extraction of a square root , and also evolution of the second power . let the number be as before 349284. the first thing to be done in the extraction of a root is punctation , or pointing the number given ; which is thus done , first set a point over the unite-place , and omitting one point every other figure thus , 349284 ; there being three points in the number , intimates three figures in the root to proceed then , enquire the greatest square number contained in those figures , under the first point on the left hand ; the greatest square number in 34 is 25 , whose root is 5 , which place in the quotient for the first figure in the root , subduct its square out of 34 , and set the remainder 9 underneath as in the example . example . the first figure in the root thus foundthe rest are found by division ; for a dividend bring down the figures under the next point , and postpone them to the last remainder , and the example will stand thus , your divisor being double the root found . then i proceed to division , always supposing the last figure in my divisor standing under the last save one in the dividend ; the number to be subducted from the dividend must always be the square of the last figure in the root , and the divisor multiplied by the last figure in the root , so added together as in this example , viz. so that the unite-place in the last number stand one place further to the right hand . which being subducted from the dividend will remain 11 , as part of a new dividend , to them bring down the two next figures , and the example will stand thus : the divisor as before is double the whole root found , and for the number to be subducted , after you have made enquiry how many times the divisor will be found in the dividend , if so placed as aforesaid , it will here be found once , then place 1 in the quotient for the third figure in the root , the number to be subducted will be as before , and the example will stand thus : the divisor multiplied by the last figure found , and the square of that figure placed as before directed . which sheweth the number was not a square number ; but if you desire to have it further , add two cyphers to the remainder for a new dividend , double your whole quotient for a new divisor , and you may have as many decimals as you please . tabula laterum quadratorum ab unitate ad 200. quadrata . latera . 1 1,00000,000000 2 1,41421,356237 3 1,73205,080757 4 2,00000,000000 5 2,23606,797750 6 2,44948,974278 7 2,64575,131106 8 2,82842,712474 9 3,00000,000000 10 3,16227,766017 11 3,31662,479036 12 3,46410,161514 13 3,60555,127546 14 3,74165,738677 15 3,87298,334621 16 4,00000,000000 17 4,12310,562562 18 4,24264,068712 19 4,35889,894354 20 4,47213,595500 21 4,58257,569496 22 4,69041,575982 23 4,79583,152331 24 4,89897,948556 25 5,00000,000000 26 5,09901,951359 27 5,19615,242271 28 5,29150,262213 29 5,38516,480713 30 5,47722,557505 31 5,56776,436283 32 5,65685,424948 33 5,74456,264654 34 5,83095,189485 35 5,91607,978310 36 6,00000,000000 37 6,08276,253030 38 6,16441,400297 39 6,24499,799840 40 6,32455,532034 41 6,40312,423743 42 6,48074,069841 43 6,55743,852430 44 6,63324,958071 45 6,70820,393250 46 6,78232,998313 47 6,85565,460040 48 6,92820,323028 49 7,00000,000000 50 7,07106,781185 51 7,14142,842854 52 7,21110,255093 53 7,28010,988928 54 7,34846,922835 55 7,41619,848710 56 7,48331,477355 57 7,54983,443527 58 7,61577,310586 59 7,68114,574787 60 7,74596,669241 61 7,81024,967591 62 7,87400,787401 63 7,93725,393319 64 8,00000,000000 65 8,06225,774830 66 8,12403,840464 67 8,18535,277187 68 8,24621,125124 69 8,30662,386292 70 8,36660,026534 71 8,42614,977318 72 8,48528,137424 73 8,54400,374532 74 8,60232,526704 75 8,66025,403784 76 8,71779,788708 77 8,77496,438739 78 8,83176,086633 79 8,88819,441732 80 8,94427,191000 81 9,00000,000000 82 9,05538,513814 83 9,11043,357914 84 9,16515,138991 85 9,21954,445729 86 9,27361,849550 87 9,32737,905309 88 9,38083,151965 89 9,43398,113206 90 9,48683,298050 91 9,53939,201417 92 9,59166,304663 93 9,64365,076099 94 9,69535,971483 95 9,74679,434481 96 9,79795,897113 97 9,84885,780180 98 9,89949,493661 99 9,94987,437107 100 10,00000,000000 101 10,04987,562112 102 10,09950,493836 103 10,14889,156509 104 10,19803,902719 105 10,24695,076596 106 10,29563,014099 107 10,34408,043279 108 10,39230,484541 109 10,44030,650891 110 10,48808,848170 111 10,53565,375285 112 10,58300,524426 113 10,63014,581273 114 10,67707,825203 115 10,72380,529476 116 10,77032,961427 117 10,81665,382639 118 10,86278,049120 119 10,90871,211464 120 10,95445,115010 121 11,00000,000000 122 11,04536,101719 123 11,09053,650641 124 11,13552,872566 125 11,18033,988750 126 11,22497,216032 127 11,26942,766958 128 11,31370,849898 129 11,35781,669160 130 11,40175,425099 131 11,44552,314226 132 11,48912,529308 133 11,53256,259467 134 11,57583,690279 135 11,61895,003862 136 11,66190,378969 137 11,70469,991072 138 11,74734,012447 139 11,78982,612255 140 11,83215,9566●0 141 11,87434,208704 142 11,91637,528781 143 11,95826,074310 144 12,00000,000000 145 12,04159,457879 146 12,08304,597359 147 12,12435,565298 148 12,16552,506060 149 12,20655,561573 150 12,24744,871392 151 12,28820,572744 152 12,32882,800594 153 12,36931,687685 154 12,40967,364599 155 12,44989,959799 156 12,48999,599680 157 12,52996,408614 158 12,56980,508998 159 12,60952,021292 160 12,64911,064067 161 12,68857,754045 162 12,72792,206136 163 12,76714,533480 164 12,80624,847487 165 12,84523,257867 166 12,88409,872673 167 12,92284,798332 168 12,96148,139682 169 13,00000,000000 170 13,03840,481041 171 13,07669,683062 172 13,11487,704860 173 13,15294,643797 174 13,19090,595827 175 13,22875,655532 176 13,26649,916142 177 13,30413,469565 178 13,34166,406413 179 13,37908,816026 180 13,41640,786500 181 13,45362,404707 182 13,49073,756323 183 13,52774,925847 184 13,56465,996625 185 13,60147,050874 186 13,63818,169699 187 13,67479,433118 188 13,71130,920080 189 13,74772,708488 190 13,78404,875209 191 13,82027,496109 192 13,85640,646056 193 13,89244,398945 194 13,92838,827718 195 13,96424,004377 196 14,00000,000000 197 14,03566,884762 198 14,07124,727947 199 14,10673,597967 200 14,14213,562373 the use of the precedent table is principally for the ease of the industrious artist ; when he hath the extraction of a square root in the solution of any question , it is but seeking the given number in the table , and just against it he shall find the root . by the subsequent examples will it plainly appear , how useful such a table to 1000 roots would be in quadratique equations , and in the cubes also , which ( were there incouragement given to the sons of art ) i doubt not but some ingenious person would enrich the world therewith ; these being long since calculated by mr. henry briggs of oxford , and given me by my honoured friend , mr. john collins , his desire being to have them made more publick , and the conveniency of such a table ( before mentioned ) shewn , by some examples upon this . of quadratique equations . mr. dary , in his miscellanies , chap. 8. saith to this , or the like purpose : 1. when any equation propos'd is incumbred with vulgar fractions , let it be reduced to its least terms in whole numbers , if possible ; if not , let it be brought to its least terms in decimals . 2. it is evident from divers authors , that if any quantity shall be signed — , then the square root , or the root of any even power of such quantity so sign'd , is inexplicable , for they cannot be generated from any binomials that shall be equal . as for example . — 9 being a negative can be made of nothing ( if taken as a square number ) but + 3 and — 3 , which roots are not equal , they being neither both affirmatives nor both negatives . 3. when you have cleared the equation by the second hereof , and that the co-efficient in the highest power is taken away , or be unity , then will quadratique equations resolve themselves into the four following compendiums . 4. let your equation be so reduced , that the highest power stand on the left side alone , the sign + being always annexed , or supposed to be annexed . example , quesita a. first equation . second equation . third equation . fourth equation . illustration by numbers , quesita a. first equation . which was to be proved . proof of the negative . example 2. second equation . example 1. example 2. third equation . example 1. example 2. fourth equation . example 1. example 2. but if in a square equation there happen to be a coefficient annexed to the highest power , it is resolved by transferring the coefficient with the sign of multiplication to the other side . admitting the equation be then the coefficient 2 being transferred ( as before directed ) they will stand as in this example . first equation . the root of +25 being +5 , then is +5+ ; = 8 , and a = +4 , the affirmative answer . and +3-5 is = -2 , and a = -1 , the negative answer . the proof is easie : first , if a be = 4 , 2 aa is = +32 , and 6a is = +24 , to which +8 being added , the sum is +32 which was to be proved . again , a = -1 , then 2 aa is = -2 , whereto +8 being added , the sum is = +6 , which also was to be done . second equation . now +13 +the √ 121 , viz. + 11 is = +24 , the 1 / 4 whereof is = +6 = a , and aa = 36. and 4 aa = +144 , +26 a = +156 , to which if -12 be added , the sum will be +144 also . again , if to +13 you add the √ 121 , viz. -11 , 4 a will be = +2 , and consequently + a = +1 / 2 , 4 aa is then = +1 , and +26 = +13 , to which add -12 , and the sum is = +1 , which was to be proved . third equation . -3 +13 = +5a , here a = +2 , 5aa = +20 , 6a = -12 , to which add +32 , the sum is also+20 . again , 3-13 = -16 = 5a , and a = -8.2 , 5aa = +51.2 : also 6a being = +19.2 , to which add +32 , the sum is = +51.2 . fourth equation . which was to be done . note , always where there is no sign annexed to any term in the equation , the sign + is supposed to be annexed . i have been the larger in these examples , that the young analist may with the more ease apprehend the several kinds by this variety ; in some of the surd roots i have on purpose omitted the large number of places , four or five being sufficient for use in most cases ; but if any desire to be more exact , he may take them as far as he pleaseth , or the table doth exhibit . of the cube root . the cube is a solid , and hath three dimensions , length , breadth , and depth , and is inclosed by six plain square superficies . example . let the side a , b , or c , d , &c. be 125 : to find the content in solid feet or inches , is the involution of the side or root . thus : and this is called the third power . the evolution hereof , is also termed the extraction of the cube root , wherein observe first your punctation , omitting two , point every third figure . example . the first figure in the root is found by taking the greatest cube number , contained in the figure or figures that stand under the first point towards the left hand , here 71 , whose root is 4 , therefore that 4 must be placed in the quotient as the first figure in the root , and the example will stand thus : then the cube of 4 is 64 , which subduct out of the first figures , and set down the remainder if any be . the first figure found in this peculiar manner , the rest are found by division thus : the dividend consists of the remainder , if any be , and the three figures under the next point postponed ; the divisor is always three times the square of the root , and three times the root it self : these two numbers being so to be added together , as that the unites of the first stand over the tens of the second . then will the example stand thus : then proceed to division , always supposing the last figure in the divisor to stand under the last save one in the dividend , and enquire , how many times 4 in 7 ? place 1 in the quotient . then for your number to be subducted out of the dividend , it always consists of three numbers , viz. then for a new dividend , bring down the three next figures , postponing them as before . which being set on the left hand the dividend , stands thus : then enquire , how many times 5 in 30 ? you will find 5 times , which place in the quotient . your subducend is as before , which shews the number was not a cube number ; if you add three cyphers , and work as before , you may have as many decimals fractions as you please . in this extraction i have not taken the same number the cube first mentioned did produce , but by adding another figure , made the number greater , that it might take in all cases ; but in the following extraction it is explicated . a short treatise of simple & compound interest : with two tables for the calculation of the value of leases or annuities by quarterly payments , at 6 per cent. per annum . by john mayne . london , printed by william godbid , for nath. crowch , in exchange-alley . m. dc . lxxiii . of simple interest . question 's in simple interest are wrought by the double rule of proportion , wherein five numbers are given to find the sixt . and if you put p = 100 principal , and t for twelve months , g = 6 l. the rate of interest , and p = any other sum greater of lesser , t = any other time ( above or under twelve months ) and also g = to the gain thereof at that rate . then if any one term of these six be unknown , it is explicated by the other five ( like symbols having the same denomination ) as in this equation . that is the fact of 100 l. multiplied by one year , and that product by 6 the interest of 25 l. for 4 years , is equal to the fact of 25 multiplied by 4 years , and that product by 6 the interest of 100 l. for one year . example . which was to be proved . now forasmuch as the usual questions of simple interest , are proposed from a sum presently due to the gain thereof , & contra ; it will be requisite you put a = the amount of a sum , forborn or due hereafter , and then you will have a = p+g , as in the former equation . example . from the precedent analogism will arise these four propositions . prop. i. a sum presently due = p , being forborn a certain time = t , at a certain rate = g , per cent. per annum : q. the amount = a ? that is , the given sum multiplied by the given time , and that product again multiplied by the given rate of interest , the last product divided by the principal , viz. 100 , in the time , viz. 1 , exhibits the gain of that sum in that time. illustration . quest. 1. 25 l. being forborn 18 months , at 6 per cent. per annum ; what doth it amount to ? the answer being 27 l. 5 s. the amount in that time . quest. 2. if 175 l. be forborn for 7 years , at 6 per cent. per annum , simple interest ; what will it amount to at the end of the said time ? prop. ii. a sum of money = a , due at a certain time hereafter = t , at a certain rate of interest = g , per cent. per annum . q. the present worth = p ? that is , the fact of the amount multiplied by the principal , 100 , in the time , viz. 1 year , divided by the said principal multiplied into the said time , more the rate of interest multiplied into the time of forbearance , the quotient is equal to the present worth . example . quest. 1. if 248 l. 10 s. be due at the end of 7 years , what is it worth in ready money , discompring interest , at 6 per cent. per annum . the answer is 175 l. quest. 2. if 950 l. be due at the end of 12 years , what is it worth in ready money , at 9 per cent. per annum simple interest ? the answer is 456 l. 14 s. 7 d. 1 / 4 ferè . prop. iii. a sum presently due = p , having been forborn a time unknown = t , di●● amount to a certain sum = a , at a rate of interest = g , per cent. per annum . q. the time of forbearance = t ? that is to say , the amount less the principal , so increased , multiplied by 100 , and that product divided by the fact of the before-mentioned principal , and rate of interest , quotes the time of forbearance . example . quest. 1. if 175 l. hath been forborn till with the interest at 6 per cent. per annum it is increased to be 248 l. 10 s. q. how long hath it been forborn ? the answer is 7 years . quest. 2. if 25 l. hath been forborn till it is amounted to 27 l. 5 s. at 6 per cent. per annum , simple interest . q. in what time is it so increased ? the answer 1 year and an half . prop. iv. a sum of money = p , being forborn a certain time = t , and at the end of that term did amount to a sum = a. q. at what rate of interest ? or from the amount subduct the principal , and the remainder multiply by 100 , that product divided by the principal multiplied by the time , the quotient will be = g the rate of interest , per cent. per annum . illustration . quest. 1. if 250 l. forborn 3 years and 6 months , did amount to 324 l. 7 s. 6 d. at what rate of interest did it so increase ? the answer is 8 l. 10 s. quest. 2. if 175 l. being forborn 7 years , did amount to 248 l. 10 s. what rate of simple interest per cent. per annum was it accompted at ? the answer is 6 l. if one month be taken for the 1\12 of a year , the business of interest and rebate is very easily performed by a small table of the amounts of 1 l. for any number of months , not exceeding 12 ; which table is made by this analogy , 100.106 : : 1.1.06 . a table of the increase of 1 l. at 6 per cent per ann. months . value . months . value . 12 1.06 6 1.03 11 1.035 5 1.025 10 1.05 4 1.02 9 1.045 3 1.015 8 1.04 2 1.01 7 1.035 1 1.005 if the question be of the amount of any sum forborn any number of months , at 6 per cent. per annum , multiply the given sum by the tabular number for that time , and the product answers the question . example . if 125 l. be forborn 10 months , what will it amount to ? the answer is 131 l. 5 s. if the question be only what is the interest of any sum for any time , then multiply the sum for that time by the tabular number less an unite . example . what is the interest of 125 l. for 10 months ? the answer is 6 l. 5 s. prout suprà . for discompt or rebate of any sum to be forborn , the present worth is found by dividing the given sum by the tabular number . example . what is the present worth of 131 l. 5 s. due at the end of 10 months ? the answer is 125 l. but if any desire to be more exact , let him multiply the interest of 1 l. for 1 day ( which is .000164384 ) by the number of days , and that product by the given sum , and the last product will be the interest for that sum forborn the time given . example . what is the interest of 125 l. forborn from the tenth of march to the tenth of january following , viz. 305 days ? the answer is 6 l. 5 s. 4 d ferè . discompt is performed by division , viz. get the amount of 1 l. for the time required , by which divide the given sum , and the quote is the present worth . of mean time. it hath been a custome amongst merchants , in their contracts upon sale of commodities , to agree upon divers times of payment , as two three-months , three six-months , &c. now to find a time between these , wherein the whole sum may be paid at one entire payment without detriment to either party , the subsequent table doth shew upon the first inspection . a table for equation of time.   1 is 1.5   1 is 2   1 is 2.5   1 is 3   2 is 3   2 is 4   2 is 5   2 is 6   3 is 4.5   3 is 6   3 is 7.5   3 is 9   4 is 6   4 is 8   4 is 10   4 is 12 2 5 is 7.5 3 5 is 10 4 5 is 12.5 5 5 is 15   6 is 9   6 is 12   6 is 15   6 is 18   7 is 10.5   7 is 14   7 is 17.5   7 is 21   8 is 12   8 is 16   8 is 20   8 is 24   9 is 13.5   9 is 18   9 is 22.5   9 is 27   1 is 3.5   1 is 4   1 is 4.5   1 is 5   2 is 7   2 is 8   2 is 9   2 is 10   3 is 10.5   3 is 12   3 is 13.5   3 is 15   4 is 14   4 is 16   4 is 18   4 is 20 6 5 is 17.5 7 5 is 20 8 5 is 22.5 9 5 is 25   6 is 21   6 is 24   6 is 27   6 is 30   7 is 24.5   7 is 28   7 is 31.5   7 is 35   8 is 28   8 is 32   8 is 36   8 is 40   9 is 31.5   9 is 36   9 is 40.5   9 is 45 the manner of making this table , is no more than adding one term to the given number of terms , and take half the sum. example . is three four-months given , add 4 to 12 , the sum will be 16 , half that sum , viz. 8 months , is the equated time of payment . this indeed is but an approximation , though near enough the truth for practice . that excellent accomptant mr. collins , in a sheet printed anno 1665. hath taught a more exact way of equation : simple interest , prop. 4. compute ( saith he ) all the present worths , and then by proportion , if all those present worths did 1 l. amount to in the said time ? from the result subtract an vnite , the remainder is the interest of 1 l. for the time sought , which divide by the interest of 1 l. for one day , and the quote is the number of days sought . example . a merchant sold wines for 300 l. and hath given the vintner three six-months for payment , viz. to pay 100 l. at the end of 6 months , another at 12 , and the third 100 l. at 18 months end ; the question is , at what time may this vintner pay 300 l together , without detriment to himself or the merchant . the interest of 1 l. for the time is .059123786 the interest of 1 l. for 1 day is = .000164384 the answer is 359 days and a half , ferè . by the table , three six-months gives twelve months for the equated time which you find above five days less than a year by this calculation . a decimal table of the present worth of one pound , quarterly payment , at 6 per cent. per annum , simple interest , for 124 quarters . 1 .985222 2 1.956095 3 2.913033 4 3.856429 5 4.786662 6 5.704093 7 6.609071 8 7.501928 9 8.382985 10 9.252550 11 10.110919 12 10.958377 13 11.795197 14 12.621643 15 13.437970 16 14.244421 17 15.041234 18 15.828636 19 16.606846 20 17.376077 21 18.136533 22 18.888413 23 19.631907 24 20.367201 25 21.094474 26 21.813898 27 22.525642 28 23.229868 29 23.926732 30 24.616387 31 25.298981 32 25.974656 33 26.643553 34 27.305804 35 27.961542 36 28.610893 37 29.253979 38 29.890922 39 30.521837 40 31.146837 41 31.766032 42 32.379529 43 32.987432 44 33.589841 45 34.186856 46 34.778572 47 35.365082 48 35.946478 49 36.522847 50 37.094275 51 37.660848 52 38.222645 53 38.779748 54 39.332235 55 39.880180 56 40.423658 57 40.962742 58 41.497501 59 42.028005 60 42.554321 61 43.076514 62 43.594649 65 44.108787 64 44.618992 65 45.125321 66 45.627833 67 46.125686 68 46.621636 69 47.113036 70 47.600841 71 48.085103 72 48.565872 73 49.043199 74 49.517133 75 49.987721 76 50.455010 77 50.919048 78 51.379877 79 51.837543 80 52.292088 81 52.743556 82 53.191986 83 53.637421 84 54.079898 85 54.519459 86 54.956140 87 55.389980 88 55.821014 89 56.249280 90 56.674811 91 57.097644 92 57.517813 93 57.935349 94 58.350287 95 58.762658 96 59.172494 97 59.579826 98 59.984684 99 60.387099 100 60.787099 101 61.184713 102 61.579970 103 61.792897 104 62.363522 105 62.751872 106 63.137972 107 63.521849 108 63.903529 109 64.283035 110 64.660394 111 65.035628 112 65.408763 113 65.779820 114 66.148824 115 66.515796 116 66.880760 117 67.243736 118 67.604747 119 67.963814 120 68.320956 121 68.676196 122 69.029553 123 69.381047 124 69.730697                         the use of the precedent table is principally to shew the present worth of any lease or annuity , payable quarterly , for any term of years under 21 , at 6 per cent. per annum , simple interest . example . there is a lease for 18 years to be sold , of the yearly value of 160 l. payable quarterly , viz. 40 l. per quarter , what is this lease worth in ready money allowing the purchaser 6 per cent. simple interest ? the answer is 1942 l. 12 s. 8 d. 1 / 4 ferè . the inversion of the question , viz. what quarterly payment for 18 years will 1942 l. 12 s. 8 d. 1 / 4 purchase ? as the former was done by multiplication , where the product exhibits the answer ; so if the sum proposed be divided by the tabular number , the quote gives your answer . example . the answer is 40 l. of compound interest . as simple interest is performed by a series of musical , so is compound interest wrought by a rank of geometrical continual proportionals . the operation whereof by the canon of logarithms , take under these four considerations . prop. i. if you shall put p = the logarithm of a principal or sum forborn , and t = the time of forbearance in years , quarters , months , or days , r = the logarithm of the rate of interest , per cent . per annum , per mensem , or per diem , a = the logarithm of the amount of the said principal for the said time , at the rate also aforesaid : then q. the amount = a ? that is , multiply the logarithm of the rate by the number of years , quarters , &c. to which product add the logarithm of the principal , and the aggregate is equal to the logarithm of the amount . example . quest. 1. if 175 l. be forborn 7 years , what will it amount to at 6 per cent. per annum , compound interest ? the answer 263 l. 2 s. 8 d. 1 / 4 ferè . quest. 2. if 1000 l. be forborn for 6 months , at 6 per cent. per annum , compound interest , what will it amount to ? the answer 1029 l. 11 s. 3 d. ferè . prop. ii. a sum of money unknown , being forborn a certain time = 1 , at a given rate of interest = r , is amounted to a given sum = a ; q what was p ? from the logarithm of the amount , subduct the logarithm of the rate , multiplied by the time , and the remainder is the logarithm of the principal . example . quest. 1. if 263 l. 2 s. 8 d. 1 / 4 be the amount of a sum forborn 7 years , at 6 per cent. per annum , compound interest , what was the principal ? the answer 175 l. quest. 2. if 102 l. 11 s. 3 d. be the principal and interest of a sum of money forborn 6 months , at 6 per cent. per annum , compound interest , what was the principal ? the answer 1000 l. prop. iii. a sum of money = p , being forborn for a time = t , did amount to a given sum = a , at a rate of interest unknown : q. the rate per cent. per annum = r ? divide the logarithm of the amount , less the logarithm of the principal , by the time , and the quote is the logarithm of the rate . example . if 25 l. forborn 4 years , did amount to 31 l. 11 s. 2 d. 1 / 4 ; at what rate of compound interest did it so increase ? prop. iv. a sum of money being forborn , at a given rate , for a time unknown , but the amount is known , how long was it so forborn ? example . if 1000 l. be increased to 1029 l. 11 s. 3 d. at 6 per cent. per annum , compound interest , in what time was it so increased ? the answer 6 months . it may here be expected that i should lay down the construction of the logarithms , having made use of them in these calculations , but this being design'd a small enchiridion , and there being large volumns of that subject in the world already , by several more learned pens , i think it unnecessary to say any thing further thereof , for as they are of excellent use , so are they easie to be had . compound interest infinite , may be so called as it relates to divers equal payments at equal times , but the number of those equal times are infinite , ( i. e. ) when an estate in fee-simple shall be sold for ever . now there being usually an interval of time , between the purchasers payment and the reception of his first rent , be it yearly , half yearly , or quarterly ; any question of this nature may be wrought by the following analogism : putting v = the rent ( yearly or quarterly ) and s = the price paid for the land , also r = the common factor of the rate of interest , per cent. per annum . hence then may arise these three propositions . prop. i. there is a fee simple to be sold , what is it worth in ready money , so that the purchaser may have 6 per cent. per annum , compound interest , allowed for his money . quest. 1. there is a manour to be sold of the clear yearly value of 969 l. 18 s. what sum of ready money is this estate worth , 6 per cent. per annum compound interest being allowed the purchaser for his money ? the annual ( or quarterly ) payment , divided by the ratio , less unity , exhibits the sum in the quotient . the answer is 16165. quest. 2. there is an estate of 969 l. 18 s. per annum , payable quarterly , what is it worth in ready money , allowing the purchaser 6 per cent. per annum compound interest ? the answer is 16524 l. 2 s. 6 d. ferè . the difference between yearly and quarterly payments in this purchase raiseth the value 359 l. 2 s. 6 d. * having the increase of 1 l. for a year , at any rate of interest , the biquadrate root of that increase , is the increase of 1 l. for a quarter at compound interest . prop. ii. a sum of money lying ready for a purchase , and it be desired to know what free-hold estate such a sum will purchase , if laid cut at a given rate per c. per ann. compound interest . or , in other terms , the sum of money multiplied by the rate , less unity , the product shall be equal to the annual half quarterly or quarterly payment . quest. a gentleman upon marriage of his daughter promiseth to lay out 1600 l. for a free-hold estate , to be settled upon her and her heirs , provided he meet with such a pennyworth as shall bring 8 per cent. per annum , compound interest for his money : q. what annual rent must it be ? the answer 128 l. per annum . prop. iii. an estate being offered for a certain sum of money , the annual rent is also known : q. what rate of interest upon interest shall the purchaser have for his money ? the annual rent being divided by the sum demanded , quotes the rate less unity . example . quest. 1. there is a free-hold estate to be sold for 1600 l. the yearly rent being 128 l. what rate of interest shall the purchaser have for his money ? quest. 2. admit there be a small farm to be sold of the value of 35 l. per annum for 500 l. what rate of compound interest shall the purchaser have for his money at that price ? furthermore , if it be inquired how many years purchase any annuity is worth , putting r = the ratio as before , and y the number of years , the rule is : that is , divide unity by the ratio less 1 , and the quote informs the number of years . example . there is a free-hold estate to be sold , q. how many years purchase is it worth at 5 per cent. per annum ? the answer is 20 years purchase . what is it worth at 6 per cent. per annum ? the answer is 16 years , and 2 / 3 of a year . again , if an estate be offered at any number of years purchase , and it be demanded what rate of interest the purchaser shall have for his money , the rule is : that is , divide unity by the number of years propos'd , and the quote exhibits the ratio , less unity . example . an estate is offered at 20 years purchase , what rate of interest shall the purchaser then have ? the answer is 5 per cent. per annum . there are many tables of compound interest printed in sundry books for the valuation of leases and annuities , but they are generally made for yearly payments , when indeed by the common and most usual covenants in leases the tenant is obliged to pay quarterly ; and in le●ses of great value , there will be found a considerable difference in the true worth , ( so great , that 25 l. per quarter is as good as 102 l. 5 s. per annum . ) i have therefore presented the reader with a table fitted to such quarterly payments , the use of which table i doubt not but will be very easily found by the examples that follow . a table of interest , for the valuation of leases or annuities for quarterly payments , at 6 per cent. per annum , compound interest , for 31 years . 1 .985538 2 1.956824 3 2.914064 4 3.857459 5 4.787313 6 5.836372 7 6.609520 8 7.496573 9 8.373700 10 9.238139 11 10.090079 12 10.929724 13 11.757176 14 12.572685 15 13.376402 16 14.168496 17 14.949134 18 15.718484 19 16.476707 20 17.223982 21 17.960417 22 18.686219 23 19.401524 24 20.106484 25 20.801250 26 21.485968 27 22.160789 28 22.825841 29 23.481282 30 24.127242 31 24.763844 32 25.391256 33 26.009595 34 26.618988 35 27.219206 36 27.811474 37 28.394861 38 28.969764 39 29.536352 40 30.094714 41 30.645034 42 31.187396 43 31.721914 44 32.248000 45 32.767870 46 33.279531 47 33.783794 48 34.280753 49 34.843000 50 35.253244 51 35.728999 52 36.197819 53 36.659861 54 37.115237 55 37.564028 56 38.006330 57 38.442234 58 38.871893 59 39.295222 60 39.712487 61 40.123777 62 40.529043 63 40.928469 64 41.322133 65 41.710087 66 42.092531 67 42.469245 68 42.841611 69 43.206601 70 43.567307 71 43.922768 72 44.273138 73 44.618415 74 44.958701 75 45.194062 76 45.624577 77 45.950311 78 46.271331 79 46.587715 80 46.899521 81 47.206817 82 47.509668 83 47.808141 84 48.102298 85 48.392200 86 48.677877 87 48.959492 88 49.236993 89 49.510486 90 49.780023 91 50.045601 92 50.307460 93 50.665471 94 50.819753 95 51.070356 96 51.317335 97 51.560742 98 51.841984 99 52.037044 100 52.271047 101 52.499677 102 52.725986 103 52.949021 104 53.134301 105 53.385474 106 53.598963 107 53.809375 108 54.016743 109 54.221113 110 54.422527 111 54.620966 112 54.816601 113 55.009461 114 55.199474 115 55.386751 116 55.571297 117 55.753185 118 55.932443 119 56.109107 120 56.283219 121 56.454811 122 56.623921 123 56.790588 124 56.954843                         the calculation of a number in the precedent table , by aid of the canon . the question being , what is the present worth of 1 l. per quarter for 21 years ? then by the rule of proportion : the answer is = 48 l. 2 s. 0 d. 1 / 2 ferè . and after this manner may a table be calculated , or the value of a lease for any number of years , may be found at any rate of interest required . the use of the table . this table sheweth the discompt of 1 l. per quarter at 6 per cent. per annum , compound interest , and if the tabular number for so many quarters as the lease is to continue be multiplied by the quarterly payment , that product is the present value of that lease in ready money . example . a lease of 40 l. per annum ( viz. 10 l. per quarter ) for 21 years , being to be sold , what is it worth in ready money ? the answer is 481 l. 0 s. 5 d 1 / 4 ferè . but if the question be , what quarterly rent for 21 years will a given sum purchase ? then divide the given sum by the tabular number for so many quarters . example . a gentleman having a lease of certain church lands , worth 200 l. per annum more than the reserved rent , for 14 years to come , surrenders the same , upon condition the chapter shall make him a new lease for 31 years without a present fine , but advancing the old rent 10 l. per quarter during the whole term of 31 years ; what doth he gain by the bargain , accompting compound interest on both sides ? the answer is 377 l. 18 s. the new lease being so much more worth than the old one . 240 l. is demanded for the lease of a house for 7 years , the tenant offers 100 l. and an advance of rent equivalent to the rest of the fine required , what ought this rent to be ? the advance of rent ought to be 6 l. 2 s. 8 d. per quarter . there is a lease of 200 l. per annum , viz. 50 l. per quarter , for 131 / 4 years , to be sold , what is it worth at 6 per cent. simple , and what at 6 per cent. compound interest ? simple . compound . where by it appears , that it is cheaper to the purchaser at compound interest than at simple interest by 106 l. six questions performed by the aid of the canon of logarithms . quest. 1. a gentleman pays 350 l. for a lease in reversion , to commence at the end of 13 years and a quarter , and to continue for 21 years and 3 quarters , what quarterly rent may he lett the premises for , after he comes to be in possession thereof , so as to gain 8 per cent. compound interest for his money ? the answer = 23 l. 3 s. 11 d. 1 / 4 ferè . quest. 2. a citizen having taken a lease of a house and shop for 21 years , at 370 l. fine , and 100 l. per annum , viz. 25 l. per quarter , rent , at the end of two years is willing to leave it for 300 l. and the old rent , or to have such an increase of rent , during the whole term yet to come , as may reimburse him his fine paid , with compound interest at 6 per cent. per annum : what ought he to receive in advance of rent , and what doth he offer to lose of his fine paid in taking 300 l. whereby it appears , there is 50 l. 18 s. 10 d. offered to be lost in putting off the house and shop aforementioned . quest. 3. a sells a house to b for 800 l. to be paid with interest upon interest by 100 l. per annum , viz. 25 l. per quarter , how many quarters rent ought b to pay before a is satisfied for his 800 l. with compound interest at 6 per cent. per annum , and what ought the last payment be ? the last payment 13 l. 3 s. 4 d. ferè . quest. 4. a lends unto b a certain sum of ready money , and accepts a rent charge of 40 l. quarterly for 7 years in satisfaction , finding it paid him his principal with interest upon interest at 8 per cent. within 13 l. 4 s. 6 d. what was the money lent ? the money lent was 968 l. 14 s. quest. 5. a testator leaving one son and two daughters , bequeaths out of his estate ( being 600 l. per annum for 11 years ) to his eldest daughter 500 l. per annum for 4 years next coming , at the end whereof , to his younger daughter 300 l. per annum for 7 years , and to his son the remainder of the estate for the whole time : q. which had the greatest portion , and by now much , calculating their several annuities at 6 per cent. compound interest ? proof . quest. 6. a merchant sold 16 kintals of cyprus cottons for 320 l. to be paid at two six-months ; the buyer having money by him , offers to pay the money presently , provided the merchant allow him discompt at 6 per cent . compound interest . q. what ought the merchant to receive ? the answer 306 l. 6 s. 4 d. ferè . stereometry : or , a new and the most practical way of gauging tunns in the form of a prismoid & cylindroid : also the frustums of pyramids and of a cone together with the art of cask-gauging . by john mayne . london , printed by william godbid , for nath. crowch , in exchange-alley . m. dc . lxxiii . to the young geometrician . i hope by this time thou art so sufficiently acquainted with the nature and use of a decimal fraction , that any operation in the six species , viz. addition , subtraction , multiplication , division , involution and evolution of the second and third powers , will not appear difficult to thee ; and these being familiar , any calculation in arithmetick , geometry , trigonometry , or other mathematical arts , will not seem strange : amongst the many pleasant walks in this tempe , i have made it my present design to give thee some diversion in that part of solid geometry called gauging , and herein passing by those blossoms that kiss the hand of every passenger , i have endeavoured ( and i hope not altogether without success ) to shew thee how to gather a rose without danger of its thorn : for the invention , the world is obliged to the ingenious mr. michael dary , the roots of these , and many other choice mathematical flowers , lying crowded together in a small treatise called dary's miscellanies , printed 1669. here , as in the former part , thou hast both precept and example in the plainest method i could possibly express them . that they may by no means seem obscure to any ingenious student , is the hearty desire of thy friend , j. m. the explanation of the signs or characters . + more . − less . = equal . > greater . < lesser . × multiplied . √ square root . q square . circle . : : proportional . difference . stereometry : or , a new and the most practical way of gauging tunns , &c. a plain and easie method for finding the solid content of a prismoid . definition . by the word prismoid is to be understood a solid contained under six plain surfaces , whereof the two bases ought to have these three qualifications : 1. rectangular parallelograms . 2. parallel . 3. alike situate . i. e. so situate , that the rectangular conjugates in both bases may be inserted by two and the same planes , and a right line extended from the center of one base to the other may be called the axis , and the other remaining four planes are the peripatasma . under this definition is comprehended the frustums of pyramids and prisms . note also , it the peripatasma be not made by the four flat sides ( spoken of before ) but shall be constituted by curveture from circles or elipse's , the solid is then called ● cylindroid , and under this definition is comprehended frustums of cones and cylinders . probl. if in a prismoid you put c = the whole content thereof . a & b = the two rectangular conjugates above . g & h = the two rectangular conjugates below . a & g opposite = their two correspondents one above the other below inserted by one plane . b & h opposite = their two correspondents above and below , and also inserted by one plane . p = the perpendicular height of the prism or prismoid . k = the increment of any two diameters , to be taken between a and g in the same plane with them , at one inch distance of the perpendicular . l = the increment of any two diameters , to be taken between b and h in the same plane with them , at one inch distance of the perpendilar . then , analogism . or , the rectangle of the two diameters at the base multiplied into the perpendicular , more the semi-sum of g l and h k , ( viz. those two diameters multiplied into their altern increments ) multiplied into the square of the perpendicular , to which add one third of the rectangle of k l ( i. e. ) the two increments multiplied into the cube of the perpendicular is equal to the content in cubick inches . by which theorem you find three fixed or stationary numbers , which mr. dary calls reserved coefficients , wherefore you shall find them hereafter called by that denomination : these three reserved coefficients thus multiplied into the perpendicular , the product is equal to the whole content , or by any part of the perpendicular gives the solidity of that part . prop. i. having a tunn in the form of a prismoid , the dimensions being , what is the solidity of this tunn in cubick inches ? first then to find the three reserved coefficients . i. e. the difference between a and g ( the two opposite diameters above and below ) divided by the perpendicular quotes k , the increment of any two diameters to be taken between them , at one inch distance in the perpendicular , and in the same plane . that is , the difference between b and h ( the two diameters opposite the one above the other below ) divided by the perpendicular quotes l , the increment of any two diameters to be taken between them , at one inch distance in the perpendicular , and in the same plane with them . now having found these reserved coefficients , i proceed , and finding that 1 / 3 of k l must be multiplied by the cube of the perpendicular , i begin with it , and call that the first coefficient ; then 1 / 4 g l h k being to be multiplied by the square of the perpendicular , i add that to the first fact , and call it the second coefficient ; lastly , g h being to be multiplied by the perpendicular , i add that to the second fact , and call it the third coefficient ; then will the work stand thus : example . now admitting this tunn have but 33 wet inches , what is the content thereof ? prop. ii. having a tunn in the form of a prismoid , the dimensions being , what is the solidity in cubick inches ? to find this tunns solidity , the rule is : i. e. the fact of a b ( the rectangular congates at the base ) multiplied by the perpendicular , from whence subduct the semi-sum of the two facts ( a and its altern decrement , b and its altern decrement , multiplied into the square of the perpendicular ) more the one third of the rectangle of k l , viz. the two decrements , multiplied into the cube of the perpendicular , and that remainder is the content in cubick inches . to find the coefficients . this rule being the converse of the former , these numbers k and l which before were affirmatives are now become negatives ( then increment , now decrement ; ) the greater conjugates being subducted from the lesser makes the dividends so much less than nothing , and consequently the quotes , the divisor being an affirmative , yet these two negatives being multiplied together , their fact becomes affirmative , according to the rule of algebra , the signs of the factors being homogeneal ( or alike ) makes the fact more , as in this example . the factors in these rectangles being heterogeneal ( or unlike ) the fact is made less . these two factors being both affirmatives , the fact is + . with these three reserved coefficients i proceed to the calculation , according to the precedent theorem . but if this tunn have only 27 inches of the perpendicular wet , the content then being required : prop. iii. there is a tun in the form of a prismoid , the dimensions are , what is the solidity in cubick inches ? prop. iv. there is a tunn in the form of a prismoid , the dimensions being , what is its solidity in cubick inches ? the reserved coefficients are found to be : the calculation . here note , if any of the precedent tunns be cloathed by curveture , ( i. e. the bases being circular or elliptical ) the last product ought to be divided by 1.27324 , then will the quotient exhibit the cubick inches in that solid . but if the question be ale gallons , let your coefficients be divided by 282 ; if beer barrels be required , divide the coefficients by 10152 , the number of inches in a beer barrel . in all flat sided figures , and for those solids , whose peripatasma is constituted by circles or ellipsis , the divisor for beer barrels is 12926 > , for ale barrels 11490 > , and for ale gallons 359 ; of which take these examples . what number of beer barrels and gallons doth the last mentioned tunn contain ? the three coefficients for beer barrels divided by 10152 are : the first = +.000007880220646 < the second = = .0067375888 > the third = +1 . 87●3404 < the three coefficients for gallons being divided by 282 are : the first = .0002837 > the second = .2425532 > the third = 67.4042553 > the coefficients being thus fitted , the calculation is after this manner : for barrels . the answer is 89 barrels , 3 firkins , and 1 gallon , or 89 barrels and 28 gallons . for gallons . the answer is 3232 gallons , which divided by 36 quotes 89 barrels 28 gallons , as before . example . a new way of gauging the frustum of a pyramid or conical tvnn . a new way of gauging the frustum of a pyramid , &c. definition . a pyramid is a solid figure , contained under many superficies , whereof one is the base , and the rest arise from the base to the vertex , and there meet in a point . the frustum of a pyramid is a solid , cut with a plane parallel to the base , and the part cut off is also a pyramid . the frustum of a cone , may not improperly be termed the frustum of a round pyramid , ( the base being circular ) nor do i think it an heresie to call a cylinder a round prism . the frustum of a pyramid , whose bases are in the form of any ordinate polygon , being alike , and alike situate , and also if a right line may be every where applied in the peripatasma from base to base , moreover a right line being extended from the center of one base to the other , may be called the axis . then if you put s = the whole solidity . b = a side above . a = a side below . p = the perpendicular . d = the common addend at one inch distance of the perpendicular , and is thus made , that is , the difference between a side above and a side below , divided by the perpendicular , quotes the increment , &c. g = the divisor . the rule is : or , in other terms : to the square of the side multiplied by the perpendicular , add the fact of one side in the increment multiplied by the square of the perpendicular , more 1 / 3 of the q. of the increment in the cube of the perpendicular , and the aggregate divided by the polygons respective divisor , the quote will be the solidity . and further it is to be well observed , if your frustum of a pyramid stand upon its greater base , the rule then is thus varied : that is to say : from the square of a side at the base multiplied by the perpendicular , subduct the rectangle of one of those sides in the decrement multiplied by the square of the perpendicular , more one third of the square of the decrement in the cube of the perpendicular , and that remainder divided by the divisor proper to the form of the base , the quote is equal to the solidity . note also , that p may be put for a part of the perpendicular , and the answer will be the content of that part required . g ) or the divisors for these 8 regular polygons , and the cone . for cubick inches .   for ale gallons .   trigon 2.30940 trigon 651.2000 tetragon   tetragon 282.0000 pentagon .58123 pentagon 157.2600 hexagon .38497 hexagon 108.5400 heptagon .27513 heptagon 77.5867 octogon .20710 octogon 58.4022 nonagon .16176 nonogon 45.6163 decagon .12997 decagon 36.6515 cone 1.27324 cone 359.0500 if your tunn be the frustum of a cone : let a or b be the diameter at the base , and d the increment or decrement of any two diameters between a and b , at one inch distance of the perpendicular , and the divisor as per table . i shall only give you some examples of the three first , and the cones frustum , which i think will be sufficient to inform any ingenious practitioner how to perform the rest . the trigon . admit a tunn be in the form of an equilateral triangle , the dimensions being , a = 126 inches , the length of a side above , b = 108 inches , the length of a side below , p = 60 inches , the perpendicular , q. the content in ale gallons ? the coefficients are found , according to the precedent directions , thus : these three divided by the divisor for ale gallons , viz. 651.2 , are as followeth : a tunn of the same dimensions standing upon its greater base , the coefficients are thus found : being divided by the same divisor with the former , they are : and are thus used : now if each of these tunns have 30 inches of the perpendicular wet , how much do they contain ? the first . the second . proof . the difference being less than a pint. the tetragon or square pyramid . there is a tunn in the form of the frustum of a square pyramid , a = 144 inches , the length of a side above , b = 108 inches , the length of a side below , p = 60 inches , the perpendicular , q. the content in gallons ? the coefficients being found by the former rule and example , viz. 1 / 3 of d d = the first coefficient .1.2 d b = the second coefficient 64.8 b b = the third coefficient 116.64 these three being divided by 282 the cubick inches in the ale gallon , are equal to if the tunn stand upon its greater base , the coefficients then are p ) b a ( = d , and the 1 / 3 d d = the first , a d = the second , and a a = the third , which divided by 282 the number of cubick inches in an ale gallon , if 40 inches of the perpendicular be wet in the first tunn , and 20 in the latter , and it be demanded what they contain in ale gallons . proof . the pentagonal pyramid . a tunn in the form of the frustum of a pyramid , whose bases are in the form of a pentagon , a = 144 inches , the length of each side above , b = 108 inches , the length of each side below , p = 60 inches , the perpendicular , q. the content in ale gallons ? the three coefficients found in the last example , viz , let another frustum of a pyramid of the same bases and altitude , stand upon its greater base , and the content in ale gallons be demanded . the coefficients so found and divided as before directed , are as followeth : if 50 inches of the perpendicular in the first tunn be wet , and 10 inches in the last , what is the content in ale gallons ? proof . a tunn in the form of a frustum of a cone , the bases being alike and alike situate , as in the precedent examples , the dimensions being , a = 144 inches , the diameter above , b = 108 inches , the diameter below , p = 60 inches , the perpendicular , q. the content in ale gallons ? p ) a b ( = d. these three divided severally by the divisor proper to a cone , as in the table mentioned , viz , 359.05 they quote : and that the young gauger may not be obliged to dray-men to repleat the horizon with liquor , of such tunns whose bases are not posited parallel thereto , ( as indeed most are not being made with a drip or fall ) let him take this example , a b c d e f g h m x , a cone or pyramid . having the length of each line in this diagram , and the content of the whole cone or pyramid in cubick inches , gallons , or barrels , &c. the quantity of the hoof h c b d is found by this analogy : as the cube of the line a c , to the whole solidity : so is the cube of a geometrical mean between a c and a h , to the content of the cone or pyramid cut off : which subducted from the whole , the remainder is the content of the hoof. some of the lines being given , the rest are to be found . example . there is a tunn taken as the frustum of a cone , c d = 144 inches , the greater base , e f = 108 inches , the lesser base , g b = 60 inches , the depth . admitting the base were raised 3 inches , as the line c h , it is then necessary to take another diameter between c h and e f to find c d. to find a b the cones axe . to find the content of the whole cone . the line a c , the line a h , and the content being known , to find the content of the fall c b d h. or thus : some practical rules & examples for cask-gavging . some practical rules & examples for cask-gavging . the corner-stone in the whole fabrick of cask-gauging , as full , was long since laid by mr. oughtred , taking a cask to be the frustum of a spheroid , under which capacity they are generally received , though indeed there have been , and daily are found some cask differing in form , and really are more parabolical than spheroidal , i shall therefore lay down a plain method for the performance of the work ( viz. finding their content ) under these four considerations : as spheroidal , as the frustum of a parabolical spindle , as the frustum of a parabolical conoid , as the frustums of two cones abutting upon one common base . these severally , with and without a table of area's of circles and forasmuch as the dimensions must be the first thing known , before the content can be found , i shall therefore shew the young tyro , how by some of the dimensions to find the rest , if any obstruction prohibit the taking of all . the boung-diameter , and head-diameter , and diagonal , to find the casks length . first subduct the semi-difference of diameters from the boung-diameter , and square the remainder , which square subduct from the square of the diagonal , and the remainder is the square of the casks semi-length . example . let b d be the boung-diameter = 29 inches , h e be the head-diameter = 23 inches , b e be the diagonal = 35.3836 > inches , s d the semi-difference = 3 inches : q. the length = l t ? this very quest. was intended by mr. smith , p. 176. but through a mistake it was left out . the boung-diameter , diagonal , and length , to find the head-diameter . the rule . from the quadrupled square of the diagonal subduct the square of the length , ( which done ) the square root of the remainder is equal to the sum of the boung-diameter and one head-diameter . example . the head-diameter , boung-diameter , and the length , to find the diagonal . the rule . to the square of the semi-length add the square of the boung-diameter , less the semi-difference of diameters , and the square root of their sum is equal to the diagonal . example . a cask taken as the frustum of a spheroid , cut with two plane parallels , each plane bisecting the axis at right angles , b the boung-diameter = 29 inches , h e the head-diameter = 23 inches , l t the length = 48 inches : q. the content in wine gallons ? the rule . to the doubled square of the boung-diameter add the square of the head-diameter , their aggregate multiply by the length , and to the product add the tenth part of it self , more one third of that tenth part , and from the sum cut off as many places toward the right hand as were in the multiplicand . example . another way . the same cask being taken as the frustum of a parabolical spindle , the content may be thus found . if taken as the frustum of a parabolical conoid , cut as before mentioned , the content may be found as in this example . if a cask of the same dimensions be taken as the middle frustum of two cones abutting upon one common base , cut with two planes parallel , and each bisecting the axis at right angles , the content in wine gallons may be found as in this example . for finding the capacity of these , or any other vessels , it is convenient to have always in readiness a table of area's of circles in wine and ale gallons : i think it unnecessary to swell this intended small volume with them , there being two lately printed , exactly calculated to every tenth part and quarter of an inch , and also a table of area's of segments of a circle , by my good friend mr. john smith , in his book of gauging , to whom in gratitude i am obliged to render my hearty acknowledgment sor many favours and kind assistances in these studies ; yet that you may be able to find any area of a circle upon demand , in wine or ale gallons , without a table , take this rule . divide the q. of the diameter by 294●1 for wine , and by 359.05 for ale gallons , and the quotient exhibits the area . or , saith mr. smith , multiply the q. of the diameter by .0034 for wine , and by .0027851 for ale gallons , and the product exhibits the area in such gallons . as in these examples . the diameter of a circle = 21.7 : q. the circles area in wine gallons ? the diameter of a circle = 26.8 : q. the area in ale gallons ? for finding the capacity of a cask , taken as spheroidal , by a table of area's of circles in gallons . example . a casks boung-diameter = 29 inches , head-diameter = 23 , and the length = 48 inches : q. the content in wine gallons ? another way . that is , 120 gallons , 1 quart , and 1 / 4 of a pint , ferè . to find the solid content of a cask , when taken as the middle frustum of a parabolical spindle , &c. the dimensions as before . that is , 113 gallons , and almost 2 quarts . and as the frustum of a parabolical conoid , the capacity is thus found : if a cask be taken as the middle frustum of two cones , abutting upon one common base , &c. the dimensions as before . the ullage , or wants in a cask , may be found under these two considerations : 1. a cask standing on the head , with the diameters parallel to the horizon . 2. a cask lying with the axe parallel to the horizon . prop. i. in a cask standing on the head , with the diameters parallel to the horizon , some liquor remaining , to find how many wine gallons it is . here are these five things necessary to be known : 1. the diameter at the boung . 2. the diameter at the head. 3. the length of the cask . 4. the depth of the liquor . 5. the diameter of the liquors superficies . example . the diameter o p is thus found , first find the axis of the whole spheroid e f , thus ; from the square of half the boung-diameter ( n h ) subduct the square of half the diameter at the head , and extract the square root of the remainder : then by the rule of proportion , say , as that q √ , is to n h , the semi-boung-diameter : so is n i , the casks semi-length , to e n half the axis sought , then , having found the diameter of the liquors superficies : then , which subducted from the whole content , leaves the ullage or wants . prop. ii. a cask lying with its axe parallel to the horizon , and having some liquor remaining in it , to find the content of the said liquor in gallons . let the dimensions be as before . in this proposition there is five requisites attending : h g the diameter at the boung = 29. a b the diameter at the head = 23. i k the length = 48. s g the depth of liquor = 11.6 . and the content of the whole cask in gallons . then by the help of a table of area's of segments of a circle , whose area is unity , and the radius divided in the ratio of 1.0000 parts , say by the rule of proportion : then seeking in the table you will find .4000 , and right against it under the title area you will find .37353 . then say : the inversion of the question , viz. to find the liquor wanting . again , finis . errata . pag. 3. l. 4. r. in the third . p. 5. l. 22. r. 20 : 13. p. 7. l. 17. r. 42 : 3 : 08 : 15 ; l. 19. r. 33 : 0 : 05 : 04. p. 9. l. 1. r. borrow of the. p. 13. l. 14. r. 5 s. the bushel . p 16. l. 13. r. 2 times . p. 19. l. 1. r. 5 from 6. p. 31. l. 19. dele always . p. 39. l. 22. r. in the decimal fractions of both factors . p. 50. l. 15. r. solid measure . p. 51. l. 15. r. 272.25 . p. 52. l. 15. r. .0041667 . p. 67. l. 14. dele as before . p. 82. l. 14. r. + a. p. 188. l. ult . r. ½ being . the rules herein mentioned , and other mathematical arts , are taught by the author , viz. arithmetick , vulgar , decimal , and logarithmetical ; the doctrine of triangles , plain and spherical ; the use of the globes , quadrant , sector , and other mathematical instruments ; fair writing , and merchants accompts , by way of debitor and creditor ; also the art of short writing . the doctrine of interest, both simple & compound explained in a more exact and satisfactory method then [sic] has hitherto been published : discovering the errors of the ordinary tables of rebate for annuities at simple interest, and containing tables for the interest and rebate of money for days, months, and years, both at simple and compound interest, also tables for the forbearance, discomps, and purchase of annulites : as likewise, equation of payments made practicable and useful for all merchants and others : together with divers other useful reflections / ... sir s. morland. morland, samuel, sir, 1625-1695. 1679 approx. 285 kb of xml-encoded text transcribed from 135 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2007-10 (eebo-tcp phase 1). a51383 wing m2778 estc r13339 11702013 ocm 11702013 48259 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a51383) transcribed from: (early english books online ; image set 48259) images scanned from microfilm: (early english books, 1641-1700 ; 542:3) the doctrine of interest, both simple & compound explained in a more exact and satisfactory method then [sic] has hitherto been published : discovering the errors of the ordinary tables of rebate for annuities at simple interest, and containing tables for the interest and rebate of money for days, months, and years, both at simple and compound interest, also tables for the forbearance, discomps, and purchase of annulites : as likewise, equation of payments made practicable and useful for all merchants and others : together with divers other useful reflections / ... sir s. morland. morland, samuel, sir, 1625-1695. [56], 203 p. printed by a. godbid and j. playford, and are to be sold by robert boulter ..., london : 1679. includes interest tables. reproduction of original in cambridge university library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng interest -tables. 2005-12 tcp assigned for keying and markup 2005-12 aptara keyed and coded from proquest page images 2007-01 ali jakobson sampled and proofread 2007-01 ali jakobson text and markup reviewed and edited 2007-02 pfs batch review (qc) and xml conversion the doctrine of interest , both simple & compound : explained in a more exact and satisfactory method then has hitherto been published . discovering the errors of the ordinary tables of rebate for annuities at simple interest . and containing tables for the interest and rebate of money for days , months , and years , both at simple and compound interest : also tables for the forbearance , discompt , and purchase of annuities . as likewise , equation of payments made practicable and useful for all merchants and others . together with divers others useful reflections . humbly presented to his most sacred majesty , charles ii. by sir s. morland , knight and baronet . printed at london , by a. godbid and j. playford . and are sold by robert boulter , at the turks-head , over against the royal-exchange in cornhill , 1679. coat of arms or blazon a necessary and useful introduction . the author of this little book hopes he has served the publick somewhat better than other arithmeticians , who have gone before him , for the following reasons . 1. in that his method is more plain and easie than that of other men ; and those things which they have left intricate and difficult to be understood , are here made evident by clear demonstrations , obvious to the meanest capacity . 2. in that his tables are calculated with greater care , and are much more correct than those that have been published of late years . for instance , all those tables in mr. newton's book , printed 1667 , are full of errors and mistakes ; and which is very remarkable , the tables which mr. dary has published as his own , are only transcribed out of mr. newton's book , and that with all the errors , which are so many , that they must needs mislead and discourage either young or old practitioners from trusting to , or making use of them . in mr. clavel's tables , which seem to be more correct than the others , there will be found many very considerable errors . as for instance , if you would know what an annuity of 600 l. to continue 21 years is worth in ready money , you will find it there to be but 6058 : 08 : 11.034 , which is too little by 1000 l. also if you would know the present worth of 60 l. annuity for the like time ( in the same page that resolves the former question ) you will find but 605 : 16 : 10.703 , which is less than the truth by 100 l. whereas in this little book , by the more than ordinary care and diligence of mr. john playford , printer , ( whom i have found the most ingenious and dexterous of any of his profession , in printing of tables , and all sorts of mathematical operations ) it is presumed that there will hardly be found one false figure ; but if there should , the tables are so framed , that what the one does by multiplication , the other proves by division , & vice versâ , whatever the one performs by division , the other makes out by multiplication to be a truth . 3. because the operations according to the rules and tables of this little book , where the sums are great , are much more easie , practicable , and satisfactory , than by mr. clavel's tables ; besides that those tables do not answer very many useful questions that will daily occur to men of business . for example . he has tables for the amount of any sum to 10000 l. for 365 days , but he has no tables of rebate for so many days , which is full as useful as the other , not only in simple , but also compound interest ; so that the practitioner must very often be forced to have recourse to the logarithms , or other tedious calculations . 4. because all the operations in this book are performed by decimal arithmetick , which of all other is the most useful and practicable , when well understood : and in order thereunto , the author has here given several examples , and explained the respective operations in such a manner , that any person who does at all understand the vulgar arithmetick , may in one hours time throughly comprehend this . addition and subtraction of decimals . as for the operations of addition and subtraction , they are the very same with the vulgar . for example . to 375.42 add 49.32 sum 424.74 . there must only care be had of setting unites under unites , and fractions under fractions , in their proper ranks and files ; as likewise that there be as many places of fractions in the total , as are found in either of the sums , before they are added together . thus : to 375.42 add 495.4 sum 870.82 or thus : to 375.42 add 95.03 sum 470.45 again , from 870.82 deduct 495.4 remainder 375.42 or , from 470.45 deduct 95.03 remainder 375.42 multiplication of decimals . rule . set one number over another , ( making only a full-point to distinguish between whole numbers and fractions ) in the very same manner as is none in ordinary multiplication , only when the product is finished , look how many places of fractions are found , both in the multiplicand and multiplicator jointly , just so many must be left in the product . for example . to multiply 342.34 by 3.123 , place them thus : explanation . because in the multiplicand there are two places of fractions , and in the multiplicator three , in all five ; therefore in the product there must be also five places of fractions . thus , here the practitioner is to observe , that the fraction which is in truth less , is set over the whole number , which is really greater . but because the fraction consists of more places , it is set uppermost , though it is a thing indifferent , for if they were set otherwise , the product would still be the same . for , which is the very same as before . by the same reason , the product must evermore be compleated , as to the number of places that are found in both multiplicand and multiplicator . an excellent method of contracting a long multiplication . 1. in the first place , wherever a multiplication consists of above three places , the author does recommend to all practitioners ( as a thing which he has sufficiently experienced to be the most safe and easie ) to make use of a tariffa , or table of multiplication for the multiplicand : and though it may and will seem at the first view to be more tedious , yet it will be found to be the shortest of all other ways whatsoever , being performed by addition only , and less subject to error ; and not only so , but whereas all other operations of multiplication do extreamly distort the eyes by looking stedfastly upon figures placed diagonally , by this tariffa the eye looks on them always in a streight line , and no otherwise . for example . suppose the two sums to be multiplied one by another were 259879.890625 , and 1.1173698 , but the product to consist of no more than eleven places . tariffa for the multiplicand . 1 259879890625 2 519759781250 3 779639671875 4 1039519562500 5 1299399453125 6 1559279343750 7 1819159234375 8 2079039125000 9 2338919015625 having made a tariffa , and placed the multiplicand and multiplicator as is before directed , because in the multiplicand there are twelve places , and eight in the multiplicator , in all twenty places ; and it is desired to contract them to eleven places . first let a line be drawn , leaving eight places to the right hand ; and then let all the imaginary places underneath be supplied with points or cyphers , decreasing in a triangular figure to nothing . then let the multiplication be performed as follows . let the last figure in the multiplicator be found in the margin of the tariffa , and the product answering to it subscribed , only let eight places be imaginary according to the number of points or cyphers , and let the remaining figures ( viz. 20790 ) be transcribed on the other side of the line . under the next figure of the multiplicator ( 9 ) , are seven points or cyphers , therefore the product answering to ( 9 ) in the margin of the tariffa being found , viz. 233891 / 9015625 , let the first seven figures to the right hand be left , and the other six inscribed , as in the example is better seen . and thus must the operation be performed , 'till all be finished ; and considering that there are eight several products , it may be well imagined , that at least ( 2 ) must be carried from the last place ; and therefore ( 2 ) being added to ( 27 ) there must be set down ( 9 ) , and ( 2 ) carried to the next place ; and thus must be wrought the whole multiplication , and at last it gives the product , as is here-under exprest , viz. and after this manner may any multiplication be contracted to any number of places , more or less . division of decimals . in division of decimals , the greatest difficulty is to know of what nature the first figure or cypher in the quotient ought to be , for that being once known , all other things are the very same as in the ordinary operation of division . and therefore i shall give this general rule , for the finding of what nature or quality the first figure or cypher of any quotient in a decimal operation ought to be . general rule . the first figure in the quotient must and will always be of the same nature and quality with that figure or cypher in the dividend , which at the first question stands over the place of vnites in the divisor . example 1. let 7.4944 be given to be divided by 32. by the foregoing rule , because the figure ( 4 ) of the dividend stands over the unite ( 2 ) of the divisor , and the figure ( 4 ) is a fraction ; therefore the first figure of the quotient ( viz. 2 ) must be a fraction , and have a point prefixed . and then all the other figures of the quotient follow in course , as in the ordinary method of division . tariffa . 1 32 2 64 3 96 4 128 5 160 6 192 7 224 8 256 9 288 example 2. direction in this last example , because the divisor may not be placed under the first figure of the dividend , nor indeed under the second , therefore are two cyphers put first in the quotient , but under the third figure it may be set , and then .0204 is found three times in 0652 , and 40 over ; then bringing down ( 8 ) , and adding it to 40 , makes the product ( 408 ) , which is just the double of ( 204 ) which gives ( 2 ) for the last figure of the quotient . and after this manner may any division be wrought , without the least difficulty or uncertainty . example 3. let. 0006258 be the dividend , and. 0032 the divisor . here must be a remove before the divisor will come under the the dividend , which is the occasion of putting one cypher in the quotient , before the figure ( 2 ) . tariffa . 1 0032 2 0064 3 0096 4 0128 5 0160 6 0192 7 0224 8 0256 9 0288 again , let the numbers in the first example be given thus : tariffa . 1 74944 2 149888 3 224832 4 299776 5 374720 6 449664 7 524608 8 599552 9 674496 explanation of the foregoing examples . explanation of the first example . in the first example a less number 7.4944 is divided by a greater , viz. 32. the young practitioner will presently object , and demand how this can be , for to divide one number by another , is to demand how many times that other number is found in the first ; that is , in this case , how many times 32 is found in 7 integers , and a fraction of .4944 . explanation . the answer in plain english is this : first , 32 is not found so much as once in 7 , and that is the reason of the full-point ( . ) in the quotient , before the figures of the fraction , to signifie , that the whole quotient consists of decimal parts . secondly , the first figure of the fraction being ( 2 ) denotes this , namely that 32 comes no nearer , being found in 7.49 , &c. than ●2 / 10 , or two tenths of once , or one time ; that is to say , it comes no nearer than 2 is to 10. and the second figure of the quotient ( 3 ) gives to understand , that 32 comes no nearer , being found in 7.49 , &c. so much as once , or one time , than 23 / 100 , or twenty three hundred parts ; that is to say , no nearer than 23 is to 100. and ( 4 ) the third figure goes farther , and says , that 32 comes no nearer , being found once , or one time , in 7.49 , &c. than 234 / 1000 , or two hundred thirty four thousand parts ; that is to say , no nearer than 234 is to 1000. and the last figure determining the question , yet somewhat more exactly ; that is to say , denotes that 32 comes no nearer , being found so much as once in 7.4944 , than 2342 / 10000 ; that is , no nearer than 2342 is to 10000. explanation of the second example . in the second example likewise a less number seems to be divided by a greater , viz. .0006528 by .0204 , and also ( in the third example ) by .0032 ; and an explanation of one of these may serve for both . and the true meaning is , 1. first .0032 cannot be found once in .0006528 , therefore is a point prefixed before the quotient . 2. the first cypher denotes that .0032 comes not so near , being found once in .0006528 , as 1 / 10 , or one tenth ; that is , not so near as 1 to 10. 3. the second cypher tells the practitioner that it comes not so near as 1 / 100 , or as 1 to 100. 4. the figure ( 3 ) in the third place , acquaints him , that 32 is no nearer , being found once in .0006528 , than 1 / 1000 , that is , three parts of a thousand , or no nearer than 3 is to 1000. and the last figure in the quotient , ( viz. 2 ) signifies that 32 is no nearer , being found once in . 0006528 , than 32 / 10000 ; that is to say , no nearer than 32 is to 10000. and this mystery being once throughly comprehended , and digested by the young practitioner , there can be no farther difficulty , about a less number being divided by a greater . 5. in the fifth and last place , by this little book may be compared together the operations of simple and compound interest , and so may be discovered how erroneous and extravagant the one is , and how true and rational the other , and only fit to be made use of by all those who deal in matters of money , or purchases , which that the reader may better comprehend , let him consider well the following animadversions , or reflections . reflections upon simple and compound interest . reflection i. let there be proposed an annuity of 100 l. to be continued 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , or 100 years , and let it be demanded , what the present worth of such an annuity is for any of the following terms , at the rate of 6 per cent. and that as well according to simple as compound interest ? answer . an annuity of 100 l. to continue for 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 , or 100 years , is worth in present money so many years purchase as is hereafter exprest , viz. number of years to be continued . years purchase , at simple interest . years purchase at compound interest . 10 7.93 7.35 20 14.27 11.46 30 20.03 13.76 40 25.52 15.01 50 30.87 15.72 60 36.13 16.16 70 41.32 16.38 80 46.48 16.50 90 51.60 16.57 100 56.71 16.61 by which table it is very observable , what a small difference there is at compound interest , between the present worth of 50 years , and the present worth of 100 years , ( viz. 00. 89 / 100 ) in comparison with the difference between 50 and 100 years , at simple interest , ( viz. 25 years purchase , more by 84 / 100 ) the one not exceeding 16 years purchase , more by 61 / 100 ; and the other still increasing as far as almost 57 years purchase ; and if continued to a greater number of years , would still swell into an extravagant sum , for the purchase , treble , or quadruple , to the usual rate of purchases in the kingdom where wo live . reflection ii. for as much as it is a truth received by all , that the purchase of an estate or revenue for ever , in most places of england , is not worth above 20 years purchase , and that to be computed according to compound interest , which is made up of so many geometrical proportional numbers : what reason can there be given , why the present worth of any payment , due at any time hereafter , should not be computed by the same proportion , although the payment be but for a year , nay , for a day , or hour , or minute to come ? thus , according to the rate of compound interest , the purchase of an estate for 30 years to come , at 4 per cent. is worth 17 years purchase , and somewhat more ; at 5 per cent. is worth 15 years purchase , more by ●9 / 100 ; at 6 per cent. is worth 13 years purchase , more by 76 / 100. the same estate for 20 years to come , at 4 per cent. is worth 13 years and a half purchase , and somewhat more ; and for 10 years to come , is worth above 8 years purchase ; and for two years to come , is worth one years purchase , more by 88 / 100 ; and all these numbers are calculated as geometrical proportionals : why then should the same estate , for a year , or 6 months to come , be calculated by any other proportion ? or indeed , how can it be rightly calculated by any other proportion , without doing wrong to either buyer or seller ? reflection iii. compound interest being made up of geometrical proportionals , the debtor ought not really to pay after the rate of 30 s. a quarter for 100 l. let out to him at 6 per cent. because , if 100 l. be put out to interest , and the interest come to 1 l. 10 s. the first quarter , that 101 l. 10 s. by the end of the next quarter ( keeping to geometrical proportion ) will become 103 l. 5 d. 1 q. more by 6● / 100 of a farthing ; that is to say , 100 l. after this manner , would amount in a years time to 106 l. 2 s. 8 d. 2 q. more by ninety hundred parts of a farthing , as may be seen by the following calculation . which in a great sum is more considerable . for suppose the crown to be indebted 1 million , or ( 1000000 l. ) and it were agreed to pay at the rate of 30 s. for each 100 l. the first quarter , and it were not paid 'till the twelve months end ; the amount would be as follows . which at the years end amounts to 60000 l. ( which ought to be the total sum of the interest for 12 months , at 6 per cent. ) and over and above the said 60000 l. there is 1363 l. 11 s. which 1 million according to such an accompt , if put out for a year , would amount to : so that in effect this is not 6 per cent. but 6 l. 2 s. 8 d. 2 q. ninety hundred parts of a farthing per cent. for he who lends money , if so soon as the first quarters interest grows due , and the creditor pay it not at the just time , ( if he so please ) obliges the creditor to acknowledge so much principal , and then it increases as aforesaid . divers other reflections of this kind might be made , and applied to the manifold abuses that may be committed , by selling according to one rate of interest , and buying by another , and so confounding together simple and compound interest , as it makes most for the advantage of the money merchant , there being very few so well versed in numbers as to contradict them . the truth is , it is as great pity that there should be two so different calculations of interest , as that there should be so many different weights and measures , and those divided and subdivided into so many heterogeneous fractions , which must of necessity create to all dealers innumerable difficulties ; whereas if coyns , weights , and measures , were divided and subdivided by decimals , all calculations would be performed with ease and pleasure . for instance , if a pound were divided into 10 shillings , a shilling into 10 pence , and a peny into 10 farthings , and only a point to distinguish integers from fractions ; then the following sum would easily be added together , viz. l. s. d. q. 15 9 6 1 39 8 3 0 48 7 2 1 for they might be set down thus : that is to say , the sum would be 104 pound , 5 shillings , 1 peny , and 2 farthings . or if these were weights , they might be , 104 pound-weight , 5 ounces , 1 dram , 2 scruples . and after this manner might all calculations be abbreviated , and made much more practicable than now they are , especially the operations of multiplication and division . for to multiply 48 l. 7 s. 2 d. 2 q. as they are now divided , by 124 , is very troublesom , and requires many operations , both of multiplication and division ; but in a decimal way , it would be plain and easie by one single multiplication , viz. that is to say , 6041 pound , 5 shillings , 2 pence , and 8 farthings . the convenience and expedition would yet be greater in long and square measures ; and all former accompts by unequal divisions , might for the present be reconciled and reduced to decimals , and in a few years utterly forgotten , and become altogether useless . but for as much as a private person can only give hints of what he conceives to be of publick use and benefit , and that it is a thing wholly in the power of those who are law-makers , to inspect and rectifie what they in their great wisdom shall judge amiss ; the author does in all humility lay by his pen , and puts a period to his discourse upon this subject . the contents of the first book . of interest in general , page 1 the reduction of shillings , pence , and farthings , into decimal fractions , 3 the interest of one pound for a year , at any rate of simple interest , from 1 to 12 per cent. 4 the interest of one pound for half a year , at any rate of simple interest , from 1 to 12 per cent. 5 the interest of one pound for a quarter of a year , at any rate of simple interest , from 1 to 12 per cent. 6 the interest of one pound for a month , at any rate of simple interest , from 1 to 12 per cent. 7 the interest of one pound for a day , at any rate of simple interest , from 1 to 12 per cent. 8. the golden table of trigonal progression , of admirable vse in all calculations of the amount or present worth of annuities , &c. 9 the number of days from the beginning of any month to the end of any other , throughout the year , 13 the amount of one pound forborn any number of years under 32 , at 6 per cent. simple interest , page 16 the amount of one pound forborn any number of equal months under 25 , at 6 per cent. simple interest , 17 the amount of one pound forborn any number of days under 366 , at 6 per cent. simple interest , 18 the present worth of one pound due after any number of years to come , not exceeding 32 , at 6 per cent. simple interest , 27 the present worth of one pound due after the expiration of any number of months under 25 , at 6 per cent. simple interest . 29 the present worth of one pound due after the expiration of any number of days under 366 , at 6 per cent. simple interest , 31 the reduction of pence and farthings into decimal fractions , to the hundredth part of a farthing , 41 the use of the foregoing tables , 46 a comparison between these and mr. clavel's tables , wherein it is proved , that the former are less troublesome , and more exact than the latter , 52 of annuities , 59 the multiplication of any rates of interest whatsoever belonging to each year , for a forborn annuity , to 100 years , 60 to find the amount of any annuity for any given time , at any rate of simple interest , page 64 this kind of interest for annuities useless and ridiculous , 65 the errors of the ordinary rules and tables for rebate relating to annuities , ibid. mr. kersey and dr. newton both mistaken , 66 diophantus alexandrinus his third proposition concerning poligonal numbers considered , 73 a second reflection on mr. kersey's and dr. newton's mistake , 87 equation of payments rectified , 93 the amount and present worth of an annuity of 100 l. for 5 years , at 1 , 2 , 3 , 4 , 5 , 6 , and 10 per cent. simple interest , page 95 , &c. observations on these tables , 102 equation of vnequal payments at times not equidistant , 123 the contents of the second book . compound interest explained , page 129 a reflection upon geometrical progression , 131 the amount of one pound put out to interest , and forborn any number of years under 32 , or quarters under 125 , at 6 per cent. compound interest , 141 the amount of one pound put out to interest for any number of months under 25 , at 6 per cent. compound interest , page 146 the amount of one pound put out to interest for any number of days under 366 , at 6 per cent. compound interest , 147 the present worth of one pound due after any number of years under 32 , or quarters under 125 , at 6 per cent. compound interest , 157 the present worth of one pound due after the expiration of any number of months under 25 , at 6 per cent. compound interest , 162 the present worth of one pound due after the expiration of any number of days under 366 , at 6 per cent. compound interest , 163 the present worth of one pound annuity , to continue any number of years under 32 , and payable by yearly payments , at 5 , 6 , 7 , 8 , 9 , and 10 per cent. compound interest , 173 what annuity to continue any number of years under 32 , and payable by yearly payments , one pound will purchase , at 5 , 6 , 7 , 8 , 9 , and 10 per cent. compound interest , 179 the present worth of any lease or annuity , for 21 , 31 , 41 , 51 , 61 , 71 , 81 , or 91 years ; as likewise the present worth of the fee-simple , at 5 , 6 , 8 , and 10 per cent. compound interest , 184 the several vses of the foregoing tables , 186 the doctrine of simple interest explained by a new and exact method , and the errors of the ordinary rules and tables of rebate discovered and rectified . chap. i. interest is either simple , or compound . 1. simple interest , is the increase which arises from the principal only , at 4 , 5 , 6 , 7 , &c. per cent. 2. compound interest , is the increase which arises from the principal , and also from the interest thereof . thus , if 100 l. be lent at simple interest for two years , at 6 per cent. the increase thereof is 12 l. but if at compound interest , it gives 6 l. for the first year , and 6 l. for the second year , together with the interest of the first 6 l. for the second year . that is to say : to which adding the principal ( viz. 100 l. ) the amount of both principal and compound interest , for two years , is 112.36 l. which by the table of reduction in the following page is 112 l. 7 s. 2 d. 1 q. more by .000626 parts of a pound . the doctrine of simple interest is plainly and clearly set forth in the following propositions . but that the practitioner may meet with no difficulty in the respective operations , he will here find made ready to his hand seven short ( but very significant ) tables . table i. reduction of shillings , pence , and farthings , into decimal fractions . shillings . decimals .   pence . decimals .       11 .0458333 19 .95   10 .0416666 18 .9   9 .0375 17 .85   8 . 03●3333 16 .8   7 .0291666 15 .75   6 .025 14 .7   5 .0208333 13 .65   4 .0166666 12 .6   3 .0125 11 .55   2 .0083333 10 .5   1 .0041666 9 .45       8 .4   farth . decimals . 7 .35       6 .3   3 .003125 5 .25   2 .0020833 4 .2   1 .0010416 3 .15   ½ .0005208 2 .1   ¼ .0002604 1 .05   1 / 8 .0001302 table ii. the interest of one pound for one year . from 1 to 12 per cent. rates per cent. interest . 1 .01 2 .02 3 .03 4 .04 5 .05 6 .06 7 .07 8 .08 9 .09 10 .10 11 .11 12 .12 table iii. the interest of one pound for one half-year . from 1 to 12 per cent. rates per cent. interest . 1 .005 2 .01 3 .015 4 .02 5 .025 6 .03 7 .035 8 .04 9 .045 10 .05 11 .055 12 .06 table iv. the interest of one pound for one quarter . from 1 to 12 per cent. rates per cent. interest . 1 .0025 2 .005 3 .0075 4 .01 5 .0125 6 .015 7 .0175 8 .02 9 .0225 10 .025 11 .0275 12 .03 table v. the interest of one pound for one month. from 1 to 12 per cent. rates per cent. interest . 1 .0008333 2 .0016666 3 .0025 4 .00333 5 .00416 6 .005 7 .00583 8 .00666 9 .0075 10 .08333 11 .09166 12 .1 table vi. the interest of one pound for one day . from 1 to 12 per cent. rates per cent. interest . 1 .00002739726 2 .00005479452 3 .00008219178 4 .00010958904 5 .00013698630 6 .00016438356 7 .00019178082 8 .00021917808 9 .00024657534 10 .00027397260 11 .00030136986 12 .00032876712 table vii . the golden table of trigonal progression . of excellent use , in all calculations of the amount or present worth of annuities , &c. arith. prog. trigonal prog. 1 1 2 3 3 6 4 10 5 15 6 21 7 28 8 36 9 45 10 55 11 66 12 78 13 91 14 105 15 120 16 136 17 153 18 171 arith. prog. trigonal prog. 19 190 20 210 21 231 22 253 23 276 24 300 25 325 26 351 27 378 28 406 29 435 30 465 31 496 32 528 33 561 34 595 35 630 36 666 37 703 38 741 39 780 40 820 41 861 42 903 43 946 44 990 45 1035 46 1081 47 1128 48 1176 49 1225 50 1275 51 1326 52 1378 53 1431 54 1485 55 1540 56 1596 57 1653 58 1711 59 1770 60 1830 arith. prog. trigonal prog. 61 1891 62 1953 63 2016 64 2080 65 2145 66 2211 67 2278 68 2346 69 2415 70 2485 71 2556 72 2628 73 2701 74 2775 75 2850 76 2926 77 3003 78 3081 79 3160 80 3240 81 3321 82 3403 83 3486 84 3570 85 3655 86 3741 87 3828 88 3916 89 4005 90 4095 91 4186 92 4278 93 4371 94 4465 95 4560 96 4656 97 4753 98 4851 99 4950 100 5050 101 5151 102 5253 arith. prog. trigonal prog. 103 5356 104 5460 105 5565 106 5671 107 5778 108 5886 109 5995 110 6105 111 6216 112 6328 113 6441 114 6555 115 6670 116 6786 117 6903 118 7021 119 7140 120 7260 121 7381 122 7503 123 7626 124 7750 table viii . a table shewing the number of days from the beginning of any month to the end of any other . january , 31. february , 59. march , 90. april , 120. may , 151. june , 181. july , 212. august , 243. september , 273. october , 304. november , 334. december , 365. february , 28. march , 59. april , 89. may , 120. june , 150. july , 181. august , 212. september , 242. october , 273. novemb. 303. decemb. 334. jan. 365. march , 31. april , 61. may , 92. june , 122. july , 153. august , 184. september , 214. octob. 245. novemb. 275. decemb. 306. jan. 337. febr. 365. april , 30. may , 61. june , 91. july , 122. august , 153. september , 183. october , 214. november , 244. december , 275. january , 306. february 334. march , 365. may , 31. june , 61. july , 92. august , 123. september , 153. october , 184. november , 214. december , 245. jan. 276. february , 304. march , 335. april , 365. june , 30. july , 61. august , 92. september , 122. october , 153. novemb. 183. december , 214. january , 245. febr. 273. march , 304. april , 334. may , 365. july , 31. august , 62. september , 92. october , 123. novemb. 153. decemb. 184. january , 215. february , 243. march , 274. april , 304. may , 335. june , 365. august , 31. september , 61. octob. 92. november , 122. december , 153. january , 184. february , 212. march , 243. april , 273. may , 304. june , 334. july , 365. september , 30. october , 61. november , 91. december , 122. january , 153. february , 181. march , 212. april , 242. may , 273. june , 303. july , 334. aug. 365. october , 31. november , 61. decemb. 92. january , 123. february , 151. march , 182. april , 212. may , 243. june , 273. july , 304. august , 335. september , 365. november , 30. december , 61. january , 92. february , 120. march , 151. april , 181. may , 212. june , 242. july , 273. aug. 304. sept. 334. octob. 365. december , 31. january , 62. february , 90. march , 121. april , 151. may , 182. june , 212. july , 243. august , 274. september , 304. october , 335. novemb. 365. note , that in every leap-year , february has 29 days , and then you must allow a day more than is here computed for that month. table ix . the amount of one pound , put out to interest , and forborn any number of years under 32. at the rate of 6 per cent. simple interest ; and that interest payable yearly . years . amount . 1 1.06 2 1.12 3 1.18 4 1.24 5 1.30 6 1.36 7 1.42 8 1.48 9 1.54 10 1.60 11 1.66 12 1.72 13 1.78 14 1.84 15 1.90 16 1.96 17 2.02 18 2.08 19 2.14 20 2.20 21 2.26 22 2.32 23 2.38 24 2.44 25 2.50 26 2.56 27 2.62 28 2.68 29 2.74 30 2.80 31 2.86 table x. the amount of one pound , for any number of equal months under 25. at the rate of 6 per cent. simple interest . months . amount . 1 1.005 2 1.010 3 1.015 4 1.020 5 1.025 6 1.030 7 1.035 8 1.040 9 1.045 10 1.050 11 1.055 12 1.060 13 1.065 14 1 070 15 1.075 16 1.080 17 1.085 18 1.090 19 1.095 20 1.100 21 1.105 22 1.110 23 1.115 24 1.120 table xi . the amount of one pound , for any number of days under 366. at the rate of 6 per cent. simple interest . days . amount . 1 1.000164383 2 1.000328767 3 1.000493150 4 1.000657534 5 1.000821917 6 1.000986301 7 1.001150684 8 1.001315068 9 1.001479452 10 1.001643835 11 1.001808219 12 1.001972602 13 1.002136986 14 1.002301369 15 1.002465753 16 1.002630136 17 1.002794520 18 1.002958904 19 1.003123287 20 1.003287671 21 1.003452054 22 1.003616438 23 1.003780821 24 1.003945205 25 1.004109589 26 1.004273972 27 1.004438356 28 1.004602739 29 1.004767123 30 1.004931506 31 1.005095890 32 1.005260273 days . amount . 33 1.005424657 34 1.005589041 35 1.005753424 36 1.005917808 37 1.006082191 38 1.006246575 39 1.006410958 40 1.006575342 41 1.006739725 42 1.006904109 43 1.007068493 44 1.007232876 45 1.007397260 46 1.007561643 47 1.007726027 48 1.007890410 49 1.008054794 50 1.008219178 51 1.008383561 52 1.008547945 53 1.008712328 54 1.008876712 55 1.009041095 56 1.009205479 57 1.009369862 58 1.009534246 59 1.009698630 60 1.009863013 61 1.010027397 62 1.010191780 63 1.010356164 64 1.010520547 65 1.010684931 66 1.010849314 67 1.011013698 68 1.011178082 69 1.011342465 70 1.011506849 71 1.011671232 72 1.011835616 73 1.011999999 74 1.012164383 75 1.012328767 76 1.012493150 days . amount . 77 1.012657534 78 1.012821917 79 1.012986301 80 1.013150684 81 1.013315068 82 1.013479451 83 1.013643835 84 1.013808219 85 1.013972602 86 1.014136986 87 1.014301369 88 1.014465753 89 1.014630136 90 1.014794520 91 1.014958903 92 1.015123287 93 1.015287671 94 1.015452054 95 1.015616438 96 1.015780821 97 1.015945205 98 1.016109588 99 1.016273972 100 1.016438356 101 1.016602739 102 1.016767123 103 1.016931506 104 1.017095890 105 1.017260273 106 1.017424657 107 1.017589040 108 1.017753424 109 1.017917808 110 1.018082191 111 1.018246575 112 1.018410958 113 1.018575342 114 1.018739725 115 1.018904109 116 1.019068492 117 1.019232876 118 1.019397260 119 1.019561643 120 1.019726027 day . amount . 121 1.019890410 122 1.020054794 123 1.020219177 124 1.020383561 125 1.020547945 126 1.020712328 127 1.020876712 128 1.021041095 129 1.021205479 130 1.021369862 131 1.021534246 132 1.021698629 133 1.021863013 134 1.022027397 135 1.022191780 136 1.022356164 137 1.022520547 138 1.022684931 139 1.022849314 140 1.023013698 141 1.023178081 142 1.023342465 143 1.023506849 144 1.023671232 145 1.023835616 146 1.023999999 147 1.024164383 148 1.024328766 149 1.024493150 150 1.024657534 151 1.024821917 152 1.024986301 153 1.025150684 154 1.025315068 155 1.025479451 156 1.025643835 157 1.025808218 158 1.025972602 159 1.026136986 160 1.026301369 161 1.026465753 162 1.026630136 163 1.026794520 164 1.026958903 day . amount . 165 1.027123287 166 1.027287670 167 1.027452054 168 1.027616438 169 1.027780821 170 1.027945205 171 1.028109588 172 1.028273972 173 1.028438355 174 1.028602739 175 1.028767123 176 1.028931506 177 1.029095890 178 1.029260273 179 1.029424657 180 1.029589040 181 1.029753424 182 1.029917807 183 1.030082191 184 1.030246575 185 1.030410958 186 1.030575342 187 1.030739725 188 1.030904109 189 1.031068492 190 1.031232876 191 1.031397259 192 1.031561643 193 1.031726027 194 1.031890410 195 1.032054794 196 1.032219177 197 1.032383561 198 1.032547944 199 1.032712328 200 1.032876712 201 1.033041095 202 1.033205479 203 1.033369862 204 1.033534246 205 1.033698629 206 1.033863013 207 1.034027396 208 1.034191780 day . amount . 209 1.034356164 210 1.034520547 211 1.034684931 212 1.034849314 213 1.035013698 214 1.035178081 215 1.035342465 216 1.035506848 217 1.035671232 218 1.035835616 219 1.036000000 220 1.036164383 221 1.036328766 222 1.036493150 223 1.036657533 224 1.036821917 225 1.036986301 226 1.037150684 227 1.037315068 228 1.037479451 229 1.037643835 230 1.037808218 231 1.037972602 232 1.038136985 233 1.038301369 234 1.038465753 235 1.038630136 236 1.038794520 237 1.038958903 238 1.039123287 239 1.039287670 240 1.039452054 241 1.039616437 242 1.039780821 243 1.039945205 244 1.040109588 245 1.040273972 246 1.040438355 247 1.040602739 248 1.040767122 249 1.040931506 250 1.041095890 251 1.041260273 252 1.041424657 day . amount . 253 1.041589040 254 1.041753424 255 1.041917807 256 1.042082191 257 1.042246574 258 1.042410958 259 1.042575342 260 1.042739725 261 1.042904109 262 1.043068492 263 1.043232876 264 1.043397259 265 1.043561643 266 1.043726026 267 1.043890410 268 1.044054794 269 1.044219177 270 1.044383561 271 1.044547944 272 1.044712328 273 1.044876711 274 1.045041095 275 1.045205479 276 1.045369862 277 1.045534246 278 1.045698629 279 1.045863013 280 1.046027396 281 1.046191780 282 1.046356163 283 1.046520547 284 1.046684931 285 1.046849314 286 1.047013698 287 1.047178081 288 1.047342465 289 1.047506848 290 1.047671232 291 1.047835615 292 1.048000000 293 1.048164383 294 1.048328766 295 1.048493150 296 1.048657533 day . amount . 297 1.048821917 298 1.048986300 299 1.049150684 300 1.049315068 301 1.049479451 302 1.049643835 303 1.049808218 304 1.049972602 305 1.050136985 306 1.050301369 307 1.050465752 308 1.050630136 309 1.050794520 310 1.050958903 311 1.051123287 312 1.051287670 313 1.051452054 314 1.051616437 315 1.051780821 316 1.051945204 317 1.052109588 318 1.052273972 319 1.052438355 320 1.052602739 321 1.052767122 322 1.052931506 323 1.053095889 324 1.053260273 325 1.053424657 326 1.053589040 327 1.053753424 328 1.053917807 329 1.054082191 330 1.054246574 331 1.054410958 332 1.054575341 333 1.054739725 334 1.054904109 335 1.055068492 336 1.055232876 337 1.055397259 338 1.055561643 339 1.055726026 340 1 . 0558●●41● day . amount . 341 1.056054793 342 1.056219177 343 1.056383561 344 1.056547944 345 1.056712328 346 1.056876711 347 1.057041095 348 1.057205478 349 1.057369862 350 1.057534246 351 1.057698629 352 1.057863013 353 1.058027396 354 1.058191780 355 1.058356163 356 1.058520547 357 1.058684930 358 1.058849314 359 1.059013698 360 1.059178081 361 1.059342465 362 1.059506848 363 1.059671232 364 1.059835615 365 1.060000000 table xii . the present worth of one pound , due after any number of years to come , under 32. at the rate of 6 per cent. simple interest . years to come . present worth. 1 .94339622 2 .89285714 3 .84745762 4 .80645161 5 .76923076 6 .73529411 7 .70422535 8 .67567567 9 .64935064 10 .62500000 11 .60240963 12 .58139534 years to come . present worth. 13 .56179775 14 .54347826 15 .52631578 16 .51020408 17 .49504950 18 .48076923 19 .46728971 20 .45454545 21 .44247787 22 .43103448 23 .42016806 24 .40983606 25 .40000000 26 .39062500 27 .38167939 28 .37313432 29 .36496350 30 .35714285 31 .34965034 table xiii . the present worth of due pound , due after the expiration of any number of months under 25. at the rate of 6 per cent. simple interest . months to come . present worth. 1 .99502487 2 .99009900 3 .98522167 4 .98039215 5 .97560975 6 .97087378 7 .96618357 8 .96153846 9 .95693779 10 .95238095 11 .94786729 12 .94339622 months to come . present worth. 13 .93896713 14 .93457943 15 .93023255 16 .92594444 17 .92165898 18 .91743119 19 .91324200 20 .90909090 21 .90497737 22 .90090090 23 .89686098 24 .89285714 table xiv . the present worth of one pound , due after the expiration of any number of days under 366. at the rate of 6 per cent. simple interest . days to come . present worth. 1 .99983564 2 .99967134 3 .99950709 4 .99934290 5 .99917876 6 .99901467 7 .99885064 8 .99868666 9 .99852273 10 .99835886 11 .99819504 12 .99803128 13 .99786757 14 .99770391 15 .99754031 16 .99737676 17 .99721326 18 .99704982 19 .99688643 20 .99672310 days to come . present worth. 21 .99655982 22 .99639659 23 .99623341 24 .99607029 25 .99590723 26 .99574421 27 .99558125 28 .99541835 29 .99525549 30 .99509269 31 .99492994 32 .99476725 33 .99460460 34 .99444201 35 .99427948 36 .99411700 37 . 993954●7 38 .99379220 39 .99362987 40 .99346761 41 .99330539 42 .99314323 43 .99298112 44 .99281906 45 .99265706 46 .99249511 47 .99233321 48 .99217136 49 .99200957 50 .99184782 51 .99168614 52 .99152450 53 .99136292 54 .99120139 55 .99103991 56 .99087848 57 .99071711 58 .99055579 days to come . present worth. 59 .99039453 60 .99023331 61 .99007215 62 .98991104 63 .98975000 64 .98958899 65 .98942804 66 .98926714 67 .98910629 68 .98894549 69 .98878475 70 .98862406 71 .98846341 72 .98830283 73 .98814230 74 .98798181 75 .98782138 76 .98766100 77 .98750067 78 .98734040 79 .98718018 80 .98702001 81 .98685989 82 .98669983 83 .98653980 84 .98637984 85 .98621993 86 .98606008 87 .98590027 88 .98574052 89 .98558081 90 .98542116 91 .98526156 92 .98510202 93 .98494253 94 .98478309 95 .98462369 96 .98446435 days to come . present worth. 97 .98430506 98 .98414582 99 .98398663 100 .98382749 101 .98366841 102 .98350937 103 .98335039 104 .98319146 105 .98303258 106 .98287376 107 .98271498 108 .98255626 109 .98239758 110 .98223896 111 .98208039 112 .98192188 113 .98176340 114 .98160498 115 .98144662 116 .98128830 117 .98113004 118 .98097183 119 .98081367 120 .98065556 121 .98049750 122 .98033949 123 .98018152 124 .98002361 125 .97986576 126 .97970795 127 .97955020 128 .97939250 129 .97923485 130 .97907725 131 .97891970 132 .97876221 133 .97860473 134 .97844734 days to come . present worth. 135 .97828999 136 .97813269 137 .97797545 138 .97781825 139 .97766111 140 .97750401 141 .97734697 142 .97718997 143 .97703304 144 .97687614 145 .97671930 146 .97656250 147 .97640576 148 .97624906 149 .97609242 150 .97593583 151 .97577928 152 .97562279 153 .97546635 154 .97530996 155 .97515362 156 .97499732 157 .97484108 158 .97468489 159 .97452875 160 .97437266 161 .97421662 162 .97406063 163 .97390470 164 .97374880 165 .97359296 166 .97343717 167 .97328143 168 .97312574 169 .97297009 170 .97281450 171 .97265896 172 .97250346 days to come . present worth. 173 .97234803 174 .97219263 175 .97203729 176 .97188199 177 .97172675 178 .97157155 179 .97141640 180 .97126131 181 .97110626 182 .97095127 183 .97079631 184 .97064141 185 .97048656 186 .97033177 187 .97017702 188 .97002232 189 .96986767 190 .96971307 191 .96955852 192 .96940401 193 .96924959 194 .96909518 195 .96894083 196 .96878652 197 .96863227 198 .96847806 199 .96832387 200 .96816976 201 .96801570 202 .96786169 203 .96770773 204 .96755382 205 .96739995 206 .96724614 207 .96709237 208 .96693865 209 .96678498 210 .96663136 days to come . present worth. 211 .96647778 212 .96632426 213 .96617079 214 .96601737 215 .96586399 216 .96571066 217 .96555738 218 .96540415 219 .96525096 220 .96509783 221 .96494475 222 .96479171 223 .96463871 224 .96448578 225 .96433289 226 .96418004 227 .96402725 228 .96387451 229 .96372181 230 .96356916 231 .96341656 232 .96326401 233 .96311151 234 .96295906 235 .96280665 236 .96265429 237 .96250198 238 .96234972 239 .96219750 240 .96204533 241 .96189322 242 .96174114 243 .96158912 244 .96143715 245 .96128522 246 .96113334 247 .96098151 248 .96082973 days to come . present worth. 249 .96067800 250 .96052631 251 .96037467 252 .96022309 253 .96007154 254 .95992004 255 .95976860 256 .95961720 257 .95946585 258 .95931454 259 .95916329 260 .95901208 261 .95886092 262 .95870981 263 .95855875 264 .95840773 265 .95825676 266 .95810584 267 .95795497 268 .95780414 269 .95765335 270 .95750262 271 .95735194 272 .95720130 273 .95705071 274 .95690016 275 .95674967 276 .95659922 277 .95644882 278 .95629847 279 .95614816 280 .95599790 281 .95584769 282 .95569753 283 .95554742 284 .95539735 285 .95524732 286 .95509735 days to come . present worth. 287 .95494742 288 .95479753 289 .95464770 290 .95449791 291 .95434817 292 .95419847 293 .95404882 294 .95389923 295 .95374967 296 .95360016 297 .95345070 298 .95330129 299 .95315192 300 .95300261 301 .95285334 302 .95270411 303 .95255493 304 .95240580 305 .95225672 306 .95210768 307 .95195869 308 .95180974 309 .95166084 310 .95151199 311 .95136318 312 .95121442 313 .95106573 314 .95091706 315 .95076844 316 .95061986 317 .95047134 318 .95032285 319 .95017442 320 .95002603 321 .94987769 322 .94972939 323 .94958114 324 .94943204 days to come . present worth. 325 .94928478 326 .94913667 327 .94898861 328 .94884059 329 .94869262 330 .94854470 331 .94839682 332 .94824898 333 . 9481●120 334 .94795346 335 .94780576 336 .94765811 337 .94751051 338 .94736295 339 .94721544 340 .94706798 341 .94692056 342 .94677319 343 .94662587 344 .94647858 345 .94633135 346 .94618416 347 .94603701 348 .94588991 349 .94574286 350 .94559585 351 .94544889 352 .94530198 353 .94515512 354 .94500829 355 .94486151 356 .94471478 357 .94456809 358 .94442145 359 .94427485 360 .94412830 361 .94398179 362 .94383533 363 .94368897 364 .94354254 365 .94339622 table xv. a most useful table for reduction of pence and farthings into decimal fractions , to the hundredth part of a farthing . farthings . dectmal fractions . 1 .0010416 2 .0020833 3 .0031250 pence & farthings . decimal fractions . ( 1 ) .0041666 1 .0052083 2 .0062500 3 .0072916 ( 2 ) .0083333 1 .0093750 2 .0104166 3 .0114583 ( 3 ) .0125000 1 .0135416 2 .0145833 3 .0156250 pence & farthings . decimal fractions . ( 4 ) .0166666 1 .0177708 2 .0187500 3 .0197916 ( 5 ) .0208333 1 .0218750 2 .0229166 3 .0239583 ( 6 ) .0250000 1 .0260416 2 .0270833 3 .0281250 ( 7 ) .0291666 1 .0302083 2 .0312500 3 .0322916 ( 8 ) .0333333 1 .0343750 2 .0354166 3 .0364583 ( 9 ) .0375000 1 .0385416 2 .0395833 3 .0406250 ( 10 ) .0416666 1 .0427082 2 .0437500 3 .0447916 ( 11 ) .0458333 1 .0468750 2 .0479166 3 .0489583 decimal fractions for every hundredth part of a farthing . hundred parts . decimal fractions . 1 .000010416 2 .000020833 3 .000031249 4 .000041666 5 .000052083 6 .000062499 7 .000072916 8 .000083333 9 .000093749 10 .000104166 11 .000114583 12 .000124999 13 .000135416 14 .000145833 15 .000156249 16 .000166666 17 .000177083 18 .000187499 19 .000197916 20 .000208333 21 .000218749 22 .000229166 23 .000239583 24 .000249999 25 .000260416 26 .000270833 27 .000281249 28 .000291666 29 .000302083 30 .000312499 hundred parts . decimal fractions . 31 .000322916 32 .000333333 33 .000343749 34 .000354166 35 .000364583 36 .000374999 37 .000385416 38 .000395833 39 .000406249 40 .000416666 41 .000427083 42 .000437499 43 .000447916 44 .000458333 45 .000468749 46 .000479166 47 .000489583 48 .000499999 49 .000510416 50 .000520833 51 .000531249 52 .000541666 53 .000552083 54 .000562499 55 .000572916 56 .000583333 57 .000593749 58 .000604166 59 .000614583 60 .000624999 61 .000635416 62 .000645833 63 .000656249 64 .000666666 65 .000677083 66 .000687499 67 .000697916 68 .000708333 hundred parts . decimal fractions . 69 .000718749 70 .000729166 71 .000739583 72 .000749999 73 .000760416 74 .000770833 75 .000781249 76 .000791666 77 .000802083 78 .000812499 79 .000822916 80 .000833333 81 .000843749 82 .000854166 83 .000864583 84 .000874999 85 .000885416 86 .000895833 87 .000906249 88 .000916666 89 .000927083 90 .000937499 91 .000947916 92 .000958333 93 .000968749 94 .000979166 95 .000989583 96 .000999999 97 .001010416 98 .001020833 99 .001031249 the use of the foregoing tables . because the usual rate of interest is 6 per cent. there are tables calculated for the more ready dispatch of questions relating either to the amount , or present worth of any sum ; but for any other rate from ( 1 ) to ( 12 ) the method will be very plain and practicable . i shall begin with some examples at 6 per cent. example 1. what is the amount of 540 l. in seven years , at 6 per cent. simple interest ? rule . see for 7 years in the margin of table ix . and against it you find 1.42 , the amount of 1 l. in 7 years ; multiply 540 by 1.42 , and the product is the answer . example 2. what is the amount of 540 l. in fifteen months , at 6 per cent. simple interest ? rule . find 15 months in the margin of table x. and against it is 1.075 ; by that multiply 540 , and the product is the answer . example 3. what is the amount of 540 l. in 279 days , at 6 per cent. simple interest ? rule . find 279 days in the margin of table xi . and against it is 1.0458 , ( you may take more or less of the fraction , according as you desire to be more or less exact ; ) then multiply 1.0458 by 540 , and the product is the answer . example 4. what is the present worth of 766.8 l. at the end of 7 years , at 6 për cent. simple interest ? rule . find 7 years in table xii . and against it is .704225 ; then multiply that by the given number 766.8 , and the product is the answer . which is within 26 hundred parts of a farthing of the truth , and is a sufficient proof of the first example . example 5. what is the present worth of 580.5 l. due after 15 months , at 6 per cent. simple interest ? rule . find 15 months in table xiii . and against it is .93023 , &c. this being multiplied by 580.5 , is an answer . which is within one farthing of the truth , and may be made within one hundredth part of a farthing of the truth , and is a clear proof of the second example . and after this manner may any question of this kind be easily and exactly resolved , and where the sums are very great , the operation will not be so tedious as that of working by mr. clavel's tables . for a proof of which , i shall here insert two examples , one of the amount , and the other of the present worth of a considerable sum. example 6. suppose the king borrows of some bankers 259879 l. 17s . 9d . 3q . for a year and 349 days ; what will be the amount of principal and interest at the expiration of a year and 349 days , allowing them 6 per cent ? the operation by mr. clavel's tables . in mr. clavel's tables i can find no more of this sum at one time than 10000 l. therefore i seek the interest of that , and find the interest of 10000 l. the odd money i reduce into decimal parts of a pound , by the decimal table in mr. russel's appendix to mr. clavel , thus , then because 200000 is twenty times 10000 , i must multiply this fraction and whole number by 20 , to find the interest of 200000 l. for a year , and 349 days : and also multiply the said whole number and fraction by 5 , for the interest of 50000 , ( there being five times 10000 contained in it ) for the like time . example . the interest of the remaining part of the aforesaid sum , viz. 9879 l. 17 s. ( omitting the 9 d. 3 q. ) is to be found in this manner : reduce the decimal fractions of the interest of 200000 , and 50000 , into shillings and pence , and then is the the answer ( without considering the interest of 9 d. 3 q. which is not to be found by mr. clavel's tables ) is 290381 l. 19 s. 2 d. 3 q. very near . the operation according to the rules of this little book is performed by simple addition , thus ; the given sum reduced by table i. is 259879.890625 the amount of 1. l. for 365 and 349 days , viz. 714 days , is 1.1173698 tariffa for the multiplicand . 1 259879890625 2 519759781250 3 779639671875 4 1039519562500 5 1299399453125 6 1559279343750 7 1819159234375 8 2079039125000 9 2338919015625 the multiplication contracted , as is directed in the introduction to this little book . this product , viz. 290381 l. 18 s. 9 d. 3 q. more by 86 / 100 of a farthing , is the answer . example 7. suppose there will be due after 349 days , upon the several branches of the king's revenue , the sum of 290381.94139 l. ( or 18 s. 9 d. 3 q. more by 36 / 100 of a farthing ; ) and his majesty have occasion to convert this into ready money , allowing the advancers 6 per cent. what is the present worth of that sum ? or what must those persons advance in ready money for the premises ? though it be the truest , and most exact way of all other , to calculate either the amount or present worth of money by days , yet there is no help at all by mr. clavel's tables to answer this question . but by this little book , the rule is , l. multiply the given sum 290381.94139 by the present worth of 1 l. due at the end of 349 days ( which you will find in table xiv . ) .94574 , and the product is an answer to the question . tariffa for the multiplicand . 1 29038194139 2 58076388278 3 87114582417 4 116152776556 5 145190970695 6 174229164834 7 203267358973 8 232305553112 9 261343747251 the multiplication contracted , as in the introduction is directed . after the same manner are resolved any questions , concerning either the amount , or present worth of any sum , either for years , months , or days . the next thing i shall treat of is annuities at simple interest , which shall be the subject of the following chapter . chap. ii. of annuities at simple interest . the increase of annuities is by multiplication of the respective rates of interest , according to a trigonal progression , which may be better seen by comparing the golden table of trigonal progression in chap. 1. with the following table of trigonal increase , or addition of ( 6 ) the rate of interest per cent. and after it short rules , which will hold for finding the amount , or present worth of any annuity , for any number of years , at any rate of simple interest whatsoever . table . the multiplication of any rates of interest whatsoever belonging to each year , for a forborn annuity to 100 years . this table is composed from the golden trigonal table . years . a trigonal increase , or addition of rates of interest . 1 0 2 1 3 3 4 6 5 10 6 15 7 21 8 28 9 36 10 45 11 55 12 66 13 78 14 91 15 105 16 120 years . a trigonal increase , or addition of rates of interest . 17 136 18 153 19 171 20 190 21 210 22 231 23 253 24 276 25 300 26 325 27 351 28 378 29 406 30 435 31 465 32 496 33 528 34 561 35 595 36 630 37 666 38 703 39 741 40 780 41 820 42 861 43 903 44 946 45 990 46 1035 47 1081 48 1128 49 1176 50 1225 years . a trigonal increase , or addition of rates of interest . 51 1275 52 1326 53 1378 54 1431 55 1485 56 1540 57 1596 58 1653 59 1711 60 1770 61 1830 62 1891 63 1953 64 2016 65 2080 66 2145 67 2211 68 2278 69 2346 70 2415 71 2485 72 2556 73 2628 74 2701 75 2775 76 2850 77 2926 78 3003 79 3081 80 3160 81 3240 82 3321 83 3403 84 3486 years . a trigonal increase , or addition of rates of interest . 85 3570 86 3655 87 3741 88 3828 89 3916 90 4005 91 4095 92 4186 93 4278 94 4371 95 4465 96 4560 97 4656 98 4753 99 4851 100 4950 prop. i. to find the amount of any annuity , for any given time , and at any rate of simple interest . general rule . to the sum of the annual , half-yearly , quarterly , or monthly payments , add the product of the annual , half-yearly , quarterly , of monthly rate , multiplied by the number in the foregoing table , answering to the number of years , half-years , quarters , or months , in the margin , that the annuity is to continue ; and the total sum is the true amount of that annuity . example 1. what is the true amount of an annuity of 100 l. in five years ? the number in the foregoing table answering to 5 in the margin , is — 10 that multiplied by 6 ( the annual interest of 100 l. ) makes — 60 to which add the five annual payments , viz. — 500 the whole amount is — 560 example 2. what is the amount of an annuity of 62 l. in four years ? the number in the foregoing table answering to 4 in the margin , is — 6 that multiplied by 3.72 ( the annual interest of 62 l. makes 22.32 to which adding the 4 annual payments , viz. 4 times 62 l. — 248.00 the whole amount is — 270.32 prop. ii. to know the present worth of any annuity for any given time , at any rate , accompting simple interest . for as much as the present worth of an annuity is in effect , and must be imagined , a principal , and the whole amount of the annuity as the amount of the said principal or present worth , in so long a time as the annuity is continued , the proportion is , as the amount of 1 l. for any time , is to 1 l. so is the amount of an annuity , to the present worth. therefore the rule is , divide the amount of the annuity by the amount of 1 l. in the given time , and the quotient is an answer . example 1. what is the present worth of an annuity of 62 l. for four years ? the amount of 62 l. per annum for four years by the foregoing rules is found to be 270.32 , and the amount of 1 l. forborn four years , by table ix . is found to be 1.24 ; wherefore i divide 270.32 by 1.24 , thus : the quotient 218 l. is the answer . example 2. what is the present worth of an annuity of 100 l. to continue 100 years ? the amount of 100 l. annuity for 100 years is 39700 l. the amount of 1 l. put out to interest for 100 years is 7 l. wherefore divide 39700 by 7 , and the quotient is the answer . for proof of this , let 5671.4 be put out to interest for 100 years , at 6 per cent. wherefore the operation is exact and just , though at the same time it is a certain argument , that the said annuity to continue 100 years at simple interest , would be valued at above 56 years purchase ; for dividing 5671 by 100 ( that is to say , cutting off the two last figures ) the remaining figures shew it to be 56 years purchase , over and above the fraction of .71 . after the same method , the amount of 100 l. annuity in 50 years is 12350 l. the amount of 1 l. put out to interest at 6 per cent. for 50 years is 4 l. wherefore dividing the said amount by ( 4 ) , 4 ) 12350 ( 3087.5 the quotient , or present worth is 3087.5 , which is above 30 years purchase . from whence it is clear and manifest , that all calculations of annuities at simple interest are absolutely useless and ridiculous : for the truth is , all present worths or purchases , either of annuities , or principal sums , due at any time hereafter , ought to be considered in a geometrical proportion , from a purchase for ever , ( or to the end of the world ) according to the several and respective rates of compound interest . and if this be a truth as to present worths , it will be also a truth as to the amounts , ( as has been sufficiently explained in the introduction to this book . ) and consequently , all calculations , according to simple interest , ought wholly to be laid aside as erroneous and useless . chap. iii. the errors of the ordinary rules and tables of rebate , relating to annuities , according to the rate of simple interest , discovered and rectified . although all tables of rebate for annuities at simple interest , ought to be wholly rejected as most ridiculous and useless , for the reasons laid down in the foregoing chapter , yet i do think it here seasonable , and indeed necessary ▪ to animadvert upon the ordinary rules relating to the present worth of such annuities , which have been composed by the respective authors upon great mistakes , and for want of due reflection upon arithmetical and geometrical progressions . i shall mention only two examples . the first is a rule laid down by mr. john kersey , in his appendix , bound up with mr. wingate's arithmetick , chap. 5. pag. 378. printed 1678. which is the very same with that made use of by dr. newton , in his scale of interest , pag. 20. when it is required to find the present worth of an annuity , by rebating or discompting at a given rate of simple interest , the operation will be as in the following example , viz. how much present money is equivalent to an annuity of 100 l. per annum , to continue 5 years , rebate being made at the rate of 6 per cent ? answer 425 l. 18s . 9d . 2q . very near : thus , for , saith he , it is manifest that there must be computed the present worth of 100 l. due at the first years end . also the present worth of 100 l. due at the second years end , and in like manner for the third , fourth , and fifth years . all which present worths being added together , the aggregate or sum will be the total present worth of the annuity , that is , 425 l. 18s . 9d . 2q . very near . i must confess i cannot but wonder how such gross mistakes should pass through the hands of so many learned and ingenious artists . for this very example i find published by the same mr. kersey , in the year 1650. and since that time , owned and made use of by several others . but for the right understanding of the truth of this , and all other questions of this kind . it is necessary to request the reader to contemplate with me a few things . 1. what is due of an annuity that is not paid , at the end of the first , second , third , fourth , and fifth years , at simple interest . 1. at the first years end .   l. at the first years end there is due the just sum of 100 ii. at the second years end . at the second years end , there is due ,   l. 1. for the first year 100 2. for the second year 100 sum 200 and besides this , for the interest of the 100 l. due at the first years end , and detained during the whole second year — 6 l. iii. at the third years end . at the third years end , there is due ,   l. 1. for the first year 100 2. for the second year 100 3. for the third year 100 sum 300 besides this , there is due ,   l. 1. for the interest of the first 100 l. for the second year 6 2. for the interest of the first 100 l. for the third year 6 3. for the interest of the second 100 l. for the third year 6 sum 18 iv. at the fourth years end .   l. 1. for the first year 100 2. for the second year 100 3. for the third year 100 4. for the fourth year 100 sum 400 besides this ,   l. 1. for the interest of the first 100 l. for the second year 6 2. the interest of the first 100 l. for the third year 6 3. the interest of the first 100 l. for the fourth year 6 4. the interest of the second 100 l. for the third year 6 5. the interest of the second 100 l. for the fourth year 6 6. the interest of the third 100 l. for the fourth year 6 sum 36 v. at the fifth years end .   l. 1. for the first year 100 2. for the second year 100 3. for the third year 100 4. for the fourth year 100 5. for the fifth year 100 sum 500 besides this ,   l. 1. for the interest of the first 100 l. for the second year 6 2. for the interest of the first 100 l. for the third year 6 3. for the interest of the first 100 l. for the fourth year 6 4. for the interest of the first 100 l. for the fifth year 6   24 5. for the interest of the second 100 l. for the third year 6 6. for the interest of the second 100 l. for the fourth year 6 7. for the interest of the second 100 l. for the fifth year 6 8. for the interest of the third 100 l. for the fourth year 6 9. for the interest of the third 100 l. for the fifth year 6 10. for the interest of the fourth 100 l. for the fifth year 6   36   24 sum total of the interest for the five years 60 to which adding the five annual payments , viz. 500 the whole amount of the annuity of 100 l. forborn five years , is 560 in the next place , i desire the ingenious reader to consider well the third prop. of diophantus alexandrinus , concerning peligonal numbers . διοφαντου αλεξανδρεως περι πολιτονων αριθμων . prop. iii. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 &c. it numbers ( how many soever they be ) exceed one another by an equal internal , then the internal between the greatest and the least , is multipler of that equal internal , according to the multitude of numbers propounded , less by one . for example . let there be five given terms , a , b , c , d , e , and let g be the common interval or difference . to apply which , let a = 100 g = 6 number of terms . then is ,     1 a = a 1 a = 100 2 b = a+g 2 b = 100+6 3 c = a+g+g 3 100+6+6 4 d = a+g+g+g 4 d = 100+6+6+6 5 e = a+g+g+g+g 5 e = 100+6+6+6+6 that is to say , the greatest term is equal to the least , and as many differences as there are more terms besides the least . so here e is equal to 100 , and 4 differences , or 4 times 6. and the sums of those numbers are the true amount of an annuity at simple interest ; thus , the annual rents , together with the annual interests the sums of annual rents , & annual interests , for therespective years . the number of annual interests , or differences , that are contained in every respective sum , besides the annual rents . 1 100 1 100   2 100+6 2 206 = 1 3 100+6+6 3 318 = 3 4 100+6+6+6 4 436 = 6 5 100+6+6+6+6 5 560 = 10 therefore the true amount of an annuity of 100 l. is as follows . year .   amounts 1 100 100 2 100+100+6 206 3 100+100+100+6+6+6 318 4 100+100+100+100+6+6+6+6+6+6 436 5 100+100+100+100+100+6+6+6+6+6+6+6+6+6+6 560 consequently the proportion is not as mr. kersey makes it , save only for the first year . but the true proportion holds thus , viz.       amounts . present worths . at the 1 years end as 106 to 100 ∷ so 100 to 94.33962 2 as 112 to 100 ∷ so 206 to 183.92856 3 as 118 to 100 ∷ so 318 to 269.49152 4 as 124 to 100 ∷ so 436 to 351.61290 5 as 130 to 100 ∷ so 560 to 430.76923 now therefore to perfect the demonstration , 1. the present worth of the first year is 94.33962 2. because 183.92856 is the present worth of the two first years , therefore if the present worth of the first year ( viz. 94.33962 ) be deducted out of it , it must needs leave the present worth of the second year , viz. 89.58894 3. because 269.49152 is the present worth of the three first years , therefore deducting out of it 183.92856 , ( viz. the present worth of the two first years ) it leaves the present worth of the third year , viz. 85.56296 4. so deducting 269.49152 out of 351.61290 , there remains the present worth of the fourth year 82.12138 5. and 430.76923 less by 351.61290 , is the present worth of the last year , viz. 79.15633 total sum of all the present worths 430.76923 to conclude , it is evident from the two last calculations , and that by clear demonstration , that ,   l. 1. the amount of the first year is 100 2. the amount of the two first years is 206 3. the amount of the three first years is 318 4. the amount of the four first years is 436 5. the amount of all five years is 560 as likewise , that the present worth , 1. of the first year is 94.33962 2. of the two first years is 183.92856 3. of the three first years is 269.49152 4. of the four first years is 351.61290 5. of all five years is 430.76923 and lastly , it is evident and plain , that the present worth , 1. of the first year is 94.33962 2. of the second year is 89.58894 3. of the third year is 85.56296 4. of the fourth year is 82.12138 5. of the fifth year is 79.15633 total sum of the present worths 430.76923 whereas mr. kersey makes the total of the present worths but 425.93933 , which is a very great mistake ; as are all his particular present worths , ( the first only excepted ) which he could not well calculate amiss . besides , if 425.93933 be put out for five years , it will amount to no more than 553.714109 . whereas 430.76923 in five years , at 6 per cent. amounts to 560 l. which is the true amount of 100 l. per annum for five years , as has been sufficiently demonstrated , and agrees exactly with the foregoing rule : so that mr. kersey in this example falls short of the truth , as to the present worth , no less than 4.8353 , that is , 4 l. 16 s. 8 d. 1 q. more by 96 / 100 of a farthing . which error , if it be so considerable in an annuity of 100 l. per annum , what would it be in an annuity of 100000 paid per annum ? no less than 4835 l. 6 s. 2 example . a second example i have borrowed from mr. dary , who has truly detected the error of it , although he has not sufficiently explained the reason of the error ; and therefore the reader will find it here more strictly examined and refuted by a plain demonstration obvious to the meanest capacity . the example is this : what is the present worth of an annual rent of 62 l. to be enjoyed four years to come , allowing the purchaser 6 per cent. simple interest ? the usual method , says mr. dary , is thus : now let the error of this operation be traced from the beginning . 1. the annual interest of 62 l. per annum , is 3.72 ; wherefore by the foregoing prop. of diophantus alexandrinus , pag. 73. the amount of therefore the true amount of an annuity of 62 l. at each years end , is as follows . at the end of the wherefore the true calculation of the present worths is as follows , viz. at the end of the now therefore , 1. the present worth of the first year is — 58.490 2. the present worth of the two first years less by the present worth of the first , that is , from 114.035 deducting 58.490 , the present worth of the second year is — 55.545 3. the present worth of the three first years ( the present worth of the two first being deducted ) that is , from 167.084 deducting 114.035 , the remainder of the present worth of the third year is — 53.049 4. deducting from 218 the present worth of all four years , 167.084 the present worth of the first three years , the remainder ( viz. 50.916 ) is the present worth of the fourth year — 50.916 so then , the present worth , whereas the usual way of rebate makes it not above 216.390 , which is less than the truth by 1.610 , which is ● l. 12 s. 2 d. 2 q. ferè . and if 216.390 be put out at interest at 6 per cent. for four years , it will amount to no more than 268.3236 , which is less than the true amount of 218 l. viz. 270.32 by 1.9964 , which being reduced , is 1 l. 19 s. 11 d. more by 11 / 100 parts of a farthing . all which may serve as a sufficient caution against such erroneous tables and calculations . a second reflection upon that example of mr. john kersey . i must confess that the present worth of 100 l. payable a year hence is 94.33962 ; and that the present worth of a single 100 l. payable two years hence , is as he has put it 89.28571 ; and the present worth of another bare 100 l. payable three years hence is 84.74576 ; and so to the end . and the total of those present worths is as he has put it , viz. and this is part of that very table which i have calculated ( being the twelfth table of the first chapter of this first book ) for the present worth of one pound after any number of years under 32. but reason tells me , that in this calculation there is no consideration had of the forbearance of interest ; for certain it is , if the first 100 l. had been paid at the first years end , it might have been put out to interest , and at the five years end would have given an increase of four times 6 l. or 24 l. at simple interest ; and so the second 100 l. would have increased in the three last years three times 6 l. or 18 l. that is to say ,   l. the first 100 l. would increase in the four last years 24 the second 100 l. would increase in the three last years 18 the third 100 l. would increase in the two last years 12 the fourth 100 l. would increase in the last year 6 the whole increase 60 therefore there would be due , if all were forborn ,   l. 1. at the first years end 100 2. at the second years end 100+06 3. at the third years end 100+12 4. at the fourth years end 100+18 5. at the fifth years end 100+24   500+60 now to calculate the present worth of any , or all of these sums , let it be considered by what proportion the calculation ought to be made . for example . suppose the annuity to be forborn only two years , and it be required to give the present worth of the two first years . whatsoever the answer is , all will agree , that the sum which is given in to be the present worth of those two years , being put out to interest , must amount to ●●● at the end of two years . therefore i say , as 112 to 100 ∷ so 206 to 183.92856 . if this be a true answer , then that sum , viz. 183.92856 , being put out to interest at 6 per cent. for two years , must amount to 206. by the former rules . now this total sum wants but ● / 100000 of 206. for , but now take the sum of mr. kersey's two years present worths , viz. let therefore this sum be put out to interest for two years . wherefore as before , which is less than 206 ( the true amount of an annuity of 100 l. for two years ) by .3396304 ; which though it be but 6 s. 8 d. and somewhat more in two years time , yet were the sum greater , or the time longer , it would prove a very considerable error . wherefore i conclude , that mr. kersey's calculations are erroneous as to annuities , and mine exact : and there needs no further illustrations or demonstrations about it . the next thing to be treated of in course , is touching the equation of several payments , and reducing them into one entire payment at a certain time , so as there may be no loss either to creditor or debtor . chap. iv. equation of payments rectified , and made practicable for all merchants , and others . equation of payments is by all agreed to be the reducing of several payments into one entire payment , at such a time , as neither creditor or debtor may be a loser by it , they being both agreed , the one to pay , and the other to receive , the said entire payment at the appointed time . now of the books that i have met with , and the men i have discoursed with , about equation of payments at simple interest , some have adventured to give rules for it , others have endeavoured to shew that such rules are erroneous , and some of the most learned of them have concluded the thing to be absolutely impracticable and impossible ; and so left the poor merchants to agree as they please about it . the truth is , they have been , and are all of them , mistaken about the present worths of annuities at simple interest , and that mistake has begot many others . the method that i shall therefore take , shall be , first , to expose to the readers view both the true amount and present worth of an annuity of 100 l. for five years , at several rates of interest . and from thence frame , and give a general rule for the reducing of several equal payments due at equi-distant times , to one entire payment . and after that , another rule for reducing of unequal payments at several times not equidistant , to one entire payment at a certain time , so as neither he who pays , nor he who receives it , shall be any loser by it . the tables of the amounts and present worths of an annuity of 100 l. for five years ( at different rates of interest ) do here follow in their order . table i. at ( 1 ) per cent. simple interest . years . the amount of 100 l. 〈◊〉 1 , 2 , 3 , 4 , or 5 years . amount of annual payments at the end of 1 , 2 , 3 , 4 or 5 years . the present worth of the first year , the first two years , the first three years , the first four years , or all the five years . the particular present worths of the first , second , third , fourth , or fifth year the amount of the total present worth of all the five payments , at the end of the first , second , third , fourth , or fifth year . 1 101 100 99.00990 99.00990 490.57142 2 102 201 197.05882 98.04892 495.42856 3 103 303 294.17475 97.11593 500.28570 4 104 406 390.38461 96.20986 505.14285 5 105 510 485.71428 95.32967 509.99999         485.71428   table ii. at ( 2 ) per cent. simple interest . years . the amount of 100 l. in 1 , 2 , 3 , 4 , or 5 years . amount of annual payments , at the end of 1 , 2 , 3 , 4 or 5 years . the present works of the first two years , the first three years , the first four years , or all the five years . the particular present works of the first , second , third fourth , or fifth year the amount of the total present worth of all the five payments , at the end of the first , second , third , fourth , or fifth year . 1 102 100 98.03921 98.03921 482.18181 2 104 202 194.23076 96.19155 491.63635 3 106 306 288.67924 94.44848 501.09089 4 108 412 381.48148 92.80224 510.54543 5 110 520 472.72727 91.24579 519.99999         472.72727 table iii. at ( 3 ) per cent. simple interest . years . the amount of 100 l. in 1 , 2 , 3 , 4 , or 5 years . amount of annual payments , at the end of 1 , 2 , 3 , 4 or 5 years . the present worth of the first year , the first two years , the first three years , the first four years , or all the five years . the particular present worths of the first , second , third , fourth , or fifth year . the amount of the total present worth of all the five payments , at the end of the first , second , third , fourth , or fifth year . 1 103 100 . 97.08737 97.08737 474.69564 2 106 203 191.50943 94.42206 488.52173 3 109 309 283.48623 91.97680 502.34782 4 112 418 373.21428 89.72805 516.17390 5 115 530 460.86956 87.65528 529.99999         460.86956   table iv. at ( 4 ) per cent. simple interest . years . the amount of 100 l. in 1 , 2 , 3 , 4 , or 5 years . amount of annual payments , at the end of 1 , 2 , 3 , 4 or 5 years . the present worth of the first year , the first two years , the first three years , the first four years , or all the five years . the particular present worths of the first , second , third , fourth , or fifth year . the amount of the total present worth of all the five payments , at the end of the first , second , third , fourth , or fifth year . 1 104 100 96.15384 96.15384 468.00000 2 108 204 188.88888 92.73504 486.00000 3 112 312 278.57142 89.68254 504.00000 4 116 424 365.51724 86.94582 522.00000 5 120 540 450.00000 84.48276 540.00000         450.00000   table v. at ( 5 ) per cent. simple interest . years . the amount of 100 l. in 1 , 2 , 3 , 4 , or 5 years . amount of annual payments , at the end of 1 , 2 , 3 , 4 or 5 years . the present worth of the first year , the first two years , the first three years , the first four years , or all the five years . the particular present worths of the first , second , third , fourth , or fifth year . the amount of the total present worth of all the five payments , at the end of the first , second , third , fourth , or fifth year . 1 105 100 95.23809 95.23809 461.99999 2 110 205 186.36363 91.12554 483.99999 3 115 315 273.91304 87.54941 505.99999 4 120 430 358.33333 84.42029 527.99999 5 125 550 439.99999 81.66666 549.99999         439.99999   table vi. at ( 6 ) per cent. simple interest . years . the amount of 100 l. in 1 , 2 , 3 , 4 , or 5 years . amount of annual payments , at the end of 1 , 2 , 3 , 4 , or 5 years . the present worth of the first year , the first two years , the first three years , the first four years , or all the five years . the particular present worths of the first , second , third , fourth , or fifth year . the amount of the total present worth of all the five payments , at the end of the first , second , third , fourth , or fifth year . 1 106 100 94.33962 94.33962 456.61538 2 112 206 183.92856 89.58894 482.46153 3 118 318 269.49152 85.56296 508.30769 4 124 436 351.61290 82.12138 534.15384 5 130 560 430.76923 79.15633 559.99999         430.76923   table vii . at ( 10 ) per cent. simple interest . years . the amount of 100 l. in 1 , 2 , 3 , 4 , or 5 years . amount of annual payments , at the end of 1 , 2 , 3 , 4 , or 5 years . the present worth of the first year , the first two years , the first three years , the first four years , or all the five years . the particular present worths of the first , second , third , fourth , or fifth year . the amount of the total present worth of all the five payments , at the end of the first , second , third , fourth , or fifth year . 1 110 100 90.90909 90.90909 440.00000 2 120 210 175.00000 84.09090 480.00000 3 130 330 253.84615 78.84615 520.00000 4 140 460 328.57142 74.72527 560.00000 5 150 600 400.00000 71.42858 600.00000         399.99999   observations upon the foregoing tables . 1. it is observable , that as the rate of interest increases , the present worth decreases ; that is to say , for the present worth of an annuity of 100 l. for five years , at 1 per cent. is 485.71428 2 472.72727 3 460.86956 4 450.00000 5 439.99999 &c. 6 430.76923 10 399.99999 &c. 2. it is no less observable , that an annuity of 100 l. increases by a trigonal progression of the respective rates . but the present worth increases by an unitarian addition of the rate to the principal for each year respectively . and these two ways are very different the one from the other , as may be seen by comparing them together , as follows in the example of an annunity of 100 l. at 6 percent . simple interest .       amount of the annuity for each of the five years . amount of the present worth of the amuity for each of the five years . at the 1 years end 100 456.61538 2 206 482.46153 3 318 508.30769 4 436 534.15384 5 560 559.99999 &c. and yet how different soever they are at their first setting out , and by the way , yet the further they go , the nearer they come together , and at last agree to an insensible difference , and such as may be diminished in insinitum , either to the hundredth , or theirsandth , or any less part of a farthing whatsoever can be desired . 3. as a consequence of the foregoing observation : if a. be to pay b. 100 l. per annum for five years , and they agree that the 500 l. shall be paid at one entire payment , they must be sure to pitch upon such a time , as that the said 500 l. being put out to interest from that time to the end of five years , may be equal to the whole amount of those five annual payments . for example . let the rate of interest be 6 per cent. per annum , and the time of paying the said 500 l. be at the end of three years , and so there are two years to come . if the said 500 l. for two years , at 6 per cent. will amount to 560 l. ( which is the whole amount of the annuity at the five years end ) the time is right , if not , it is a false time. but the annual interest of 500 l. is 30 l. therefore in two years it is 60 l. and that added to 500 , makes 560 l. and therefore it was a just time to pay the said 500 l. at one entire payment . for so b. has at the five years end , the whole effect of his annuity improved to the utmost , at 6 per cent. simple interest . and b. having paid nothing before of the annuity , and being obliged to pay nothing of it afterwards ; but having enjoyed it for three years ( which is the best part of it ) already , and being to enjoy it two years more ; the 500 l. he now pays , is only as a purchase of the amount of the whole annuity , which will be due at the five years end , viz. 560 l. and so gives the present worth of 560 l. from the three years end to the 5 years end ; and so he pays not a farthing more than the true worth of it . and for that true worth of it , to the end of the 5 years he has enjoyed , and must enjoy the said annuity it self to the end of the said five years . and so neither a. nor b. have the least wrong or loss , neither the one by paying , nor the other by receiving , this one entire payment of 500 l. at the three years end ; and if either or both should sell their concerns , it would be the same thing . 4. it is observable that the present worth of the said annuity , at any rate of interest , does at the three years end exceed the aggregate of the said five sums , ( or 500 l. ) for example . the present worth of an annuity of 100 l. per annum to continue five years , does at the end of three years , amount , at 1 per cent. to 500.28570 2 501.09089 3 502.34782 4 504.00000 5 505.99999 6 508.30769 10 520.00000 5. it being as evident from this last observation , that the present worth of the whole annuity being put out to interest for three years , will at any rate of interest , exceed the aggregate of all the five payments , and the greater the rate of interest is , the greater is that excess . for example . at ( 1 ) per cent. the excess is but . 28570 ; at ( 2 ) per cent. the excess is somewhat more , viz. 1.09089 ; at ( 3 ) per cent. it is 2.34782 ; at ( 10 ) per cent. it is 20 l. and at ( 15 ) per cent. it would be much more . and it being likewise evident by all the foregoing tables , whatever the rate of interest be , that 500 l. more by the interest of 500 l. for two years , is equal to the whole amount of the annuity of 500 l. for five years . that is to say , the interest of 500 l. for two years , at ( 1 ) per cent. is 10 l. which added to 500 l. makes the amount 510 l. at ( 2 ) per cent. is 20 l. which added to 500 l. makes the amount 520 l. at ( 3 ) per cent. is 30 l. which added to 500 l. makes the amount 530 l. at ( 4 ) per cent. is 40 l. which added to 500 l. makes the amount 540 l. at ( 5 ) per cent. is 50 l. which added to 500 l. makes the amount 550 l. at ( 6 ) per cent. is 60 l. which added to 500 l. makes the amount 560 l. and lastly , it being sufficiently evident by the third observation , that if the 500 l. be paid at one entire payment , at the end of three years , or , which is all one , two years before the annuity be at an end ; neither creditor nor debtor can have the least wrong , or suffer the least loss . it may therefore be safely concluded , that it is practicable and possible to give a good and true rule for equation of several payments ; and likewise , that it is no way necessary ( as some very learned artists would needs have perswaded me ) to try that rule by this mark , viz. that the present worth of the said 500 l. at the three years end , must be the present worth of the whole amount of the said annuity . for by what has been already proved , the present worth of the whole annuity at any rate of interest , will at the three years end exceed the said 500 l. now therefore i shall proceed to give two general rules . the first , for equation of several equal payments at equi-distant times . the second , for equation of several unequal payments at several times not equi-distant . 1. general rule . for equation of any given number of equal payments due at equi-distant times . rule . out of the whole amount of the annuity , of monthly payment , deduct the aggregate of the several payments , and the remainder , if annual , multiply by 365 ; if monthly , by 30.416 ; then divide the product by the annual , or monthly interest of the said aggregate , and the quotient is the number of days , before the end or term of the annuity , or monthly payment , when the said aggregate may be paid without loss to either creditor or debtor . 1. example . let the annuity be 100 l. the time it is to continue five years . the whole amount of the annuity 560 the aggregate of the several payments 500 the annual interest of the aggregate ( viz. 500 ) 30 now suppose a. be obliged to pay to b. 100 l. per annum for five years , but they both agree that a. shall pay to b. the aggregate 500 l. at one entire payment . and then the question is , at what time the said 500 l. is to be paid ? therefore as the rule directs , that divided by 30 , gives a quotient , which is the true number of days before the end of the said annuity , when the said 500 l. is to be paid , viz. 730 those 730 days divided by 365 , gives a quotient of two years . so then the true time of paying the said aggregate of several payments , ( viz. 500 l. ) is two years before the end of five years ; that is at the end of the third year . 2. example . a. is to pay b. 62 l. per annum for four years ; but they agree that a. shall pay the aggregate of the several sums , ( viz. 248 ) at one entire payment . if the annual payment be 62.00 the amount of that in four years , at 6 per cent. will be 270.32 the aggregate of the several payments , or four times 62 , is 248.00 the annual interest of the said aggregate 14.88 wherefore , this 22.32 is first to be multiplied by 365 , which is 8146.80 . that product 8146.80 being divided by the annual interest of the aggregate 248 , viz. 14.88 , gives a quotient of 547.5 days . this quotient 547 days and ● / 10 , or a half , is a true answer to the question ; that is to say , 547 days and a half , or one year , and 172 days and a half , before the end of four years , is the just time to pay the said aggregate , or 248 , at one entire payment ; so as neither he who pays it , nor he who receives it , may be a loser . but that all things may be exposed clearly to the readers view , i shall here repeat the thing , and set down the whole operation . 1. the annual payment for four years is 62.00 l. 2. the whole amount of this in four years is 270.32 l. 3. the aggregate , or four years payments , that is , four times 62 l. is 248.00 l. 4. the annual interest of the said aggregate is 14.88 l. now the question is , what is the true time for paying the said aggregate , or 248 , at one entire payment ? to answer this , i proceed according to the aforesaid rule . 2. i multiply this remainder by 365 , thus , 3. this product i divide by the annual interest of the aggregate , viz. 14.88 . tariffa for the divisor . 1 1488 2 2976 3 4464 4 5952 5 7440 6 8928 7 10416 8 11904 9 13392 10 14880 and the quotient 547.5 , is an answer to the question . that is to say , ( as before ) one year , and 172 days , and a half , before the end of four years . or , which is the same thing , two years , and 192 days and a half , after the agreement , must the 248 l. be paid at one entire payment ; and for the reasons aforesaid , there is no loss to either a. or b. for proof of this , let 248 l. be put out to interest at 6 per cent. for one year , and 172 days and a half , that is , 547.5 days ( which is the quotient , or the time given from the payment thereof to the end of the annuity ) and if it make up the whole amount of the annuity , viz. 270.32 , the operation is right . tariffa for the multiplicand . 1 00016438356 2 00032876712 3 00049315068 4 00065753424 5 00082191780 6 00098630136 7 00115068492 8 00131506848 9 00147945204 10 00164383560 for example . then i make the following tariffa , and proceed to multiply the foregoing product by 248. tariffa for the multiplicand . 1 089999999100 2 179999998200 3 269999997300 4 359999996400 5 449999995500 6 539999994600 7 629999993700 8 719999992800 9 809999991900 wanting but 1 / 10000 ( which is not the hundredth part of a farthing ) of the true amount of the whole annuity , viz. 270.32 , and therefore the operation is just . and thus may any question of this nature be resolved , to a day , and parts of a day ; for if both these last questions had been made for months , the same rule must have been observed . for example . if a. is to pay to b. 100 l. per month for five months , when may he pay the 500 l. at one entire payment , at the rate of 6 per cent ? the payments being monthly , therefore , in pursuance of the aforesaid general rule . let therefore 5 be multiplied by 30.416 , or the true number of days that are in one equal month. and let that ( 152.080 ) be divided by 2.500 , or the monthly interest of 500 l. at 6 per cent. tariffa for the divisor . 1 25 2 50 3 75 4 100 5 125 6 150 7 175 8 200 9 225 the quotient ( 60.832 ) is a true answer in days . that is to say , 60 days and 832 / 1000 of a day , ( which makes two equal months ) before the end of five months ; or ( which is all one ) three months after the agreement , or after the first day , when the said debt was growing due , is the just time of paying the 500 l. at one entire payment . for proof of this . if 500 l. be put out to interest at 6 per cent. for two equal months , or 60.832 days , and does give 5 l. it makes the 500 l. become 505 l. which is the full amount of those five months payments , and is a just answer to the question . but , and the operation is exact . and this i take to be sufficient for the resolution of any question of this nature . i shall proceed in the next place to discourse about unequal payments , at times not equi-distant . a brief discourse concerning the equation of unequal payments at times not equi-distant . for example . a merchant owes 500 l. to be paid at three several unequal payments , viz. at the end of four months 300 l. at the end of six months 100 l. and at the end of twelve months 100 l. but the debtor agrees with the creditor to discharge the debt ( viz. 500 l. ) at one entire payment . the question is , at what time this 500 l. may be paid , without damage or prejudice to either creditor or debtor ? the general rule is this . first find the true amount of each of the sums , from the first day of the agreement , to the last day of payment , as supposing them to be forborn to the last . then out of that deduct the aggregate of the respective payments , and multiply the remainder , if annual , by 365 ; if monthly , by 30.4166 ; and the product divide by the annual or monthly interest of the said aggregate , and the quotient is the number of days from the last day of payment , accompting backwards . the operation is as follows . first , the length of time from the day of the agreement , to the last day of payment , is just twelve months . so then , 1. in the first place , 300 l. payable after 4 months , and being forborn to the end of 12 months , has 8 months interest to accompt for , viz. 12.000 2. in the second place , 100 l. payable after 6 months , and being forborn to the end of 12 months , has 6 months interest to accompt for , viz. 3.000 3. to these sums adding the 500.000 the whole amount is 515.000 then , and the proportion is this . if 2.5 be the interest of 500 l. for one month , how many months interest will 15 make ? wherefore divide 15 by 2.5 , and the quotient is the answer to the question . tariffa for the divisor . 1 25 2 50 3 75 4 100 5 125 6 150 7 175 8 200 9 225 the operation is this . that is to say , if the said 500 l. be paid six months before the end of twelve months or ( which is all one ) at the end of six months , there will be no loss or damage either to creditor or debtor . for proof of this , 1. in the first place , 300 l. was due at 4 months end , and being continued 2 months longer , the interest thereof for 2 months is 3 l. the whole amount is 303 l. 2. in the next place , 100 l. paid at 6 months end , is the time it was due 100 l. 3. in the last place , the other 100 l. paid 6 months before the time , there must be an abatement made of 3 l. 97 l. total sum 500 l. so that in the first sum there is an increase of 3 l. and in the last there is a decrease of 3 l. which are to be set one against the other ; and the whole amount is the aggregate of the respective sums , and being paid at the end of 6 months makes the equation just 500 l. after this manner may any number of unequal sums payable at any number of times not equi-distant , be equated , and a time set for the payment of the aggregate ; and not only so , but if the debtor a. owe to b. 100 l. per annum , or per month , for any number of years or months , and a. and b. agreeing together that it shall be in the power of a. to pay to b. the true value of his pretensions at the end of any of the years or months , it is very practicable , for the present worth of the whole amount at the end of any of the years or months resolves the doubt , and is an answer the question . for example . a. owes to b. 100 l. per annum for five years , and they agree that a. shall buy it off at the end of any of the four years , for at the end of 5 years nothing less than the whole 560 l. will pay the dein . 1. the present worth of 560 l. ( or the whole amount ) at the first years end , is 451.6129 2. the present worth of 560 l. at the second years end , is 474.5762 3. the present worth of 560 l. at the third years end , is 500 , 0000 4. the present worth of 560 l. at the fourth years end , is 528.3018 5. the present worth of 560 l. at the fifth years end , is 560 , 0000 thus i have as briefly as the nature of the thing would permit , explained the doctrine of simple interest , as likewise that of annuities , and equation of several payments at simple interest , which is of excellent use for 6 12 , or 18 months , because the difference between simple and compound interest is not material in so short a time . but for as much as the business of an●uities , or purchases , for any considerable number of years , does most properly and truly belong to the doctrine of compound interest , i shall make that the subject of the following book . the doctrine of compound interest . lib . ii. chap. i. the doctrine of compound interest explained . compound interest , or interest upon interest , increases not only from the principal , but also from the interest , in the manner hereafter exprest . that is to say , if 100 l. be put out to interest at 6 per cent. 1. the first year there will be due 106.0000 2. the second year that ( 106 l. ) is made a principal , and being put out for a year , becomes 112.3600 3. the third year that ( 112.360 ) is made a principal , and being put out to interest , amounts to 119.1016 and so in infinitum . so that the respective amounts for each respective year , are so many geometrical proportional numbers . for , as 100 to 106 , for the first year ∷ so 106 to 112.36 , for the second year . again , as 106 to 112.36 ∷ so 112.36 to 119.1016 , for the third year . item , as 112.36 to 119.1016 ∷ so 119.1016 to 126.247016 , for the fourth year . &c. but to the end , that the ingenious practitioner may have entire satisfaction in the business of interest upon interest , it will be necessary to make some reflection upon geometrical proportion and progression . reflection upon geometrical progression . if numbers ( how many soever they be ) contain the one the other by an equal ratio , then the greatest of those numbers is multipler of the powers of the denomination of that equal ratio multiplied by the least , according to the multitude of the given numbers less by one . let the given numbers be 2 , 6 , 18 , 54. then by the hypothesis , the first multiplied by ( 3 ) is equal to the second ; and the second multiplied by ( 3 ) is equal to the third ; and so in infinitum . that is to say , first term 2 = 2 — — — — 2 second 6 = 2 into 3 — — — 6 third 18 = 2 into 3 into 3 — — 18 fourth 54 = 2 into 3 into 3 into 3 — 54 that is to say in a symbolical way , let there be any number of proportionals , a , b , c , d , e , f , g , and the ratio r. first term a = a second b = a into r third c = a into r into r fourth d = a into r into r into r fifth e = a into r into r into r into r sixth f = a into r into r into r into r into r seventh g = a into r into r into r into r into r into r to apply this to the present purpose , let the first geometrical term be ( 1. ) the ratio ( . 06 )   first power . second power . third power . fourth power . fifth power . sixth power . geometrical proportional numbers . a = 100             100.000 b = 100 into 1.06           106.000 c = 100 into 1.06 into 1.06         112.360 d = 100 into 1.06 into 1.06 into 1.06       119.101 e = 100 into 1.06 into 1.06 into 1.06 into 1.06     126.247 f = 100 into 1.06 into 1.06 into 1.06 into 1.06 into 1.06   133.823 g = 100 into 1.06 into 1.06 into 1.06 into 1.06 into 1.06 into 1.06 141.851 the geometrical numbers at length are these that follow , though there is no necessity of making use of them all , the difference being indiscernable . years . amount at 6 per cent. compound interest . 1 1.06 2 1.1236 3 1.191016 4 1.26247696 5 1.3382255776 6 1.418519112256 7 1.50363025899136 8 1.5938480745308416 9 1.689478959002692096 10 1.79084769654285362176 now for as much as these geometrical proportional numbers swell into a great number of places , and the multiplications become tedious , it has been look'd upon as impracticable to find them out by any way , but by the help of the logarithms . but i shall endeavour to shew a way how it may be very practicable to find out any of these numbers , for any year under 32 , without much trouble or difficulty . for example . let it be demanded to give the amount of i l. in eight years , at 6 per cent. compound interest , not having any help of a table . the operation is thus . first , i square 1.06 , which is 1.1236 , and the product is the amount in two years . secondly , i square 1.1236 , and that gives me the proportional number answering to ( 4 ) in the margin , viz. 1.26247 , &c. thirdly , i square 1.26247 , and that gives me the proportional number answering to ( 8 ) in the margin , which was the thing proposed , viz. 1.59384 , &c. now if it had been demanded to find the proportional number answering to ( 16 ) in the margin , it is the square of 1.59384 , &c. and the square of 1.59384 gives the proportional number answering to ( 32 ) in the margin . thus far the method is clear for all even numbers ; but for the odd numbers , the rule is this : having found the proportional number answering to the greater half of the given number in the margin , square it , and divide it by the least and first proportional number , and the quotient is the number desired . for example . let it be demanded to find the proportional number answering to ( 3 ) in the margin , and let ( 1.06 ) be the least proportional number . having found 1.1236 to be the proportional number answering to ( 2 ) in the margin , which ( 2 ) is the greater half of ( 3 ) , i square 1.1236 , and it gives 1.26247 , which i divide by 1.06 , and the quotient ( 1.1910 , &c. ) is the proportional number desired . again , let it be demanded to find the proportional number answering to ( 5 ) in the margin . having found the proportional number answering to ( 3 ) in the margin , ( which 3 is the greater half of 5 ) viz. 1.1910 ; the square thereof , viz. 1.4185 , being divided by 1.06 , the quotient is the number desired , viz. 1.3382 . thus ( 9 ) is the greater half of ( 17 ) , and therefore the proportional number answering to ( 9 ) in the margin being squared , and that square divided by 1.06 , gives 3.700 , for the proportional number answering to ( 17 ) in the margin . and so may the proportional number of any odd number in the margin be found out , without the help of logarithms . but for as much as exact tables truly calculated are most ready for use , i have with no small pains and charge ( not transcribed other mens tables and errors , but ) carefully and exactly calculated several tables of my own ; by the help of which , may easily and readily be found out either the amount , or present worth of any sum , at any rate of compound interest , and the like for annuities and purchases , after the same manner , and in the same method as i have done in the first book of this small treatise , for the amount and present worth of either principal sums , or annuities , at simple interest . table i. the amount of one pound put out to interest , and forborn any number of years under 32 , or quarters under 125. at the rate of 6 per cent. compound interest . years and quarters . amount . ( 0 ) 1.000000 1 1.014674 2 1.029563 3 1.044670 ( 1 ) 1.060000 1 1.075554 2 1.091336 3 1.107351 ( 2 ) 1.123600 1 1.140087 2 1.156817 3 1.173792 ( 3 ) 1.191016 1 1.208493 2 1.226226 3 1.244219 ( 4 ) 1.262477 1 1.281002 2 1.299799 3 1.318872 ( 5 ) 1.338225 1 1.357862 2 1.377787 3 1.398005 ( 6 ) 1.418519 1 1.439334 2 1.460455 3 1.481885 ( 7 ) 1.503630 1 1.525694 2 1.548082 3 1.570798 ( 8 ) 1.593848 1 1.617236 2 1.640967 3 1.665046 ( 9 ) 1.689479 1 1.714270 2 1.739425 3 1.764949 ( 10 ) 1.790847 1 1.817126 2 1.843790 3 1.870846 ( 11 ) 1.898298 1 1.926154 2 1.954418 3 1.983096 ( 12 ) 2.012196 1 2.041723 2 2.071683 3 2.102082 ( 13 ) 2.132928 1 2.164226 2 2.195984 3 2.228207 ( 14 ) 2.260904 1 2.294080 2 2.327743 3 2.361900 ( 15 ) 2.396558 1 2.431725 2 2.467407 3 2.503614 ( 16 ) 2.540351 1 2.577628 2 2.615452 3 2.653831 ( 17 ) 2.692773 1 2.732286 2 2.772379 3 2.813061 ( 18 ) 2.854339 1 2.896223 2 2.938722 3 2.981844 ( 19 ) 3.025599 1 3.069996 2 3.115045 3 3.160755 ( 20 ) 3.207135 1 3.254196 2 3.301948 3 3.350400 ( 21 ) 3.399564 1 3.449448 2 3.500065 3 3.551424 ( 22 ) 3.603537 1 3.656415 2 3.710069 3 3.764509 ( 23 ) 3.819749 1 3.875800 2 3.932673 3 3.990380 ( 24 ) 4.048934 1 4.108348 2 4.168633 3 4.229803 ( 25 ) 4.291870 1 4.354849 2 4.418751 3 4.483591 ( 26 ) 4.549383 1 4.616139 2 4.683876 3 4.752607 ( 27 ) 4.822346 1 4.893108 2 4.964909 3 5.037763 ( 28 ) 5.111686 1 5.186695 2 5.262803 3 5.340029 ( 29 ) 5.418388 1 5.497896 2 5.578571 3 5.660431 ( 30 ) 5.743491 1 5.827770 2 5.913284 3 6.000054 ( 31 ) 6.088101 table ii. the amount of due pound , put out to interest for any number of months under 25. at the rate of 6 per cent. compound interest . months . amount . 1 1.004867 2 1.009758 3 1.014673 4 1.019612 5 1.024575 6 1.029562 7 1.034574 8 1.039610 9 1.044670 10 1.049755 11 1.054865 12 1.060000 13 1.065159 14 1.070344 15 1.075554 16 1.080789 17 1.086050 18 1.091337 19 1.096649 20 1.101987 21 1.107351 22 1.112741 23 1.118158 24 1.123600 table iii. the amount of due pound , put out to interest for any number of days under 366. at the rate of 6 per cent. compound interest . days . amount . 1 1.000160 2 1.000319 3 1.000479 4 1.000639 5 1.000798 6 1.000958 7 1.001118 8 1.001278 9 1.001438 10 1.001598 11 1.001757 12 1.001917 13 1.002077 14 1.002237 15 1.002397 16 1.002557 17 1.002717 18 1.002878 19 1.003038 20 1.003198 21 1.003358 22 1.003518 23 1.003678 24 1.003839 25 1.003998 26 1.004159 27 1.004320 28 1.004480 29 1.004640 30 1.004801 31 1.004961 32 1.005121 33 1.005282 34 1.005442 35 1.005603 36 1.005764 37 1.005924 38 1.006085 39 1.006245 40 1.006406 41 1.006567 42 1.006727 43 1.006888 44 1.007049 45 1.007209 46 1.007370 47 1.007531 48 1.007692 49 1.007853 50 1.008014 51 1.008175 52 1.008336 53 1.008497 54 1.008658 55 1.008818 56 1.008980 57 1.009141 58 1.009302 59 1.009463 60 1.009624 61 1.009786 62 1.009947 63 1.010108 64 1.010269 65 1.010431 66 1.010592 67 1.010753 68 1.010915 69 1.011076 70 1.011237 71 1.011398 72 1.011560 73 1.011722 74 1.011883 75 1.012045 76 1.012207 77 1.012368 78 1.012530 79 1.012691 80 1.012853 81 1.013015 82 1.013177 83 1.013338 84 1.013500 85 1.013662 86 1.013824 87 1.013986 88 1.014147 89 1.014309 90 1.014471 91 1.014633 92 1.014795 93 1.014957 94 1.015119 95 1.015281 96 1.015443 97 1.015605 98 1.015768 99 1.015930 100 1.016093 101 1.016254 103 1.016417 103 1.016579 104 1.016741 105 1.016903 106 1.017066 107 1.017228 108 1.017391 109 1.017553 110 1.017715 111 1.017878 112 1.018040 113 1.018203 114 1.018365 115 1.018528 116 1.018691 117 1.018853 118 1.019016 119 1.019179 120 1.019341 121 1.019504 122 1.019667 123 1.019830 124 1.019992 125 1.020155 126 1.020318 127 1.020481 128 1.020644 129 1.020807 130 1.020970 131 1.021133 132 1.021296 133 1.021459 134 1.021622 135 1.021785 136 1.021948 137 1.022112 138 1.022275 139 1.022438 140 1.022601 141 1.022765 142 1.022928 143 1.023091 144 1.023254 145 1.023418 146 1.023581 147 1.023745 148 1.023908 149 1.024072 150 1.024235 151 1.024399 152 1.024562 153 1.024726 154 1.024889 155 1.025053 156 1.025217 157 1.025380 158 1.025544 159 1.025708 160 1.025871 161 1.026035 162 1.026199 163 1.026363 164 1.026527 165 1.026691 166 1.026855 167 1.027018 168 1.027182 169 1.027346 170 1.027510 171 1.027675 172 1.027839 173 1.028003 174 1.028167 175 1.028331 176 1.028495 177 1.028659 178 1.028824 179 1.028988 180 1.029152 181 1.029316 182 1.029481 183 1.029645 184 1.029809 185 1.029974 186 1.030138 187 1.030302 188 1.030467 189 1.030632 190 1.030796 191 1.030961 192 1.031126 193 1.031290 194 1.031455 195 1.031619 196 1.031784 197 1.031949 198 1.032114 199 1.032278 200 1.032443 201 1.032608 202 1.032773 203 1.032938 204 1.033103 205 1.033268 206 1.033433 207 1.033598 208 1.033763 209 1.033928 210 1.034098 211 1.034258 212 1.034423 213 1.034588 214 1.034753 215 1.034919 216 1.035084 217 1.035249 218 1.035414 219 1.035580 220 1.035745 221 1.035910 222 1.036076 223 1.036241 224 1.036407 225 1.036572 226 1.036737 227 1.036903 228 1.037069 229 1.037234 230 1.037400 231 1.037565 232 1.037731 233 1.037897 234 1.038062 235 1.038228 236 1.038394 237 1.038560 238 1.038725 239 1.038891 240 1.039057 241 1.039223 242 1.039389 243 1.039555 244 1.039721 245 1.039887 246 1.040053 247 1.040219 248 1.040385 249 1.040551 250 1.040717 251 1.040883 252 1.041050 253 1.041216 254 1.041382 255 1.041548 256 1.041715 257 1.041881 258 1.042047 259 1.042214 260 1.042380 261 1.042546 262 1.042713 263 1.042879 264 1.043046 265 1.043212 266 1.043379 267 1.043545 268 1.043712 269 1.043879 270 1.044045 271 1.044212 272 1.044379 273 1.044545 274 1.044712 275 1.044879 276 1.045046 277 1.045213 278 1.045380 279 1.045546 280 1.045713 281 1.045880 282 1.046047 283 1.046214 284 1.046381 285 1.046548 286 1.046715 287 1.046883 288 1.047050 289 1.047217 290 1.047384 291 1.047551 292 1.047719 293 1.047886 294 1.048053 295 1.048220 296 1.048388 297 1.048555 298 1.048723 299 1.048890 300 1.049057 301 1.049225 302 1.049393 303 1.049560 304 1.049728 305 1.049895 306 1.050063 307 1.050230 308 1.050398 309 1.050566 310 1.050734 311 1.050901 312 1.051069 313 1.051237 314 1.051405 315 1.051573 316 1.051741 317 1.051908 318 1.053076 319 1.052244 320 1.052412 321 1.052580 322 1.052748 323 1.052916 324 1.053084 325 1.053253 326 1.053421 327 1.053589 328 1.053757 329 1.053925 330 1.054094 331 1.054262 332 1.054430 333 1.054599 334 1.054767 335 1.054935 336 1.055104 337 1.055272 338 1.055441 339 1.055609 340 1.055778 341 1.055946 342 1.056115 343 1.056284 344 1.056452 345 1.056621 346 1.056790 347 1.056958 348 1.057127 349 1.057296 350 1.057465 351 1.057633 352 1.057802 353 1.057971 354 1.058140 355 1.058309 356 1.058478 357 1.058647 358 1.058816 359 1.058985 360 1.059154 days . amount . 361 1.059323 362 1.059492 363 1.059661 364 1.059830 365 1.060000 table iv. the present worth of due pound , due after any number of years under 32 , or numters under 125. at the rate of 6 per cent. compound interest . years and quarters . present worth. ( 0 ) .0000000 1 .9855383 2 .9712858 3 .9572394 ( 1 ) .9433962 1 .9297531 2 .9163074 3 .9030560 ( 2 ) .8899964 1 .8771256 2 .8644409 3 .8519397 ( 3 ) .8396193 1 .8274770 2 .8155103 3 .8037167 ( 4 ) .7920936 1 .7806387 2 .7693493 3 .7582233 ( 5 ) .7472581 1 .7364516 2 .7258013 3 .7153050 ( 6 ) .7049605 1 .6947656 2 .6847182 3 .6748160 ( 7 ) .6650571 1 .6554393 2 .6459606 3 .6366189 ( 8 ) .6274123 1 .6183389 2 .6093967 3 .6005839 ( 9 ) .5918984 1 .5833386 2 .5749026 3 .5665885 ( 10 ) .5583947 1 .5503194 2 .5423609 3 .5345175 ( 11 ) .5267875 1 .5191693 2 .5116612 3 .5042618 ( 12 ) .4969693 1 .4897823 2 .4826993 3 .4757187 ( 13 ) .4688390 1 .4620588 2 .4553767 3 .4487912 ( 14 ) .4423009 1 .4359045 2 .4296006 3 .4233879 ( 15 ) .4172650 1 .4112307 2 .4052836 3 .3994226 ( 16 ) .3936463 1 .3879535 2 .3823430 3 .3768137 ( 17 ) .3713644 1 .3659939 2 .3607010 3 .3554847 ( 18 ) .3503438 1 .3452772 2 .3402839 3 .3353629 ( 19 ) .3305130 1 .3257332 2 .3210226 3 .3163801 ( 20 ) .3118047 1 .3072955 2 .3028515 3 .2984718 ( 21 ) .2941554 1 .2899014 2 .2857089 3 .2815771 ( 22 ) .2775051 1 .2734919 2 .2695367 3 .2656388 ( 23 ) .2617972 1 .2580112 2 .2542799 3 .2506026 ( 24 ) .2469785 1 .2434068 2 .2398867 3 .2364176 ( 25 ) .2329986 1 .2296291 2 .2263082 3 .2230355 ( 26 ) .2198100 1 .2166312 2 .2134983 3 .2104108 ( 27 ) .2073679 1 .2043690 2 .2014135 3 .1985008 ( 28 ) .1956301 1 .1928010 2 .1900128 3 .1872648 ( 29 ) .1845567 1 .1818877 2 .1792573 3 .1766649 ( 30 ) .1741101 1 .1715924 2 .1691113 3 .1666663 ( 31 ) .1642569 table v. the present worth of one pound , due after the expiration of any number of months under 25. at the rate of 6 per cent. compound interest . months . present worth . 1 .9951560 2 .9903355 3 .9855383 4 .9807644 5 .9760136 6 .9712858 7 .9665810 8 .9618988 9 .9572394 10 .9526026 11 .9479884 12 .9433962 13 .9388264 14 .9342788 15 .9297531 16 .9252494 17 .9207676 18 .9163074 19 .9118689 20 .9074518 21 .9030561 22 .8986817 23 .8943285 24 .8899964 table vi. the present worth of one pound , due after the expiration of any number of days under 366. at the rate of 6 per cent. compound interest . days . present worth. 1 .9998404 2 .9996808 3 .9995212 4 .9993616 5 .9992021 6 .9990426 7 .9988831 8 .9987237 9 .9985643 10 .9984048 11 .9982455 12 .9980861 13 .9979268 14 .9977675 15 .9976083 16 .9974490 17 .9972898 18 .9971306 19 .9969714 20 .9968123 21 .9966532 22 .9964941 23 .9963350 24 .9961759 25 .9960169 26 .9958579 27 .9956990 28 .9955400 29 .9953810 30 .9952222 31 .9950633 32 .9949045 33 .9947457 34 .9945869 35 .9944282 36 .9942694 37 .9941107 38 .9939520 39 .9937934 40 .9936347 41 .9934760 42 .9933175 43 .9931590 44 .9930004 45 .9928419 46 .9926834 47 .9925250 48 .9924665 49 .9923081 50 .9921497 51 .9919914 52 .9917330 53 .9915747 54 .9914165 55 .9912582 56 .9911000 57 .9909418 58 .9907836 59 .9906254 60 .9904673 61 .9903092 62 .9901511 63 .9899930 64 .9898350 65 .9896769 66 .9895190 67 .9893611 68 .9892031 69 .9890452 70 .9888874 71 .9887297 72 .9885718 73 .9884139 74 .9882561 75 .9880983 76 .9879406 77 .9877829 78 .9876252 79 .9874676 80 .9873100 81 .9871523 82 .9869948 83 .9868372 84 .9866797 85 .9865222 86 .9863647 87 .9862073 88 .9860498 89 .9858924 90 .9857350 91 .9855777 92 .9854204 93 .9852631 94 .9851058 95 .9849486 96 .9847913 97 .9846341 98 .9844770 99 .9843198 100 .9841627 101 .9840056 103 .9838485 103 .9836914 104 .9835344 105 .9833774 106 .9832204 107 .9830635 108 .9829066 109 .9827497 110 .9825928 111 .9824359 112 .9822791 113 .9821223 114 .9819656 115 .9818088 116 .9816521 117 .9814954 118 .9813387 119 .9811821 120 .9810254 121 .9808688 122 .9807123 123 .9805557 124 .9803992 125 .9802427 126 .9800862 127 .9799298 128 .9797733 129 .9796169 130 .9794606 131 .9793042 132 .9791479 133 .9789916 134 .9788353 135 .9786791 136 .9785228 137 .9783666 138 .9782105 139 .9780543 140 .9778982 141 .9777421 142 .9775860 143 .9774300 144 .9772739 145 .9771179 146 .9769620 147 .9768060 148 .9766500 149 .9764942 150 .9763383 151 .9761824 152 .9760266 153 .9758708 154 .9757150 155 .9755593 156 .9754036 157 .9752479 158 .9750922 159 .9749366 160 .9747809 161 .9746253 162 .9744697 163 .9743142 164 .9741587 165 .9730032 166 .9738477 167 .9736922 168 .9735368 169 .9733814 170 .9732260 171 .9730707 172 .9729154 173 .9727600 174 .9726047 175 .9724495 176 .9722942 177 .9721390 178 .9719839 179 .9718287 180 .9716736 181 .9715185 182 .9713634 183 .9712084 184 .9710534 185 .9708983 186 .9707433 187 .9705884 188 .9704334 189 .9702785 190 .9701236 191 .9699688 192 .9698140 193 .9696591 194 .9695044 195 .9693496 196 .9691949 197 .9690400 198 .9688954 199 .9687308 200 .9685762 201 .9684216 202 .9682670 203 .9681124 204 .9679579 205 .9678033 206 .9676489 207 .9674944 208 .9673400 209 .9671855 210 .9670311 211 .9668768 212 .9667224 213 .9665681 214 .9664138 215 .9662596 216 .9661053 217 .9659511 218 .9657969 219 .9656428 220 .9654886 221 .9653345 222 .9651804 223 .9650263 224 .9648723 225 .9647183 226 .9645643 227 .9644103 228 .9642563 229 .9641024 230 .9639485 231 .9637946 232 .9636408 233 .9634870 234 .9633332 235 .9631794 236 .9630256 237 .9628719 238 .9627182 239 .9625645 240 .9624109 241 .9622573 242 .9621037 243 .9619500 244 .9617965 245 .9616430 246 .9614895 247 .9613360 248 .9611825 249 .9610291 250 .9608757 251 .9607223 252 .9605690 253 .9604157 254 .9602623 255 .9601091 256 .9599558 257 .9598026 258 .9596494 259 .9594962 260 .9593430 261 .9591799 262 .9590369 263 .9588837 264 .9587306 265 .9585775 266 .9584245 267 .9582715 268 .9581185 269 .9579656 270 .9578127 271 .9576598 272 .9575069 273 .9573541 274 .9572013 275 .9570485 276 .9568957 277 .9567430 278 .9565902 279 .9564375 280 .9562849 281 .9561322 282 .9559796 283 .9558270 284 .9556744 285 .9555219 286 .9553693 287 .9552168 288 .9550644 289 .9549119 290 .9547595 291 .9546071 292 .9544547 293 .9543023 294 .9541500 295 .9539977 296 .9538454 297 .9536932 298 .9535409 299 .9533887 300 .9532365 301 .9530843 302 .9529322 303 .9527800 304 .9526280 305 .9524759 306 .9523239 307 .9521719 308 .9520199 309 .9518679 310 .9517160 311 .9515640 312 .9514121 313 .9512603 314 .9511084 315 .9509566 316 .9508048 317 .9506530 318 .9505013 319 .9503495 320 .9501978 321 .9500462 322 .9498945 323 .9497429 324 .9495913 325 .9494397 326 .9492881 327 .9491366 328 .9489851 329 .9488336 330 .9486822 331 .9485307 332 .9483793 333 .9482279 334 .9480766 335 .9479251 336 .9477739 337 .9476226 338 .9474713 339 .9473201 340 .9471689 341 .9470177 342 .9468665 343 .9467154 344 .9465642 345 .9464131 346 .9462621 347 .9461110 348 .9459600 349 .9458090 350 .9456580 351 .9455071 352 .9453561 353 .9452052 354 .9450543 355 .9449035 356 .9447526 357 .9446018 358 .9444511 359 .9443003 360 .9441495 361 .9439988 362 .9438481 363 .9436975 364 .9435468 365 .9433962 table vii . the present worth of one pound annuity , to continue any number of years under 32 , and payable by yearly payments , at 5 , 6 , 7 , 8 , 9 , and 10 per cent. compound interest . the present worth of one pound annuity , comp. int. at years . 5 per cent. 6 per cent. 7 per cent. 1 0.95238 0.94339 0.93457 2 1.85941 1.83339 1.80801 3 2.72324 2.67301 2.62431 4 3.54595 3.46510 3.38721 5 4.32947 4.21236 4.10019 6 5.07569 4.91732 4.76653 7 5.78637 5.58238 5.38928 8 6.46321 6.20979 5.97129 9 7.10782 6.80169 6.51523 10 7.72173 7.36008 7.02358 11 8.30641 7.88687 7.49867 12 8.86325 8.38384 7.94268 13 9.39357 8.85268 8.35765 14 9.89864 9.29498 8.74546 15 10.37965 9.71224 9.10791 16 10.83776 10.10589 9.44664 17 11.27406 10.47725 9.76322 18 11.68958 10.82760 10.05908 19 12.08532 11.15811 10.33559 20 12.46220 11.46992 10.59401 21 12.82115 11.76407 10.83552 22 13.16300 12.04158 11.06124 23 13.48857 12.30337 11.27218 24 13.79864 12.55035 11.46933 25 14.09394 12.78335 11.65358 26 14.37518 13.00316 11.82577 27 14.64303 13.21053 11.98671 28 14.89812 13.40616 12.13711 29 15.14107 13.59072 12.27767 30 15.37245 13.76483 12.40904 31 15.59283 13.92908 12.53187 years . 8 per cent. 9 per cent. 10 per cent. 1 0.92592 0.91743 0.90909 2 1.78326 1.75911 1.73553 3 2.57709 2.53129 2.48685 4 3.31212 3.23971 3.16986 5 3.99270 3.88965 3.79078 6 4.62287 4.48591 4.35526 7 5.20636 5.03295 4.86841 8 5.74663 5.53481 5.33492 9 6.24688 5.99524 5.75902 10 6.71008 6.41765 6.14456 11 7.13896 6.80519 6.49506 12 7.53607 7.16072 6.81369 13 7.90377 7.48690 7.10335 14 8.24423 7.78614 7.36668 15 8.55947 8.06068 7.60608 16 8.85136 8.31255 7.82371 17 9.12163 8.54363 8.02155 18 9.37188 8.75562 8.20141 19 9.60359 8.95011 8.36492 20 9.81814 9.12854 8.51356 21 10.01680 9.29224 8.64869 22 10.20074 9.44242 8.77154 23 10.37105 9.58020 8.88322 24 10.52875 9.70661 8.98474 25 10.67477 9.82258 9.07704 26 10.80997 9.92897 9.16094 27 10.93516 10.02658 9 . 237●● 28 11.05107 10.11613 9.30656 29 11.15840 10.19828 9.36960 30 11.25778 10.27365 9.42691 31 11.34981 10.34284 9.47901 table viii . shewing what annuity , to continue any number of years under 32 , and payable by yearly payments , one pound will purchase , at the rate of 5 , 6 , 7 , 8 , 9 , and 10 per cent. compound interest . a table shewing what annuity one pound will purchase , at several rates of comp. int. years . 5 per cent. 6 per cent. 7 per cent. 1 1.05000 1.06000 1.07000 2 .53780 .54543 .55309 3 .36720 .37411 .38105 4 .28209 .28859 .29519 5 .23097 .23739 .24389 6 .19701 .20336 .20979 7 .17281 .17913 .18555 8 .15472 .16103 .16746 9 .14069 .14702 .15348 10 .12950 .13586 .14237 11 .12038 .12679 .13335 12 .11282 .11927 .12590 13 .10645 .11296 .11965 14 .10102 .10758 .11434 15 .09634 .10296 .10979 16 .09226 .09895 .10585 17 .08869 .09544 .10242 18 .08554 .09235 .09941 19 .08274 .08962 .09675 20 .08024 .08718 .09439 21 .07799 .08500 .09228 22 .07597 .08304 .09040 23 .07413 .08127 .08871 24 .07247 .07967 .08718 25 .07095 .07822 .08581 26 .06956 .07690 .08456 27 .06829 .07569 .08342 28 .06712 .07459 .08239 29 .06604 .07357 .08144 30 .06506 .07264 .08058 31 .06418 .07181 .07983 years . 8 per cent. 9 per cent. 10 per cent. 1 1.08000 1.09000 1.10000 2 .56076 .56846 .57619 3 .38803 .39505 .40211 4 .30192 .30866 .31547 5 .25045 .25709 .26379 6 .21631 .22291 .22960 7 .19207 .19869 .20545 8 .17401 .18067 .18744 9 .16007 .16679 .17364 10 .14902 .15582 .16274 11 .14007 .14694 .15396 12 .13269 .13965 .14676 13 .12652 .13356 .14077 14 .12129 .12843 .13574 15 .11682 .12405 .13147 16 .11298 .12029 .12781 17 .10962 .11704 .12466 18 .10670 .11421 .12192 19 .10412 .11173 .11954 20 .10184 .10954 .11745 21 .09983 .10761 .11562 22 .09803 .10590 .11400 23 .09642 .10438 .11257 24 .09497 .10302 .11126 25 .09367 .10180 .11016 26 .09250 .10071 .10915 27 .09144 .09973 .10825 28 .09048 .09885 .10745 29 .08961 .09805 .10672 30 .08882 .09733 .10607 31 .08814 .09670 .10550 table ix . the present worth of any lease , or annuity , for 21 , 31 , 41 , 51 , 61 , 71 , 81 , or 91 years ; as likewise the present worth of the see simple . at 5 , 6 , 8 , and 10 per cent. compound interest . years to be purchased . at 5 per cent. the purchase of freehold land. at 6 per cent. the purchase of copyhold land , or leases of land.   years . qua. mo. years . qua. mo. 21 12 3 1 11 3 0 31 15 3 1 13 3 2 41 17 0 1 15 0 1 51 18 1 0 15 3 0 61 18 3 2 16 2 0 71 19 1 1 16 1 2 81 19 2 1 16 2 0 91 19 3 0 16 2 0 fee simple . 20 0 0 16 2 2 years to be purchased . at 8 per cent. the purchase of very good houses . at 10 per cent. the purchase of leases of ordinary houses .   years . qua. mo. years . qua. mo. 21 10 0 0 8 3 2 31 11 1 1 9 3 0 41 11 3 2 9 3 2 51 12 1 0 9 3 2 61 12 1 1 10 0 0 71 12 1 2 10 0 0 81 12 2 0 10 0 0 91 12 2 0 10 0 0 fee simple . 12 2 0 10 0 0 chap. ii. the use of the preceding tables of compound interest . having with all imaginable care framed and calculated divers tables relating to compound interest , it will be needful to apply the same to use and practice . the use of the first table , shown in two examples . example i. suppose it be demanded to give the amount of 136 l. 15 s. 6 d. being forborn 20 years , at 6 per cent. compound interest . direction . the given sum must first be reduced by the first table of the first book , and made 136.775 , and then multiplied by the number in the first table answering to ( 20 ) , in the margin of pag. 144 , viz. 3.20713 . tariffa for the multiplicand . 1 136775 2 273550 3 410325 4 547100 5 683875 6 820650 7 957425 8 1094200 9 1230975 the operation may be contracted , according to the rule in the introduction . the product 438.6552 is the true answer , and being reduced by the fifteenth table of the first book , makes 438 l. 13 s. 1 d. 1 q. example 2. suppose it be demanded to give the amount of the aforesaid sum in 20 years and 3 quarters . direction . multiply the aforesaid sum of 136.775 , by the number which answers to 20 years and 3 quarters , viz. 3.35040 . the operation may be contracted as before . the product 458.2509 is the answer to the question , and being reduced by the fifteenth table of the first book , makes 458 l. 5 s. more by 22 / 100 ( or ninety two hundred parts ) of a farthing . the use of the second table . suppose it be desired to know the amount of 42 l. in 7 months , at 6 per cent. compound interest . direction . seek the number in table ii. answering to ( 7 ) in the margin , viz. 1.034574 , and multiply it by 42 , and the product is the answer . which product being reduced is 43 l. 9 s. 2 q. more by 2 / 100 ( or two hundred parts ) of a farthing . the use of the third table . suppose it be demanded to find the amount of 42 l. in 104 days . direction . find the number in table iii. answering to ( 104 ) in the margin , viz. 1.016741 , and multiply that by 42 , and the product is the answer . which product being reduced , makes 42 l. 14 s. 2 q. more by 99 / 100 ( or ninety nine hundred parts ) of a farthing . the use of the fourth table . let it be demanded to find the present worth of 438 l. 13 s. 1 d. 1 q. due and payable after the expiration of 20 years , at 6 per cent. compound interest . direction . the given sum being converted into a decimal number is 438.65520 , then find the number in table iv. answering to ( 20 ) in the margin , viz. .3118047 , and multiplying one by another , the product is the answer . tariffa for the multiplicand . 1 4386552 2 8773104 3 13159656 4 17546208 5 21932760 6 26319312 7 30705864 8 35092416 9 39478968 and the operation may be contracted thus to seven places , by the rule in the introduction . the product 136.7747 is a manifest proof of the truth of the operation in the first example of the use of the first table , pag. 186. there being not so much as the hundredth part of a farthing difference . the use of the fifth table . let the present worth of 43.452108 l. due after the expiration of 7 months , be sought , according to the rate of 6 per cent. compound interest . tariffa for the multiplicand . 1 43452108 2 86904216 3 130356324 4 173808432 5 217260540 6 260712648 7 304164756 8 347616864 9 391068972 the operation contracted by the rule in the introduction . which product 41.99997 is a clear and manifest proof of the truth of the operation in the use of the second table , pag. 190. the use of the sixth table . let it be required to find the present worth of 42.703122 l. after the end of 104 days , at the rate of 6 per cent. compound interest . tariffa for the multiplicand . 1 42703122 2 85406244 3 128109366 4 170812488 5 213515610 6 256218732 7 298921854 8 341624976 9 384328098 the operation contracted by the rule in the introduction . which product 41.99997 , is a clear and manifest proof of the truth of the operation in the example , calculated to shew the use of the third table , pag. 191. the use of the seventh and ninth tables . let it be required to find the present worth of an annuity of 56 l. to continue 21 years , and payable by yearly payments , at the rate of 6 per cent. compound interest . direction . first find the number in table vii . answering to ( 21 ) in the margin , which is 11.76407 ; then multiply it by 56 , without a tariffa , because there are but two places in the multiplicator , and the product is the answer . which product being reduced by the fifteenth table of the first book , makes 657 l. 15 s. 9 d. more by 40 / 100 ( or forty hundred parts ) of a farthing , which agrees with mr. kersey's example , in his appendix to mr. wingate's arithmetick , pag. 412. only this calculation is more exact than his , and somewhat nearer to the truth . the use of the eighth table . let it be demanded what annuity , to continue 14 years , and payable by yearly payments , will 320 l. buy , allowing 6 per cent. compound interest . direction . seek in the margin of table viii . the number ( 14 ) , and the number answering to it , under the title of 6 per cent. viz. .10758 ; which multiply by 320 , and the product is the answer . which product 34.42560 , being reduced by the fifteenth table of the first book , makes 34 l. 8 s. 6 d. more by 57 / 100 ( or fifty seven hundred parts ) of a farthing . a farther use of the seventh table . to convert a present sum or fine into an annual rent ; or on the contrary , to bring down an annual rent by a present sum or fine . example 1. a landlord le ts a lease of a house and land for 21 years , and is to have 100 l. for that lease , and a yearly payment of 30 l. what fine or present money must the tenant give , to bring down the rent from 30 l. to 10 l. per annum , allowing 6 per cent. compound interest ? direction . first find the difference of 10 l. and 30 l. which is 20 l. then find by table vii . pag. 176. what an annuity of 1 l. to continue 21 years , is worth in present money , which is 11.76407 l. then multiply 11.76407 by 20 , and the product gives the present worth of 20 l. per annum for 21 years . the operation . which product 235.28140 being reduced , is 235 l. 5 s. 7 d. 2 q. more by 14 / 100 ( or fourteen hundred parts ) of a farthing . example 2. a landlord demands a fine , or present sum , for a lease of 127 l. per annum , to continue 7 years ; what is the sum , allowing 6 per cent. compound interest ? direction . find by table vii . the present worth of 1 l. annuity for 7 years , at 6 per cent. viz. 5.58238 , which multiply by 127 , and the product is the answer . the operation . which product 708.96226 being reduced by the fifteenth table of the first book , makes the just sum of 708 l. 19 s. 2 d. 3 q. more by 77 / 100 ( or seventy seven hundred parts ) of a farthing . and here the reader is desired to take notice of a printed sheet sold in westminster-hall , entituled , “ a president for purchasers , &c. or anatocisme ( commonly called compound interest ) made easie , &c. computedly w. leybourn . the principal table in this sheet is printed from a copper plate , but so full of gross errors and mistakes , that it is not sit to be used : for in this last example , that table makes tho sum but 706 l. 16 s. 6 d. which the table of this book makes 708 l. 19 s. 2 d. 3 q. and more , ( which sum agrees with mr. clavel's tables ) . but in very many places there is no less than 4 , 5 , 6 , and 10 pound mistaken , which must needs deceive all those , who do in the least rely upon , or give any credit to it . so that the author of this little book hopes , that the manifold errors in the calculations of other writers , will occasion a more kind acceptance of his more than ordinary care and diligence in all the foregoing tables ; if not , — redit labor actus in orbem . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . finis . advertisement . there is newly printed a vade mecum , or necessary companion ; containing , 1. sir samuel morland ' s perpetual almanack , in copper plates , with many useful tables proper thereto . 2. the computation of years , comparing the years of each king's reign from the conquest with the years of christ . 3. reduction of weights and measures . 4. the ready casting up any number of farthings , half-pence , pence , shillings , nobles and marks ; with sir samuel morland ' s new table for guinneys . 5. the interest and rebate of money , the forbearance , discompt , and purchase of annuities , at 6 per cent. 6. the rates of post-letters , both inland and outland , with the times for sending or receiving them ; also the post-stages , shewing the length of each stage , and the distance of each post-town from london . 7. the rates or fares of coach-men , carr-men , and water-men . and are sold by r. northcot , bookseller , either next st. peter's alley in cornhill , or at the anchor and mariner on fish-street-hill ; by john playford , printer , near the blew-anchor inn in little britain ; and by charles blount , bookseller , at the black-raven in the strand , near the savoy . the necessity of abating usury re-asserted in a reply to the discourse of mr. thomas manly entituled, usury at six per cent. examined, &c. together with a familiar and inoffensive way propounded for the future discovery of summes at interest, that so they may be charged with their equal share of publick taxes and burthens, the long defect whereof hath exceedingly fomented usury, embased land, and much decay'd the better half of the kingdom. by sr. thomas culpeper, jun. knight. culpeper, thomas, sir, 1626-1697. 1670 approx. 145 kb of xml-encoded text transcribed from 33 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2004-03 (eebo-tcp phase 1). a35408 wing c7560 estc r204213 99825325 99825325 29705 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a35408) transcribed from: (early english books online ; image set 29705) images scanned from microfilm: (early english books, 1641-1700 ; 1828:9) the necessity of abating usury re-asserted in a reply to the discourse of mr. thomas manly entituled, usury at six per cent. examined, &c. together with a familiar and inoffensive way propounded for the future discovery of summes at interest, that so they may be charged with their equal share of publick taxes and burthens, the long defect whereof hath exceedingly fomented usury, embased land, and much decay'd the better half of the kingdom. by sr. thomas culpeper, jun. knight. culpeper, thomas, sir, 1626-1697. [6], 57, [1] p. printed by t.l. for christopher wilkinson, at the black-boy against s. dunstans church in fleet-street, london : 1670. reproduction of the original in the british library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng manley, thomas, 1628-1690. -usury at six per cent. examined, and found unjustly charged by sir tho. culpepper and j.c. with many crimes and oppressions, whereof 'tis altogether innocent -controversial literature -early works to 1800. interest rates -england -early works to 1800. great britain -economic conditions -17th century -early works to 1800. 2003-07 tcp assigned for keying and markup 2003-08 spi global keyed and coded from proquest page images 2003-10 stephanie batkie sampled and proofread 2003-10 stephanie batkie text and markup reviewed and edited 2003-12 pfs batch review (qc) and xml conversion the necessity of abating usury re-asserted ; in a reply to the discourse of m r. thomas manly entituled , vsury at six per cent. examined , &c. together with a familiar and inoffensive way propounded for the future discovery of summes at interest , that so they may be charged with their equal share of publick taxes and burthens , the long defect whereof hath exceedingly fomented usury , embased land , and much decay'd the better half of the kingdom . by s r. thomas culpeper , jun. knight . london , printed by t. l. for christopher wilkinson , at the black-boy against s. dunstans church in fleet-street , 1670. to the reader . the answer lately published to my discourse concerning the abatement of usury was so farre from surprising mee , that , indeed , it was no other then i long expected and much desired ; not from any overweening of my own cause , ( which yet perhaps would justifie some degree of confidence , ) but from a reall wish , that important truths may be cleared , which they can hardly be , till they have been roundly contradicted and severely scanned : and therefore i am in the first place to thank my plain dealing adversary for this opportunity of resuming the argument , that by due enquiry , either convincing my errour , or confirming my judgement , the impartial reader may be however satisfied . when first i saw it , and observed its bulke , i looked at least for some arguments which had never been offered before , and prepared my self with much curiosity to read it ; but finding my expectation herein disappointed , i could not but take it for a happy omen , that since the reasons urged for the present fall are either parallel , or certainly more pregnant than those in former times , and the objections against it , little or nothing varied , the like successe would probably attend it . it was then with equal tumult and acrimony suggested , that no wisdom could foresee the tragical consequences ; that half our cash would be buried under ground , and the rest exported to better profit ; that no young beginner could ever hope to borrow five pounds ; that wee should be beggered meerly by the with-drawing of forraign loanes ; that eight per cent , was not worth whistling after , nor scarce telling ; that brokage and securities would be intolerable , that lawes were but cobwebs to necessity , that improvement was a brainsick project ; that orphanes and widowes would crie for vengeance ; that the disasters of riot and sloath were falsely charged upon usury ; and that it was frivolous herein to quote the wise , frugal and industrious hollander . sutable to the arguments , the adversaries were then the same , for it was principally opposed by the dons and ruffes , the eminent traders and other sages of that time , who either being ( some of them , ) at least parcel-usurers , or foreseing that it would raise that land which they were yet to purchase , or disperse that benefit of trade which they desired still to monopolize , or disdaining to learn ought from their inferiours , brow-beat it as the project of bankrouts , derided it as the frenzy of novices and state-empyricks , and thought it sufficiently baffled by their dis-owining it : herein seconded by the usurer with his numerous gang , deeply concerned that so goodly a shrine should be prophanely touched , and shrewdly misliking the precedent : abetted by many faint-hearted borrowers , who , mistrusting the event of a good cause , maintain'd , ( as they thought ) by dwarfes , but assai'ld by gyants , either cried quarter● ; and layd down their armes , or ran over to the enemy , to the great encrease of his forces , and hazard of the enterprise . the same crisis had it in point of time , being moved three years before it took effect ; for in the year 1620 , my father wrote his treatise , as appeares by the date of its first edition , and in the year 1623. i take it , the act passed ; now this interval was spent in eager disputes , and the daily gaining of proselytes ; ( wherin , by the way , it is observable , that , for ought appeares , that age was not yet brave enough to assert even the height of publick usury in print , ) for being first propounded by a few country gentlemen and merchants , ( for the smalnesse of their party and boldnesse of their assertions then censured as fanaticks in trade , ) in that space of time , it won in effect all true lovers of their country , and convinced farr the major part of unbrassed auditours : these circumstances i hold it pertinent enough for me to relate , as i received them by conversation with my deceased father , or collected them from his treatises , partly to shew how difficult it is to dislodge a potent oppressour , partly to satisfie the present assertours of this argument , that they ought not to despayre , though they meet with greater hardships then have yet encountred them , but rather assuredly promise themselves , that cause must and will at length prevayle , which hath not hitherto been opposed but by flouts and frowns . in the reading of m r. manlies answer , i find exception taken both at my frequent mention of the term usurer , and at divers blunt expressions upon that subject ; but i hope it may easily be salved with this candid distinction of a ranke or common usurer , and a lender upon usury ; it is the trade which i abhorre , not the bare practise ; common usurers i defie , as the scandals of the church , and cankers of the state ; lenders upon usury i partly excuse , knowing many of them to be persons truly conscientious , and such , as were they convinced of the oppression , would not only desist but restore : yet even these i cannot but admonish seriously to consider , whether such practise have any better ground to support it , then general custome , and seeming convenience , countenanced by the pulpits silence , and whether in the purpose of humane lawes , impunity come not farre short of right : to such as yet further expostulate my meaning , i answer with a late eminent states-man in the like case , whosoever feels himself concerned , him i mean ; or with a friend of mine , who being asked where the usurer dwelt , protested he knew not , and hoped there was no such man. two capital errours in my former treatise i must acknowledge , but withal excuse ; the first , that i did not previously clear this great probleme , that the abatement of usury hath a natural and mathematical energy to rayse land , and augment trade ; for that being granted , all the advantages propounded had been sufficiently proved by but naming them ; whereas , for want of this ground-work the foundation seemed too sleight for the building , and my ensuing assertions to unprepared readers appear'd no better then bold presumptions , like the imposing of authority without first proving it authentick : the second , that charged our present sufferings wholy , ( or at least principally , ) upon the rate of usury , and not as well upon our long unequal burthens , which perhaps have had a greater share in the embasing of land then even usury it self , and without which usury would now much lesse have needed reducing : to the first , i answer , that in truth i could not foresee the denial of that maxime , which so immediately referres to the infallible rule of three in arithmetick , hath been ever granted , and never till now questioned by the usurer himself , and is , by way of admittance , solemnely declared , not only by that notable statute 21. jacobi , but even by an act of this present parliament : to the second , that i rather chose frequently to glance , as it were , upon those unequal pressures , than lay the main stresse upon them , if i could avoyd it , partly from my reverence to the authority imposing them , partly from my foresight of an answer , which obliging me , in my own defence , to produce them as manifest causes of the fall of land and rents , will , i hope , absolve me for it . for brevities sake , i have chosen to reply by way of dialogue , having ever observed that in such familiar discourses , doubtful matters are best explained ; glosses and sophismes prevented , and taedious circum-locutions avoyded , which at best signifie somewhat to style and forme , but nothing to sense : only for an antidote to my former omission , i shall first ground my future arguments concerning land , upon the impartial narrative of our publick burthens , for forty years past , here ensuing . a summary account of our publick taxes and burthens , and how they have been born for forty years past . to clear my antithesis of land and usury , i shall distinguish the time into three stages or periods , 1. before the war , 2. during the war , 3. after the war. 1. before the war , it hath ever been the known grievance of this kingdom , that all the hardships of the common wealth were born by land : our land-lords only exposed to be lords and deputy lieutenants , sheriffes , commanders in the militia , justices of the peace , jury-men , with divers other chargeable employments general and parochial ; our tenants to be constables , bosholders , surveyours , collectours , &c. prest to the war , and charged even in peace ; both of them , in their degrees , obliged to residence and hospitality , subject to payment of tithes , maintenance of the poor , employment of labourers at certain cost , but uncertain profit , repayring of churches , mills , bridges , high-wayes , sewers , &c. rarely pretending to matters of much advantage : neither is it a new complaint , that usury hath always sculked and shifted like the running gout , and like a faery or goblin , which tortures and scares without ever appearing ; that it was to the commonwealth , at best , like a lame legge , uselesse , deceitful , and troublesome ; profitable only to it self ; craftily avoyding all charges and duties , how just and equall soever , but watching all the advantages of wealth and leisure for gainfull offices and penny worths : tithe he never payd , i will not swear he never received it , since the first fall of interest , in doubtful times he is presently upon the wing , and if you do but talke reason to him , threatens to lurch or leave you ; for the world is his country , ●and perhaps in six moneths time , he can be as good dutch or french , as ever he was englishman , being now , at the best , but a denizen : with great reason therefore my father , in his second treatise , even then inferred , that since the usurer payd little to subsidies , nothing to fifteens , little to the poor mans boxe , repayred nor built no churches , set no labourers a● worke for the good of the commonwealth , employed none but scriveners and brokers , and those at the charge of the borrower , no man needed doubt , but there would be enough of the occupation , though mony were brought to five , ( he might now have sayd to three , ) in the hundred . 2. during the war , most remarkable it is , how generally and fatally the land was engaged , most of it actively in raysing of troopes and regiments , for the assistance and support of the parties contending , towards which the land-lords , as their perswasions led them , not only staked and pawned their own estates , but procured their neighbours and tenants to embarke with them ; all of it passively , by plunder , freequarter , contribution , and other exactions so insupportable , that an indifferent summe was then worth a fair lordship , taxes being commonly in surplussage to rents , and stock on all sides looked upon as lawful prise , so as land-lords were ruined by hundreds , and tenants by thousands ; not to mention the irreparable wasts committed by fire and other warlike violences . the usurer , in the mean time , felt none of these earth quakes , but ( like a devout hermite in his cell , ) retired to his beads , little concerned in secular or sublunary affaires , unlesse it were in the special case of an assumpsit or single band : wee heard little of his chivalry , and lesse of his martyrdom : some have been reported by the black art to be stick-free , and others shot-free ; the usurer , in the late times , was both . 3. after the war , it is but too fresh in our memories , what grievous pressures have ever since lain upon the land ; for the clear discovery whereof , i shall consider it under the fourefold capacity of compounder , owner , farmer , and borrower : the compounder , ( of which quality were perhaps our most and greatest land-lords , ) upon payment of two years compleat revenue for a fine , the lowest rate i have heard of , ( debts being rarely considered , ) was graciously restored to his house empty and half ruined , to his land stripped of wood and timber , ill tenanted and unfenced , his meadows perhaps broken up , his plantations , hop-grounds , nurseries , &c. at best neglected ; nor was hee thus dismissed , but exposed to the repayring of all pretended trespasses by him unavoydably committed in the war ; still molested , and forced , ( as the least of evils in appearance , though in consequence perhaps the greatest , ) by residing in london , to shelter himself from some ill neighbourhood . the owner , besides many other ruinous losses , hath for above twenty years past , commumbus annis , in land-taxes , military charges , and the encrease of parochial duties , pay'd at least one fourth part of his yearly income strictly valued . without the least consideration of fall or losse of rents , repayrs and divers other incident defalcations . the farmer having been impoverished by free quarter , and owing , ( at least in part , ) for his stock , hath been , and still is , by the like sufferings , together with his growing debts , kept so low , that it is great pity to see how painfully and innocently he cheats himself by holding on the farme , being neither able profitably to stock , nor afford it ordinary and necessary amendment , nor keep his grayn for tolerable market : the borrower , if compounder , and in debt before the war , ( as divers were , ) must needs be desperate ; it could then be no otherwise with him then thus , take all , and pay the baker ; for what estate almost could buoy up against such a fine , with many years losse of income , and growth of interest at eight per cent ? but though neither compounder , nor formerly in debt , can he well be imagined a clear man , having lived so long in effect upon the main ? and then let us take a survey of his condition ; borrow he could not then , without excessive brokage , for the glut of compounders had strangely improved extortion , besides the circumstantial mischiefs and traps of chargeable attendance , conveyance , suretyships , counter-securities , and trusts , which have furnished us with sutes and incumbrances scarce to be cleared in an age , and which , without fall of interest , may amount to a reasonable land-taxe , twenty , ( perhaps forty ) years hence ; sell he could not in due time , but to the losse of almost half his inheritance , so much was land embased by the miseries of the war , multitude of sellers , and land-taxes : subsist without selling long he could not , how ever ought not , for taxes and interest mony , ( like heavy bruises meeting with foul humours , ) would soon gangreen : all this while , the monyed man eat the fat of the land , being a kind of lord-dane in every houshold ; the common rate of interest , with choice of security real or personal , ( for borrowers were forced to helpe one another with joynt and mutual suretyships , ) came clear to him , for the acceptance whereof he was even treated as a benefactour ; but the common usurer , ( being generally his own broker , like bawd and curtesan , ) was double greased ; he swaggered like the lord of a great mannour , the demeans whereof are holden by villenage , having the very carkasses of his betters , as it were , in his clutches : his harvest lasted many years , betwixt pernicious loanes and seisures , dog-cheap penny-worths of goods , and half-purchases of lands both private and publick : for like a raven , he feasts upon carrion , and thrives by the calamities of his country . i have claimed the losers priviledge in the blunt narrative of these plain truths , ( irksome indeed to the memory , but in use medecinal ) partly to silence their un reasonable clamour , who most absurdly impute our present damp of land , to the reducing of interest , chiefly to lay open , even to vulgar capacities , the original and ground-work of our present maladies , so industriously palliated by most of those that procured , so unhappily mistaken or sleighted by many that feel it , whom i dayly hear lamenting the hardship of the times , but withal imputing it to causes , either scandalous to authority , or in themselves so frivolous , as one would blush to mention , as if they should tell me , we are sick for want of health , idle for want of businesse , and insolvent for want of mony : these i would willingly acquaint , what evil spirits haunt them , and what familiar spels may drive them away ; for to mee it seems most evident , that the disproportion of usury to trade , but principally to rents , not timely observed and redressed , together with the advantage constantly taken by usurers to decline all publick burthens , ( especially in civil broyles , after them , ) hath and , since our current practise of usury , made greater havock of noble families , hopefull traders , and honest farmers , then all other oppressions and casualties , within that time , summed up together . for the better applying of this history to my present argument , give mee leave to propound these following quaeries . doth not publick welfare mainly depend on the avoyding of oppression by equality of taxes ? ought not every one that hath a certain revenue to contribute his share to the common burthens of his country , is it not a condition reasonably annexed to property ? supposing interest of money to be lawful rent , ( as it pretends , ) and admitting it the speediest , clearest , and securest income , ( as doubtlesse it is , ) ought it not , even in that respect , to be most strictly charged ? are not summes of money at usury , goods , chattels , indeed the principal ones , were they not then comprehended in all our late lawes for taxes , even those of the late usurpers ? were they not , in some of our latest acts , since his majesties return , particularly charged by name ? admitting it assault to steal customes and excise , is it not at least equivalent in the lender upon usury to decline taxes imposed by one and the same authority ? is not the prejudice to king and kingdom finally as great , but the immediate wrong to neighbours palpably greater ? hath not the encrease of our poor , military burthens , and farmers taxes , for twenty years past , embased farmes at least ten per cent. in value ? have not the like pressures more immediately cost the land-lord at least fifteen per cent. of his yearly income , and what hath the usurer contributed to any of them ? hath not every purchaser of late years , by reason of their long prescription , purchased with allowance for them , in the nature of quit-rents clogging inheritance ? hath not then every necessitous seller clearly sacrificed the fourth part of his estate to his exigence , and have not purchasers thriven to the same proportion by their neighbours misery , and so made double benefit of their own wrong ? have not the hopes of land-lords and doubts of tenants concerning the end or ease of taxes justly hindred the letting of good leases , and multiplied tenancies at will , to the manifest ruine of farmes , and publick detriment , but advantage of lurching purchasers ? have not the like hopes suspended many sellers upon exigence to their greater ruine , and the contrary doubts so amused fair purchasers , that they knew not what justly to offer ? have not borrowing land-lords pay'd all this while six per cent. indeed to the usurer , but otherwise , ( considering the clog of their inheritances , ) much more then double that rate ; and have not lenders , in effect , received neer two per cent. overplus , which , in all equity , they should have payd to the publick ? will not the usurer , without due caution always , serve us with the same sawce in all future broyles , or extraordinary levies ? may not this kingdom be presumed still to feel the effects of the late civil war , as men do sometimes old bruises or the sinnes of their youth very long after ? admitting land-taxes should cease , may not the continuance ( perhaps encrease , ) of other burthens , especially the poor , without effectual redresse , be sufficient to perpetuate the embasement of our farmes , now so impoverished ? will any man now marvel at the deadnesse , and not rather at the quicknesse of our lands and markets ? must we not impute this suspension of our utter ruine to our intermediate growth of trade by our last fall of usury , and its exemption from new clogs ? may not an indifferent charity suppose , that the land-lord may be now incumbred , and tenant impoverished , without rank prodigality ? doth not even six per cent. grievously bite the land , it being now notorious , that ( all things computed ) rents in the country do not generally answer three ? can the borrower ever hope , without abatement of usury , to clear himself , but to half ruine in sale , or extreme mischief by delay , may not the usurer , at his pleasure , relieve himself , perhaps with advantage , by purchasing in time ? can the retrenching of usury , which by visible experience hath always proved successeful , be ever so just and necessary , as to farmers generally drooping , and a gentry incumbred by loyal sufferings ? is not the improvement of land , and support of gentry farre more considerable to his majesties service , then any pretence of usurers can be ? if our taxes and burthens had been equally born , must not the due rate of land have been maintained , to at least 24. years purchase ? if land could have escaped all these burthens , and money born them , without consideration of desperate and uncertain debts , ( as surely little we have had of incumbrances or fayler of rents . ) what would probably have been the purchase of land ? if all our payments had been charged upon customes and forrain imposts ( money and land being both exempted , ) what would have been our account of trade ? may it not yet be seasonable , ( because profitable , and most just , ) to expose money at interest to publick taxes and duties ? if creditours at interest be obliged , at their peril , to taxe themselves , so as by their declining it , they be construed to disown their principal , and forfeit it , either wholy to the borrower , or half to the king , may not this probably be effected , without either the temptation of perjury , or prejudice of informing ? where were the inconvenience ? were not this , concurrent with the fall of usury , a likely way speedily to raise the value of land , for want of which only the country now droopes ? i shall now proceed in my reply to mr. manly by questions and propositions naturally arising from his own words , or sense , for brevities sake , collected with the same fidelity ; which i would desire him , or any other , hereafter to use towards me . the preface . t. m. is not the hiring of mony , ( seeing it cannot be borrowed for gods sake , ) as necessary for the well-being of mankind , as hiring of land or houses ? t. c. divines will first tell you , your very hypothesis is stark naught , de jure , i mean , though de facto it be too true ; and then withal they will direct you to wholsomer expedients for traffick , on all sides , than hiring of mony , viz. trading with our own stocks , honest partnership , and discreet factorage : besides , as to the difference of land and money , they will , ( amongst other things ) inform you , that your letting of mony at the same price to all borrowers , looks somewhat like the expecting an equal rent for all lands by the acre , without examining their quality , scituation , &c. to vary is impracticable , and not limit the rate , hath been found by experience , in uncharitable times , the highway to jewish extortion . t. m. do you not lay an unreasonable stresse upon the interest payd by his majesty for monies borrowed in the late war ? t. c. my meaning was the same with yours , ( though not asserted with the like confidence and authority , ) viz. that his majestie gave excessive rates , now this , say i , happened through his not commanding mony , as the states did , the reason whereof i clearely referre to the plenty and security attending low interest . t. m. doth not the frugal hollander grow rich with the gaines of seven or eight per cent. whilst fifteen per cent. will not support our expensive traders ? t. c. five or six , i doubt , is generally fair for them , ours , i suppose , may thank you for it ; they would fain perswade the usurer either to trie himself , or be their ensurer ; but , it seems , he desires none of their egges for his mony , for he lovingly thanks them , and had rather they should be his . t. m. i desire the reader to take notice , that all europe exceeds us in the rates of vsury , the states of holland , and some commonwealths of italy only excepted ? and some or all of these are unrestrained by their lawes , and at liberty to take as much for interest as they can get . t. c. we differ partly in fact , but more in the issue by you put ; for lawes may not only be proper but necessary in a kingdom grievously incumbred by civil war , and that hath so much good land for its fund ; when , in commonwealths of unequal and slender territory , free from exigents , possessed of trade , and chiefly founded in it ; current security , with good policies , may both supply the want of them , and perhaps better effect their design : as for rates , i think it were happy , if ours were the lowest . t. m. i say , ( speaking as a man , ) 't is no wrong to the commonwealth , if men of estates drink , drab , live profusely , and die beggars , so long as every penny comes to the natives , &c. t. c. i say ( speaking as an englishman , ) interest reipublicae , nequis male utatur suis : this is indeed , a rare doctrine for usurers , but baneful to the commonwealth ; such a vermine , as you describe , it no more wants , then it doth the usurer himself , or than the farmer , in a cheap time , doth rats and mice , or lazy and disorderly hinds to devour his fruits ; for so necessity , ( the mother of incumbrance , and gran-dame of extortion● would both fatally embase our lands , and poyson our trade with bankrouts ; besides he is a scabby sheep and infects the flock ; i now leave the reader to judge , who speaks most in favour of luxury , you or i ; cato or seneca , i presume , taught you no such lewd and vulgar politicks . t. m. well then ! a taxe we must have , be it only to dispose authority to subdue interest , &c. t. c. me thinks , sir , we are already half agreed ; the kings debts , i presume , you would have payd , and his real occasions supplied , land-taxes , it seems , you abborre as much as i , and i trust , you wish so well to trade , as you would not have that bear all our burthens ; what then remains , but that our future levies be upon mony at interest ? if you please then , and publick occasions require it , ( as 't is like they may ) monytaxes let them be : let two or three per cent. be charged upon all interest mony for seven years , and let usurers always afterwards be double taxed like aliens , as , in effect , they are , and say you are gently dealt with : but four per cent. with an effectual provision for the future taxing of mony its due share , seems to be the cleanlier way . t. m. is not this gratifying the borrower with a vengeance for one years payment to eternity , out of an honest creditours purse ? t. c. how honest i know not , i am sure , of late we have tasted little of his justice ; let me again acquaint him , that admitting even his fairest pretence , and hardest measure , i suppose , it were scarce a rowland for his oliver , but our soundest divines , i doubt , will tell you , you mistake your vice for your estate . t. m. who layd this excise , as you terme it , upon your land , the borrower , or the vsurer ? he swears , he sought not for the gentleman or trader , he had something else to do with his mony , &c. t. c. i could answer you perhaps without just exception , it was the rebel and the usurer betwixt them ; but , pray sir , is not this as good a plea for the highest extortions as for common interest ? my surly host , when i question his reckoning , may as well reply , who sent for you ? the prostitute , having picked her lovers purse , may as well aske him , who sollicited you ? i durst likewise swear , ( but that i doubt a borrowers oath may not be taken without a voucher , since his band i find will not passe without two or three sureties , ) the usurer would never lend for pure good nature or importunity , or if he thought he could otherwise deale to better effects ; and therefore i have a little curiosity to know , what that something else was , for , if it were a purchase , ( though a lurching one , ) beshrew those , say i , whoever they were , that diverted him . t. m. what would you have him do ? let his neighbour sinke ? go to prison ? &c. t. c. such a deliverance or jubile as this had esops horse , protected from the stagge , but ridden to death by the man ; i 'll tell you , what i would have him do , not give his friend poyson for physick , or , at best , cold water in a calenture ; what then ? why lend him mony grais , or at a tolerable and saving rate , to be sure , what ever it be : but he who now premises that usury is charity , may shortly , i doubt conclued , that gaine is godlinesse . t. m. he kept his mony by him these six moneths to lend , &c. t. c. 't was his own folly , he should once for all , ( according to your discreet advertisement page 44 , ) have fairely layd it out upon land , and for ever prevented the like losse ; but , it seems he knows better what to do , then you or i can direct him . t. m. he lends it to a man , that gaines fifteen per cent. ( for so much i believe all traders do , ) is it not reasonable the lender should have at least one half thereof ? &c. t. c. nay , if once you come to reason , you are gone , stick to your opus and usus , if you be wise ; for what if he lend it to a man who looses fifteen per cent. ( so much , i doubt , some traders do , ) is it not then reasonable the lender should bear one half of the losse , since he looked for one half of the gaine ? i marvel , sir , i should need , now to tell you , that trading at interest is a deceitful lottery , consisting of blanks without number for a few great lots , an errand quack , that proclaims his cures , but conceales his murthers ; a few field-officers it hath , who by chance surviving , and carrying away the fruit and glory of the whole service , are celebrated for their exploits ; and well they may , for they are almost as strange as knight-errandry ; but common souldiers are slaine by thousands and forgotten ; my comfort is , that i hope by this time , our merchants , and usurers too so well perceive it , that the one is not forward to trust , nor the other eager to be trusted ; and that the blessing of forraigne loanes hath quite forsaken us ; otherwise , it would aske no conjuring to read the destiny of our trade . t. m. no man will keep mony by him to lend for so small a praemium as four per cent. which will hardly reward selling in and out , and make good the brass mony , much less answer the hazard of lending , which is so considerable , in this deceitful age , that i perswade my self , the ensurance office would demand above 30 s. per 100 to secure all the mony lent on security in england . t. c. t'other angel , and 't is done : there is now no more , for ought i see , betwixt your hazard and our ensurance , troth , be good natur'd , and do not stand for a trifle : but surely , sir , you speak at a great rate ; tell mr. usurer from me , his poor bayliffe the gentleman , ( as you rightly terme him , ) is content with half the salary , sometimes with a bit and a knock from his benefactour , and that his worship puts me in mind of some great goodfellows , who were so long accustomed to swill in spirits , brandy , sack , metheglin , northdown , and mum , as houshold beer would not down with them , it was but rock-water , even cyder they took but for clarified whey : but our hope is malt will shortly rise , and then we must brew smaller for him then of late we have done ; yet even at four per cent. i doubt , he will fare but too well ; better , i am sure for the present , then many who better deserve : as for his hazards , he ensures himself with a witnesse ; nor do i suppose , he desires to loose so sweet a pretence . however , if at any time he be bitten , he is but pay'd in his own coyne , for not purchasing fairely , in stead of lending shrewdly , and lying in ambush , as he doth , for lurching pennyworths . t. m. i am yet to learn , what puts our gentry upon considerable borrowing , except such things as i am not willing to record , since not one in seven borrowes to advance any laudable improvement . t. c. our late usurpers could better resolve you then i , unless you will take my preface in part of payment , but in truth , the question comes strangely from you in this place ; who tell us but a page or two before , of marrying daughters , and going to prison ; good sir , look about , or you will lose your self in the wood . t. m. there is another sort of men , ( gentlemen not in debt , ) concern'd in this conditional taxe , who are not to expect present advantage by subduing interest , but are to solace themselves with an assurance of future improvement of their inheritances in value , as certain as if it were in their purses , saith my discourser , &c. t. c. i say so indeed , and i doubt not but most of those gentleman will believe me , for the thing is manifest both as to the purchase and rents of land ; for purchase , the resemblance of land and mony to two buckets was never questioned till now ; and rents must needs be governed by the very same maximes with the land it self and trade , the farmer being no other then a country marchant , and , with your patience , i shall offer you divers familiar instances to prove , the tenant hath equal benefit in the fall of usury with his land-lord , his stock will be so much cheaper to him , his ordinary yet necessary amendments , fences , repairs , &c. will be cheaper , he may the better afford to sell at common and low markets , or wait for higher , and , upon the encouragement of a long and good lease , he ( but much more the owner ) will be enabled to venture on improvements chargeable and expectant , the profit whereof will vastly accrue not to himself only , but the commonwealth , viz. building , planting , enclosing , drayning , flouding , marling , &c. these are so obvious , as i cannot but admire the vulgar capacities of some , who in discourse on this subject are apt to say , alas ! what is it to me , that neither lend nor borrow ? but say i , do you neither hire nor let ? neither sell nor buy ? neither build nor repayre ? neither plant nor enclose ? neither wear nor cloath neither travel nor sojourn ? neither entertain nor eat ? which way soever you turn , six per cent. stares in your face ; you meet him on the road and sup with him at your inne ; his intruding you cannot avoyd , yet shun , if you can , his acquaintance ; and in case you design to build a church or chappel , or found an hospital , or plant a colony , or enlarge a navigation , or bravely serve your prince , or worthily oblige your friend , or seasonably assist your neighbour , or encourage manufacture , or advance learning , or maintain hospitality , or uphold your degree , or improve your estate , or adorn your mansion , or enclose your park , or compleat your library , or liberally breed your son , or well match your daughter , or any way exemplifie your christian profession , publick spirit , or private conduct , to the purchasing of brass or marble , nay to the bare rescuing your name even from present oblivion , consult him not , for you will find him sacrilegious , selfish , difficult and costly ; but let me freely recommend to your four per cent. for besides his fidelity and dispatch , he may chance in the upshot , ( all things computed , ) save you more then half in half . t. m. but how will this rayse a farme now 100 l. per annum to 130 l. in the future ? &c. t. c. me thinks the usurer , disclayming good works , might have a little more faith , and not argue so sceptically and perversely since nothing seems clearer , then that what you take from interest , you give to land and stock ; those two rents being all along the same buckets ; but if he will yet suspect his reason , let him hearken to great authority , viz. the stat. 21. iacobi , which declares its main drift to be the upholding of rents , and incouragement of tillage , then decaying ; the act of this present parliament , which recites , that by notable experience , improvements had ensued ; and the edict of that wife king ; henry the fourth of france , anno 1601. recording the very same design . t. m. but our happinesse is , we have a third sort of land-lords , ( whom you did not please to think on , ) and , i hope one third part of the land-lords in england , at least in weight , who are so farre from being in debt , that , by happy conduct , they are masters of considerable summes , and that upon vsury ; now to deal alike with the land-lord lender and land-lord-borrower is monstrous unequal . t. c. excellent news , i profess ! that we have so many weighty land-lords ; seriously i have not had the honour to know many of these worthi●s , or weighty gentlemen ; but i the less marvel , having generally converst with royallists ; yet if such gentlemen there be , ( which upon your credit i shall admit , let them know , i desire their acquaintance , not to trouble them with the impertinency of getting in the shire what they loose in the hundred ; but purely to tell them this story from my deceased fathers mouth ; when he went to oxford in 1642. he owed a considerable summe at 8 percent to a certain creditour of principles different from him , ( whom he ever mentioned with respect , ) at their meeting in 1647. my father told him , he hoped for some abatement of interest , and forbearance of the principal , in regard of the fine he was then to pay ; his answer was , sir , take your own time for payment , as for interest , god forbid , i should require any when you had no rents , nor could my father prevail with him to take any part of it : a rare pattern for conscientious lenders , and a lively decision of our present argument : now by the happy conduct of these weighty land-lords , i understand their dextrous shifting of publick duties , and otherwise making hay while the sun shined ; if they can , at length , be ( in some small measure ) fairely met with , let king adonibezek acquaint them with the justice of it . t. m. i humbly conceive , it were much better to keep up vsury , and find out a way like that of a register , ( so long and passionately desired , ) which at once might enable the solvent gentleman to borrow easily , ( which now he cannot do , ) on all occasions reasonably secure the mony lent , affright men from running greatly into debt , least their nakednesse appear , prevent ten thousand frauds , and as many law sutes , defer none but insolvent and ill-minded men , and direct the state , upon all emergencies to lay impositions on it equal to land-taxes . i humbly perceive , usury is your noli me tangere ; well , however , i am glad to find you grant equall taxing just , it savours of some ingenuity still , though , i doubt , you may think it will not be in your time , and that you are safe enough at your close guard : as for a register , it hath indeed been long desired , and long , i fear , yet may be , at least , ere it operate , considering the difficulties of agreeing , settling , and purging it : this six per cent. well knows , and therefore , as his last stake , drives the argument to that issue , just in the welshmans rhetorick , let her but alone , till that daycomes ; we , on the other side , desire a register , ( as surely it is chiefly our interest , ) farre more sincerely then he , and wish no time were lost , that at least the next age may reap the fruit of it ; but we hope our redresse needs no such long prorogation , for he that must dine late , wants a good breakfast , and we suppose some fall of usury , in our involved condition , to be the necessary harbinger or pioneer to an effectual register , judging it more likely and proper to begin with the egge , then the hen. by the way , i cannot but with trouble reflect , that land and trade should so conspire to play the usurers game against themselves , as by their discord all along they have done ; the trader crying , taxe land , in gods name , for that will bear it , trade cannot ; and the land-lord of late , spare land , for gods sake , it hath already been taxed to death ; taxe now our superfluous trade , and therein our luxury ; giving , it seems , the usurer over to his reprobate sense , and therefore freely permitting him to thrive in this world ; but little , in the mean time , considering , that tillage and trastick lay in one belly the earth , sayle in one bottom upon the sea , and fear one pyrate or vermine , the usurer , like a slie make-bate circumventing , and secretly no doubt deriding them , withal applauding his own happy conduct , ( as my authour hath it : ) for as when theeves disagree , true men recover their goods , so whilst honest men quarrel , pockets are the more securely picked . t. m. do you really believé , that abatement of vsury will rayse the purchase and revenue of land , and performe such wonderful feats ? t. c. i have heard of divers great politicians , and some , in my dealings , i have met with , who being a little thick of hearing , kept notwithstanding one ear constantly open to good tydings , and another shut to bad : near of kinne to these is our usurer ; no man so nimble in apprehending , so subtle in calculating profit as he ; but if any thing be offered crosse to his purpose , he counterfeits himself a changeling ; poor man ! i dare say , he cannot tell ten : at this close lock we have him all along : if he find purchasing commonly gainful , in three moneths time he is our land-lord , however , if he meet with a lurching penny worth , he snaps it ; he then lookes bigge and is a man of business , he would have you know ; but if times be doubtful , taxes high , and rents falling , he is then a poore orphane , a silly cock-nay , not versed in country affaires ; if trade be in a thriving way , and yield above his rate of usury , ( which he critically observes and understands as well as most that drive it , for there is not a better weathercock , to tell us where the wind sits , ) being naturally shrewd , and pensive : a rare accomptant , and by conversation , at least , no stranger to those affaires , he plies the exchange , examines the rates of impost , soon acquaints himself with prices and markets , and is as brisk as the best : but finding little to be got , but hazard , and that , all things considered , he may repose himself more profitably upon his downbed of interest , he is then wholy defective in business of that kind , his friends undid him by not giving him more learning , or putting him early out to prentice ; or he is a crazy old man , weary of the world , glad to retire , and beginning to doat : were it not for this imposture of affected impotency , how could men the acurest and exactest judges of advantage in their generation , at this time of the day , so peremptorily deny the raysing of land by the fall of usury ; a problem full of self conviction , compelling assent to the very mention of it , and which themselves , i dare say , have formerly granted a hundred times over : but truly here is the intrigue , before the usurer had dived into the bottome of the argument , and spied the vast invincible consequences of it , not only in the various improvements of land , but in their immediate affinity to those of trade , ( and one would marvel so sharp a nostril should not sooner smell so strong a scent , ) his common reflexions , were these , yes indeed , this is good for you in the country , but it will undo us citizens ; you gentlemen care not what becomes of trade , so your lands rise ; now you would fain be raysing your rents again , and racking your tenants to maintain your prodigality : these and divers other unwary confessions have i my self , and i dare say most that read this page heard from some even of those who now sing another note ; for finding themselves , by their own admission , utterly gravelled , and unable to gainsay the necessary great and good effects of raysing land , they soon swallowed their own spittle , and now the crie is , 't is absurd thus to argue against experience ; we utterly deny it , prove it if you can ; well then , i am ready to prove it , ( which yet i supposed i should never have been driven to , ) and not only prove , but in good measure demonstrate it , if at least arguments of this nature be capable of such evidence . purchasing is the exchanging of mony for land to a supposed equal value , the proper measure whereof is yearly income or revenue ; he then that purchases according to rule , compares the income of his mony which he quits , with the revenue of his land which he acquires , and thereby examines his gain or loss : now , in regard of the dignity and stability of land , it hath alwayes had , caeteris paribus , some preheminence allowed it in the ballance , to a fourth or third part , perhaps more in very clear times , so as six pounds per annum good rents were counted of equal intrinsecal value to eight or nine pounds per annum interest ; he then that would lay out a hundred pounds upon a purchase , ( mony being at six per cent. ) expected land to the yearly value of four pound , or at most four pounds and ten shillings , which is about four and twenty years purchase , whereas , ( mony being at four per cent. ) less then three pounds per annum becomes his due , which is about six and thirty years purchase : this estimate , i dare maintain , must generally hold , if there be certainty in the rules of proportion ; and that it doth so , appears even in our present case , which i take for a pregnant and marvellous instance , considering the number and extremity of sellers ; for supposing land now to carry eighteen years purchase , ( as good rents have all along done , ) and abating a fourth part for the rent charges of publick duties , by purchasers cruelly defalked ; the present purchase is just reconciled to my presumed rate : as for rents , i must again mind you , of five years actual war , five years anarchie , ten years usurpation , and above twenty years unequal burthens , sufficient , one would think , much more to have impoverished our farmers , and embased our farms . but as for the feats and projects which you so deride , i again affirm , they are not monstrous , but most natural , even so familiar ? that every country , almost every year presents us with notable patterns of them ; your self have instanced in some which may only serve for a relish of many incomparably more important : do but cast your eye upon our lands now adjacent to good towns , and observe what the industrie of man , meanly and but accidentally encouraged hath there effected ; and then , ( if you can ) deny , that a perfect enablement , and withal prudent compulsion of the same industrie , doubled and redoubled , would , through the necessary progresse of improvement , make indeed a strange and happy metamorphosis ; even by planting cities , in time , where are now scarce hamlets , and multiplying towns almost to the number of our parishes ; since god , who sends meat for our mouths doth likewise ever send mouths for our meat , and that not by miracle in our vulgar account , but the ordinary successe of just laws , and prudent endeavours ; for sure there is nothing that so fatally and universally wasts and depopulates as usury , if once it grow rank and rampant ; no not war or pestilence it self , which have always had their periods , intermissions and exemptions ; whereas this , like a general and perpetual contagion and secret canker , supplants the present age , and undermines posterity ; for who , that hath common sense , observes not , that dark and drooping times , ( the fruitful harvest of our silversmiths , ) drive out natives , and keep out strangers , cut off the thred of life untimely with want , care , anguish , and disorder , oblige even the richer sort , ( as it were in their own defence , ) to decline or deferre marriage , and compel the poorer , at best to neglect , but shrewdly tempt them even to expose their children ? and who may not easily thence conclude , that the flourishing of trade and tillage , ( which to our worms and weeds is a most nipping frost , ) endeares any country to its people , allures forreiners , prolongs lives , and makes posterity even the tenants welcomest stock , but the land-lords only treasure and jewels ? t. m. where is now the treasure of the nation , lying idle , locked up in misers chests ? or if it be now employed at six per cent. it can be but employed , reduce interest to what you please . t. c. indeed a rare ground-work for the raysing of interest to forty or fifty per cent. for , i● seems , you make no difference betwixt the general employment of our stock to profit or losse : my father , i take it , in his first treatise , hath laid down a sounder maxime , viz. that where particulars thrive not , the commonwealth is seldom greatly advanced . t. m. will our encrease oblige forreigners to sit still , and take their food and rayment of our providing , granting it cheap . t. c. truly in many things , it is like , it may oblige divers of them , as the cheapness of polish corn hoarded by the dutch too oft obliges us to buy it at great rates in dear years ; but i presume , there are , amongst others , two pregnant and mighty instances , wherein a cheap growth , ( justified by large crops , and flourshing improvements , ) manifestly conduces to great vent , viz. the foundation of manufacture , and victualling of ships . t. m. 't is well known , most of our lands are upon their best improvements , &c. t. c. t is better known , that you impose herein a shameful mistake ; for visibly the better half of them are still common fields , and perhaps neer a quarter commons or wasts . t. m. i would appeale to the impartial and industrious , whether six per cent. hath discouraged improvements , or whether they have nor rather feared a cheap year , want of vent , &c. t. c. i would appeal to common sense , whether six per cent. in name , but at least twelve in effect as to the land , computing our unequal burthens , did not , and must not necessarily produce this want of vent , by impoverishing tenants , disabling them to wait for good markets , and so leaving them to the buyers courtesy . t. m. we have vast quantities of fruit in england , and more we might have , without reducing vsury , would our gallants spend more of their time and mony upon laudable improvements in the country , instead of wasting so much in london . t. c. store , saith the old proverb , is no sore ; but any thing must be said , how little pertinent soever , rather then infringe the usurers supposed charter : i tell you , sir , in short , borrowers are bad planters , and worse preservers of plantation , but the usurer , methinks , might do rarely well in both ; for planting , to successe i take it , requires great leisure and continual care , with a strong purse . t. m. but in good earnest , shall we undersel our neighbours , and will they long endure it ? by what rare arts shall we keep the knowledge of this hidden vein from them , will not they , if that will do , take the same course ? t. c. let them take what course they please : god and nature , with the blessing and freedom of a just and gentle government , have furnished us with advantages enough , even to some good latitude , if we abuse them not , and that the usurer and his gang , with their wiles , do not undermine us , and blast our spring in its early blossom . t. m. will the hollander , who lives cheaper , workes cheaper , sayles cheaper , builds ships cheaper , navigates cheaper , and hath a noble for our nine pence , be ever undersold by us in the same commodity ? &c. t. c. you will , anon make the hollander a very fine monster , of five heads , ten hands , twenty pockets , and never a mouth ; and poor england , for ought i see , is wholy given over by the doctour ; well now , say i , may be a fit time for the mountebanck , ( as you call him ) to trie a dose upon his patient ; recover him , with gods blessing , it may , for while there is life , there is hope ; hurt him it cannot , for you have pronounced him a dead man : sir , i have lived in holland , and know in point of fact , that all provisions are there at a rate , neer double to what they are here , as needs they must be , not only from the smalnesse and populousness of their territory , but from their vast charges of embanking , duties , and tolls ; and then i leave it to the reader to inferre , whether their wages , ( even to keep them alive , being thrifty enough in conscience , ) must not be greater , as i affirm they generally are , with a confidence , i am sure , better grounded then yours can be : some artificial advantages , indeed , they have of us , which , god be thanked , are reasonably ballanced by our natural ones , and we have divers defects , which would soon be cured , if our best heads and stocks were employd in trade , and not in usury , whereby our dwarfes are put to grapple with their gyants . t. m. will this make the french king revoke his edicts against our drapery , suffer his people to sit idle , eat our bread and wear our manufactures , merely in regard of cheapnesse ? &c. t. c. for the first and last of these , i suppose , it may , viz. by keeping our wool at home for our own working , and shrewdly pinching him , as well in his ingredients as vent : for their eating our bread , we aym not much at that , but desire and hope never more to eat theirs ; however we may promise our selves , our drapery thus encouraged will assuredly carry the market , and that out gallants shall have no longer any pretence to wear french druggets , as they now say , for cheapness . t. m. to what neighbours standard would you have vsury adjusted ? to the french ? no sure , they pay more then we , &c. t. c. it is now almost seventy years , since usury in france was abated from eight to six pounds and five shillings per cent. by that wise king henry the fourth , as a prime expedient to repayr the breaches , and desolations of thirty years cruell war , judging , no other medicine adaequate to the disease , for so it appeares by his solemne and excellent edict in the french story thus noted and related : the king , by these edicts , had nothing relieved the necessities of the nobility , if he had not provided for vsuries , which have ruined many good and antient houses , filled towns with unprofitable servants , and the countrys with miseries and inhumanities : he found the rents constituted after ten or eight in the hundred did ruine many good families , hindred the traffick and commerce of merchandise , and made tillage and handicrafts to be neglected ; many desiring , through the easiness of a deceitful gain , to live idely in good towns of their rents , ( mark this , for it is now become just our own ease , mony having so long escaped all our heavy burthens , ) then to give themselves , with any paines to liberal arts , or to till or husband their inheritances ; for this reason , ( meaning to invite his subjects to enrich themselves with more just gaine , ) to content themselves with more moderate profit , and to give the nobility means to pay their debts , he did forbid all vsury or constitution of rents , at a higher rate , then six pounds five shillings for the hundred : the edict was verified in the court of parliament , which considered , that it was always prejudicial to common-weal to give mony to vsury , for it is a serpent , whose biting is not apparent , and yet it is so sensible , that it pierceth the very heart of the best families . it was yet early-day , i take it , when this law was made in france , anno 1601. at least twenty years before usury had its first reducement from ten to eight per cent. in this kingdom , a thing , in it self , very observable ; for had it not been for the miserable servitude of that people , and their other insupportable taxes , ( the very twins of usury , ) it is scarce by any mans wit imaginable what effects so great and early a foundation of wealth and trade , ( as perhaps the then lowest rate of interest , ) might before this time have produced in that ample and fruitful territory , or what influence it might have had upon all its neighbours : truly i never heard , it was since raysed , and will hold you great oddes it was not ; and i durst likewise hold you an even wager , ( having it from very good hands , ) that the french king hath newly reduced interest to five per cent. sweden , our licensed gazette acquainted us in a solemne narrative , the last year , brought it from ten to six at one large stride ; little , it should seem , regarding your profound objection of forcing nature by a law , even in a remote northern tract , or rather desart , desperate , ( one would think , ) as to much improvement or trade : if yet you ask mee , to what neighbours standard i would have usury adjusted , i answer , certainly to the lowest in christendom , if it might be , for that is evidently best , though somewhat more may for the present serve turn , the rather , because we hope , that with this seasonable lift at the brow of the hill , it may tumble downward of it self , which , without it , it will never do , but rather rise in extortion ; for as to high and low interest , it is equally natural for the one to soar with its own wings , and the other to sink with its proper weight . t. m. have not the french beaten us out of our hamburghs trade as to the manufacture of gloves , meerely by underselling us therein to a great proportion , being favoured by their cheap labour only ? &c. t. c. quote not the french for wages , least your country-men stone you , their condition indeed is worse then the gibeonites in israel , or israelites in egypt , their king hath nine pence in the shilling of their earnings : and yet like spiders , spinning their webs out of their bellies , a sorry shift they make , and a trade they drive for their task masters profit ; for much may be done and payd , where men work almost without eating : but mark the consequence ; france , the happiest soyl and climate for the extent now known , lies half of it wast , the natives even loathing their own country , and burthening all the habitable world with their beggarly colonies , one third of the lackeys and valets in europe being frenchmen , witnesse doctour heylin , who tells us , that once at madrid , they banished them all as dangerous for their numbers , finding the french servants in that town only , to exceed 30000. so just and natural is it for oppression to disarme it self ; and even thus the usurer murtherd his own security , as appears by my authours most genuine complaints , page 4. and 22. t. m. surely we need not be long in quest after that which give the forraigner the great advantage over us , since i believe we have as good mechanicks and as lusty labourers to dispatch worke as any of them : how can wee then avow any other reasons , then cheapnesse of provisions , course diet , and worse drinke , parsmonious living and small wages ? whereby , through a constant practise , forreigners will do that for foure pence which our people will not willingly perform for six pence ? t. c. but are wages higher with us then our neighbours ? a blessed grievance ! god continue and encrease it ; i do not hear that scotland or ireland are so opprest ; wages are fairely cheaper at york then at london , yet i do not find either york greatly boast , or london much repine ; wages are the highest in kent of any county in england , except middlesex , is it therefore our folly . at rochester you exceed those in the weld , yet they , i suppose , would change with you : if once you could reconcile great trade to small wages , farewel hans , the philosophers stone were a trifle to it ; good mechanicks and lusty labourers you grant we have , and i could acquaint , ( if i thought it needed , ) that we have good brains and stocks , even those prodigious summes by you owned page 35. scowr this armory bright from the rust of usury , to employ in trade or improvement of land , and our work is done at once , for all these cavills will sink , like froth , as indeed they are , if any disproportion there be in wages , ( as some in every thing may there be , where the ballance it self is faulty , and the main wheel out of frame , ) the remedy falls in of course , and wages will , without more adoe , recover and keep their due standard ; otherwise to dream of augmenting trade by stinting wages , too much resembles the judicious contrivance of that worthy squire , whom nothing would please but to let his meadow for forty shillings the acre , and buy his hay at ten shillings the load . t. m. will our fuell and labour which is the main charge of iron be ever as cheap as in sweden , though we knew not what interest meant ? t. c. no man , i dare say , can define , what the total extirpation of usury might or might not effect ; yet probably speaking , i shall admit they never will : and therefore in this , and possibly some parallel cases must referre you to the common practice of rival states , when both equally possess the ingredients of some important manufacture , but the one , by reason of some circumstance , ( like this of cheap fuell in a remote northern countrey , ) cannot compasse it so cheap for market as the other ; what do they then do but help their own commodity , ( at least as to their own use , ) by charging the forraigne with an impost wisely proportioned to their own defect : thus have the french to our cost lately clogged the importation of most of our manufactures , especially our draperies , and thus have we very successefully , without forbidding flemish hops , in effect excluded them , to the great improvement of our own so necessary growth ; whether any other temporary respect of league or trade with sweden may ballance so weighty an interest as this of iron , i leave to the wisdom of authority , acknowledging , that i cannot see into the milstone ; otherwise i dare pronounce , posterity may deeply repent our easiness herein , both in the future price of iron , neglect of woods , and encrease of the poor ; however , do we our utmost , repel swedish iron , and recover our forges , yet the present rate of usury shall undermine our woods , and render the price of that staple commodity insupportable to us even among our selves . t. m. the general conspiracy amongst artificers and labourers is so apparent , that , within forty miles of london , artificers are raysed , ( against all reason , ) from 18 or 20 d. to 2 s. 6 d. or 3 s. and meer labourers from 10 d. or 12 d. a day to 16 or 20 d. t. c. your conspiracy of artificers and labourers is a dangerous plot indeed , much like that of usurers , not to lend at abated interest , but 't is strange , say i , they should conspire only within forty miles of london ? surely , the only inconvenience as to our wages consists in the present disproportion betwixt trade and land ; for our manifest growth in the bulk of our trade since the last fall of usury having deserved , advanced wages in all our maritine and trading towns , hath necessarily imposed the same upon the countries adjacent , which , under their unequal pressures and impoverishment they cannot bear , so fruitful of mischief is errour , this is at present a reall and accumulative grievance , particularly to us in kent , by reason of the special influence we receive both from the city and navy ; but to retrive it otherwise , then by easing land for the future in the rate of taxes and usury were indeed a work worthy of your art. t. m. but since vsury hath been reduced , hath not the vent of our manufactures dayly lessened , and doth not tht whole nation dwindle into extrem poverty ? t. c. usury in respect of land hath been so farre from abatement , ( as i have often prooved , ) that it hath been , in effect , excessively raised by our unequal burthens , though usurers perhaps will not allow that bitter to others , which to them was so delicious ; for they have all this while , ( no doubt , like true israelites , ) dwelt in the land of goshen ; as for trade , which , god be thanked , hath had easier fetters , and whose exemption hath been our only support , by all the measures of it that can be taken , it is , ( all things considered ) miraculously advanced , as your self also confesse , page 43. where you justly observe the prodigious riches of london , and our merchants plentyful way of living : but it is common with sophisters in a bad cause to contradict themselves . t. m. sure i am , i know many artificers , and trades-men , who now live well and borrow , &c. t. c. but how many do you know , that have borrowed and broke ; 't is a hard battle , say i , where none survive . t. m. you are so sharp set in the quarrel , the poor fisherman , who never owed above twenty pounds in vsury cannot scape you , &c. t. c. surely , sir , i aymed not at the poor fisherman or huckster , ( though perhaps the use of twenty pounds to him , in his model , may be likewise paenal enough , ) but at the royal fishing trade , which i take it , requires even a national stock , and cannot now be effectually promoted , but at very low interest . t. m. who shall judge what moderate benefit the borrower may cheerfully afford the lender ? &c. t. c. you have , by the way , ( unwarily , i suppose , ) urged one of the best arguments for condemning all usury , and reducing it to the honest participation of gaine or losse , so abhorred by usurers ; but my answer is , the usurer doth , upon the whole matter , in our case , prejudge and conclude himself , even by his choyce . t. m. but will you not by way of gratitude and requital allow the vsurer a liberal reward for hazards as great as an east-india voyage ? t. c. when he hath tried the hazards of an east-india vayage , he may the better measure his demands by it : but i doubt he finds it easier and better pastime to talk of robin hood , then draw his bow : yet let him examine whether the hazards he objects be not of his own creating by uncharitable contracts , and whether a due abatement of his profit would not mend his security ; for two per cent. we offer him competent ensurance . t. m. what mean those swarms of lewd and idle persons , who prowle about in every part of the kingdom , or those gangs of gypsies , that appear amongst us at noon-day ? &c. t. c. because your present objection seems to be grounded upon our pretended general want of ingenuity and industrie , i shall endeavour previously to remove this vulgar prejudice ; and first for ingenuity , i say , it appeares reasonable to suppose , that people , at least , of the same or neer the same climate and meridian are born with the same or neer the same principles of ingenuity : that which afterwards makes the difference , is law , example , education , custome , and other forraigne accidents of life , either ennobling or depraving our natures : thus the examples of princes and generals active and always present in battles and campes , together with military rewards and punishments maks nations and armies valiant : pure doctrine enlivened by diligent preachers , adorned by holy patternes , and advanced by wholsome constitutions civil and ecclesiastical , makes people orthodoxe and devout ; hope of successe in their affaires , with a nimble spurre to endeavour , and prudent curbe of sloath , makes men inquisitive and ingenious : i say then we are now , caeteris paribus , as ingenious as any people living , for every one , by a kind of civil instinct , understands and closly pursues his best interest , and what would you have more ? to begin with the usurer , ( for with him indeed we must begin ) he , i am sure , of all men is in the right ; for you , in your first page , have resolved and secured him in point of conscience , by positively affirming , that hiring of mony is as necessary for the well being of mankind as hiring of land or houses ; and those , we know , were never questioned by any casuist : then you lay him down a second doctrine every whit as wholsome ; that his profit should reward his hazard , which sometimes , you say , is excessive ; be●wixt these two , what should hinder him from concluding , that what we now call extortion , may be , in many cases , every whit as just as common interest ; the latter having no more reall stamp of authority , then the former : thus i have heard that highway-men fancy they acquit themselves and come off with honour , by pleading , that they see no difference betwixt their courses , and some worshipful trades , but the danger , which , they suppose , much improves their title , and so , by your rule , evidently it doth . being thus inwardly fortified , his next consideration is profit , and surely that affords no dispute : i have heard , that an eminent person , to prove that beasts have logick , would introduce a hound or beagle thus discoursing ; the hare went not that way , for there i smell nothing ; nor that way , for there i smell nothing neither ; but this way , for here , indeed , i have a seent of her . to the usurers choyce three wayes are propounded for the employment of his stock ; land , trade , and usury ; and thus i presume him to argue : land i like not , for there i smell taxes , duties , and losse of rents ; trade i like not , for there i smell pyrates , shipwrack , trusts , customes , and flemings ; but for usury , surely there went the hare , for there is the sweet savour of mortgages and vayles with immunity ease and dominion . of the borrower i have little to say , for i looke upon him all along not as a free but necessary agent or rather patient : what would you expect from the labourer ? he workes not if he can chuse , and in effect tell us , if you find working so good , work your selves ; is not this a witty answer from a labourer ? hath he not , thinke you conferred notes with six per cent : to thrive by pain-taking he sees little hope ; live from hand to mouth , it seems he can , tying one hand behind him . if then he work in dear years , take his ease in cheap , and cast himself upon the parish in age or sickness , doth he not very discreetly ? even those gangs of gypsies you mention , i doubt not but the usurers , wholesome principles , applied to their condition , may likewise bear then out in conscience and prudence ; the usurer himself being ( qua vsurer , ) to the common-wealth but a bigger and graver sort of gypsie now for our industry , it appeares by the premisses , that is meerly frustrate by our ingenuity from one end of the board to the other ; for if usury and sloath be more pleasant , profitable , and secure , industrie becomes folly , and that so it is , who can doubt seeing it by so intelligent persons so dearly preferred : it must then be lawes grounded upon equity and vertue , which must clear this endless laborynth , and correct this vicious habit , and that of subduing usury must march in the van . and for infallible high-water markes to know the tide or season , take this ; when rich and experienced citizens leave off trading , and betaks themselves to interest ; when monied men in the country generally decline purchasing , but enquire for security and hug good mortgages ; when honest men make it the business of their lives to sell at any tolerable rate , and pay their debts , but cannot ; when the mortgage , being at first but half , is become full or neer equal in account to the land ; when statutes , judgements , and recognisances grow as familiar as bonds , and new shaped securities are dayly minted ; when the ruine of all borrowers and most farmers is bespoken ; when it is weightily objected , that there are many borrowers for one lender , ( though surely as much lent as borrowed ; ) when professions are overcharged , but the land understocked ; when , by reason of the farmers indigence , markets run low with mean crops ; when , according to the french kings edict , many good and antient houses are ruined , towns fined with unprofitable servants , and the countries with miseries and inhumanities , traffick and commerce of merchandise hindred , tillage and handicrafts neglected , &c. when usurers would passe for orphanes , and in their own defence , turn preachers and patriots ; when parish duties encrease , yet vagabonds swarm ; then , then , i say , the fruit is ripe , gather it , or expect abundance of windfals ; yet even then , i doubt not , but abatement of usury , and equal taxing , will with gods blessing , and some allowance of time , ( for betwixt ebbing and flowing is always still water , ) retrive our after-game , revive farmers , excite improvements , and largely answer all the benefits specified in my former treatise . t. m. were our poor industrious and frugal , and wages reasonable , ( which i fear will never be , till the abused ( rutch of state-maintenance be rescinded , or better regulated , ) they could not want employment , though vsury were at eight per cent. t. c. i agree with you in the rescinding of state-maintenance , as a provision only proper for the times it was made in , when monasteries were newly dissolved , and trade in its infancy ; but if you will take from the poor this crutch , you must withal cure their lameness , and set them upright upon their own legs , lest they lye too heavy at your doors : this , i affirm , neither eight nor six per cent. will do , nor any thing but the turning of our main stocks out of the muddy chamel of usury into the pure streams of husbandry and traffick , by a round abatement and equal taxing of interest-mony ; for did you not marke , how eight per cent. in france , even seventy years since , when perhaps that rate was lesse in proportion then five is now , filled towns with unprofitable servants , spoyld traffick , tillage , and handicrafts ? t. m. i am perswaded , few men come into great poverty , but by their own idle , irregular and wicked courses , &c. t. c. censure not so uncharitably , at least declayme not so freely ; for , i dare say , if it were examined , there are more and severer texts of scripture , canons of the church , sentences of fathers and eminent doctours , condemning usurers , then ●uthrifts or vagabonds ; but the truth is , if men be commonly idle , they will be lewd of course , ( for standing waters will putrefie ; ) and if poor men want work , or can live at half work , they will be commonly idle ; if farming and handicrafts decline they will want work , and yet perhaps may miserably live at half work ; all things being cheap not for reall plenty , but by reason of the seller's exigence ; and if usury still oppresse industrie , farming and handicrafts must naturally decline : and if the usurer , having thus oppressed the poor , do likewise reproach them ; he seems to speak in pharaohs proper dialect . t. m. who can but admire , that whilst our poor are thus lazy , wastful , and disorderly ; the dutch and walloons , who live under the same laws , should notwithstanding , by some innate vertue , or peculiar rules of their own , preserve themselves in their ancient simplicity , and be so remarkably industrious ? t. c. no man need admire it , if he will but consider , what they were from their first arrival here , viz. a choyce band of people , who being famous artificers , bringing good stocks with them , and forsaking their country for their conscience , gave indeed abundant proof of their integrity and innate vertue , which they have derived to their posterity ; who , ( as you rightly note , ) still observe certain peculiar rules of their own ; the chief whereof are , that they dread borrowing , cherish industrie , hate oppression and discord , provide liberally for their reall poor , and preferre honest labour and trade before usury , though more easy , and perhaps more profitable ; which gods blessing will always attend . t. m. our fathers could count one two and three , and some of them pay ten per cent. for mony , and had sons and daughters too to provide for , and yet suffered thriving timber to stand to its full growth , &c. t. c. i could alledge another manner of reason , then you dream of for the standing of timber to full growth in our fathers time , viz. their general abhorrence of multiplying mony by mony , now so current and orthodox ; witness the statute 13. elizabeth which in its preamble recites , that all usury , being against the law of god is sinful and detestable , thereby convincing us of the sense of that age ; as also the act 21. iacobi , which foreseeing , what perverse use might be , made of their limitation , by construing it to an allowance of usury , notably provides against the mistake ; but i will admit , the inconsiderable value of their timber , at least in places remote from market , must needs have been a second motive , ( proper for such as then owed or wanted mony ) to let it stand : otherwise , if our fathers could have had tolerable prizes for their timber , and yet would either pay ten per cent. or decline the receiving it with a safe conscience , i durst , without irreverence to them , pronounce , that they could not count one , two and three . t. m. can we well hope , that any thing but severe laws can make half the nation wise in this particular ? &c. t. c. the only laws , in this and most other cases , are those of encouragement ; those of compulsion , by experience , signifie little ; and what encouragement so manifest , as abating usury ? t. m. i say this course , ( forementioned , ) or the like , being duely observed , would bring mutual benefit to the commonwealth and planter . t. c. believe me , sir , the planters benefit is not so clear as you surmise ; for to the planting of groves , i take it , more is required , then the bare notion , or written direction , viz. chargeable fencing , losse of rent , constant residence , perfect leisure , and long forbearance , with allowance , not withstanding , for dammage , so as , it seems to be the proper work only of rich and contemplative men ; wherefore you might for the present have reserved your good rules , till we be in somewhat a a better condition of planting , or , at least , of preserving what we plant , by abating usury and delivering us from the bondage of debt , which will either intercept or interrupt most improvements of this nature . t. m. what improvident actions , ( besides the calamities of the late ill times , ) have contracted great debts upon many of our gentry , is too apparent to be covered with figleaves , &c. t. c. methinks , sir , i cannot better resemble most of your arguments upon this subject , then to the sentence of a country doctour , who , in a visit to his patient , dying of the stone , gravely pronounced , that if he could pisse freely , he might doe well , or to the right witty prevention of vomiting at sea by holding a large peble in the mouth : for , when we demand a remedy to our present incumbrance and embasement of land and rents , you bid us look better to the decay of our manufacture , and exporting our coyne : you recommend to us the reforming our luxury and avoyding idleness , you tell the gentleman , he must get and keep out of debt , reside in the country , plant groves and orchards , and read seneca ; the labourer you direct to be always at work , and accept such wages , as his master may afford to give ; the vagabond you admonish to keep at his home , or , if he have none , to get one , to mend his manners , and be a better commonwealthsman , then he hath hitherto been ; why do you not likewise chide the farmer ; because , in truth , his farme is understocked , ill fenced , and out of heart ? seriously , your discourse is very charming , the beasts and trees , one would think , should again dance to such a pipe : now , for the party here accused , viz. the gentleman , you advise him to sell timely , he entreats you to purchase fairely , for unlesse you will buy , he cannot sell ; he protests , he offers you almost half under value , and makes it his chief business in this world to sollicite you ; but you sleightingly tell him , land stinks of taxes nothing , is sweet but mony ; thus you wish him to keep close at home , but will you suffer him there to stay ? live he should within compasse , it must be a very narrow compasse , if it be your reversion , you will teach him to play the epicure , you will reform him with a witness , before you leave him ; by all means , he must plant , but is it not that you may gather ? surely , sir , you speak all this while ironically , for when you list to be a little more serious , you have other language within call , you can tell us , page 2. of borrowing to keep out of prison ; of 1500. per annum brought to a trifle without ill husbandry , page 10. of hazards by tenants , paying taxes of all sorts for what is really none of his , being a sort of bayliffe to the savage usurer , page 36. of keeping up interest in terrorem , page 40. you can , i presume , pronounce of a person greatly incumbred , as of one that hath plague-tokens ; nay you can foresee ruine upon its march in a great estate , ( once dipped as you terme it , ) at ten , perhaps twenty years distance without present sale , be the owner never so provident ; you require vast mortgages , and other dayly new invented securities , to borrowers as paenal as usury it self : the fact therefore , i am sure , you too well know , give me leave to acquaint you with the cause ( since those you offer are but accidents ; ) a poor man that had a very sore leg , shewd ' it the chirurgeon , and mournfully asked him , if it must not be cut off , to which he pleasantly replied , that trouble , perhaps , might be saved , let it alone for a while longer , and lay but diaculum to it , it will soon enough rot off without more adoe : such surgery , me-thinks , is the best you can here afford , viz. trivial cheap , but therefore destructive to us , who , i take it , want effectual means ; for incumbrance is to the commonwealth an ulcer , deeply rooted in a viciated habit , fed by a rebellious humour , viz. usury , with its accomplices , unequal burthens ; conquer or tame this humour , the ulcer heals ; but plasters shall never mitigate , diet shall never alone correct it ; having once got this head , it is too proud and stubborn for any thing but cauteries , and radical courses ; else it will need no other inflammation then its own to fester and spread . crescit , indulgens sibi , dirus hydrops , nec sitim pellit , nisi causa morbi fugerit venis , & aquosus albo corpore languor . t. m. sure i am , nothing more argues a nation ripe for destruction , then . intemperance , corruption of manners , and exorbitancy of expence in all degrees of men , &c. t. c. if you will , indeed , reclayme our extravagants , begin with the usurer , 't is he that needs your moralls ; he is the captain of our banditti ; reduce him , and they will soon disband for want of a head ; his life is a state of outlawry , no man , like him , persists in defiance of authority ; lay what taxes you please , be they never so just , necessary , and clearly imposed , he laughes and tells you to your face , hee 'l not pay a groat : taxe usurers , in good time , taxe princes ! all the other brood you mention are but the litter and spawn of this venemous beast or serpent ; pardon the expression , i only borrow it from the parliament of paris . you will say , this is very odd , indeed , to arraigne usurers for excesse ; but , alas ! all our madness is not in bedlam , nor all our riot in tavernes : there is a more grave and dangerous debauch , whose thrift is the kingdoms prodigality : i have heard of a plain country fellow in a great house at christmasse ▪ who being made drunk for spor● , and disgorging , called the butler , and sold him , see , see now , what you have done ; let the countryman be who you please , the butler , i am sure , is the usurer , well known by his box . t. m. have we our selves been sensible of improvements of land in purchase , proportionable to the several retrenchments of vsury ? t. c. ask the parliament now sitting , they tell you , our improvements of land are visible ; whether sensible then , or no , do you consider . t. m. when mony was at ten per cent. land was worth , ( as several discreet and aged persons informe me , ) 15 or 16 years purchase , &c. t. c. this i affirm to be a bold mistake , and prove my averment , 1. from the ballance of land and interest , which never fayls but to the prejudice of land in bad times ; 2. from the plain recital of the act 21. iacobi declaring then a fall of land , even below its due proportion , as the natural effect of high interest ; 3 from the testimony of my father , dedicating his tract to that parliament , wherein he sate , and avowing twelve years purchase , then not controuled , and sure , not modestly to be questioned fifty years after : but i see you are one of those deaf men i mentioned , that hear only what you list . t. m. when mony was at eight per cent. ( being the time of our greatest prosperity ) land yielded but 17 or 18 years purchase , and not frequently 20 , &c. t. c. surely a faire rise in so short a period , being but 13 or 14. years inclusive at most , for about the year 1637. i take it , began our scotish commotions , which might reasonably check its progresse , ( as my father in his second treatise insinuates they did , ) for civil war and usury are closer confederates , then you are aware of , and both sworn enemies to the land : 't was multis utile bellum that succoured his friend at a dead lift , and enabled him thus to trample upon freeholders and farmers ; high interest and free-quarter , me thinks , are first cousins . t. m. but now by our unhappy expence of forraigne growths and manufactures , over and above our native commodities exported , and a succession of taxes , great and heavy like the waves of the sea are not our land-lords in debt , many borrowers and few lenders , and land fallen to 16 or 17 years purchase , where t is like to continue , for ought i see , ( though interest were reduced ) till we have more mony , fewer borrowers , and lesse land to sell : for if subduing interest would have done the desired feat , 't is strange to me , that falling from ten to six per cent. which is almost one half , should not appear ere now so visibly , as to stop the mouths of all gainsayers . t. c. nothing will stop the mouths of some gainsayers ; yet to stop all mouths but those that gape on purpose , ( as usurers , we observe , do , and that very wide , ) i will not referre you to your self for an answer , though well i might , for surely your question amounts but to this , how come our land-lords ; having been so long and grievously opprest ; to be so deeply incumbred ? neither will i barely thank you for so strongly and pertinently urging my arguments for me , but will likewise , in requital , set you on your way , which it seems , you have lost by a fog : you alledge , that there are many borrowers and few lenders , but is there not , say i , as much lent as borrowed ? is there a borrower without a lender ? and might not our lenders , ( who , it appeares , are great ones , being few to many borrowers , ) soon become purchasers , if , ( as the phrase is , ) they were free ? and is not the pinching of usury in rate and taxes the readiest way to make them free , that is forward to purchase ? and may not such forwardnesse of theirs make borrowers likewise free , that is , able to sell at tollerable prices , for the payment of their debts , which now , it is certain , they cannot ? and may not such sales and payments soon clear and contract the number of debts and debtours ? and will not such clearing of debts in time make few exigents ? and will not few exigents make sellers thin ? and will not the thinnesse of sellers , even by your own confession marvellously rayse land ? you reproach us with the present fall of land in purchase , but doth not your tenant paying you 75 pound in mony , and 25 pound in lawful bills , reckon that he pays you 100 pound per annum ? and do you not believe his account ? and have not most usurers treated and purchased accordingly ? and doth not this , by your own allowance come pretty neer my account ? and is it not much , that it should still do so , considering the extremities of some , and moderation of others ? you object the expence of forraine commodities above our own exportation , but have not land-taxes : ( the usurers darling , however you now exclaim against them , for old friends may sometimes wrangle , and shake hands again , ) dispatched many of our freeholders and farmouts half undone by the war ? and hath not their ruine made much of our land lie waste , and more be ill husbanded ? and must not such waste miserably impair and decay our growth ? and must not such decay starve our exportation ? and may not trade so founded easily exceed in its importation ? shew me , if you can , the weaknesse of these chaines . t. m. none will lend at three or four per cent. but upon some other speciall consideration , &c. t. c. too many , i doubt , will still lend at four per cent. as well for the rents reserved , and thereby secured , as also for divers other good causes and considerations ; the chief whereof , i suppose , will be , that they can no other way , for the present , get so much , so easily , safely , and to them conveniently , yet more , 't is hoped , will purchase , which i take for much the wholsomest kind of loane , wishing that usurers thought so too . t. m. must not trade , ( to the infinite losse of the nation , ) be hereby engrossed by a few , who have prodigious summes at command , to the excluding of small-stocked traders , and young beginners with little money ? t. c. you are still for pedlers and higlers , the usurers cattle , whom he milkes almost dayly , and at last must eat them lean , ( for fat they can never be , ) i am for the worshipfull trader , even the usurer himself , that hath stock to cope with a fleming viz. those prodigious summes at command or interest , ( so i take your meaning ) which , methinks , i had rather see generously employ'd in forraign conquests , then , like intestine warre , eating our own bowells , and praying on our vitals : as for the engrossing of trade , that is , indeed , your wisest argument , for have you not noted all along , how trade was dispersed by high interest , but , engrossed by lower ? and may not i observe , how the builders tongues are confounded ? nine in ten of your brethren , at least , your sages objecting , ( directly in your teeth ) the inevitable growth of a mechanick trade , ( as they call it ) meaning thereby , i suppose , a trade , not so profitable , as some of them now possesse , nor so easy , lordly , and secure , as the present rate of u sury . having hitherto shewn , how little your generall invectives against our luxury , and other reigning vices signifie to your purpose , i shall now , ( with lesse noyse , but i hope more evidence ) turn your own weapons against you , by proving , that abatement of usury is , in its own nature , the greatest sumptuary law , perhaps the only effectuall one , that policy , with justice can contrive ; therefore , no doubt , recommended by god himself to his own people ; therefore , by the wisest of common-wealths , both antient and modern , layd as the very corner-stone of their fabrick ; therefore , by king henry the fourth of france , a prince of vast experience , after the desolations of civil warre , aptly chosen , both for a restorative of past , and antidote against future distempers ; therefore , by that politick emperour tiberius approved , who , though he justly sleighted the pedantick notion of reforming popular excesse by coercive lawes , ( as appeares by his notable speech to the senate upon that subject ) yet , as a main provision for publick security and good order , from his own treasury , erected a bank for noble romans , of declining fortune , ( though of the patrician faction ) to borrow for divers years without paying interest ; by that single act , redeeming in great measure the scandals of his tyranny ; finally therefore , by most familiar proofes , asserted ; for who sees not that the excesses of this , and indeed every state , are fed by three plentifull and indulgent nurses , viz. drooping debtours , easy gainers , and impotent vagrants ? the first of these , ( like those that project to live but from hand to mouth ) loathing to day , and fearing to morrow , resign themselves to dissolute habits , that so they may forget those miseries which they cannot prevent , and be in part revenged on disaster by sleighting it , perhaps they judge it nor altogether unreasonable for them to partake with an oppressour in their own spoyls , as persons unhappily matched , sometimes think it just to share with their licentious mates : the second , ( wallowing in their superfluity , through an unweildy stock managed to certain profit with little burthen or trouble , whilst their betters carke and droop ) neigh and praunce , like high-fed horses , and by the old proverbe , light come , light go , care not what they squander , perhaps at dice , because their very sheepes tayles , they think will pay the reckoning , be it what it will ; and though this character may not fit the usurer himself ( who seldom revels but wisely , and at the borrowers charge ) yet his executor , possessing an estate , with a curse appendant , without proportion to his quality and breeding , oft-times consumes it as dissolutely as his ancestour shrewdly got it : the third and most general , finding vertuous courses servile and unprofitable , and nothing sweet but summes usuniously improved , which they want , and see not how to compasse , first turne tayle to industry , and then meeting with common frailty in the ● , fill up the measure of our disorders : now whither a convenient corrosive applied to usury may not , with allowance for humane drosse , by relieving the first , retrenching the second , and employing the third , probably in time , reclaym and refine them all , i leave to found and impartial judgments . t. m. why doe you taxe high interest with injustice and oppression though the law tolerate it ? t. c. high interest , i take it , is a terme of scandalous sound , equivalent to that of excessive or biting usury , which no man that owned conscience had ever yet the face of brasse to defend : even for common and general rates , give me leave again to tell you , you still abound in your wilfull mistake of limitation for toleration ; since no assembly of christians , that deserved the name , or had the face of a church , ( no not heretical ) ever gave usury the least approbation , other then their silence , finding , perhaps , the sons of zerviah too hard for them ; no christian authority that i have heard of , popular , or despotick , ever allowed it a current stamp : mahomet himself hath prohibited it . t. m. i dare avow , that since vsury became so tame , we have two gentlemen in debt for one that was before , &c. t. c. i durst referre it even to the usurer himself , if i had any hope he would speak out , whether interest be now a tame beast ; and whether , betwixt its bear-like rage , and fox-like wiles , it hath not been of late more savage then ever : whither , if it had continued at ten or eight per cent. it would not , long ere this , have strewd our highwayes with carkasses ; and whither already it have not so sufficiently worried us , that it needs no longer be upheld for a bugbeare . t. m. is not this to robbe peter to pay paul , and as bad as stealing sheepe , and giving the trotters to the poor for gods sake ? &c. t. c. boast nor too loud of this spanish proverb , at least , be not so fond of it , as to bring it in by the head and shoulders ; for , to my knowledge , it is one of the best and aptest similitudes commonly used to check the arrogance of usurers in their pretended almes . t. m. sir francis bacon saith , it is a vanity to conceive ; that there would be borrowing without profit , that is , a proportionable reward for the disservice the lender oft-times gives himself , and hazard he runs . t. c. were sir francis bacon now living , i verily believe , he would grant three or four per cent. to be no incompetent reward for loans in general : 't is true , in respect of ten , the rate wherewith he was acquainted , it seems a trifle ; but nothing upon earth is great or small , save in comparison , as the dogge is a dwarfe to an oxe , but to the mouse a monster : in pagan kingdomes , where weekly or monthly encrease is usually exacted , any thing per cent. would perhaps be counted moderate ; in colonies and new plantations , where neither the situation and commerce of the place , nor quality of the inhabitants affords security or credit , fifteen , nay twenty and thirty per cent. hath been current ; and he that so trusted , was reputed charitable , ( as charity there went ) though it beggered them all : in tributary provinces , and mis-governed countries , or remote from traffick or sun-shine , exigence it self almost commands high rates ; neither , indeed is it much material in some of them , what the rates be , where nature scarce admits of any improvement , or employment , but for mean stocks : in england , about sixty or eighty yeares since , trade was in its early non-age , traders were few , builders , planters , and improvers thinne , and small competition we had with our neighbours , whereby the returns of stock must needs be generally large , even liberally to reward any tolerable interest ; but now to argue upon that principle , were a paradoxe , like that of maintaining the antient rates of purveyance , statute , ( or as my author judiciously propounds ) stinted wages ; for , i take it , the reason of varying them from time to time , is the same through out , with this single , yet notable diversity , that as all other things advance , usury must abate ; upon which account , i verily hope , or rather doubt not , but that ( with gods blessing ) the next generation may judge even four per cent. an extravagant rate for money . t. m. the vsurer sayes , rather then venture at three or four per cent. he will keep his money , and once in a year get more by lurching , &c. t. c. see my mistake ! i took the usurer for an orphane , an impotent person , at least a very harmlesse fellow , till you proclaymed him , at need , an errand lurcher . well! it seems , he is a good man , and a fair gamester , that he should not all this while , so much as think of his tricks , till he was put to his trumpes : but let him take his course , your own author , sir francis bacon acquaints us , that bigge words and menaces are the constant marks of imbecillity , and we all know the great usurer too wise to play much , or commonly , at that game , for fear of mischief ; yet to do him perfect right beyond any future cavill or exception , i shall fairly examine , upon what ground of reason and justice he sleights the benefit of four per cent : the usurer , you say , thinks that profit too small , but is not rather his eye too bigge ? i affirm , it is still great , perhaps excessive and offer to prove it by all the measures of square and honest gain , whither you will consider his title , his stock , his pains , his skill , or compare him with others ; his title is meerly advantage taken of his brothers exigence ; his stock , ( sever it from his farm ) scarce equals a barbers , or indeed a rat-catchers , his agents and servants being all maintain'd by others ; his skill comes short of a fidlers or juglers , minors and ideots being free of the company ; his pains doe not much exceed the vagabonds or gypsies he so upbraids : now to compare him with his neighbours , who , one would think might somewhat better mer from their country ; his neighbours , i suppose , are freehc●ders , farmers , and traders ; for freeholders you tell us almost in every page , what their profit is , for you wonder they are so mad to borrow , you advise them at their peril to sell upon any terms , and you deride their imaginary improvements : of farmers , i think i need not offer a syllable , res ipsa loquitur ; we are then reduced to traders , who are of two sorts , forraign and domestick ; the domestick , being shopkeepers and artificers , depending on the casualty of vent or custom , have a benefit so contingent , as no rule concerning them can well be framed , nor other observation made , then this in generall , that some indeed thrive , and many fayl , even of those that set up with their own stocks , but still were borrowers : forraign traders are either in those few trades , which we naturally or politically engrosse , or those many , wherein we intercommon with the dutch and others ; the former indeed , i suppose , may oft-times yeild good returns to the merchant ; but neither is their foundation very large , nor , perhaps altogether so found as to build our fortune , on them : in the latter , being of more vast and solid advantage and behoof , the present rate of interest must of necessity , as to many of them , wholy exclude , in all , so encounter and curbe us , that we cannot expect any cheerfull progresse , or otherwise than to truckle under the hollander , a trade , whose benefit is not , ( one would think ) very hard to calculate : whence then is our usurers lofty pretence , or but colourable claim even to four per cent. t. m. few will sit down so contented , having been used to greater profit , but will rush upon several projects and undertakings , which , for want of skill to manage , may redound to the equall prejudice both of themselves and the commonwealth . t. c. sure i think , i may now sing nunc dimittas , for i have lived to hear the usurer talk of projects and undertakings too ; his businesse hitherto hath been only to sit warm , and unconcerned , applaud his own happy conduct , for thriving with such ease ; censure and deride the tenant for taking such pains to be undone , the landlord for not falling near half of his rent , and consequently his inheritance , but trying the most probable conclusions he could think on , to make it ; in some measure good to him , and venturing to turn farmer of his land himself , upon meer constraint , rather then let it to the growes ; the stander by , it seems , could then see more then the gamester ; but four per cent. belike , 2 little alters the case , and infuses such metal into a roguish usurer ▪ poor wretch , that all on the sudden he is on fire , and a perfect knight-errant , for what would you expect more of don quixot himself , then to rush upon projects and undertakings ? well sir , 't is the best thing said in your book : turn him loose , say i , he is throughly fledged , having got , god be thanked , store of feathers upon his back ; and the common-wealth , i dare say , will freely venture her share in his flight . t. m. is not the greatest part of trade driven by young men with small stocks ? t. c. i hope , sir , you mean the costardmongers trade , or the poor fishermans before mentioned ; sure i am , if our principal trade be so driven , it is high time to reduce usury , to some purpose , and call in to our rescue the prodigious summes you boast of ; neither will i pretend to urge a greater argument for the restraint of it , then you have here contrived : but our comfort is , the usurer now understands trade too well to trust the trader upon meer credit , or with a small stock , very farre . t. m. is not your answer to widowes and orphanes very harsh and churlish ? t. c. really , i much marvel you should think so ; for first i tell them of other widows and orphanes mainly concerned in land , who , by the uneasie rates of interest and taxes now receive prejudice , at least equal to the benefit of these ; secondly i mention a numerous train of unhappy but honest borrowers , perhaps no lesse worthy of support then themselves , who , by the same pressures have been , and are dayly almost ruined ; these , being evidently relievable by restraint of usury , i desire may likewise be considered , and put into the counterscale : thirdly , i conjure them to deal as they would be dealt with , ( a hard lesson , i know , for any oppressour to learn , ) in not exacting from their borrowers , that which i calmly say they cannot afford , or which my authour himself , in other language , ( perhaps , more effectual and peremptory , ) often affirms , must ruine at least all our borrowing land-lords to give . but wholy to silence the rage of these masked usurers , who exclaim as if christianity were expiring , when usury only is reducing , i shall distinguish the plaintiffs into two ranks , viz. truly impotent and intelligent ; for the truly impotent , or infants and orphanes properly so called , i offer these considerations . 1. that they are certainly beholden to the several falls of interest for their present ample provision , which is much better even at four per cent. ( all things computed , ) then those of their rank , generally , enjoyed at ten . 2. the orphanes of london , ( who , by reason of their assurance , fare , i suppose the best of any , ) complain not much of that rate . 3. abatement of their profit will certainly facilitate and improve security for other orphanes , and may so turn to better account . 4. by raysing the value of land , their fellow orphanes , the children of loyal and worthy parents , ( for number and quality , perhaps more considerable , ) may be likewise provided for , who otherwise can never look for portions , at least , to their degrees : the intelligent i fairly admonish , to save their stakes by purchasing betimes , which , in mortgages , where the title hath been scanned , were , methinks , an easie exchange : this , i hope , is no such cruel hardship , or dangerous doctrine ; for though some doctours hold usury to be consistent with good conscience , yet few , that i have heard of , maintain it necessary to good life : and further to prove it most reasonable , thus i argue ; either the rents of land do now competently ballance the interest of mony , or they do not ; if not , where is their justice ? if they do , where is their prejudice ? besides , i am directed by an honest gentleman and their special advocate , one mr. manly , to acquaint them , that five pounds five shillings a year in land once surely settled , whereby they shall only venture their rent , which is commonly secured by stock upon the ground , is better then a hundred pounds in mony at six per cent. sometimes tumbled and tossed at usury like a ship in a tempest , and utterly lost , and sometimes remayning uselesse by them , like a vessel becalmed : if now they will not be ruled by their best friends , what hope is there say i of persons so refractory and self conceited ? in case their genius be not for land , let them trie the seas in forraign trade ; if they can be brought neither to fancy the land , nor trust the sea , let them build granaries , to deal for grain and other commodities in cheap times , and keep them for better markets , and with as much ease , as a usurers heart would wish , sometimes double their stock , so employ'd ; or let them advance our national manufactures with clean hands , and no doubt with competent gain : if nothing but usury will content them , tell them from me , i smell an evil savour , and that it were great pity , but they were pinched in their superfluous , and ( to the commonwealth ) every way pernicious revenue . t. m. is not interest with us the lowest by law in europe ? t. c. i verily believe , there is no law in europe for interest , save only the law of restraint , which you are pleased still to misconstrue for licence ; but i apprehend you , sir , you would have us stay , till usury reduce it self without law : very fine ! you maime us , throw us into a deep ditch , and crie , god help you . t. m. will you or any other land-lord sink his rent , because his tenants complain of hard pennyworths ? t. c. are not usurers ever the first to reproach gentlemen at least with folly , for not sinking their rents , if they but seem too dear for the land ? are not all land-lords even now upon abatement , and glad at any rates to get tenants , though surely not so sufficient as yours ? do they not freely discount for taxes and extraordinary burthens ? and do not all good land lords allow for bad times , nay even for very bad years ? i tell you , sir , i ever did , shall , nay , at my peril , must sink my rent , if the tenant produce but the tithe of those reasons , which most borrowers now may : for though i shall never admit , that letting of land is usury , yet will i not deny , that racking of rents , and taking extreme advantage of strict covenants is extortion : and yet by the way , i must note , that the worst of land-lords will find it a harder matter thus to extort , then the best of usurers doth , the trade of letting land not being driven in the dark ; and there being , i take it , no procurement , continuance , double mort-gages , or treble bands-men in his case to be got ; nor other probable security , then barely the penny-worth , but the markets of land being free and open , and the values , to a trifle , publickly known and allowed . t. m. that trade will regularly bear present interest , who hath not observed , that the careful managers thereof have had a thriving time of it ? t. c. that trade will not regularly bear present interest , who hath not observed , that the carefullest managers thereof , ( if borrowers , ) have been eaten out and undone ? and that our old foxes are so well aware of it , as to preferre english mutton before outlandish venison ? however the main stresse of this argument , i must tell you , lies upon land , for surely few but land-lords either do , or , now , can borrow considerably : to land therefore the fall and taxing of usury is most indispensably just and necessary ; to trade , undeniably wholsome and profitable . t. m. as for idlenesse sucking the brests of industrie , 't is no mor applicable to lending mony upon a valuable consideration to them , who by industrie and skill live thereon , then to my land-lords hiring his farm to the laborious husbandman , &c. t. c. when you produce me any one text of scripture , church-canon , or christian sect , that deserves a civil name , disallowing the rents of land , or any one temporal law restraining them , your bold assertion shall be considered : i , on the other side , offer to prove , that the laws of this and many countries , ( how tender soever they were of propriety and freehold , as indeed it concerned them to be , ) have , as they saw occasion , from time to time , retrenched usury without scruple , or saying so much as , by your leave , mr. usurer ; which , ( notwithstanding your categorical thesis , ) shrewdly argues , that the justice and title of them hath not been reputed altogether the same ; nor doth the usurer himself , i suppose , pretend to be our lawful land-lord , for then he would be readier to keep hospitality , serve upon enquests , find armes , repayre churches , and pay taxes , then of late , methinks , he hath been . t. m. is it reasonable to imagine , that all men are of equal brains or education to traffick in one sort or other ? &c. t. c. you will prove anon , that borrowers have more brains , then lenders , though formerly you told them , in effect , that if they had any brains at all , they would not be borrowers : truly 't is a comfort still , thus to be cajoul'd into our ruine ; and that though we find our selves the poor , yet an oracle , it seems , hath pronounced us the wiser : sure , apollo was of another mind , when he made my alderman his laureat ; nor doth six per cent. i take it , much glory in the improvement of his sons knowledge and experience , when he runs out , and borrowes ; nor would any sneaking usurer , i suppose , like to be taken at his word , and have a guardian by the king assigned him , which methinks , were a charitable work , he having so slender a capacity with so fair an estate ; in which case , land-lords are of course , provided for ; but , alas , too sure it is , that when a usurer is made , there is commonly as good a merchant marred , as most that walk the exchange . t. m. the present interest , ( admitting much were borrowed , ) can be no just scare-crow to the builders , since all builders i have yet met with , may have eight , nine , or ten per cent. and very good rents for their ground besides . t. c. i rejoyce at your good news , though it be yet early day : but give me leave , sir , from thence to observe , how signally trade having groaned under few or no new burthens , hath thriven and flourished , even in uncertain times , since the last fall of usury ; whilst the land is even sinking under the load of its chayns ; for , ( not accounting losses and hazards , which perhaps would deserve other-like ensurence then your mony , ) three per cent. i must tell you , goes farre with us in the country . t. m. he that employes his own mony , matters not much , whether it be six or four . t. c. quoth the good huswife , we have all provisions of our own , and a figge for the market , sure , it were happy for england , if usurers were in all their affayrs so indifferent . t. m. it is a contradiction , that many lenders and low interest live together in a declining commonwealth . t. c. you say very right , a contradiction there is throughout , for where low interest is , the state can scarce naturally decline , nor will there need much lending . t. m. for the credit of six per cent. i will appeal to all the world , if the rebuilding of london goes not on much faster then could be reasonably imagined . t. c. for the credit of former abatements , you should say , and encouragement of future . t. m. what pity is it , i must conclude , that having examined , and found how little likelyhood there is , that subduing interest will encrease the fruit and revenue of the kingdom , we have small reason to hope , it will augment the revenue of the king. t. c. land will certainly be improved by it , if we may believe either reason , experience , or authority ; and , i suppose , what is good for the land , is not bad for the land-lord ; trade will evidently be augmented by the instance of most flourishing commonwealths , which have ever begun with it , and the proverb tells us , what is sawce for a goose , is sawce for a gander . t. m. your expression of land being in safe hands seems very odd and dividing . t. c. it is , i am sure , no new maxime , that the crown , ( without competition of title ) ever was , and probably would be safe in the majority of landlords ; neither did , i suppose , our late experience disprove it : doubtlesse in distracted times , they have most at stake , and lie most to pawn : usurers and pyrates are own countrey-men . the pretended mischiefs briefly examined . t. m. low interest will draw the treasure of the nation into a few hands , and endanger the hoarding up of the same , &c. t. c. yes indeed sir , money is dangerously hoarded in holland , is it not ? the usurer , i must tell you , thankes god , he never did , nor shall willfully bury his talent in that sense . t. m. it will necessitate active young men with small stocks , ( who are the best merchants ) to sell their goods at great losse , because they cannot stay for the best market . t. c. what an errour was that of mine to think , that old experienced men with great stocks were the best merchants ? they , it seems , were ordained still to be usurers ; but what will you now say , if four per cent should even disappoint their fate ? t. m. it will expose an infinite number of widowes , orphanés , and other impotent persons to great want and extremity . t. c. i remember oft to have seen a picture full of strange sights , very odd and uncouth to behold , viz. the horse riding the man , the lawyer feeing the client , the mouse devouring the cat , &c. 't is pitty , say i , that of the borrower oppressing the usurer hath not yet been added ; for if four per cent. should suddenly passe , some think , it may come too late . t. m. it will encourage our gentry to run in debt , by making most of them bolder in borrowing , ( if any one will lend . ) t. c. 't is a comfort to hear you make an if of it already ; methinkes you begin to relent and come to , as if you would have us hope , or not altogether despayr : but surely , sir , you are in very good jest , and will shortly perswade a man that hath the french disease , to reject his present cure , for fear of future claps . t. m. it will oblige the nobility and gentry to provide greater portions for their younger children . t. c. yes , and enable them too , i hope , after such provision , to leave better estates to their eldest sons . t. m. it will introduce a thousand tricks among the rank usur●rs , brokers , and scriveners , whereby the hasty borrower shall be indirectly wormed out of more money , then when interest was at eight per cent ? t. c. i doubt , they must pump hard for new ones : but hold a while , say i , rayse but the intrinseal value of our lands , and let them doe their worst ; double our security , and a fig for his empty threats : for if once the divel were dead , we should not , i suppose , much regard jackadandy . t. m. was not this worshipfull brat of low interest begot in the crafty noddle of a great moneyed man ? &c. t. c. that were , indeed , a mighty project , much like its opposite of raysing usury for the borrowers case , maintain'd by some of our discretest debtours : but the right usurer , i take it , is not for merit or pennance , and therefore sure would not mangle his own flesh . t. m. it will cause the dutch to withdraw their money from us to the great stop of trade . t. c. tell me the story of eighty eight ; alas ! that , god be thanked , was long since done to our hands by the fall of interest to six per cent. yet , it seemes , the old mumpsimus runs still in some of our noddles ; well! since you have such a love to forraign chink , by all means , let interest be raysed to eight per cent. for a year , to decoy some strangers money , and then seise it as a deodand or stray ; for under , i assure you , it will not come , if then : now pray sir , doe you not observe , what a desperate stop of trade we have ever since ? was it not a foul mistake of our good friend mr. manly so to extoll the riches of london page 43. or have you the confidence still to maintain , that we have yet a million of dutch money , because you find it easy to affirm , and think it hard to disprove ? consider , i beseech you , whither the present difference of our rates could in reason tempt any sober dutch-man , ( not reckoning factorage ) to run so many risques as he must doe ; since besides the general hazards here , which you declare equall to an east-india voyage , and worrhy of 30 s. per 100 pound ensurance even amongst our selves , he must likewise trust the sufficiency and integrity of his own agent , in a degree to dutch-men and usurers very uneasy : but i am too serious for the subject ; the very notion of trade , ( for any bulk of it ) driven at interest , is abominable , whither the loan be forrain or domestick , with this graduall difference ; that the one amounts to a ruinous tribute , the other to a dangerous impost . t. m. men will not quickly borrow at the intended rate , nor willingly sell their concernments , on reasonable terms , to such as have money , and so the building of london will be retarded . t. c. hath not the wisdom of the law provided at least against such willfull defaulters , by a forfeiture and lapse of time , perfixed ? and if building be so generally profitable , as you suppose , will any man , in case of disability , obstinately incurre it by not selling ? nay will he not make hard shift to borrow upon security , which , i must tell you , is that which only , ever did , and ever shall command money ? something you would fain object , if you knew what . t. m. the gentry , who shall be in debt at the passing of such a law , will be exposed to many and great exigents ; before they shall get clear of their creditours , it being ten to one the debtours estates will become so many sacrifices , ere any man will be found to come in to their rescue , though chancery , or the intended act should allow them a considerable time for redemption ; so that , i dare affirme , this nation never saw such seisures , arrests , extents , executions , &c. as will infallibly follow upon passing such a law , &c. t. c. is it not the known device of cruell and insulting pedants , to threaten their innocent and awfull fry with severe correction , if they tell tales out of school ? is it not the proper language of orthodoxe goalers to scare their prisoners with gibets or dungeons , if they offer to attempt an escape ? even so , methinkes , doth the usurer treat his poor vassall and tenant at will , the borrower : if he do but mutter at the perpetual taxes and burthens even of his mortgaged land , without any allowance , the finger or ferula is held up ; sirrah look to your carkasse , or if a member of parliament , the house will one day prorogue . if he presume to dispute the justice or rate of usury , and fainly appeal to his king and country for relief ; hough man ! what ? break prison ? but let the serpent hisse , so his sting be out ; and what is the sting of usury , ( if at least it be nót all sting ) but its disproportionable rate ? i my self have perhaps had my share of these menaces , and more i expect for this freedom of my pen ; but they are musick to me ; for i was never yet , ( i thank god ) so rowted and bereft of judgment , as to distrust my benefit by the fall of interest : and i hope , fear , the betrayer of reason , will not so dazle and benum any of our patriots ( being englishmen , though borrowers ) as not to see and feel their own and the publick concernment in it . and now , sir , i hope , i have in good measure re-asserted all the benefits in my former treatise propounded , by abatement of usury ; and shewn , that your objections and declamations upon the several heads thereof are either reall mistakes , or flourishes and digressions : your appendix concerning the valuation of our coyn i have declined , considering it as forraign to our dispute , and leaving it to be examined , ( as occasion shall require ) by some abler pen-man , more versed in exchange , then i pretend to be : offence , at least personal , i trust , i have given none , looking upon that as a paltry way of arguing : that i answer you under a character , which i am perswaded you abhorre , you will pardon me , in regard i could not otherwise well direct my speech ; you , in the conference , personating the usurer , as i the borrower : other animadversions , or expressions , how keen or resenting soever they be , the bitternesse of my subject will indemnifie . if either you have new matter to alledge ; or can reinforce your former arguments , or shew me any thing material , by me omitted in my reply , i candidly invite you to rejoyn , with promise , upon good evidence on your side , to lay down the buckler , and recant : but if nothing more be offered , save endlesse repetitions and unfriendly cavills , i shall fairly spare my paper , and demurre in judgement . a brief appendix touching the proposal of taxing mony at interest . for a more forcible inducement to this great work of discovering summes at interest , and subjecting them to all manner of publick taxes and burthens , i shall endeavour further to clear the businesse , by shewing , that it is most honest , necessary , and practicable without inconvenience . the justice of it is , methinks , so apparent , that i durst almost referre it to the usurers own conscience , ( and it had need be a very plain matter , ( saith our late reverend bishop sanderson , ) that one would referre to the conscience of an usurer , ) for the question , modestly put , is , i take it , barely this , whether it be reasonable , that one part of the kingdom should constantly bear the burthens of the whole ; to which the ready answer seems to be , that it is , ( in mr. manlies phrase , ) monstrous unequal ; even to such degree , that i might well say , no wonder if it hath not thriven : neither , having been proposed to divers champions of usury , ( to give them their due , ) hath any of them hitherto offered ought against it : only they have gravely demurred ; and therefore i look that time and thought may produce somewhat to disprove , discountenance , or , at least , divert it : for we live in an acute age , which hath much improved the oratours maxime , oportet posse contraria persuadere , by adding , etiam velle : to excite vertue or explode vice is now but a school-boyes theme ; he is , indeed a wit , that argues packing the cards more honourable ( because more ingenious , ) then square play ; can maintain felony better then others can do property , prove the true man robbed the thiefe , and say more , perhaps , for keeping a brothel-house , then i can do for building an almes-house ; thus , since the publishing of my reply , our saviours questioning the sloathful servant , for not putting his talent to the bankers , was mainly urged to convince me of the lawfulnesse and expedience of usury , leaving me to inferre , ( for follow it needs must , ) that usury is necessary to salvation , the party there , ( if you take the literal sense , ) being evidently condemned for not being an usurer ; a clear case , one would think , and past controule : and i expect some or other should shortly start this doctrine , that it is the special duty or priviledge of christians to practise usury , since mahomet hath forbidden it : thus my learned adversary hath in his preface asserted , that an unthrift , drunkard , or whore-master , ( and consequently , no doubt , an oppressour , highway-man , or curpurse , ) may passe for a tolerable commonwealths-man , ( if an englishman born , ) because every penny comes to the natives ; thus he hath convinced us page 2. that there cannot well be a more seasonable almes-deed then an usurious loan ; thus , in the same page , he acquaints us , how the restraint of usury is the defrauding of honest creditours ; that the state , ( at least for shame of the world , ) may not still persist in picking pockets , ( and that with a vengeance , ) as twice , it seems , already they have done ; thus he confidently assures us , page 3. the lender got his mony by great industrie , and thereupon surmises that he lends it to a trader , who certainly gains fifteen per cent. whereas we thought , he had gotten part of it by happy conduct , and lent most of it to a gentleman or farmer , who never makes three , and who , by his own admission , must be thereby undone : thus he possesses us , sect 2. that improvement is , in effect , ridiculous , implying , that it may shortly become a kind of project in the farmer , to dung or fence his farme , because , it seems , the wisest and worthiest improvement is that of interest mony , whereas i took that of land to be the more natural and commendable of the two : thus he blesses himself at raysing the purchase of land by fall of interest , a question , which , i presumed , might soon be determined , ( as to the value of leases , ) by comparing some of our yearly almanacks , made , when mony was at eight per cent. with others , since it came to six : thus he intimates , sect 3. that the stinting of wages would instantly cure us , but the subduing of usury never , whereas i simply imagined , that in the reducing of mony , wages , ( being mony , ) were best reduced , viz. insensibly , without exception or prejudice , nay to vast and universal benefit : thus he admitts , page 18. that wages about london are raysed by meer confederacy , which makes me wonder , the welch , and northern men should not joyn with them , conclude , that , most callings being combined in the same league , catilines conspiracy was not to be mentioned in respect of this , and only comfort my self , that land-lords in the country , for ought i hear , continue loyal , and are not of the plot : thus he makes it appear , page 33. that we want wherewithal to purchase , whereas a classical authour , page 35. makes it likewise appear , that there are prodigious summes at command : and lastly , ( for there is no end of his witty paradoxes , ) thus , with a delicate flourish , page 17. he demonstrates , that the substracting of one third from usury , and adding it to industrie , ( which i took to be greatly important in all undertakings and affairs , ) signifies no more to trade , then the wrens pissing in the ocean . now since all these fundamentals are so cleared and reconciled , who would despaire , that the same , or some other genius of the like sagacity may not henceforth infallibly teach us , that the redresse of our hardships will no more import to the benefit of land , then , belike , the rate of interest doth in manufacture , nay further inform us , that honesty is destructive of commonweal , and equal taxing monstrous unequal ? for the importance , and indeed necessity , of this proposal , hear the late excellent prelate , before cited , in his sermon on the nature of callings , where , having directed three main enquiries , 1. whether the thing be simply and in it self lawful , 2. whether it be lawful so as to be made a calling , 3. whether it will be profitable or rather hurtful to the commonwealth , and shrewdly mated the usurer in the first two , he thus proceeds as to the third article ; but say yet our usurer should escape , at least in the judgment of his own hardened conscience , from both these rules , as from the sword of jehu and hazael , there is yet a third rule , like the sword of elisha to strike him stone dead , and he shall never be able to escape that ; let him shew , wherein his calling is profitable to humane society ; he keeps no hospitality , if he have but a barr'd chest and a strong lock , to keep his god and his scriptures , ( his mammon and his parchments in , ) he hath house-room enough ; he fleeceth many , but cloatheth none ; he biteth and devoureth , but eat●th all his morsels alone ; he giveth not so much as a crumme , no not to his dearest broker or scrivener , only where he biteth , he alloweth them to scratch what they can for themselves : the king , the church , the poor are all wronged by him , and so are all that live near him ; in every common charge , he slippeth the collar , and leaveth the burthen upon those that are lesse able : it were not possible , vsurers should be so bitterly inveighed against by sober heathen writers , so severely censured by civil and canon laws so uniformely condemned by godly fathers and councells , so universally hated by all men of all sorts , and in all ages and countries , as histories and experience manifest they have been and are , if their practise and calling had been any way profitable , and not indeed every way hurtful and incommodious both to private men , and publick societies : if any thing can make a calling unlawful , certainly the vsurers calling cannot be lawful . thus preached that accurate casuist neer fifty years since , when land-taxes , properly so called , were not in being , when the militia was rather an exercise and holyday sport then a burthen , and when our parochial duties were not , i dare say , generally the fourth part in bulk to what they now are ; for my authour himself tell us , page 25. that in his own parish within these five and thirty years , the maintenance of the poor is swelled from six or seven pounds per annum to above an hundred , which is at least sixteen for one , even neer a great road , adjoyning to chatham , and in the very mouth of trade : and in most places of decayed cloathing , it is too well known , the rates for the poor run from three to five shillings in the pound , ( and still , like a creeping soar , they spread , ) wherewith the land is frequently charged , though un-tenanted and un-stocked ; however , if such farms be eased , ( as surely 't is but reason they should , ) still the neighbours are the more oppressed , and so must needs gallop into the same ruine : as for the variety of other rates and duties , the reckoning hath therein been likewise so inflamed , that , by a modest estimate , i cannot judge interest of mony to be fairly endebted to land , upon the balance of our publick burthens , so little as twenty millions principal , since the year 1641. it is therefore high time , at length , to make some hue and cry after that notable goodfellow , which hath so oft , so largely , nay gallantly robbed us ; and if we cannot get him to refund , yet at least to look better to the bottom of the bagge , where his fingers are , methinks , as busie as ever . that it is practicable without inconvenience , to me appeares by this certain measure , that it having been already propounded to many intelligent persons of different byasse , all of which found themselves concern'd , there was never yet any thing moved , which received not its present answer ; neither indeed do i see , what can be colourably objected : for what , i pray , is lesse difficult , then that mortgages being local and fixed , their taxes and duties should attend the estate , and be of course defalked by the debtour , ( to his great ease , ) as well as now by the tenant ? and that the rates of other summes and debts should always follow the person and present habitation of the creditour , even as now , in some small measure , they doe ? if any pretend , it is hard for the creditour to be so paenally compelled to taxe himself ; i answer , what remedy ? since his debtour dares not , for fear of trouble , his neighbours cannot for want of evidence , and himself will not for love of gain ; for should he not , in good conscience , all along have done it without compulsion , at least not have avoyded it by shifts , covenants and threats ? if they plead , mens ability or weakenesse will be thereby discovered , is it not fit , say i , it should ? doth not my adversary himself press for such discovery , page 5 ? but what can this discover ? surely not very many personal debts , and for mortgages , either they are now known , or it is pity they are not : if they alledge , that it is too shrewd for creditours to taxe certainly for uncertain debts , i ask , whether there be almost any gentleman of estate in england , who hath not taxed for land , when either by want of tenants , losse of rents , or divers other charges incident to estates , it hath yielded him little or nothing , and whether all this while the lender have not thought it very just and commodious for the half-ruined borrower , ( even in such extreme cases , ) to pay likewise his taxes , as my authour himself frankly confesses , page 36. but some will yet , perhaps , further object , that there the annual income only is ventured , here the capital : my reply then is , that debts upon personal security are either clearly secured , desperate , or doubtful : of the clear , ( which must needs include all considerable summes , the creditour in great loanes having always divers strings to his bow , ) there can be no question made , those being equivalent to mortgages , and of double value , in point of steady receipt , to the generality of our rents : debts really desperate should , methinks , without more adoe , be quitted , the continuance of their claim serving only to wound charity , molest the insolvent , hurt and disturb the commonwealth by rendring many of its members uselesse , male-content and fit only for mischief ; as for doubtful , ( and therefore hopeful , ) debts , whereof farre the greater number , by reason of suretyships , are finally ensured with a witnesse , do not they who now sue for them effectually , venture a large taxe to atturnies , lawyers , officers and sheriffes ? and why should they grudge the commonwealth its due to preserve their own ? besides they have always , at the worst , their ready amends in their own hand ; for may they not honestly purchase and turn their biting usury into a healing rent , to the just relief of their neighbour , benefit of their country , and quiet of their conscience ? it being now our greatest and most general complaint , that there is so much land upon sale , and so few chapmen , seconded by my authour himself , page 33. which way soever i look , the objections are either frivolous or inconsiderable to our grievance and prospect ; for i dare maintain , that a taxe of three shillings in the pound , indifferently charged , will not now so bite the land by embasing its fund , and consequently cannot finally so much prejudice the state , as a taxe of twelve pence in the pound , partially imposed , must inevitably doe : from whence i inferre , that ( comparing our present condition and rates with the great likelyhood of their future growth , by reason of the dangerous encrease of our neighbours in shipping , ) whosoever argues , that interest of mony should not , or cannot be taxed , in effect , rings his countrys passing-bel ; for it is notorious , that no good plant ever did or can thrive together in the same soyle with usury ; which , ( being thus exempted and cherished , ) infects our land much worse then the sowing it with mustardseed . wherefore , as a fair adieu to the usurer , i shall now take my leave of him with this hearty and christian admonition , that he first pluck the beam , ( of avarice and sordid partiality , ) out of his own eye , and then , perhaps , he may see clearer ( then as yet , methinks , he doth ) to take the more ( of excesse or sloath , ) out of his brothers eye . finis . errata . page 1. line ult . for conclued , r. conclude . pag. 11. line 29. for selling , r. telling . pag. 12. l. 31. for gentleman , r. gentlemen . pag. 13. l. 19. for enlarge a navigation , r. enlarge navigation . pag. 4. l. 20. for broyles , after them ) hath and , r. broyles , and after them ) hath . socius mercatoris: or the merchant's companion: in three parts. the first, being a plain and easie introduction to arithmetick, vulgur and decimal, the extraction of the square and cube roots, with a table of 200 square roots, and their use in the resolution of square equations. the second, a treatise of simple and compound interest and rebate, with two tables for the calculation of the value of leases or annuities, payable quarterly, the one for simple, the other compound interest, at 6 per cent. per annum, with rules for making the like for any other rate. the third, a new and exact way of measuring solids in the form of a prismoid and cylindroid, with the frustums of pyramids and of a cone: whereunto is added, some practical rules and examples for cask-gauging. by john mayne, philo-accomptant. mayne, john, fl. 1673-1675. 1674 approx. 145 kb of xml-encoded text transcribed from 113 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2003-11 (eebo-tcp phase 1). a50425 wing m1484 estc r214155 99826364 99826364 30766 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a50425) transcribed from: (early english books online ; image set 30766) images scanned from microfilm: (early english books, 1641-1700 ; 1764:5) socius mercatoris: or the merchant's companion: in three parts. the first, being a plain and easie introduction to arithmetick, vulgur and decimal, the extraction of the square and cube roots, with a table of 200 square roots, and their use in the resolution of square equations. the second, a treatise of simple and compound interest and rebate, with two tables for the calculation of the value of leases or annuities, payable quarterly, the one for simple, the other compound interest, at 6 per cent. per annum, with rules for making the like for any other rate. the third, a new and exact way of measuring solids in the form of a prismoid and cylindroid, with the frustums of pyramids and of a cone: whereunto is added, some practical rules and examples for cask-gauging. by john mayne, philo-accomptant. mayne, john, fl. 1673-1675. [16], 206, [2] p. printed by w[illiam] g[odbid] for n. crouch, in exchange-alley, over against the royal-exchange in cornhill, london : 1674. "a short treatise of simple & compound interest" and "stereometry" have separate title pages dated 1673; "a new way of gauging the frustum of a pyramid or conical tunn" and "some practical rules & examples for cask-gauging" have half titles; register and pagination are continuous. errata on recto of final leaf. reproduction of the original in the bodleian library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng interest -tables -early works to 1800. interest rates -early works to 1800. 2000-00 tcp assigned for keying and markup 2001-11 spi global keyed and coded from proquest page images 2002-02 tcp staff (oxford) sampled and proofread 2003-04 spi global rekeyed and resubmitted 2003-08 emma (leeson) huber sampled and proofread 2003-08 emma (leeson) huber text and markup reviewed and edited 2003-10 pfs batch review (qc) and xml conversion socius mercatoris : or the merchant's companion : in three parts . the first , being a plain and easie introduction to arithmetick , vulgar and decimal , the extraction of the square and cube roots , with a table of 200 square roots , and their use in the resolution of square equations . the second , a treatise of simple and compound interest and rebate , with two tables for the calculation of the value of leases or annuities , payable quarterly , the one for simple , the other compound interest , at 6 per cent. per annum , with rules for making the like for any other rate . the third , a new and exact way of measuring solids in the form of a prismoid and cylindroid , with the frustums of pyramids and of a cone : whereunto is added , some practical rules and examples for cask-gauging . by john mayne , philo-accomptant . nunquam nimis quod nunquam satis dicitur . sen. london , printed by w g. for n. crouch , in exchange-alley , over against the royal-exchange in cornhill . 1674. to his honoured friend tho. williams , m. d. physician in ordinary to his s. majesty . sir , though the happiness which i formerly enjoyed in your converse , hath been , to my great loss , for some years discontinued ; yet i easily perswade my self , that the favour of a great prince , and the best master in the world , has not wrought such a change upon your even virtue , but that you will still descend to remember him whom you were once pleased to honour with the name of friend . this confidence has embold'ned me to present you with this small trifle ; too mean indeed and trivial for your acceptance , but that i know you are wont to admit of any thing that proceeds from an honest undesigning gratitude . and though i am not at all inclin'd to vanity from the merits of the work it self , yet i am proud that it affords me an opportunity to discover the lasting impressions , which your many favours have made upon my breast . geometry , with arithmetick her woman , are beauties , that having truth written in their foreheads , dare appear in the court of the greatest monarch , and i doubt not but they will find very easie and courteous admittance into your appartment ; where if they shall afford you any divertisement when you return wearied from your ingenious elaboratory , i shall then accompt that i have written to very good purpose . however , they certainly assure you , that it is impossible the teeth of time should obliterate the honourable esteem conserved for you , in the heart of , sir , your most humble servant , iohn mayne . the preface . i shall not trouble thee , reader , nor my self , with a long apology for the publishing this treatise . how demurely soever i should pretend to the contrary , i fear thou wilt still be apt to imagin , that i had a tolerable good opinion of it , before i ventur'd it to the press ; and truly i my self cann't well conceive , how any man should be over ambitious of being publickly laught at . if it be in any measure suited to the general good , ( for which i intended it , ) i may at least expect thy pardon ; but if upon the perusal thou shalt find it otherwise , i ingenuously acknowledge my self to have been mistaken . my design in this work is , to render the rules of those excellent arts , which the title-page pretends to , so plain and obvious , as that they may be easily apprehended without the assistance of a living master . and if there were nothing new in the whole , but the perspicuity of the principles , and easiness of the method ( which out of civility to my self i must deny ) yet those alone are sufficient to vindicate me in this publication ; and i hope thou wilt not be angry , that i am a well-wisher to thy vnderstanding . for when i consider'd , that among the many good books of this nature , that are abroad in the world ( though written by persons of greater knowledge than i dare pretend to ) some were so learned and obscure , as not to be understood , unless by those who have already made a considerable proficiency in these things ; others , so voluminous and prolix that they fright the endeavours of such who cannot spend their whole time this way : i was willing , according to my abilities , to obviate both these inconveniences , and accordingly applied my self to the composure of something , which for its plainness and brevity might be accommodated to those of mean capacities and small leisure ; and this book is the result of those contemplations . whether i have accomplish'd my purpose or no , i make thee the iudge ; requiring only that thou censure impartially of the author and his endeavours , without being offended that he is desirous to do thee a courtesie . i shall not here expatiate in the praise of the arguments i treat of , nor give thee one line of encomium : though out of the great affection i bear to these arts , i find a strange inclination in my self to be rhetorical , yet i am resolv'd not to affront thee ; for truly their usefulness and excellency is so universally known , that to tell thee of it as a new thing , were to suppose thee a person of more than ordinary ignorance ; only ( as i said before ) i must be so civil to my self too , as to inform thee , that ( besides the introduction to arithmetick and the treatise of interest , of which i challenge no more than thou shalt find thy self very willing to give me ) that part which concerns the measuring of solids , viz. the prismoid , cylindroid , &c. is wholly new , and never before made publick . the bulk is bigger than at first by me intended ; but to gratifie the book-seller , the vulgar arithmetick was an appendix , though previous to the rest . but if one , or other , or all , prove either profitable or pleasant to thee , i am sufficiently oblig'd to subscribe , thy friend , john mayne . from my house at the golden-ball in shaws-court , near st. georges church , southwark ; iuly 29. 1673. to the ingenious author , concerning his decimals . 1 sir , by your art , and pythagorean pen , i 'd prove a metempsychosis agen ; and were his soul of decimals but made , 2 as plato's soul o' th' world of seven is said , i 'd swear 't was slunk to you ; but that you shew 3 more skill than e're his rambling fancy knew . let roving rabbies praise their seven and four ; 4 we 'l shew them mysteries enough and more : the heav'nly orbs are ten , their motions all 5 conspire to make a perfect decimal : this is their musick , and they shall be thus , 6 in spight of tycho or copernicus . 't is said the muses are but nine , but who 7 ( rather than fail ) cann't add apollo too ? thus may we range the world , and quickly find , 8 we all to th' number of our fingers bind . thus logick all the wandring species brings , 9 and places under tenfold heads of things . thus i , to give the author praise in all , 10 reduce my verses to a decimal . on his gauging . your circles , sir , would make my folly ghess , you were a conjurer , though you wo'n't confess . and gauging is the rugged dev'lish name of some hobgobling imp , the very same that brought in custome ; but what e're he be , he 's a rare fellow at the rule of three : he doth just square the circle ; nay so true , that the king 's right is given to a cue . there 's none else such impossibles can do : you give the king's , i give this right to you . i. w. on his worthy friend mr. j. mayne , the author of this book . ingenious artist , whither do'st aspire ? or why t' outvye the ancients do'st desire ? have they not left enough to following ages ? no : thou their master art , they but thy pages . my feeble muse can never soar so high , as thy deserts herein extend , nor nigh . yet give me leave hereof to speak my mind : no man could better teach us in this kind , each part so useful , and so plain i find . t. w. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . to his ingenious friend the author mr. john mayne . who reads thy book with an impartial eye , will see how plain , and how ingeniously thy rules are fram'd ; here every child may learn arithmetick , which doth the truth discern . the iudges of our realm could not dispence to all men iustice , were 't not fetch'd from hence : those sons of mars that furrow neptune's brow , unto this science must their labours bow : the wealthy merchant , and all traders , hence must calculate their gain , or their expence : the greedy miser , here may plainly see his pelf's increase at compound vsurie : the purchaser of farms , may also here , value his lordships , whether cheap or deer . thy squares and cubes , methinks , so plain do seem , that i old euclid should thy father deem . all humane arts , mechanical and free , for this companion are oblig'd to thee . by lines and numbers , we our buildings bring in due proportion , framing every thing . by these our wooden walls and towers are fram'd , which guard our island , and the seas command : these fill our stores with rich and costly things , born from both indies under canvas wings : these fortifie our towns with forts , by line ; by these we learn our foes to undermine : by these th' excise and customs we do scan , without injustice to the trading man. thanks to our author then , that hath set forth these arts so plain , and of abundant worth : which do to sea and land such profit yield , in court , in city , garrison , and field . hugh handy , philomath . a table of the contents . the first book . notation or numeration . pag. 1 addition . 4 subtraction . 8 multiplication . 12 division . 17 reduction . 20 the rule of three . 22 the rule of practice . 28 notation of decimals . 34 addition of decimals . 37 subduction of decimals . 38 multiplication of decimals . ib. division of decimals . 41 reduction of decimals . 48 a table of reduction . 52 the golden rule . 54 the double golden rule . 61 of the square root . 66 a table of square roots . 71 of quadratique equations . 80 of the cube root . 91 the second book . of simple interest . pag. 99 prop. 1. to find the interest of any sum , forborn any time , at any given rate . 100 prop. 2. to find the present worth of any sum , due at any time hereafter , at any given rate of interest . 102 prop. 3. having the principal , amount , and rate of interest , to find the time of forbearance . 103 prop. 4. having the principal , the time , and the amount , to find the rate . 105 a table of the amounts of 1 l. from one to twelve months . 107 to find the interest or discompt of any sum of money by that table . 107 , 108 a table for equation of time. 110 a more exact way of equation . 111 , 112 , 113 a decimal table of the present worth of 1 l. per quarter for 124 quarters , at 6 per cent. per annum , simple interest . 114 the vse of the table . 117 of compound interest . 118 prop. 1. to find the increase of any given sum , forborn any known time , at a known rate per cent. per annum . 118 prop. 2. the amount of a sum of money , the rate of interest per cent. per annum , and the time being known , to find what was the principal . 120 prop. 3. the principal , the time , and the amount of a sum of money being known , to find the rate of interest per cent. per annum . 121 prop. 4. the principal , the rate , and the amount being known , to find the time in which it hath so increased . 122 of compound interest infinite . 123 prop. 1. to find the present worth of an estate in 〈◊〉 simple , at any rate of interest per c. per ann. 123 prop. 2. to find what free-hold estate any sum of money will buy , as any rate of interest per c. per ann. 126 prop. 3. an estate being offered for a sum of money , the annual rent being known , to find what rate of interest the purchaser shall have for his money . 126 to find how many years purchase any free-hold estate is worth at any given rate of interest . 128 the number of years purchase being propos'd , to find the rate of interest it is offered at . 129 a decimal table for the valuation of leases or annuities● payable quarterly , at 6 per cent. per annum , interest upon interest for 31 years . 130 the way of making the table before-mentioned , for this , or any other rate of interest . 133 the vse of the table . 134 six questions performed by aid of the canon of logarithms . 137 the third book . the definition of a prismoid . pag. 151 to find its solidity 153 prop. 1. an example in numbers . ib. prop. 2. the inversion of the former solid upon its opposite base , the rule and example . 157 prop. 3. another example . 161 prop. 4. the inversion . 163 the definition of a pyramid . 171 to find its solidity . 172 a table of divisors for reduction of the polygons , and the cone , to cubick inches or gallons . 173 an example of a trigon . 174 of a tetragon . 179 of a pentagon . 18● of a cone . 184 to find the fall of a conical tunn . 186 of ca●k-gauging . 191 to find a casks length . 192 to find the head-diameter . 193 to find the diagonal . ib. to find the content as spheroidal . 194 as parabolical . 196 as conical . 197 by a table of area's . 199 , 200 , &c. to find the vllage . 202 , 205 arithmetick in whole numbers . notation . it is necessary , that all persons that would acquaint themselves with the nature and use of numbers , do first learn to know the characters by which any quantity is expressed . these characters are in number nine , who with a cypher are the foundation of the whole art of arithmetick . their form and denomination as in this example . 0. cypher 1. one. 2. two. 3. three . 4. four. 5. five . 6. six . 7. seven . 8. eight . 9. nine . these characters standing alone express no more than their simple value , as 1 is but one , 2 standing by it self signifies but two , and so of the rest ; but when you see more than one of those figures stand together , they have then another signification , and are valued according to the place they stand in , being dignified above their simple quality , according to the examples in this table .                 unites .               tens . 1             hundreds . 1 2           thousands . 1 2 3         ten thousands . 1 2 3 4       hundred thousands . 1 2 3 4 5     millions . 1 2 3 4 5 6   ten millions . 1 2 3 4 5 6 7 hundred millions . 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 the denomination of places according to this table , must be well known , and are thus exprest ; those standing in the place of unites , signifie no more than their value before taught ; but standing in the second place toward the left hand , they are increased to ten times the value they had before , 1 or one in the unite place signifies but one ; if it stand in the second place toward the left hand , and a cypher before it thus 10 , it hath ten times its simple value , and is called ten ; if 2 stand in the place of the cypher thus 12 , it is then twelve , being ten and two unites ; 1 , 2 , or 3 , standing in third place , with figures or cyphers toward the right hand of it , doth signifie hundreds , as 100 is one hundred , 123 is one hundred twenty three , 321 is three hundred twenty one , 213 is two hundred thirteen ; and so any three of the other figures have like value , according to their stations , the first to the right hand in the unite place signifies so many unites , the second , or that in the place of tens , is increased to ten times its simple value , and in the third place , or place of hundreds , any figure there standing hath a hundred times the value it would have had were it in the unite place . the fourth place is the place of thousands , any figures standing there , with three figures or cyphers to the right hand of it , is so many thousands as simply it contains unites , so 3000 is three thousand , 9825 is nine thousand eight hundred twenty five , &c. the fifth place is ten thousands , and any five figures placed together , are to be read after this manner : example . 45326 forty five thousand three hundred twenty six . 12345 twelve thousand three hundred forty five . the sixt place hath the denomination of hundred thousands , and those six in the table that stand in a rank are to be read , one hundred twenty three thousand four hundred fifty six . the seventh is the place of millions , and the seven in the table are , one million two hundred thirty four thousand five hundred sixty seven . and the eighth rank of figures are to be read , twelve millions three hundred forty five thousand six hundred seventy eight . the ninth rank is , one hundred twenty three millions four hundred fifty six thousand seven hundred eighty nine . and so any greater number of places , every figure one place more toward the left hand , is increased ten times in value more than in the place it stood before . addition . addition , is a gathering or collecting of several numbers or quantities into one sum , by placing all numbers of like denomination under one another , carrying all above ten to the next place , as in these examples . there is likewise another kind of addition , that is not of whole quantities , wherein is necessary to be known the number of parts the integer or whole number is divided into , as pounds and shillings , every pound is divided into 20 shillings , and one shilling is divided into twelve pence , one penny into four farthings . now being to add a number of pounds and shillings together , they are thus set down with a small line or point between them . 3-5 6 : 16 if these be added together , observe in casting up your shillings , so many times as you have 20 in the shillings , you must carry unites to the pounds , and set down the remainder , being under 20 , as in these examples . l. s. 3 : 5 6 : 16 10 : 01 l. s. 4 : 17 3 : 15 5 : 9 6 : 12 19 : 13 in the first example , i find in adding the shillings together , they make 21 , so i set down 1 and carry 1 pound to the pounds : in the second example , i find among the shillings 53 , which is 2 pounds 13 shillings , so i set down 13 under the shillings , and 2 to the pounds . any number of shillings and pence being to be added together , if your number of pence amount to above 12 , carry 1 to the shillings , and set down the remainder under the pence ; if they make above 24 , carry 2 shillings , and set down the remainder , as before . examples . s. d. 1 : 6 2 : 7 4 : 1 s. d. 8 : 9 2 : 8 3 : 10 15 : 03 s. d. 1 : 7 2 : 6 3 : 9 4 : 8 5 : 11 18 : 05 in the first example , you carry one shilling ; in the second , two ; and in the third , three . in addition of pence and farthings , carry so many times four as you find in the number of farthings to the pence , setting down the remainder under the farthings , as in these examples . when you would know the sum of any number of pounds , shillings , pence , and farthing , they are to be placed thus : addition of weight and measure is performed after the same manner . 16 ounces averdupois , make a pound . 28 pounds , make a quarter . 112 pound , or 4 quarters , make an hundred gross . 20 hundred , make a tun. examples . where observe , that so oft as i find 16 ounces , i carry 1 to the pounds ; so often as i find 28 pounds , i carry 1 to the quarters ; and as many times as i find 4 in the quarters , so many times 1 do i carry to the hundreds . subtraction . svbtraction is the taking a lesser number from a greater , and exhibits the remainder . in subtraction the numbers are placed one under another , as in addition , thus : the first of these numbers is called the minorand , the second the subducend , and the third number , or the number sought , is the residuum . 8 the minorand 6 the subducend 2 the residuum or remainder examples of coins . but when the number of pence or shillings , are greater than the number that stands over it in the minorand , you must borrow the next denomination , as in this example . this example i work after this manner , saying 9 d. out of 3 d. i cannot have , wherefore i borrow 1 s. from the shillings , and subduct the 9 d. from that , and there will remain 3 d. which added to the other 3 d. maketh 6 d. i place therefore 6 d. in the place of pence , and proceed saying , 1 s. that i borrowed and 19 is 20 from 1 i cannot , wherefore i borrow 1 l. from the pounds , and subduct from that the 20 s. and there remains nothing but the 1 s. which i place under the shillings , and say , 1 that i borrowed and 6 is 7 from 7 and there remains nothing , then i place a cypher under the 6 , and say , 1 from 2 and there remains 1 , which i set down , and 1 from 1 and there resteth nothing . after this manner is performed subduction of weight and measure . examples . by which examples , the learner may perceive , that where the number to be subducted is greater than the number standing over it , i then borrow one from the next greater denomination , adding the remainder , if any be , to the lesser number before-mentioned , and setting them underneath those of like denomination with them . the proof of subtraction is by adding the subducend and remainder together , and their aggregate must always be equal to the minorand , as you may see by the last example . i could here add many more examples of weight and measure , but to the ingenious practitioner i hope it will be enough , all other being wrought af●er the same manner , respect being had to the number of lesser denominations contained in each greater . as in troy weight , 24 grains make a penny-weight . 20 penny-weight one ounce . 12 ounces one pound . long measure . 4 nails make a quarter of a yard . 4 quarters one yard . 5 nails one quarter of an ell. 4 quarters one ell. 12 inches a foot. 3 feet a yard . 16½ a perch . 40 perches a furlong . 8 furlongs make an english mile . liquid measure . 8 pints make a gallon . 63 gallons make a graves hogshead . 4 hogsheads make a tun. 36 gallons make a beer barrel . 32 gallons make an ale barrel . dry measure . 8 gallons of corn make a bushel . 8 bushels make a quarter . multiplication . mvltiplication is a kind of addition , and resolveth questions to be performed by addition in a different manner : in order whereunto , it is necessary the learner do well acquaint himself with this table ; the having this table perfectly by heart , will make both this rule and division also very facile , otherwise they will be both troublesome and unpleasant . 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72 7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 110 121 132 12 24 36 48 60 72 84 96 108 120 132 144 in the first rank of this table , you have an arithmetical progression from 1 to 12 , and also in the first column toward the left hand downwards . this table doth at first sight exhibit the sum of any number , so often repeated as you shall require , provided the numbers do neither of them exceed 12. multiplication hath three members , thus called , a multiplicand , a multiplicator , and a product : the multiplicand , is the number to be repeated ; the multiplicator , is the number of times the first is to be repeated ; and the product , is the sum of the multiplicand so often repeated . as for example . a countrey-man sold 6 bushels of wheat for 5 s. how many shillings ought he to receive ? by addition 6 must be 5 times set down thus : or 5 six times repeated thus : but by multiplication it is done thus : 6 the multiplicand . 5 the multiplicator now if you look in the table precedent , in the first column find 5 , then look in the first rank for 6 , and cast your eye down to their angle of meeting , and you will find 30 standing under 6 and against 5 , i then conclude that 5 times 6 is 30 ; that is called the product , and they will stand thus : 6 the multiplicand . 5 the multiplicator . 30 the product . but when you have a number to multiply , greater than any in the table , as for example : a gentleman having forborn his rent of a farm , at 157 l. per quarter , for 3 quarters , what ought he to receive ? the multiplication will stand thus : 157 the multiplicand . 3 the multiplicator . 471 the product . i then say , 3 times 7 is 21 , i set down 1 and carry 2 ; then , 3 times 5 is 15 and 2 is 17 , i set down 7 next the 1 , and carry 1 ; saying , 3 times 1 is 3 and 1 is 4 , as in the example before-going ; and the product is 471 l. there is yet more variety , of which take these examples following . if 65 ships do carry 536 men in every ship , how many men will there be in all ? i say 5 times 6 is 30 , set down 0 and carry 3 ; then 5 times 3 is 15 and 3 is 18 , set down 8 and carry 1 ; then 5 times 5 is 25 and 1 is 26 , which i set down : then for the next figure , i say , 6 times 6 is 36 , i set down 6 one place short of the former rank , and carry 3 ; then 6 times 3 is 18 and 3 is 21 , set down 1 and carry 2 ; again , 6 times 5 is 30 and 2 is 32 , these i set down : then draw a line , and cast them up as they are placed , and the sum is the product and answer to the question , viz. 34840 men. in multiplication , always make the lesser number the multiplicator , for it is all one whether i multiply 5 by 15 , or 15 by 5 , the product is always the same . if 128 men of war have each made 746 shot , how many shot were made in all ? begin as before with the unites place , and say , 8 times 6 is 48 , set down 8 and carry 4 ; 8 times 4 is 32 and 4 is 36 , set down 6 and carry 3 ; then 8 times 7 is 56 and 3 is 59 , which set down : then go forward with the 2 , ( but remember to place your remainder one figure short of the former ) saying , 2 times 6 is 12 , set down 2 under the 6 and carry 1 ; 3 times 4 is 8 and 1 is 9 , which set down ; twice 7 is 14 , which set down : also then , once 6 is 6 , which place under the 9 ; once 4 is 4 , which set under the 4 ; and once 7 is 7 , which set under the 1 : then cast th●● up , as in addition , and the sum is the product , and answers the question , viz. 95488 shot . if any number be to be multiplied by 1 with cyphers , it is but adding so many cyphers to the multiplicand as there is in the multiplicator . as for example . if 35678 be to be multiplied by 10 , add one cypher to the multiplicand , thus , 356780 ; if by 100 , add two cyphers , thus , 3567800 ; &c. and when any number is to be multiplied by any other number , that hath cyphers annexed , always place the cyphers immediately under the line , as in these examples . division . division is also a kind of subduction , and informs the querent , how many times one number is contained in another . there is in division these three things to be observed , viz. the dividend , the divisor , and the quotient . the dividend is a number to be divided into parts , the divisor is the quantity of one of those parts which the former is to be divided by , the quotient is the number of such parts as the dividend doth contain . there is also by accident a fourth number in this rule necessary to be known , which is a remainder , and that happens when the dividend doth not contain an equal number of such quantities as it is divided by , as when 15 is to be divided by 4 , the dividend is 15 , the divisor is 4 , and there is a remainder 3. in division you may place your numbers thus . multiplication is positive , but division is performed by essays or tryals , after this manner : here i first inquire how many times 3 i can have in 14 , i find 4 times , i place 4 in the quotient , and then multiply the divisor by that 4 , placing the product underneath the dividend , as in the example ; say , 4 times 5 is 20 , set down a cypher under the 6 and carry 2 , then 4 times 3 is 12 and 2 is 14 , which i set down also , as in the example ; then subduct this product from the figures standing over them , and set down the remainder . then for a new dividend , i bring down the next figure , and postpone that to the remainder , and inquire how many times 3 in 6 , i cannot have twice , bacause i cannot have twice 5 from 5 , i say then once , and place 1 in the quotient , proceeding as before saying , once 5 is 5 , which i place under the first 6 toward the right hand , and once 3 is 3 , which i set down under the other 6 ; subducting these as the former , i find the remainder to be 31. a●ter which i bring down the next figure in the dividend , and postpone it to the remainder , as in this example : then i inquire how many times 3 in 31 , i suppose 9 times , placing 9 in the quotient i multiply again , saying 9 times 5 is 45 , 5 and carry 4 ; then 9 times 3 is 27 , and 4 is 31 ; these being set down , as before directed , and subducted , there will remain nothing . i then conclude , that the divisor is so often contained in the dividend as i● expressed in the quotient , viz. 419 times . for further instructions , take these examples . reduction . reduction is twofold , viz. bringing greater denominations into smaller , and that by multiplication , as pounds into shillings , shillings into pence , &c. also lesser denominations are reduced into greater , by division as pence into shillings , shillings into pounds minutes into hours , hours into days , and days into years , &c. having any number of pounds to reduc● into pence , multiply them by 240. example . in 869 pounds how many pence ? answ. 208560 pence . in 2486 shillings how many farthings ? answ. 119328 farthings . how many minutes are there in 9476 hours ? the answer 568560 minutes . how many pounds , shillings , and pence , are contained in 22929 farthings ? in 544542 cubique inches , how many beer barrels , firkins , and gallons ? inches in 1 b. bar. 10152 ) 544542 ( 53 : 2 : 5 bar. firk . g. inches in 1 firkin 2538 ) 6486 inches in 1 gallon 282 ) 1410 the rule of three . this rule is so called , because herein are three numbers given to find a fourth ; of these three numbers , two are always to be multiplied together , and their product is to be divided by the third , and the quotient exhibits the fourth number , or the number sought . and here note , that of the three given numbers , if that number that asketh the question be greater than that of like denomination with it self , and require more , or if i● be less , and require less , then the number of like denomination is the divisor . or , if the number that asketh the question be less than that of like denomination , and require more ; or if it be more , and require less , then the number that asketh the question is the divisor . example . if 3 yards of sarcenet cost 15 s. what shall 32 yards cost ? which 3 numbers if you please may stand thus : here you may see the term that asketh the question is greater than that of like denomination , being 3 , and the other 32 , and also requires more , viz. a greater number of shillings ; therefore , according to the rule , the first term , or the term of like denomination to that which asketh the question , is the divisor . and the answer is 160 shillings , which being divided by 20 will be found 8 l. again , if 32 ells of holland cost 160 s. what shall 3 ells cost ? in this question ( being the converse of the former ) you may see the term that asketh the question , here 3 , is lesser than that of like denomination , being 32 ells , and also requires less ; therefore the first term here also is the divisor . and the answer is 15 s. if 36 men dig a trench in 12 hours , in how many hours will 144 men dig the same ? 144 ) 432 ( 3 hours , the fourth number . in this question , the term that asketh the question is greater than that of like denomination , and requireth less ; wherefore the term that asketh the question is the divisor . if 144 workmen build a wall in 3 days , in how many days will 36 workmen build the same ? this question you may perceive to be the converse of the former , here the term that asketh the question is less than that of like denomination , and requires more , the term that asketh therefore is the divisor . if 125 lb. of bisket be sufficient for the ships company for 5 days , how much will victual the ship for the whole voyage , being 153 days ? this question is of the same kind with the first example ; here the two terms of like denomination are 5 days and 153 days , the term that asketh the question being more than the term of like denomination , and also requiring more ; so , according to the general rule , the term of like denomination to that which asketh the question is the divisor . it matters not therefore in what order they ar● placed , so you find your true divisor ; but if you will you may set them down thus : the answer is 3825 lb. weight of bisket . a ship having provision for 96 men during the voyage , being accompted for 90 days , but the master taking on boord 12 passengers , how many days provision more ought he to have ? which is no more than this : if 96 men eat a certain quantity of provision in 90 days , in how many days will 108 men eat the same quantity ? the answer is 80 , so that for 108 men he ought to have 10 days provision more . if the assize of bread be 12 ounces , corn being at 8 s. the bushel , what ought it to weigh when it is sold for 6 s. the bushel ? in this question , the term inquiring being less than the term of like denomination , and requiring more ; therefore is the term so inquiring the divisor . the answer is 16 ounces . the rule of practice . it is necessary that the learner get these two tables perfectly by heart , which are only the aliquo● parts of a pound and of a shilling . the parts of a shilling . d. q.   0 1 forty eighth . 0 2 twenty fourth . 0 3 sixteenth . 1 0 twelfth . 1 2 eighth . 2 0 sixth . 3 ● fourth . 4 0 third . 6 0 half. the parts of a pound . s. d. q.   0 00 1 the nine hundred and sixtieth . 0 00 2 the four hundred and eightieth . 0 00 3 the three hundred & twentieth . 0 01 0 the two hundred and fortieth . 0 01 2 the hundred and sixtieth . 0 02 0 the hundred and twentieth . 0 03 0 the eightieth . 0 04 0 the sixtieth . 0 05 0 the forty eighth . 0 06 0 the fortieth . 0 08 0 the thirtieth . 0 10 0 the four and twentieth . 1 00 0 the twentieth . 1 03 0 the sixteenth . 1 04 0 the fifteenth . 1 08 0 the twelfth . 2 00 0 the tenth . 2 06 0 the eighth . 3 04 0 the sixth . 4 00 0 the fifth . 5 00 0 the fourth . 6 08 0 the third . 10 00 0 the half. having these tables perfectly in memory , any question propounded will be readily resolved , only by dividing the given number of yards , ells , feet , inches , gallons , quarts , pounds , or ounces . of which take some examples . 145 ells of cloth at 3d. per ell. 36 s. 3 d. three pence being the fourth part of a shilling , i divide the number by 4 , and the quote is the number of shillings it is worth . 728 at 4.d . 242s . 8d . four pence being the third part of a shilling , i divide by 3. 654 at 6d . 327 s. here take the half . 321 at 1d . 2q . 40s . 1d . 2q . here the eighth part . here take the sixth and the eighth part of the quote . having any number of shillings to reduce into pounds , cut off the last figure toward the right hand by a line , and the figures on the left hand of the line are so many angels as they express unites ; draw a line under them , and take the half of them , and you have the number of pounds . examples . any commodity , the value of 1 yard being the aliquot part of a pound , is thus cast up : 836 yards of broad cloth at 6s . 8d . per yard . 278l . 13● . 4d . take the one third part , and that is the answer in pounds : 3 in 8 twice , and carry 2 ; 3 in 23 seven times , and carry 2 ; 3 in 26 eight times , and carry 2 ; the third part of 2 l. is 13 s. 4 d. where always observe , that the remainder is always of the same denomination with the dividend . 654 lb. of cloves at 5s . per lb. 163l . 10s . take the fourth part . 9464 gall. of brandy at 3s . 4d . 1577l . 6s . 8d . the sixth . where the price is not aliquot . 625 at 3s . per ounce . here i take the tenth and the half of that tenth . 348 dollers at 4s . 6d . the fifth and the eighth of that fifth . 245 lb. at 2s . 3d. the tenth and the eighth of that quote . to cast up the amount of any commodity , sold for any number of farthings by the pound , i borrow from the dutch a coin called a guilder , whose value is 2 s. english. then if a question be proposed of the amount of an hundred weight of any commodity , by the hundred gross , viz. 112 lb. so many hundred as there be , the amount is so many guilders so many groats , as there are farthings in the price of 1 lb. as for example . a hundred weight of iron is sold for 5 farthings the pound , comes to 5 guilders , that is 10 s. and 5 groats , which together is 11 s. 8 d. again . a hundred weight of lead is sold for 2 d. farthing the pound , that is 9 guilders and 9 groats , which is 21 shillings . but if it be the subtil hundred , it is then but so many guilders so many pence : as if a hundred weight of tobacco be sold for 5 d. farthing the pound , the hundred comes to twenty one guilders and twenty one pence , that is forty three shillings and nine pence . arithmetick in decimals . notation . integers . decimals . 3 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 thousand millions . hundred millions . ten millions . millions . hundred thousands . ten thousands . thousands . hundreds . tens . unites . tenths . hundredths . thousandths . ten thousandths . hundred thousandths . millioneths . ten millioneths . hundred millioneths . thousand millioneths . as in whole numbers , the value or denomination of places do increase by tens , from the unite place toward the left hand ; so in decimals , the value or denomination of places do decrease by tens , from the unite-place toward the right hand , according to the precedent table . a fraction or broken number is always less than a unite , as pence are parts of a shilling , and shillings of a pound , inches of a foot , and minutes of an hour , &c. fractions are of two kinds , and are thus called vulgar , & decimal . a vulgar fraction is commonly expressed by two numbers set over one another , with a small line between them , after this manner ⅔ , the uppermost being called the numerator , and the lower the denominator . the denominator expresseth into how many parts the integer or whole number is divided , and the numerator sheweth how many of those parts is contained in the fraction . example . if the integer be a shilling ⅔ is 8 d. if it be 1 l. or 20 shillings , it is 13 s. 4 d. if a foot , it is then 8 inches . or if an hour , it will be 40 minutes . a decimal fraction hath always a common number for a numerator , and a decimal number for its denominator . a decimal number is known by unity , wi●h one or more cyphers standing before it , as 10 , 100 , 1000 , &c. a decimal fraction is known from a whole number by a point , or some other small mark of distinction , whether it stand alone , or be joyn'd with whole numbers ; as in these following examples . or else with a point over the head of unity , or the unite place ; as in these examples . in decimal fractions , the numerators only are set down , the denominator being known by the last figure in the numerator . example . .2 is two tenths . .25 is twenty five hundredths . .257 is thousandths . .2575 is ten thousandths , &c. as cyphers before a whole number have no value , so cyphers after a decimal fraction are of no signification : but cyphers before a decimal fraction , are of special regard ; for as cyphers after a whole number do increase that number , so before a decimal fraction they diminish the value of that fraction . example . .25 twenty five hundredths . .025 twenty five thousandths . .0025 twenty five ten thousandths . each cypher so added removing the fraction further from unity , making it ten times less than before . addition . addition in decimals , whether in pure decimals , or whole numbers mixt with decimals , differs not from addition in whole numbers , only care must be had to the seperating lines or points , that all places of like denomination stand one under another , both in the addends and in the sum ; as in these examples . subtraction . as in addition , so in subtraction care must be had to the placing each figure under that of like denomination with it self , then it is the same with subtraction in whole numbers . examples . multiplication . mvltiplication in whole numbers serveth instead of many additions , and teacheth of two numbers given to increase the greater as often as there are unites in the lesser . it likewise consists of three requisites , viz. a multiplicand , a multiplicator , and a product . the multiplicand is the number to be increased . the multiplicator is the number by which it is to be increased . and the product is the sum of the first number so often repeated as there are unites in the second . in decimal fractions , or whole numbers mixt with fractions , the two first numbers are called factors , and the last is called the fact. multiplication , whether in decimal fractions , or whole numbers mixt with fractions , differeth not ( in the operation ) from multiplication in whole numbers . the last figures in both the factors may be placed under one another , without respect to the distinction of places , or places of like denomination standing under one another , as in addition and subduction ; yet from the product must be cut off by a line or point so many places as there are figures in decimal fractions in both factors of the last figures standing toward the right hand . examples . if it happen when the multiplication is ended , that there be fewer figures in the product● than there are places in decimals in both the factors , then put cyphers before the product till the number of places be equal to those in both the factors : as in these examples . whereby may be observed , that the multiplication of two fractions doth not increase them as in whole numbers , but they are hereby made less , and the fact is removed further from unity than either of the factors . if a whole number be to be multiplied by a decimal number , put so many cyphers after the whole number as there are in the decimal number , and that number will be the product . if 48 be multiplied by 10 , it will be 480 ; by 100 , 4800 ; &c. in multiplying decimal fractions , or mixt numbers , by a decimal number , you need only remove the point or seperating line so many places toward the right hand as there be cyphers in the decimal number . if you multiply .2845 by 10 , the fact will be 2.845 ; by 100 , it will be 28.45 ; by 1000 , 284.5 ; &c. division . division , both in whole numbers and fractions , is by young practitioners found to be more difficult than any of the four species ; it will therefore require a little more industry in the learner : but when once had , there will appear small difference between the operation herein , as in any the precedent . division is also constituted by three requisites , and a fourth by accident , viz. a dividend , a divisor , and a quotient : the fourth is a remainder , which doth not always happen to be . the dividend is the number to be divided . the divisor is the number by which the other is to be divided . the quotient is the number found out by the division . and the remainder is that which is left of the dividend after the division is ended , and is always less than the divisor . example . if 12 be to be divided by 4 , then is 12 the dividend , 4 the divisor , and the quotient will be 3. if 13 be divided by 3 , then 13 is the dividend , 3 the divisor , 4 the quotient , and there will be a remain , which is here 1. decimal fractions , or mixt numbers , are divided after the same manner as whole numbers are divided , only care must be had in giving a true value to the quotient . to perform which , observe well this general rule . the first figure in the quotient is always of the same denomination with that figure which stands ( or is supposed to stand ) over the unity place in the divisor . as to the manner of placing your figures , and the way of dividing , there are many published by divers writers of arithmetick : the way of placing the divisor under the dividend , is the most apt for giving a value to the quotient ; but the rasing of figures , and repeating the divisor so often , is found an inconvenience ; which to avoid , observe the following examples . being to divide 2487.04 by 53.6 , i place them in this order : 53.6 ) 2487.048 ( then i consider if the divisor were placed under the dividend , the unity place in the divisor , here 3 would stand under the 8 in the dividend , i then set a mark over the head of the 8 , and conclude the first figure in the quotient to be of the same denomination with it , which is tens , in whole numbers . having thus found the value of the first figure in the quotient , i proceed to the division , and inquire , how many times 5 in 24 ? i find 4 ; i then set 4 in the quotient , and go back , multiplying the whole divisor by that figure , and subduct the product out of the dividend , placing the remainder underneath as part of a new dividend : thus 4 times 6 is 24 , from 27 , and there remains 3 , which i place under the 7 ; again , 4 times 3 is 12 , and 2 that i borrowed is 14 , from 18 , and there remains 4 , which i place under the 8 , as in the example ; then 4 times 5 is 20 , and 1 i borrowed is 21 , from 24 , and there remains 3 , which i place under the 4. for my new dividend , i bring down the next figure , here a cypher , and postpone it to the remainder , and the example will stand thus : then proceeding in my division , i ask , how many times 5 in 34 ? finding 6 times , i then place 6 in the quotient , and as before say , 6 times 6 is 36 , from 40 , and there remains 4 , which i set down under the cypher ; then 6 times 3 is 18 , and 4 i borrowed is 22 , from 23 , and there remains 1 , which i place under the 3 ; then 6 times 5 is 30 , and 2 i borrowed is 32 , from 34 , and there will remain 2 , which i place under the 4 ; then to this remainder i bring down the next figure in the dividend , postponing it as i did the cypher , and they will stand thus : i now inqui●e , how many times 5 in 21 ? and find 4 times , i then place 4 in the quotient , and go on as before ; there being yet a remainder , i add a cypher , and proceed as before ; and find , upon the adding one cypher , my divisor greater than the dividend , i place a cypher in the quotient : example . having placed a cypher in the quotient , i add another to the dividend , and make it 800 ; and then inquire , how many times 5 in 8 ? finding once , i put 1 in the quotient , working as before : where note , so long as there is a remainder , if you add cyphers and work after this manner , you may have as many decimals as you please . it doth often happen in division , in decimal fractions , or mixt numbers , that the unite place in the divisor will stand beyond all the significant figures in the dividend , either toward the right hand or toward the left ; in which case , that you may the better find out the value of the first figure in your quotient ( according to the precedent general rule ) add cyphers to the right or to the left hand of the dividend , till you come over the unity place in the divisor , and what value or denomination that place is of , that is the denomination of the first figure in the quote ; as in these examples . if in division in whole numbers , there happen to be a remainder , it is the numerator of a common fraction , and the divisor is the denominator , and this fraction is part of the quotient . example . if you divide 66 by 8 , the quotient will be 8 and ● / 8 , according to the way of vulgar fractions , but in decimal fractions it will be 8.25 . common way . decimal way . if you be to divide a whole by a decimal number , cut off so many places by a mark , as there are cyphers in the decimal number : if 468 be divided by 10 , the quote is 46.8 ; by 100 , 4.68 ; and by 1000 , quotes .468 . if a decimal fraction , or a mixt number , be to be divided by a decimal number , remove your line or point so many places toward the left hand , as there are cyphers in your decimal number , supplying the vacant places with cyphers , if there be occasion : 69.5 divided by 10 , is 6.95 ; by 100 , it will be .695 ; by 1000 , .0695 ; and by 10000 , quotes .00695 ; &c. division being the converse of multiplication , as multiplying a mixt number or decimal fraction by a decimal number , you remove your mark of distinction toward the right hand ; so in dividing a decimal fraction or mixt number by a decimal number , the mark is removed toward the left hand , as in the foregoing examples . reduction . to reduce a vulgar fraction into a decimal fraction , your rule is : divide your numerator by your denominator , and the quotient will be a decimal fraction of the same value with the vulgar fraction . so ¼ , if reduced into a decimal fraction , will be .25 . example . here note , that only the even parts of an integer will be exactly reduced into a decimal fraction , as ½ , 2 / 8 , 2 / 16 , &c. in all surds , there will be some remainder , but if you carry your decimal fraction to four or five places , making the last one more than it is , if the sixth figure be above 5 , or else leave them out , and your calculation will come near the truth ; but if any desire to be more exact , he may take as many as he please . examples . to reduce any decimal fraction out of a greater denomination into a lesser , multiply the fraction by those parts of the integer into which you would have it reduced ; as .65 being the parts of a pound , you would know how many shillings are contained in the fraction , multiply it by 20 : if you desire the pence therein contained , multiply it by 240 ; or if farthings , multiply by 960 , the number of farthings in a pound or 20 shillings . the decimal parts of a foot are reduced , by multiplying them by 12 ; if parts of a foot square , by 144 ; and the decimal parts of a foot solid , by 1728 , the cubick inches in a foot of solid . the decimal parts of a pound , are reduced by 16 , the ounces in a pound averdupois ; and 12 , the ounces in a pound troy. the decimal parts of a beer barrel by 36 , and by 32 reduceth the parts of an ale barrel , into gallons ; and gallons into pints , by 8 ; gallon● into cubick inches , by 282 ; and for win● gallons , by 231 , the number of cubick inches in such a gallon , &c. as greater denominations are reduced to lesser , by a multiplication of the several part● of the integer ; so lesser denominations ar● reduced to greater , by division . any number of shillings are reduced into pounds , and the decimal parts of a pound , if you divide them by 20 ; and pence , if divided by 240. example . hours are reduced into the decimal parts of a day , if you divide them by 24 , the hours in a day natural ; and minutes into the parts of an hour , if divided by 60. perches are reduced into the decimal parts of an acre , if you divide them by 160 , the number of square poles or perches in an acre ; and any number of feet into poles , and the decimal parts of a pole , if you divide them by 16.5 the feet in a pole , or by 158.25 the number of square feet in a square pole ; but if wood-land measure by 18 , or if a square pole by 324 , the square feet in a pole or perch of such measure . any number of inches are reduced into the parts of a beer barrel , if divided by 10152 ; and into ale barrels and parts , by 9024 ; &c. for the ease of the reader here is made a table of english coin reduced into the decimal parts of a pound sterling . a table of reduction of english coin , the integer being one pound . shillings . decimals .   pence . decimals of a pound . 19 .95   11 .0458333 18 .9   10 .0416667 > 17 .85   9 .0375 16 .8   8 .0333333 < 15 .75   7 .0291667 > 14 .7   6 .025 13 .65   5 .0208333 12 .6   4 .0166667 > 11 .55   3 .0125 10 .5   2 .0083333 < 9 .45   1 .0441667 > 8 .4       7 .35       6 .3       5 .25   farthings . decimals of a pound . 4 .2   3 .15   3 .003125 2 .1   2 .0020833 1 .05   1 .0010417 > the vse of the table . having any quest. wherein pounds , shillings & pence , are required to be under one denomination , viz. pounds , and the parts of a pound : first seek in the column of shillings for your shillings , and set down the fraction that stands against it ; then in the column of pence , seek your pence ; in the farthings , your farthings ; add all these together , and the sum is the decimal fraction desired . example . what is the decimal fraction for 17 s. 9 d. ¾ ? first as the decimal parts of a pound seek for 17 s. and the fraction against it in the other column is .85 ; which set down thus .85 then against 9 d. i find .0375 and against 3 farthings .003125 their sum is .890625 which is the number required , and is the decimal fraction for 17 s. 9 d. ¾ , as parts of a pound . again , having a decimal fraction in the parts of a pound , and its desired to know the value thereof in lesser denominations : let it be the fraction before found , viz. .890625 : i seek in the table of fractions for the neerest to it , and find .85 , and against it 17 s. i then set .85 down , and subduct it from the other , and there remains .040625 ; i look over the table again , and find the next neerest is .0375 , against it 9 d. i subduct that ; and find the remainder .003125 , stand against 3 farthings . so finding the value of any other decimal fraction : if any thing remain after the last subduction , being less than a farthing , i cast it away as of small regard . the golden rule . this rule is called the rule of three , because herein are three numbers given , to find a fourth . it is also called the rule of proportion , for as the first is in proportion to the second , so is the third to the fourth : and the converse . this rule is called the golden rule for its excellent use in the solution of questions of various kinds , and great advantage is made of it in almost all kind of calculations arithmetical . two of the three numbers given in every rule of proportion are of one denomination , and the third is of the same kind with the fourth sought ; and one of the two numbers that are of like species doth always ask the question . arithmeticians distinguish this rule by two denominations , one they call the direct , and the other the inverse or backer rule of three . one of the three given numbers of like denomination in any rule of proportion is a divisor , the other remaining two are multipliers . to find which of the forementioned numbers is the divisor , take these following rules . 1. if that term to which the question is annexed be more than that of like denomination , and also requires more ; or if it be less , and require less than the term of like denomination ; then that term of like denomination to that which asketh the question is the divisor , and the question is in the direct rule of three . 2. if the term which asketh the question be more than that of like species , and requires less ; or less , and requires more ; then that term which asketh the question is the divisor , and the question is in the backer or inverse rule of three . having by the precedent rules discovered the divisor , multiply the other two numbers , and divide by the divisor , your quote will be the answer to the question . note , if any of the numbers given be in several denominations , they must be reduced into one , either greater or lesser , as before directed . example . quest. 1. if 12 ½ yards of taffaty cost 5 l. 7 s. 9 d. 3 q. what shall 5 ½ yards cost ? in this example , of the three numbers given there are two of like denomination , and they are 12 ½ and 5 ½ , the latter of which is the term which asketh the question , known always by the words what or how much . and this term is less than that of like kind with it self , and also requires less , therefore according to the precedent rule , this question is in the golden rule direct . these three numbers may be placed in what order you please , provided you mistake not your divisor , but according to the general way , being reduced into decimals , and of one species , they will stand thus : yards . l. yards . 12.5 5.390625 ∷ 5.5 then , as before directed , multiply the second and third numbers , and divide by the first , and the quotient exhibits the fourth proportional or the number sought . the answer is 2 l. 7 s. 5 d. 1 q. quest. 2. if 6 yards of broad cloth cost 4 l. what shall 32 yards cost ? here the term which asketh the question is greater than the term of like denomination , and requires more ; therefore the term of like denomination to the term that asketh the question is the divisor . the answer is 21 l. 6 s. 8 d. quest. 3. if 320 men raise a breast-work in 6 hours , in what time will 750 men do the same ? here the term that asketh the question is more than the term of like denomination , and requires less ; therefore the term that asketh the question is the divisor , and this is the backer rule of three . the answer is 2 hours , 33 minutes , and 36 seconds . quest. 4. if 756 men dig a trench in 12 hours , in how many hours will 126 dig the same ? here the term that asketh the question is less than the term of like denomination , and requires more ; then according to the rule the term demanding is the divisor , and this question is also in the inverse rule of three . the answer is 72 hours . there is sometimes four numbers given in a question , yet is it but a single rule of three , for one of the four numbers is of no signification , and might as well have been left out . example . quest. 5. if 10 workmen build a wall 40 foot long in 3 days , in what time might 50 men have done the same ? here note , there is four numbers given , and yet there is but three to be used in working the question , you must therefore find which those 3 are that are necessarily to be used : thus , first , you must take the term that asketh the question , here 50 workmen ; secondly , you must have the term of like denomination with it , which is 10 workmen ; thirdly , the term sought , being days ; you must take the term of like denomination with that also , which is here 3 days : the superfluous term then in the question is 40 , which might have been left out , and they will then stand thus : the answer is half a day or 12 hours . this question is in the rule of three inverse . quest. 6. if 100 l. gain 6 l. in 12 months , what shall 32 l. gain in the same time ? in this question the 12 months is the superfluous term , being of no use in the calculation , the terms required being 100 l. 6 l. and 32 l. note , though the terms in this question be all money , and so may seem to be of one species , yet they are not ; 100 l. and 32 l. are of one kind , being both principal , and the other term is of the same denomination with the term sought , viz. gain or interest . the answer is 1 l. 18 s. 4 d. 3 q. ferè . and this question is in the direct rule of three , the term that asked the question being less than the term of like denomination , and also requiring less , &c. the double golden rule . this rule is called the double golden rule , or double rule of three , because it requires two distinct calculations , before you can answer the question . and in this rule there are five numbers given to find a sixth sought . this differs not in the operation from the single rule , only the calculation is twice repeated . of the five numbers given , the question is sometimes annexed to two , and sometimes but to one . if the question be annexed to two of the five given numbers , then are there two of the other three of the same species with those that ask the question , and the third is proportional to the number sought . for the due regulation of these two calculations , wh●n the question is annexed to two of the five numbers , take these directions . first , take one of the numbers demanding , and let that ask the question in the first operation ; secondly , take that of the same species , and also that of the like quality with the respondent , of these three constitute your first rule of proportion ; then find which is your divisor , according to your rule pag. 55. and proceed to find the fourth in proportion . then for your second rule of three , take the other of the two numbers to which the question is annexed , and let that ask the question ; take also the number of like kind , and the fourth number found in the first calculation ; judge which is your divisor , and work accordingly ; the last quotient will be the sixth number , or the number sought . example . if a trench be 20 perches in length , and made by 12 men in 18 days ; how long may that trench be , that shall be wrought be 48 men in 72 days ? here the question is annexed to two of the five numbers , viz. 48 men and 72 days ; now according to the foregoing direction , take one of the two numbers inquiring , 48 , and say , then take the other of the two numbers inquiring , and say , if 6 lighters bring 60 tuns of ballast in 5 tides , how many tun will 15 bring in 12 ? if a man travel 160 miles in 4 days , when the days are 10 hours long ; in how many days will he travel 195 miles , when the days are 14 hours long ? when a question is stated in the double rule of three , so that there is but one number inquiring , first , take that number , and let it ask the question in the first rule ; take also the number of like denomination , together with the number joyn'd to that of like denomination ; and of these three numbers constitute your first rule of proportion . secondly , let that number which was found in the first operation , ask the question in the second ; then take the number of like denomination to it , and also the number joyn'd with that like number ; of these three is your second compounded ; find your divisor , and proceed ; the last quote exhibits the answer . example . if 4 crowns at london make 2 ducates at venice , and 8 ducates at venice make 20 patacoons at genoa ; how many patacoons at genoa will make 120 crowns at london ? of the square root . a square is a plain superficies bounded with four right lines of equal length , the angles also are equal , being all right angles , as ( a b c d ) the measure of a square is by a square , that is , when it is known how many square inches , feet or perches , is contain'd in any superficies , the content or area of the said superficies is then said to be known . and in a square , it is found by multiplying the length by the breadth , which being equal , it is called squaring of a number , and by the learned dr. pell , involution , and the product or area is the second power ; now the side of such a square is by geometricians called a root or the first power . let the side a b be 222 inches , feet , or perches , &c. 49284 the area or q square . number . now having the area of a square or square number given , and the side or root be required . this is called the extraction of a square root , and also evolution of the second power . let the number be as before 349284. the first thing to be done in the extraction of a root is punctation , or pointing the number given ; which is thus done , first set a point over the unite-place , and omitting one point every other figure thus , 349284 ; there being three points in the number , intimates three figures in the root to proceed then , enquire the greatest square number contained in those figures , under the first point on the left hand ; the greatest square number in 34 is 25 , whose root is 5 , which place in the quotient for the first figure in the root , subduct its square out of 34 , and set the remainder 9 underneath as in the example . example . the first figure in the root thus found , the rest are found by division ; for a dividend bring down the figures under the nex● point , and postpone them to the last remainder , and the example will stand thus , your divisor being double the root found . then i proceed to division , always supposing the last figure in my divisor standing unde● the last save one in the dividend ; the number to be subducted from the dividend must always be the square of the last figure in the root , and the divisor multiplied by the last figur● in the root , so added together as in this example , viz. so that the unite-place in the last number stand one place further to the righ● hand . nine times the divisor 90 and 9 multiplied by it self 81 981 which being subducted from the dividend will remain 11 , as part of a new dividend , to them bring down the two next figures , and the example will stand thus : the divisor as before is double the whole root found , and for the number to be subducted , after you have made enquiry how many times the divisor will be found in the dividend , if so placed as aforesaid , it will here be found once , then place ●r in the quotient for the third figure in the root , the number to be subducted will be as before , and the example will stand thus : the divisor multiplied by the last figure found , and the square of that figure placed as before directed . rectangle — 118 square — 1 1181 1181 subducted from the dividend 1184 there will remain but — 3 which sheweth the number was not a square number ; but if you desire to have it further , add two cyphers to the remainder for a new dividend , double your whole quotient for a new divisor , and you may have as many decimals as you please . tabula laterum quadratorum ab unitate ad 200. quadrata . latera . 1 1 , 00000 , 000000 2 1 , 41421 , 356237 3 1 , 73205 , 080757 4 2 , 00000 , 000000 5 2 , 23606 , 797750 6 2 , 44948 , 974278 7 2 , 64575 , 131106 8 2 , 82842 , 712474 9 3 , 00000 , 000000 10 3 , 16227 , 766017 11 3 , 31662 , 479036 12 3 , 46410 , 161514 13 3 , 60555 , 127546 14 3 , 74165 , 738677 15 3 , 87298 , 334621 16 4 , 00000 , 000000 17 4 , 12310 , 562562 18 4 , 24264 , 068712 19 4 , 35889 , 894354 20 4 , 47213 , 595500 21 4 , 58257 , 569496 22 4 , 69041 , 575982 23 4 , 79583 , 152331 24 4 , 89897 , 948556 25 5 , 00000 , 000000 26 5 , 09901 , 951359 27 5 , 19615 , 242271 28 5 , 29150 , 262213 29 5 , 38516 , 480713 30 5 , 47722 , 557505 31 5 , 56776 , 436283 32 5 , 65685 , 424948 33 5 , 74456 , 264654 34 5 , 83095 , 189485 35 5 , 91607 , 978310 36 6 , 00000 , 000000 37 6 , 08276 , 253030 38 6 , 16441 , 400297 39 6 , 24499 , 799840 40 6 , 32455 , 532034 41 6 , 40312 , 423743 42 6 , 48074 , 069841 43 6 , 55743 , 852430 44 6 , 63324 , 958071 45 6 , 70820 , 393250 46 6 , 78232 , 998313 47 6 , 85565 , 460040 48 6 , 92820 , 323028 49 7 , 00000 , 000000 50 7 , 07106 , 781185 51 7 , 14142 , 842854 52 7 , 21110 , 255093 53 7 , 28010 , 988928 54 7 , 34846 , 922835 55 7 , 41619 , 848710 56 7 , 48331 , 477355 57 7 , 54983 , 443527 58 7 , 61577 , 310586 59 7 , 68114 , 574787 60 7 , 74596 , 669241 61 7 , 81024 , 967591 62 7 , 87400 , 787401 63 7 , 93725 , 393319 64 8 , 00000 , 000000 65 8 , 06225 , 774830 66 8 , 12403 , 840464 67 8 , 18535 , 277187 68 8 , 24621 , 125124 69 8 , 30662 , 386292 70 8 , 36660 , 026534 71 8 , 42614 , 977318 72 8 , 48528 , 137424 73 8 , 54400 , 374532 74 8 , 60232 , 526704 75 8 , 66025 , 403784 76 8 , 71779 , 788708 77 8 , 77496 , 438739 78 8 , 83176 , 086633 79 8 , 88819 , 441732 80 8 , 94427 , 191000 81 9 , 00000 , 000000 82 9 , 05538 , 513814 83 9 , 11043 , 357914 84 9 , 16515 , 138991 85 9 , 21954 , 445729 86 9 , 27361 , 849550 87 9 , 32737 , 905309 88 9 , 38083 , 151965 89 9 , 43398 , 113206 90 9 , 48683 , 298050 91 9 , 53939 , 201417 92 9 , 59166 , 304663 93 9 , 64365 , 076099 94 9 , 69535 , 971483 95 9 , 74679 , 434481 96 9 , 79795 , 897113 97 9 , 84885 , 780180 98 9 , 89949 , 493661 99 9 , 94987 , 437107 100 10 , 00000 , 000000 101 10 , 04987 , 562112 102 10 , 09950 , 493836 103 10 , 14889 , 156509 104 10 , 19803 , 902719 105 10 , 24695 , 076596 106 10 , 29563 , 014099 107 10 , 34408 , 043279 108 10 , 39230 , 484541 109 10 , 44030 , 650891 110 10 , 48808 , 848170 111 10 , 53565 , 375285 112 10 , 58300 , 524426 113 10 , 63014 , 581273 114 10 , 67707 , 825203 115 10 , 72380 , 529476 116 10 , 77032 , 961427 117 10 , 81665 , 382639 118 10 , 86278 , 049120 119 10 , 90871 , 211464 120 10 , 95445 , 115010 121 11 , 00000 , 000000 122 11 , 04536 , 101719 123 11 , 09053 , 650641 124 11 , 13552 , 872566 125 11 , 18033 , 988750 126 11 , 22497 , 216032 127 11 , 26942 , 766958 128 11 , 31370 , 849898 129 11 , 35781 , 669160 130 11 , 40175 , 425099 131 11 , 44552 , 314226 132 11 , 48912 , 529308 133 11 , 53256 , 259467 134 11 , 57583 , 690279 135 11 , 61895 , 003862 136 11 , 66190 , 378969 137 11 , 70469 , 991072 138 11 , 74734 , 012447 139 11 , 78982 , 612255 140 11 , 83215 , 956620 141 11 , 87434 , 208704 142 11 , 91637 , 528781 143 11 , 95826 , 074310 144 12 , 00000 , 000000 145 12 , 04159 , 457879 146 12 , 08304 , 597359 147 12 , 12435 , 565298 148 12 , 16552 , 506060 149 12 , 20655 , 561573 150 12 , 24744 , 871392 151 12 , 28820 , 572744 152 12 , 32882 , 800594 153 12 , 36931 , 687685 154 12 , 40967 , 364599 155 12 , 44989 , 959799 156 12 , 48999 , 599680 157 12 , 52996 , 408614 158 12 , 56980 , 508998 159 12 , 60952 , 021292 160 12 , 64911 , 064067 161 12 , 68857 , 754045 162 12 , 72792 , 206136 163 12 , 76714 , 533480 164 12 , 80624 , 847487 165 12 , 84523 , 257867 166 12 , 88409 , 872673 167 12 , 92284 , 798332 168 12 , 96148 , 139682 169 13 , 00000 , 000000 170 13 , 03840 , 481041 171 13 , 07669 , 683062 172 13 , 11487 , 704860 173 13 , 15294 , 643797 174 13 , 19090 , 595827 175 13 , 22875 , 655532 176 13 , 26649 , 916142 177 13 , 30413 , 469565 178 13 , 34166 , 406413 179 13 , 37908 , 816026 180 13 , 41640 , 786500 181 13 , 45362 , 404707 182 13 , 49073 , 756323 183 13 , 52774 , 925847 184 13 , 56465 , 996625 185 13 , 60147 , 050874 186 13 , 63818 , 169699 187 13 , 67479 , 433118 188 13 , 71130 , 920080 189 13 , 74772 , 708488 190 13 , 78404 , 875209 191 13 , 82027 , 496109 192 13 , 85640 , 646056 193 13 , 89244 , 398945 194 13 , 92838 , 827718 195 13 , 96424 , 004377 196 14 , 00000 , 000000 197 14 , 03566 , 884762 198 14 , 07124 , 727947 199 14 , 10673 , 597967 200 14 , 14213 , 562373 the use of the precedent table is principally for the ease of the industrious artist ; when he hath the extraction of a square root in the solution of any question , it is but seeking the given number in the table , and just against it he shall find the root . by the subsequent examples will it plainly appear , how useful such a table to 1000 roots would be in quadratique equations , and in the cubes also , which ( were there incouragement given to the sons of art ) i doubt not but some ingenious person would enrich the world therewith ; these being long since calculated by mr. henry briggs of oxford , and given me by my honoured friend , mr. iohn collins , his desire being to have them made more publick , and the conveniency of such a table ( before mentioned ) shewn , by some examples upon this . of quadratique equations . mr. dary , in his miscellanies , chap. 8. saith to this , or the like purpose : 1. when any equation propos'd is incumbred with vulgar fractions , let it be reduced to its least terms in whole numbers , if possible ; if not , let it be brought to its least terms in decimals . 2. it is evident from divers authors , that if any quant●ty shall be signed − , then the square root , or the root of any even power of such quantity so sign'd , is inexplicable , for they cannot be generated from any binomials that shall be equal . as for example . − 9 being a negative can be made of nothing ( if taken as a square number ) but + 3 and − 3 , which roots are not equal , they being neither both affirmatives nor both negatives . 3. when you have cleared the equation by the second hereof , and that the co-efficient in the highest power is taken away , or be unity , then will quadratique equations resolve themselves into the four following compendiums . 4. let your equation be so reduced , that the highest power stand on the left side alone , the sign + being always annexed , or supposed to be annexed . example , quesita a. first equation . second equation . third equation . fourth equation . illustration by numbers , quesita a. first equation . proof of the affirmative . the square of 9 = 81 six times the root = 54 to which add 27 81 which was to be proved . proof of the negative . example 2. second equation . example 1. example 2. third equation . example 1. example 2. fourth equation . example 1. example 2. but if in a square equation there happen to be a coefficient annexed to the highest power , it is resolved by transferring the coefficient with the sign of multiplication to the other side . admitting the equation be then the coefficient 2 being transferred ( as before directed ) they will stand as in this example . first equation . the root of +25 being +5 , then is +5+3 = 8 , and a = +4 , the affirmative answer . and +3 − 5 is = − 2 , and a = − 1 , the negative answer . the proof is easie : first , if a be = 4 , 2 aa is = + 32 , and 6 a is = +24 , to which +8 being added , the sum is +32 which was to be proved . again , a = − 1 , then 1 aa is = − 2 , whereto +8 being added , the sum is = +6 , which also was to be done . second equation . now + 13 + the √ 121 , viz. + 11 is = +24 , the ¼ whereof is = +6 = a , and aa = 36 , and 4 aa = +144 , +26 a = +156 , to which if − 12 be added , the sum will be +144 also . again , if to +13 you add − the √ 121 , viz. − 11 , 4 a will be = +2 , and consequently + a = +½ , 4 aa is then = +1 , and +26 = +13 , to which add − 12 , and the sum is = +1 , which was to be proved . third equation . − 3+13 = +5 a , here a = +2 , 5 aa = +20 , − 6 a = − 12 , to which add +32 , the sum is also +20. again , − 3 − 13 = − 16 = − 5 a , and a = − 3.2 , 5 aa = +51.2 : also − 6 a being = +19.2 , to which add +32 , the sum is = +51.2 . fourth equation . which was to be done . note , always where there is no sign annexed to any term in the equation , the sign + is supposed to be annexed . i have been the larger in these examples , that the young analist may with the more ease apprehend the several kinds by this variety ; in some o● the surd roots i have on purpose omitted the large number of places , four or five being sufficient for use in most cases ; but if any desire to be more exact , he may take them as far as he pleaseth , or the table doth exhibit . of the cube root . the cube is a solid , and hath three dimensions , length , breadth , and depth , and is inclosed by six plain square superficies . example . let the side a , b , or c , d , &c. be 125 : to find the content in solid feet or inches , is the involution of the side or root . thus : the solidity . and this is called the third power . the evolution hereof , is also termed the extraction of the cube root , wherein observe first your punctation , omitting two , point every third figure . example . the first figure in the root is found by taking the greatest cube number , contained in the figure or figures that stand under the first point towards the left hand , here 71 , whose root is 4 , therefore that 4 must be placed in the quotient as the first figure in the root , and the example will stand thus : then the cube of 4 is 64 , which subduct out of the first figures , and set down the remainder if any be . the first figure found in this peculiar manner , the rest are found by division thus : the dividend consists of the remainder , if any be , and the three figures under the next point postponed ; the divisor is always three times the square of the root , and three times the root it self : these two numbers being so to be added together , as that the unites of the first stand over the tens of the second . three times the q square . of the √ = 48 three times the √ = 12 divisor 492 then will the example stand thus : then proceed to division , always supposing the last figure in the divisor to stand under the last save one in the dividend , and enquire , how many times 4 in 7 ? place 1 in the quotient . then for your number to be subducted out of the dividend , it always consists of three numbers , viz. three times the q square . of the first figure = 48 multiplied by the second 1 product of the first by the second 48 3 times the q square . of the second by the first 12 and the cube of the second 1 the subducend 4921 the q square . of 41 = 1681 3 q square of 41 × 3 = 5043 then for a new dividend , bring down the three next figures , postponing them as before . the divisor thrice the q square . of the √ 41 = 5043 and three time the √ 41 = 123 50553 which being set on the left hand the dividend , stands thus : then enquire , how many times 5 in 30 ? you will find ● times , which place in the quotient . your subducend is as before , 3 times the square of 41 × 5 = 25215 3 times the square of 5 × 41 = 3075 and the cube of 5 = 125 the subducend 2552375 which being subducted from 3032125 there will remain 479750 which shews the number was not a cube number ; if you add three cyphers , and work as before , you may have as many decimals fractions as you please . in this extraction i have not taken the same number the cube first mentioned did produce , but by adding another figure , made the number greater , that it might take in all cases ; but in the following extraction it is explicated . three times the square of the root = 3 three times the root is also = 3 the first divisor = 33 three times the square of 1 = 3 2 three times the square of 1 × 2 = 6 three times the square of 2 × 1 = 12 the cube of 2 = 8 the first subducend = 728 three times the square of the root = 432 three times the root = 36 the second divisor = 4356 three times the square of the √ 12 = 432 5 three time the square of 12 × 5 = 2160 three times the square of 5 × 12 = 900 the cube of 5 = 125 the second subducend = 225125 a short treatise of simple & compound interest : with two tables for the calculation of the value of leases or annuities by quarterly payments , at 6 per cent. per annum . by iohn mayne . london , printed by william godbid , for nath. crowch , in exchange-alley . m. dc . lxxiii . of simple interest . question 's in simple interest are wrought by the double rule of proportion , wherein five numbers are given to find the sixt . and if you put p = 100 principal , and t for twelve months , g = 6 l. the rate of interest , and p = any other sum greater or lesser , t = any other time ( above or under twelve months ) and also g = to the gain thereof at that rate . then if any one term of these six be unknown , it is explicated by the other five ( like symbols having the same denomination ) as in this equation . ptg = ptg that is the fact of 100 l. multiplied by one year , and that product by 6 the interest of 25 l. for 4 years , is equal to the fact of 25 multiplied by 4 years , and that product by 6 the interest of 100 l. for one year . example . which was to be proved . now forasmuch as the usual questions of simple interest , are proposed from a sum presently due to the gain thereof , & contra ; it will be requisite you put a = the amount of a sum , forborn or due hereafter , and then you will have a = p+g , as in the former equation . example . p t p+g as 100 in 1 to 106 so 25 in 4 to 31 = p+g from the precedent analogism will arise these four propositions . prop. i. a sum presently due = p , being forborn a certain time = t , at a certain rate = g , per cent. per annum : q. the amount = a ? equation a = that is , the given sum multiplied by the given time , and that product again multiplied by the given rate of interest , the last product divided by the principal , viz. 100 , in the time , viz. 1 , exhibits the gain of that sum in that time. illustration . quest. 1. 25 l. being forborn 18 months , at 6 per cent. per annum ; what doth it amount to ? the answer being 27 l. 5 s. the amount in that time . quest. 2. if 175 l. be forborn for 7. years , at 6 per cent. per annum , simple interest ; what will it amonut to at the end of the said time ? the answer = 248.5 that is 248 l. 10 s. prop. ii. a sum of money = a , due at a certain time hereafter = t , at a certain rate of interest = g , per cent. per annum . q. the present worth = p ? equation , p = that is , the fact of the amount multiplied by the principal , 100 , in the time , viz. 1 year , divided by the said principal multiplied into the said time , more the rate of interest multiplied into the time of forbearance , the quotient is equal to the present worth . example . quest. 1. if 248 l. 10 s. be due at the end of 7 years , what is it worth in ready money , discompting interest , at 6 per cent. per annum . the answer is 175 l. quest. 2. if 950 l. be due at the end of 12 years , what is it worth in ready money , at 9 per cent. per annum simple interest ? the answer is 456 l. 14 s. 7 d. ¼ ferè . prop. iii. a sum presently due = p , having been forborn ● time unknown = t , did amount to a certain sum = a , at a rate of interest = g , per cent. per annum . q. the time of forbearance = t ? equation , that is to say , the amount less the principal , so increased , multiplied by 100 , and that product divided by the fact of the before-mentioned principal , and rate of interest , quotes the time of forbearance . example . quest. 1. if 175 l. hath been forborn till with the interest at 6 per cent. per annum it is increased to be 248 l. 10 s. q. how long hath it been forborn ? the answer is 7 years . quest. 2. if 25 l. hath been forborn till it is amounted to 27 l. 5 s. at 6 per cent. per annum , simple interest . q. in what time is it so increased ? the answer 1 year and an half . prop. iv. a sum of money = p , being forborn a certain time = t , and at the end of that term did amount to a sum = a. q. at what rate of interest ? equation , or from the amount subduct the principal , and the remainder multiply by 100 , that product divided by the principal multiplied by the time , the quotient will be = g the rate of interest , per cent. per annum . illustration . quest. 1. if 250 l. forborn 3 year● and 6 months , did amount to 324 l. 7 s. 6 d. at what rate of interest did it so increase ? the answer is 8 l. 10 s. quest. 2. if 175 l. being forborn 7 years , did amount to 248 l. 10 s. what rate of simple interest per cent. per annum was it accompted at ? the answer is 6 l. if one month be taken for the 1 / 12 of a year , the business of interest and rebate is very easily performed by a small table of the amounts of 1 l. for any number of months , not exceeding 12 ; which table is made by this analogy , 100. 106 : : 1.1.06 . a table of the increase of 1 l. at 6 per cent per ann. months . value . 12 1.06 11 1.055 10 1.05 9 1.045 8 1.04 7 1.035 6 1.03 5 1.025 4 1 . 0● 3 1.015 2 1.01 1 1.005 if the question be of the amount of any sum forborn any number of months , at 6 per cent. per annum , multiply the given sum by the tabular number for that time , and the product answers the question . example . if 125 l. be forborn 10 months , what will it amount to ? the principal = 125 the tabular number for 10 months = the answer is 131 l. 5 s. if the question be only what is the interest of any sum for any time , then multiply the sum for that time by the tabular number less an unite . example . what is the interest of 125 l. for 10 months ? the principal = 125 the tabular number less an unite = .05 6.25 the answer is 6 l. 5 s. prout suprà . for discompt or rebate of any sum to be forborn , the present worth is found by dividing the given sum by the tabular number . example . what is the present worth of 131 l. 5 s. due at the end of 10 months ? the answer is 125 l. but if any desire to be more exact , let him multiply the interest of 1 l. for 1 day ( which is .000164384 ) by the number of days , and that product by the given sum , and the last product will be the interest for that sum forborn the time given . example . what is the interest of 125 l. forborn from the tenth of march to the tenth of ianuary following , viz. 305 days ? the answer is 6 l. 5 s. 4 d ferè . discompt is performed by division , viz. get the amount of 1 l. for the time required , by which divide the given sum , and the quote is the present worth . of mean time. it hath been a custome amongst merchants , in their contracts upon sale of commodities , to agree upon divers times of payment , as two three-months , three six-months , &c. now to find a time between these , wherein the whole sum may be paid at one entire payment without detriment to either party , the subsequent table doth shew upon the first inspection . a table for equation of time.   1 is 1.5   2 is 3   3 is 4.5   4 is 6 2 5 is 7.5   6 is 9   7 is 10.5   8 is 12   9 is 13.5   1 is 2   2 is 4   3 is 6   4 is 8 3 5 is 10   6 is 12   7 is 14   8 is 16   9 is 18   1 is 2.5   2 is 5   3 is 7.5   4 is 10 4 5 is 12.5   6 is 15   7 is 17.5   8 is 20   9 is 22.5   1 is 3   2 is 6   3 is 9   4 is 12 5 5 is 15   6 is 18   7 is 21   8 is 24   9 is 27   1 is 3.5   2 is 7   3 is 10.5   4 is 14 6 5 is 17.5   6 is 21   7 is 24.5   8 is 28   9 is 31.5   1 is 4   2 is 8   3 is 12   4 is 16 7 5 is 20   6 is 24   7 is 28   8 is 32   9 is 36   1 is 4.5   2 is 9   3 is 13.5   4 is 18 8 5 is 22.5   6 is 27   7 is 31.5   8 is 36   9 is 40.5   1 is 5   2 is 10   3 is 15   4 is 20 9 5 is 25   6 is 30   7 is 35   8 is 40   9 is 45 the manner of making this table , is no more than adding one term to the given number of terms , and take half the sum. example . is three four-months given , add 4 to 12 , the sum will be 16 , half that sum , viz. 8 months , is the equated time of payment . this indeed is but an approximation , though near enough the truth for practice . that excellent accomptant mr. collins , in a sheet printed anno 1665. hath taught a more exact way of equation : simple interest , prop. 4. compute ( saith he ) all the present worths , and then by proportion , if all those present worths amounted to the total of all those payments , what did 1 l. amount to in the said time ? from the result subtract an vnite , the remainder is the interest of 1 l. for the time sought , which divide by the interest of 1 l. for one day , and the quote is the number of days sought . example . a merchant sold wines for 300 l. and hath given the vintner three six-months for payment , viz. to pay 100 l. at the end of 6 months , another at 12 , and the third 100 l. at 18 months end ▪ the question is , at what time may this vintner pay 300 l. together , without detriment to himself or the merchant . 100l . at 6 months is worth — 97.087 100l . at 12 months is worth — 94.34 100l . at 18 months is worth — 91.826 the present worths = 283.253 the interest of 1 l. for the time is .059123786 the interest of 1 l. for 1 day is = .000164384 the answer is 359 days and a half , ferè . by the table , three six-months gives twelve months for the equated time , which you find above five days less than a year by this calculation . a decimal table of the present worth of one pound , quarterly payment , at 6 per cent. per annum , simple interest , for 124 quarters . 1 .985222 2 1.956095 3 2.913033 4 3.856429 5 4.786662 6 5.704093 7 6.609071 8 7.501928 9 8.382985 10 9.252550 11 10.110919 12 10.958377 13 11.795197 14 12.621643 15 13.437970 16 14.244421 17 15.041234 18 15.828636 19 16.606846 20 17.376077 21 18.136533 22 18.888413 23 19.631907 24 20.367201 25 21.094474 26 21.813898 27 22.525642 28 23.229868 29 23.926732 30 24.616387 31 25.298981 32 25.974656 33 26.643553 34 27.305804 35 27.961542 36 28.610893 37 29.253979 38 29.890922 39 30.521837 40 31.146837 41 31.766032 42 32.379529 43 32.987432 44 33.589841 45 34.186856 46 34.778572 47 35.365082 48 35.946478 49 36.522847 50 37.094275 51 37.660848 52 38.222645 53 38.779748 54 39.332235 55 39.880180 56 40.423658 57 40.962742 58 41.497501 59 42.028005 60 42.554321 61 43.076514 62 43.594649 65 44.108787 64 44.618992 65 45.125321 66 45.627833 67 46.125686 68 46.621636 69 47.113036 70 47.600841 71 48.085103 72 48.565872 73 49.043199 74 49.517133 75 49.987721 76 50.455010 77 50.919048 78 51.379877 79 51.837543 80 52.292088 81 52.743556 82 53.191986 83 53.637421 84 54.079898 85 54.519459 86 54.956140 87 55.389980 88 55.821014 89 56.249280 90 56.674811 91 57.097644 92 57.517813 93 57.935349 94 58.350287 95 58.762658 96 59.172494 97 59.579826 98 59.984684 99 60.387099 100 60.787099 101 61.184713 102 61.579970 103 61.792897 104 62.363522 105 62.751872 106 63.137972 107 63.521849 108 63.903529 109 64.283035 110 64.660394 111 65.035628 112 65.408763 113 65.779820 114 66.148824 115 66.515796 116 66.880760 117 67.243736 118 67.604747 119 67.963814 120 68.320956 121 68.676196 122 69.029553 123 69.381047 124 69.730697 the use of the precedent table is principall● to shew the present worth of any lease or a●nuity , payable quarterly , for any term 〈◊〉 years under 31 , at 6 per cent. per annu● simple interest . example . there is a lease for 18 years to be sold , of the yearly value of 160 l. payable quarterly , viz. 40 l. per quarter , what is this lease worth in ready money , allowing the purchaser 6 per cent. simple interest ? 72 quarters per table = 48.565872 the answer is 1942 l. 12 s. 8 d. ¼ ferè . the inversion of the question , viz. what quarterly payment for 18 years will 1942 l. 12 s. 8 d. ¼ purchase ? as the former was done by multiplication , where the product exhibits the answer ; so if the sum proposed be divided by the tabular number , the quote gives your answer . example . the answer is 40 l. of compound interest . as simple interest is performed by a serie● of musical , so is compound interes● wrought by a rank of geometrical continua● proportionals . the operation whereof by th● canon of logarithms , take under these four considerations . prop. i. if you shall put p = the logarithm of a principal or sum forborn , and t = the time o● forbearance in years , quarters , months , or day , r = the logarithm of the rate of interest , per cent . per annum , per mensem , or per diem , a = the logarithm of the amount of the said principal for the said time , at the rate also aforesaid : then q. the amount = a ? equation , a = rt + p. that is , multiply the logarithm of the rate by the number of years , quarters , &c. to which product add the logarithm of the principal , and the aggregate is equal to the logarithm of the amount . example . quest. 1. if 175 l. be forborn 7 years , what will it amount to at 6 per cent. per annum , compound interest ? log. of the rate = 0,02530586 = r log. of the sum = 2,24303805 = 175 = p the answer 263 l. 2 s. 8 d. ¼ ferè . quest. 2. if 1000 l. be forborn for 6 months , at 6 per cent. per annum , compound interest , what will it amount to ? log. of the former rate divided by 12 , the months in a year , is = 0,00210882 = r add the log. of 1000 viz. 3,00000000 1029.563 = log. amount 3,01265292 = a the answer 1029 l. 11 s. 3 d. ferè . prop. ii. a sum of money unknown , being forborn a certain time = t , at a given rate of interest = r , is amounted to a given sum = a ; q what was p ? equation , p = a − rt . from the logarithm of the amount , subduct the logarithm of the rate , multiplied by the time , and the remainder is the logarithm of the principal . example . quest. 1. if 263 l. 2 s. 8 d. ¼ be the amount of a sum forborn 7 years , at 6 per cent. per annum , compound interest , what was the principal ? log. of the rate = 0,02530586 = r log. of the amount 2,42017910 log. of the principal 2,24303805 = p = 175 the answer 175 l. quest. 2. if 102 l. 11 s. 3 d. be the principal and interest of a sum of money forborn 6 months , at 6 per cent. per annum , compound interest , what was the principal ? log. of rate for 1 mo. 0,00210882 log. of 1029.563 = 3,01265292 log. of the principal 3,00000000 = 1000 the answer 1000 l. prop. iii. a sum of money = p , being forborn for a time = t , did amount to a given sum = a , at a rate of interest unknown : q. the rate per cent. per annum = r ? equation , divide the logarithm of the amount , less the logarithm of the principal , by the time , and the quote is the logarithm of the rate . example . if 25 l. forborn 4 years , did amount to 31 l. 11 s. 2 d. ¼ ; at what rate of compound interest did it so increase ? logarithm of the amount = 1,49808345 logarithm of the principal = 1,39794001 a − p divide by 4 ) 0,10014344 the log. of the rate = r = 0,02503586 prop. iv. a sum of money being forborn , at a given rate , for a time unknown , but the amount is known , how long was it so forborn ? equation , example . if 1000 l. be increased to 10●9 l. 11 s. 3 d. at 6 per cent. per annum , compound interest , in what time was it so increased ? the answer 6 months . it may here be expected that i should lay down the construction of the logarithms , having made use of them in these calculations , but this being design'd a small enchiridion , and there being large volumns of that subject in the world already , by several more learned pens , i think it unnecessary to say any thing further thereof , for as they are of excellent use , so are they easie to be had . compound interest infinite , may be so called as it relates to divers equal payments at equal times , but the number of those equal times are infinite , ( i. e. ) when an estate in fee-simple shall be sold for ever . now there being usually an interval of time , between the purchasers payment and the reception of his first rent , be it yearly , half yearly , or quarterly ; any question of this nature may be wrought by the following analogism : putting v = the rent ( yearly or quarterly ) and s = the price paid for the land , also r = the common factor of the rate of interest , per cent. per annum . hence then may arise these three propositions . prop. i. there is a fee simple to be sold , what is it worth in ready money , so that the purchaser may have 6 per cent. per annum , compound interest , allowed for his money . quest. 1. there is a manour to be sold of the clear yearly value of 969 l. 18 s. what sum of ready money is this estate worth , 6 per cent. per annum compound interest being allowed the purchaser for his money ? equation , the annual ( or quarterly ) payment , divided by the ratio , less unity , exhibits the sum in the quotient . the answer is 16165. quest. 2. there is an estate of 969 l. 18 s. per annum ▪ payable quarterly , what is it worth in ready money , allowing the purchaser 6 per cent. per annum compound interest ? the answer is 16524 l. 2 s. 6 d. ferè . the difference between yearly and quarterly payments in this purchase raiseth the value 359 l. 2 s. 6 d. ☞ having the increase of 1 l for a year , at any rate of interest , the biquadrate root of that increase , is the increase of 1 l. for a quarter at compound interest . prop. ii. a sum of money lying ready for a purchase , and it be desired to know what free-hold estate such a sum will purchase , if laid out at a given rate per c. per ann. compound interest . theorem , v = s × r − 1. or , in other terms , the sum of money multiplied by the rate , less unity , the product shall be equal to the annual half quarterly or quarterly payment . quest. a gentleman upon marriage of his daughter promiseth to lay out 1600 l. for a free-hold estate , to be settled upon her and her heirs , provided he meet with such a pennyworth as shall bring 8 per cent. per annum , compound interest for his money : q. what annual rent must it be ? the answer 128 l. per annum . prop. iii. an estate being offered for a certain sum of money , the annual rent is also known : q what rate of interest upon interest shall the purchaser have for his money ? equation , v ÷ s = r − 1. the annual rent being divided by the sum demanded , quotes the rate less unity . example . quest. 1. there is a free-hold estate to be sold for 1600 l. the yearly rent being 128 l. what rate of interest shall the purchaser have for his money ? quest. 2. admit there be a small farm to be sold of the value of 35 l. per annum for 500 l. what rate of compound interest shall the purchaser have for his money at that price ? furthermore , if it be inquired how many years purchase any annuity is worth , putting r = the ratio as before , and y the number of years , the rule is : that is , divide unity by the ratio less 1 , and the quote informs the number of years . example . there is a free-hold estate to be sold , q. how many years purchase is it worth at 5 per cent. per annum ? the answer is 20 years purchase . what is it worth at 6 per cent. p●r annum ? the answer is 16 years , and ⅔ of a year . again , if an estate be offered at any number of years purchase , and it be demanded what rate of interest the purchaser shall have for his money , the rule is : that is , divide unity by the number of years propos'd , and the quote exhibits the ratio , less unity . example . an estate is offered at 20 years purchase , what rate of interest shall the purchaser then have ? the answer is 5 per cent. per annum . there are many tables of compound interest printed in sundry books for the valuation of leases and annuities , but they are generally made for yearly payments , when indeed by the common and most usual covenants in leases the tenant is obliged to pay quarterly ; and in leases of great value , there will be found a considerable difference in the true worth , ( so great , that 25 l. per quarter is as good as 102 l. 5 s. per annum . ) i have therefore presented the reader with a table fitted to such quarterly payments , the use of which table i doubt not but will be very easily found by the examples that follow . a table of interest , for the valuation of leases or annuities for quarterly payments , at 6 per cent. per annum , compound interest , for 31 years . 1 .985538 2 1.956824 3 2.914064 4 3.857459 5 4.787213 6 5.836372 7 6.609520 8 7.496573 9 8.373700 10 9.238139 11 10.090079 12 10.929724 13 11.757176 14 12.572685 15 13.376402 16 14.168496 17 14.949134 18 15.718484 19 16.476707 20 17.223982 21 17.960417 22 18.686219 23 19.401524 24 20.106484 25 20.801250 26 21.485968 27 22.160789 28 22.825841 29 23.481282 30 24.127242 31 24.763844 32 25.391256 33 26.009595 34 26.618988 35 27.219206 35 27.811474 37 28.394861 38 28.969764 39 29.536352 40 30.094714 41 30.645034 42 31.187396 43 31.721914 44 32.248000 45 32.767870 46 33.279531 47 33.783794 48 34.280753 49 34.843000 50 35.253244 51 35.728999 52 36.197819 53 36.659861 54 37.115237 55 37.564028 56 38.006330 57 38.442234 58 38.871893 59 39.295222 60 39.712487 61 40.123777 62 40.529043 65 40.928469 64 41.322133 65 41.710087 66 42.092531 67 42.469245 68 42.841611 69 43.206601 70 43.567307 71 43.922768 72 44.273138 73 44.618415 74 44.958701 75 45.194062 76 45.624577 77 45.950311 78 46.271331 79 46.587715 80 46.899521 81 47.206817 82 47.509668 83 47.808141 84 48.102298 85 48.392200 86 48.677877 87 48.959492 88 49.236993 89 49.510486 90 49.780023 91 50.045601 92 50.307460 93 50.665471 94 50.819753 95 51.070356 96 51.317335 97 51.560742 98 51.841984 99 52.037044 100 52.271047 101 52.499677 102 52.725986 103 52.949021 104 53.134301 105 53.385474 106 53.598963 107 53.809375 108 54.016743 109 54.221113 110 54.422527 111 54.620966 112 54.816601 113 55.009461 114 55.199474 115 55.386751 116 55.571297 117 55.753185 118 55.932443 119 56.109107 120 56.283219 121 56.454811 122 56.623921 123 56.790588 124 56.954843 the calculation of a number in the precedent table , by aid of the canon . the question being , what is the present worth of 1 l. per quarter for 21 years ? the logarithm of the increase of 1 l. at 6 per cent. for three months = 0,0063264664 the number of quarters = 84 discompt of 1 l. for 84 qrs. 0,5314231776 then by the rule of proportion : if 1,467384617 com . arithm . 9,8334569382 have 100 l. for its principal , 2,0000000000 what shall 1 l. have for its pr. 0,0000000000 68.148601 = 1,8334569382 the log. of the discompt = 0,5314231776 the answer is = 48 l. 2 s. 0 d. ½ ferè . and after this manner may a table be calculated , or the value of a lease for any number of years , may be found at any rate of interest required . the vse of the table . this table sheweth the discompt of 1 l. per quarter at 6 per cent. per annum , compound interest , and if the tabular number for so many quarters as the lease is to continue be multiplied by the quarterly payment , that product is the present value of that lease in ready money . example . a lease of 40 l. per annum ( viz. 10 l. per quarter ) for 21 years , being to be sold , what is it worth in ready money ? 84 quarters per table = 48.102221 the quarterly rent = 10 the answer is 481 l. 0 s. 5 d. ● / 4 ; ferè . but if the question be , what quarterly rent for 21 years will a given sum purchase ? then divide the given sum by the tabular number for so many quarters . example . a gentleman having a lease of certain church lands , worth 200 l. per annum more than the reserved rent , for 14 years to come , surrenders the same , upon condition the chapter shall make him a new lease for 31 years without a present fine , but advancing the old rent 10 l. per quarter during the whole term of 31 years ; what doth he gain by the bargain , accompting compound interest on both sides ? 56 quarters per table = 38.006 the quarterly rent = 50 124 quarters per table = 56.955 the answer is 377 l. 18 s. the new lease being so much more worth than the old one . 240 l. is demanded for the lease of a house for 7 years , the tenant offers 100 l. and an advance of rent equivalent to the rest of the fine required , what ought this rent to be ? the advance of rent ought to be 6 l. 2 s. 8 d. per quarter . there is a lease of 200 l. per annum , viz. 50 l. per quarter , for 13 ¼ years , to be sold , what is it worth at 6 per cent. simple , and what at 6 per cent. compound interest ? simple . 53 quarters per table = 38.779748 compound . 53 quarters per table = 36.659861 which subtracted from 1938.987440 leaves 105.99439 whereby it appears , that it is cheaper to the purchaser at compound interest than at simple interest by 106 l. six questions performed by the aid of the canon of logarithms . quest. 1. a gentleman pays 350 l. for a lease in reversion , to commence at the end of 13 years and a quarter , and to continue for 21 years and 3 quarters , what quarterly rent may he lett the premises for , after he comes to be in possession thereof , so as to gain 8 per cent. compound interest for his money ? the logarithm of 350 l. = 2,544008 worth of 1 l. forborn 53 quarters = 0,442865 log. of the increase of 350 l. = 2,986873 worth of 1 l. for 87 quarters = 1,621420 log. of 23.198 = 1,365453 the answer = 23 l. 3 s. 11 d. ½ ferè . quest. 2. a citizen having taken a lease of a house and shop for 21 years , at 370 l. fine , and 100 l. per annum , viz. 25 l. per quarter , rent , at the end of two years is willing to leave it for 300 l. and the old rent , or to have such an increase of rent , during the whole term yet to come , as may reimburse him his fine paid , with compound interest at 6 per cent. per annum : what ought he to receive in advance of rent , and what doth he offer to lose of his fine paid in taking 300 l. 2,568202 = 370l . 1,682165 = the worth of 1 l. per quarter for 84 quarters . 0,886037 the advance of rent ought to be 7 l. 13 s. 10 d. ¼ ferè . 1,652198 the worth of 1 l. per quarter for 76 quarters . 2,545235 the present fine ought to be 350 l. 18 s. 10 d. whereby it appears , there is 50 l. 18 s. 10 d. offered to be lost in putting off the house and shop aforementioned . quest. 3. a sells a house to b for 800 l. to be paid with interest upon interest by 100 l. per annum , viz. 25 l. per quarter , how many quarters rent ought b to pay before a is satisfied for his 800 l. with compound interest at 6 per cent. per annum , and what ought the last payment be ? the last payment 13 l. 3 s. 4 d. ferè . quest. 4. a lends unto b a certain sum of ready money , and accepts a rent charge of 40 l. quarterly for 7 years in satisfaction , finding it paid him his principal with interest upon interest at 8 per cent. within 13 l. 4 s. 6 d. what was the money lent ? 1,602060 the logarithm of 40 l. 1,565196 the logarithm of the worth of 1 l. quarterly for 48 quarters . 3,167256 the logarithm of the worth of 40 l. per quarter for 48 quarters . 0,177140 the logarithm of the increase of 1 l. forborn 28 quarters . 2,986188 the logarithm of 968.7 . the money lent was 968 l. 14 s. quest. 5. a testator leaving one son and two daughters , bequeaths out of his estate ( being 600 l. per annum for 11 years ) to his eldest daughter 500 l. per annum for 4 years next coming , at the end whereof , to his younger daughter 300 l. per annum for 7 years , and to his son the remainder of the estate for the whole time : q. which had the greatest portion , and by how much , calculating their several annuities at 6 per cent. compound interest ? 0,539716 logarithm of the worth of 1 l. per annum for 4 years . 2,698970 the logarithm of 500 l. 3,238686 = 1732.55 . 0,746820 the logarithm of the worth of 1 l. per annum for 7 years . 2,477121 the logarithm of 300 l. 0,101232 the logarithm of the worth of 1 l. forborn 4 years . 3,122709 = 1326.47 . 0,896905 the log. of the present worth of 1 l. per annum for11 years . 2,896905 = 788.68 0,746820 the log. of the present worth of 1 l. per annum for 7 years . 2,301029 the logarithm of 200 l. 0,101232 the logarithm of the worth of 1 l. forborn 4 years . the sons portion — 1673 : 00 : 05 the eldest daughters portion 1732 : 11 : 00 the youngest daughters — 1326 : 09 : 04¾ proof . 0,896905 the logarithm of the worth of 1 l. per annum for 11 years . 2,778151 the logarithm of 600 l. 3,675056 the logarithm of 4732 l. quest. 6. a merchant sold 16 kintals of cyprus cottons for 320 l. to be paid at two six-months ; the buyer having money by him , offers to pay the money presently , provided the merchant allow him discompt at 6 per cent . compound interest . q. what ought the merchant to receive ? 2,505149 the logarithm of 320l . 0,018979 the logarithm of 1 l. forborn 9 months , the equated time , acording to the table of mean time , pag. 110. 2,486170 the logarithm of 306.316 . the answer 306 l. 6 s. 4 d. ferè . stereometry : or , a new and the most practical way of gauging tunns in the form of a prismoid & cylindroid : also the frustums of pyramids and of a cone . together with the art of cask-gauging . by iohn mayne . london , printed by william godbid , for nath. crowch , in exchange-alley . m. dc . lxxiii . to the young geometrician . i hope by this time thou art so sufficiently acquainted with the nature and use of a decimal fraction , that any operation in the six species , viz. addition , subtraction , multiplication , division , involution and evolution of the second and third powers , will not appear difficult to thee ; and these being familiar , any calculation in arithmetick , geometry , trigonometry , or other mathematical arts , will not seem strange : amongst the many pleasant walks in this tempe , i have made it my present design to give thee some diversion in that part of solid geometry called gauging , and herein passing by those blossoms that kiss the hand of every passenger , i have endeavoured ( and i hope not altogether without success ) to shew thee how to gather a rose without danger of its thorn : for the invention , the world is obliged to the ingenious mr. michael dary , the roots of these , and many other choice mathematical flowers , lying crowded together in a small trea●ise called dary's miscellanies , printed 1669. here , as in the former part , thou hast both precept and example in the plainest method i could possibly express them . that they may by no means seem obscure to any ingenious student , is the hearty desire of thy friend , j. m. the explanation of the signs or characters . + more . − less . = equal . > greater . < lesser . × multiplied . √ square root . q square square . ⊙ circle . ∷ proportional . ∽ difference . stereometry : or , a new and the most practical way of gauging tunns , &c. a plain and easie method for finding the solid content of a prismoid . definition . by the word prismoid is to be understood a solid contained under six plain surfaces , whereof the two bases ought to have these three qualifications : 1. rectangular parallelograms . 2. parallel . 3. alike situate . i. e. so situate , that the rectangular conjugates in both bases may be inserted by two and the same planes , and a right line extended from the center of one base to the other may be called the axis , and the other remaining four planes are the peripatasma . under this definition is comprehended the frustums of pyramids and prisms . note also , if the peripatasma be not made by the four flat sides ( spoken of before ) but shall be constituted by curveture from circles or elipse's , the solid is then called a cylindroid , and under this definition is comprehended frustums of cones and cylinders . probl. if in a prismoid you put c = the whole content thereof . a & b = the two rectangular conjugates above . g & h = the two rectangular conjugates below . a & g opposite = their two correspondents one above the other below inserted by one plane . b & h opposite = their two correspondents above and below , and also inserted by one plane . p = the perpendicular height of the prism or prismoid . k = the increment of any two diameters , to be taken between a and g in the same plane with them , at one inch distance of the perpendicular . l = the increment of any two diameters , to be taken between b and h in the same plane with them , at one inch distance of the perpendil●r . then , analogism . or , the rectangle of the two diameters at the base multiplied into the perpendicular , more the semi-sum of g l and h k , ( viz. those two diameters multiplied into their altern increments ) multiplied into the square of the perpendicular , to which add one third of the rectangle of k l ( i. e. ) the two increments multiplied into the cube of the perpendicular is equal to the content in cubick inches . by which theorem you find three fixed or stationary numbers , which mr. dary calls reserved coefficients , wherefore you shall find them hereafter called by that denomination : these three reserved coefficients thus multiplied into the perpendicular , the product is equal to the whole content , or by any part of the perpendicular gives the solidity of that part . prop. i. having a tunn in the form of a prismoid , the dimensions being , inches . above . a = 126 and b = 144 below . g = 102 and h = 108 p = 60 what is the solidity of this tunn in cubick inches ? first then to find the three reserved coefficients . i. e. the difference between a and g ( the two opposite diameters above and below ) divided by the perpendicular quotes k , the increment of any two diameters to be taken between them , at one inch distance in the perpendicular , and in the same plane . that is , the difference between b and h ( the two diameters opposite the one above the other below ) divided by the perpendicular quotes l , the increment of any two diameters to be taken between them , at one inch distance in the perpendicular , and in the same plane with them . .6 = l .4 = k .24 = the rectangle of lk .08 = ⅓ of lk , the first coefficient . now having found these reserved coefficients , i proceed , and finding that ⅓ of k l must be multiplied by the cube of the perpendicular , i begin with it , and call that the first coefficient ; then ½ g l h k being to be multiplied by the square of the perpendicular , i add that to the first fact , and call it the second coefficient ; lastly , g h being to be multiplied by the perpendicular , i add that to the second fact , and call it the third coefficient ; then will the work stand thus : example . the answer 866160 cubick inches . now admitting this tunn have but 33 wet inches , what is the content thereof ? the answer = 423248.76 cubick inches . prop. ii. having a tunn in the form of a prismoid , the dimensions being , inches . above . g = 102 and h = 108 below . a = 126 and b = 144 p = 60 what is the solidity in cubick inches ? to find this tunns solidity , the rule is : i. e. the fact of a b ( the rectangular congates at the base ) multiplied by the perpendicular , from whence subduct the semi-sum of the two facts ( a and its altern decrement , b and its altern decrement , multiplied into the square of the perpendicular ) more the one third of the rectangle of k l , viz. the two decrements , multiplied into the cube of the perpendicular , and that remainder is the content in cubick inches . to find the coefficients . this rule being the converse of the former , these numbers k and l which before were affirmatives are now become negatives ( then increment , now decrement ; ) the greater conjugates being subducted from the lesser makes the dividends so much less than nothing , and consequently the quotes , the divisor being an affirmative , yet these two negatives being multiplied together , their fact becomes affirmative , according to the rule of algebra , the signs of the factors being homogeneal ( or alike ) makes the fact more , as in this example . the factors in these rectangles being heterogeneal ( or unlike ) the fact is made less . these two factors being both affirmatives , the fact is + . with these three reserved coefficients i proceed to the calculation , according to the precedent theorem . the answer = 866160 cubick inches . but if this tunn have only 27 inches of the perpendicular wet , the content then being required : prop. iii. there is a tun in the form of a prismoid , the dimensions are , inches . above . a = 132 and b = 144 below . g = 108 and h = 108 p = 60 what is the solidity in cubick inches ? the answer = 911520 cubick inches . prop. iv. there is a tunn in the form of a prismoid , the dimensions being , inches . above . g = 108 and h = 108 below . a = 132 and b = 144 p = 60 what is its solidity in cubick inches ? the reserved coefficients are found to be : the calculation . the answer = 911520 cubick inches . here note , if any of the precedent tunns be cloathed by curveture , ( i. e. the bases being circular or elliptical ) the last product ought to be divided by 1.27324 , then will the quotient exhibit the cubick inches in that solid . but if the question be ale gallons , let your coefficients be divided by 282 ; if beer barrels be required , divide the coefficients by 10152 , the number of inches in a beer barrel . in all flat sided figures , and for those solids , whose peripatasma is constituted by circles or ellipsis , the divisor for beer barrels is 12926 > , for ale barrels 11490 > , and for ale gallons 359 ; of which take these examples . what number of beer barrels and gallons doth the last mentioned tunn contain ? the three coefficients for beer barrels divided by 10152 are : the first = +.000007880220646 < the second = − .0067375888 > the third = +1.8723404 < the three coefficients for gallons being divided by 282 are : the first = .0002837 > the second = .2425532 > the third = 67.4042553 > the coefficients being thus fitted , the calculation is after this manner : for barrels . the answer is 89 barrels , 3 firkins , and 1 gallon , or 89 barrels and 28 gallons . for gallons . the answer is 3232 gallons , which divided by 36 quotes 89 barrels 28 gallons , as before . example . a new way of gauging the frustum of a pyramid or conical tvnn . a new way of gauging the frustum of a pyramid , &c. definition . a pyramid is a solid figure , contained under many superficies , whereof one is the base , and the rest arise from the base to the vertex , and there meet in a point . the frustum of a pyramid is a solid , cut with a plane parallel to the base , and the part cut off is also a pyramid . the frustum of a cone , may not improperly be termed the frustum of a round pyramid , ( the base being circular ) nor do i think it an heresie to call a cylinder a round prism . the frustum of a pyramid , whose bases are in the form of any ordinate polygon , being alike , and alike situate , and also if a right line may be every where applied in the peripatasma from base to base , moreover a right line being extended from the center of one base to the other , may be called the axis . then if you put s = the whole solidity . b = a side above . a = a side below . p = the perpendicular . d = the common addend at one inch distance of the perpendicular , and is thus made , that is , the difference between a side above and a side below , divided by the perpendicular , quotes the increment , &c. g = the divisor . the rule is : g ) aa p+a dpp+⅓ ddppp ( = s or , in other terms : to the square of the side multiplied by the perpendicular , add the fact of one side in the increment multiplied by the square of the perpendicular , more ⅓ of the q. of the increment in the cube of the perpendicular , and the aggregate divided by the polygons respective divisor , the quote will be the solidity . and further it is to be well observed , if your frustum of a pyramid stand upon its greater base , the rule then is thus varied : g ) : bb p − b dpp+⅓ ddppp ( = s that is to say : from the square of a side at the base multiplied by the perpendicular , subduct the rectangle of one of those sides in the decrement multiplied by the square of the perpendicular , more one third of the square of the decrement in the cube of the perpendicular , and that remainder divided by the divisor proper to the form of the base , the quote is equal to the solidity . note also , that p may be put for a part of the perpendicular , and the answer will be the content of that part required . g ) or the divisors for these 8 regular polygons , and the cone . for cubick inches . for ale gallons . trigon 2.30940 trigon 651.2000 tetragon   tetragon 282.0000 pentagon .58123 pentagon 157.2600 hexagon .38497 hexagon 108.5400 heptagon .27513 heptagon 77.5867 octogon .20710 octogon 58.4022 nonagon .16176 nonogon 45.6163 decagon .12997 decagon 36.6515 cone 1.27324 cone 359.0500 if your tunn be the frustum of a cone : let a or b be the diameter at the base , and d the increment or decrement of any two diameters between a and b , at one inch distance of the perpendicular , and the divisor as per table . i shall only give you some examples of the three first , and the cones frustum , which i think will be sufficient to inform any ingenious practitioner how to perform the rest . the trigon . admit a tunn be in the form of an equilateral triangle , the dimensions being , a = 126 inches , the length of a side above , b = 108 inches , the length of a side below , p = 60 inches , the perpendicular , q. the content in ale gallons ? the coefficients are found , according to the precedent directions , thus : these three divided by the divisor for ale gallons , viz. 651.2 , are as followeth : the answer = 1201.9020 ale gallons . a tunn of the same dimensions standing upon its greater base , the coefficients are thus found : being divided by the same divisor with the former , they are : and are thus used : the answer as before = 1201.9080 ale gallons . now if each of these tunns have 30 inches of the perpendicular wet , how much do they contain ? the first . the answer = 537.84750 ale gallons . the second . the answer = 663.9630 ale gallons . proof . the difference being less than a pint. the tetragon or square pyramid . there is a tunn in the form of the frustum of a square pyramid , a = 144 inches , the length of a side above , b = 108 inches , the length of a side below , p = 60 inches , the perpendicular , q. the content in gallons ? the coefficients being found by the former rule and example , viz. p ) a − b ( = d. ⅓ of dd = the first coefficient .12 db = the second coefficient 64.8 bb = the third coefficient 11664 these three being divided by 282 the cubick inches in the ale gallon , are equal to the answer = 3400.8960 ale gallons . if the tunn stand upon its greater base , the coefficients then are p ) b − a ( = − d , and the ⅓ d d = the first , a d = the second , and a a = the third , which divided by 282 the number of cubick inches in an ale gallon , they do appear to be = +.00042553 and if the content be required the answer = 3400,855680 if 40 inches of the perpendicular be wet in the first tunn , and 20 in the latter , and it be demanded what they contain in ale gallons . the first . the second . proof . the pentagonal pyramid . a tunn in the form of the frustum of a pyramid , whose bases are in the form of a pentagon , a = 144 inches , the length of each side above , b = 108 inches , the length of each side below , p = 60 inches , the perpendicular , q. the content in ale gallons ? the three coefficients found in the last example , viz. for ale gall. the answer = 6099.46920 ale gall. let another frustum of a pyramid of the same bases and altitude , stand upon its greater base , and the content in ale gallons be demanded . the coefficients so found and divided as before directed , are as followeth : the answer = 6099.45120 if 50 inches of the perpendicular in the first tunn be wet , and 10 inches in the last , what is the content in ale gallons ? the first . the last . proof . a tunn in the form of a frustum of a cone , the bases being alike and alike situate , as in the precedent examples , the dimensions being , a = 144 inches , the diameter above , b = 108 inches , the diameter below , p = 60 inches , the perpendicular , q. the content in ale gallons ? p ) a − b ( = d. these three divided severally by the divisor proper to a cone , as in the table mentioned , viz. 359.05 they quote : the answer = 2671.0440 ale gall. and that the young gauger may not be obliged to dray-men to repleat the horizon with liquor , of such tunns whose bases are not posited parallel thereto , ( as indeed most are not being made with a drip or fall ) let him take this example , a b c d e f g h m x , a cone or pyramid . having the length of each line in this diagram , and the content of the whole cone or pyramid in cubick inches , gallons , or barrels , &c. the quantity of the hoof h c b d is found by this analogy : as the cube of the line a c , to the whole solidity : so is the cube of a geometrical mean between a c and a h , to the content of the cone or pyramid cut off : which subducted from the whole , the remainder is the content of the hoof. some of the lines being given , the rest are to be found . example . there is a tunn taken as the frustum of a cone , c d = 144 inches , the greater base , e f = 108 inches , the lesser base , g b = 60 inches , the depth . admitting the base were raised 3 inches , as the line c h , it is then necessary to take another diameter between c h and e f to find c d. to find a b the cones axe . as 18 , the semi . diff . of diam . co . ar . 8,744728 to 72 , the semi-diam . at the base : 1,857332 so is 60 , the tuns depth , 1,778151 to 240 , the cones axe . log. of the sum of their q square . the logarithm of ac 250.567 2,398924 the logarithm of ab 247.567 2,393692 a geometrical mean 2,396308 to find the content of the whole cone . the square of 144 4,316724 ⅓ of ab = 80 1,903090 359 &c. complement arithm . 7,444842 content in ale gallons 4620 ferè 3,664656 the line a c , the line a h , and the content being known , to find the content of the fall c b d h. as the cube of ac , co.ar. 2,803228 to the whole content : 3,664656 so is the cube of the mean , 7,188924 to the content of the cone cut off . 3,656808 82.6 the content of the fall. or thus : as the cube of ac , co . ar . 2,803228 to the whole cones solidity : 3,664656 so is the cube of ah , 7,181076 to the lesser cones solidity . 3,648960 the whole cone = 4620 the frustum mxhcbd = 164 the being ½ the fall or hoof = 82 some practical rules & examples for cask-gavging . some practical rules & examples for cask-gavging . the corner-stone in the whole fabrick of cask-gauging , as full , was long since laid by mr. oughtred , taking a cask to be the frustum of a spheroid , under which capacity they are generally received , though indeed there have been , and daily are found some cask differing in form , and really are more parabolical than spheroidal , i shall therefore lay down a plain method for the performance of the work ( viz. finding their content ) under these four considerations : as spheroidal , as the frustum of a parabolical spindle , as the frustum of a parabolical conoid , as the frustums of two cones abutting upon one common base . these severally , with and without a table of area's of circles . and forasmuch as the dimensions must be the first thing known , before the content can be found , i shall therefore shew the young tyro , how by some of the dimensions to find the rest , if any obstruction prohibit the taking of all . the boung-diameter , and head-diameter , and diagonal , to find the casks length . first subduct the semi-difference of diameters from the boung-diameter , and square the remainder , which square subduct from the square of the diagonal , and the remainder is the square of the casks semi-length . example . let bd be the boung-diameter = 29 inches , he be the head-diameter = 23 inches , be be the diagonal = 35.3836 > inches , sd the semi-difference = 3 inches : q. the length = lt ? the square of be = 1252 square of bd − sd = 676 sqaure of semi-length = 576 √ 24 48 = lt this very quest. was intended by mr. smith , p. 176. but through a mistake it was left out . the boung-diameter , diagonal , and length , to find the head-diameter . the rule . from the quadrupled square of the diagonal subduct the square of the length , ( which done ) the square root of the remainder is equal to the sum of the boung-diameter and one head-diameter . example . the square of diagonal = 5008 square of the length = 2304 remainder = 2704 √ = 52 subduct the boung-diameter = 29 head-diameter = 23 the head-diameter , boung diameter , and the length , to find the diagonal . the rule . to the square of the semi-length add the square of the boung diameter , less the semi-difference of diameters , and the square root of their sum is equal to the diagonal . example . square of semi-length = 576 square of 26 = 676 square of diagonal = 1252 √ 35.3836 > a cask taken as the frustum of a spheroid , cut with two plane parallels , each plane bisecting the axis at right angles , b the boung-diameter = 29 inches , h e the head-diameter = 23 inches , l t the length = 48 inches : q. the content in wine gallons ? the rule . to the doubled square of the boung-diameter add the square of the head-diameter , their aggregate multiply by the length , and to the product add the tenth part of it self , more one third of that tenth part , and from the sum cut off as many places toward the right hand as were in the multiplicand . example . the doubled square of 29 = 1682 the square of 23 = 529 the aggregate = 2211 the answer = 120.2784 wine gallons . another way . the q square . of the boung-diameter = 841 the q square . of the head-diameter = 529 the sum of their squares = 1370 the semi-sum = 685 the semi-diff . of squares = 156 their aggregate = 2211 the length = 48 16788 8844 the product = 106128 the tenth part = 106128 the part or ⅓ of = 35376 the answer in wine gall. 120.2784 the same cask being taken as the frustum of a parabolical spindle , the content may be thus found . q square . of the boung-diameter = 841 q square . of the head-diameter = 529 their aggregate = 1370 the semi-sum = 685 the tenth part of the diff. = 312 the length = 48 the product = 1001376 tenth of the product = 1001376 ⅓ of the answer in wine gall. 113.48928 if taken as the frustum of a parabolical conoid , cut as before mentioned , the content may be found as in this example . q square . of the boung-diameter = 841 q square . of the head-diameter = 529 the sum = 1370 the product = 98640 tenth part of the product = 98640 the answer in wine gall. 111.7920 if a cask of the same dimensions be taken as the middle frustum of two cones abutting upon one common base , cut with two planes parallel , and each bisecting the axis at right angles , the content in wine gallons may be found as in this example . q square . of the boung-diameter = 841 q square . of the head-diameter = 529 the sum = 1370 the semi-sum = 685 semi q square . of diff . of diam . = 18 the answer in wine gall. 110.8128 for finding the capacity of these , or any other vessels , it is convenient to have always in readiness a table of area's of circles in wine and ale gallons : i think it unnecessary to swell this intended small volume with them , there being two lately printed , exactly calculated to every tenth part and quarter of an inch , and also a table of area's of segments of a circle , by my good friend mr. iohn smith , in his book of gauging , to whom in gratitude i am obliged to render my hearty acknowledgment for many favours and kind assistances in these studies ; yet that you may be able to find any area of a circle upon demand , in wine or ale gallons , without a table , take this rule . divide the q. of the diameter by 294.1 for wine , and by 359.05 for ale gallons , and the quotient exhibits the area . or , saith mr. smith , multiply the q. of the diameter by .0034 for wine , and by .0027851 for ale gallons , and the product exhibits the area in such gallons . as in these examples . the diameter of a circle = 21.7 : q. the circles area in wine gallons ? the diameter of a circle = 26.8 : q. the area in ale gallons ? for finding the capacity of a cask , taken as spheroidal , by a table of area's of circles in gallons . example . a casks boung-diameter = 29 inches , head-diameter = 23 , and the length = 48 inches : q the content in wine gallons ? ⅓ of the area of the boung ⊙ = .9531 ⅓ of the area of the head ⊙ = .5996 their sum = 1.5527 semi-sum = .7763 semi ∽ = .1768 area of mean circle = 2.5058 the length = 48 the answer in wine gall. 120.2784 another way . ⅓ of the area of boung ⊙ = 1.9062 ⅓ of the area of head ⊙ = .5996 the area of mean ⊙ = 2.5058 the length = 48 the answer = 120.2784 that is , 120 gallons , 1 quart , and ¼ of a pint , ferè . to find the solid content of a cask , when taken as the middle frustum of a parabolical spindle , &c. the dimensions as before . ⅓ of the area of boung ⊙ = .9531 ⅓ of the area of the head ⊙ = .5996 their sum = 1.5527 semi-sum = .7763 tenth of the difference = .03535 area of mean ⊙ = 2.36435 the length = 48 the answer in wine gall. 113.48880 that is , 113 gallons , and almost 2 quarts . and as the frustum of a parabolical conoid , the capacity is thus found : ⅓ of the area of the boung ⊙ = .9531 ⅓ of the area of the head ⊙ = .5996 their sum = 1.5527 semi-sum = .7763 area of the mean ⊙ = 2.3290 the length = 48 the answer in wine gall. 111.792 if a cask be taken as the middle frustum of two cones , abutting upon one common base , &c. the dimensions as before . ⅓ of the area of the boung ⊙ = .9531 ⅓ of the area of the head ⊙ = .5996 their sum = 1.5527 the semi-sum = .7763 of area of 6 the ∽ of diam . .0204 area of mean ⊙ = 2.3086 the length = 48 the answer in wine gall. 110.8128 the ullage , or wants in a cask , may be found under these two considerations : 1. a cask standing on the head , with the diameters parallel to the horizon . 2. a cask lying with the axe parallel to the horizon . prop. i. in a cask standing on the head , with the diameters parallel to the horizon , some liquor remaining , to find how many wine gallons it is . here are these five things necessary to be known : 1. the diameter at the boung . 2. the diameter at the head. 3. the length of the cask . 4. the depth of the liquor . 5. the diameter of the liquors superficies . example . the diameter o p is thus found , first find the axis of the whole spheroid e f , thus ; from the square of half the boung-diameter ( n h ) subduct the square of half the diameter at the head , and extract the square root of the remainder : then by the rule of proportion , say , as that q √ , is to n h , the semi-boung-diameter : so is n i , the casks semi-length , to e n half the axis sought . diameter of the liquors superficies 27.4 having found the diameter of the liquors superficies : then , to ⅔ of the area of that circle = 1.70173 add ⅓ of area of the head circle = .59953 the depth of liquor = 11.6 the answer in wine gallons = 26.694616 which subducted from the whole content , leaves the ullage or wants . prop. ii. a cask lying with its axe parallel to the horizon , and having some liquor remaining in it , to find the content of the said liquor in gallons . let the dimensions be as before . in this proposition there is five requisites attending : h g the diameter at the boung = 29. a b the diameter at the head = 23. i k the length = 48. s g the depth of liquor = 11.6 . and the content of the whole cask in gallons . then by the help of a table of area's of segments of a circle , whose area is unity , and the radius divided in the ratio of 1.0000 parts , say by the rule of proportion : versed sine or arrow of segment . then seeking in the table you will find .4000 , and right against it under the title area you will find .37353 . then say : whole content 1.0000 . .37353 ∷ 120.2784 . 44.9276 the liquor remaining . the inversion of the question , viz. to find the liquor wanting . as 29. 17.4 ∷ 1.0000 . .6 again , the ullage . as 1.0000 . .62647 ∷ 120.2784 . 75.3509 the liquor remaining = 44.9276 which together make 120.2785 the casks whole capacity . finis . errata . pag. 3. l. 4. r. in the third . p. 5. l. 22. r. 20 : 13. p. 7. l. 17. r. 42 : 3 : 08 : 15 ; l. 19. r. 33 : 0 : 05 : 04. p. 9. l. 1. r. borrow of the. p. 13. l. 14. r. 5 s. the bushel . p 16. l. 13. r. 2 times . p. 19. l. 1. r. 5 from 6. p. 31. l. 19. dele always . p. 39. l. 22. r. in the decimal fractions of both factors . p. 50. l. 15. r. solid measure . p. 51. l. 15. r. 272.25 . p. 52. l. 15. r. .0041667 . p. 67. l. 14. dele as before . p. 82. l. 14. r. + a. p. 188. l. ult . r. ½ being . the rules herein mentioned , and other mathematical arts , are taught by the author , viz. arithmetick , vulgar , decimal , and logarithmetical ; the doctrine of triangles , plain and spherical ; the use of the globes , quadrant , sector , and other mathematical instruments ; fair writing , and merchants accompts , by way of debitor and creditor ; also the art of short writing . the country-survey-book: or land-meters vade-mecum wherein the principles and practical rules for surveying of land, are so plainly (though briefly) delivered, that any one of ordinary parts (understanding how to add, substract, multiply and divide,) may by the help of this small treatise alone and a few cheap instruments easy to be procured, measure a parcel of land, and with judgment and expedition plot it, and give up the content thereof. with an appendix, containing twelve problems touching compound interest and annuities; and a method to contract the work of fellowship and alligation alternate, very considerably in many cases. illustrated with copper plates. by adam martindale, a friend to mathematical learning. martindale, adam, 1623-1686. 1692 approx. 245 kb of xml-encoded text transcribed from 96 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2006-02 (eebo-tcp phase 1). a52120 wing m854a estc r217468 99829133 99829133 33569 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a52120) transcribed from: (early english books online ; image set 33569) images scanned from microfilm: (early english books, 1641-1700 ; 1917:11) the country-survey-book: or land-meters vade-mecum wherein the principles and practical rules for surveying of land, are so plainly (though briefly) delivered, that any one of ordinary parts (understanding how to add, substract, multiply and divide,) may by the help of this small treatise alone and a few cheap instruments easy to be procured, measure a parcel of land, and with judgment and expedition plot it, and give up the content thereof. with an appendix, containing twelve problems touching compound interest and annuities; and a method to contract the work of fellowship and alligation alternate, very considerably in many cases. illustrated with copper plates. by adam martindale, a friend to mathematical learning. martindale, adam, 1623-1686. collins, john, 1625-1683. [12], 225 [i.e. 226], 229-234 p., plates, folding printed for r. clavel, at the peacock in st. pauls church-yard, and t. sawbridge, at the three flower-de-luces in little-britain, london : 1692. "an appendix containing xii. problems touching compound interest & annuities" has separate title page with imprint: london, printed in the year 1692. register and pagination are continuous. errata on p. [12]. "to the reader" signed: john collins. page 226 misnumbered 225. reproduction of the original in the british library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng surveying -early works to 1800. interest -early works to 1800. mathematics -early works to 1800. 2005-07 tcp assigned for keying and markup 2005-08 aptara keyed and coded from proquest page images 2005-12 judith siefring sampled and proofread 2005-12 judith siefring text and markup reviewed and edited 2006-01 pfs batch review (qc) and xml conversion the country-survey-book : or land-meters vade-mecvm . wherein the principles and practical rules for surveying of land , are so plainly ( though briefly ) delivered , that any one of ordinary parts ( understanding how to add , subtract , multiply and divide , ) may by the help of this small treatise alone , and a few cheap instruments easy to be procured , measure a parcel of land , and with judgment and expedition plot it , and give up the content thereof . with an appendix , containing twelve problems touching compound interest and annuities ; and a method to contract the work of fellowship and alligation alternate , very considerably in many cases . illustrated with copper plates . by adam martindale , a friend to mathematical learning . frustra sit per plura quod fieri potest per pauciora . london , printed for r. clavel , at the peacock in st. pauls church-yard , and t. sawbridge , at the three flower-de-luces in little-britain , 1692. to the right honourable the lord delamer , baron of dunham-massie , &c. my lord , this small tract comes to your lordship , not as to a patron to protect its errors ( if any such there be ) but as to a critical noble friend , that will be sure faithfully to tell the author of them . which favour , together with a chearful acceptance of this poor present , he humbly hopes for , because of its relation , being writ at dunham , by your humble servant , who besides his domestick dependance , cannot forbear without ingratitude to tell the world that your lordship's kindness hath very much encouraged and assisted him in mathematical studies , not only by a free communication of many a choice notion both vivâ voce , and by the loan of manuscripts . but also by a considerable number of excellent books and costly instruments bountifully bestowed upon him : who wanting other ways to express his many singular obligations , and deep sence thereof , humbly offers this punie treatise for your lordships diversion at spare hours ; and is ambitious to write himself , oct : 26. 1681. my lord , an humble and faithful ( though unworthy ) servant to all your lordship's noble family a. m. mr. collins to the reader . courteous reader , the learned mr. adam martindale formerly writ two excellent almanacks , called country almanacks , which were printed , and esteemed by several members of the royal society very useful , especially for country affairs , but meeting with some discouragements from such as knew not how to judge of the authors worth , he gave over that undertaking , contrary to the desires of many ingenious men. and having since writ a little treatise of survey , in which he hath had experience , as well as theory , and being willing to have the approbation or dislike of others , that it might either be printed or stifled , imparted the same to some of the members of the aforesaid illustrious body . upon the perusal of whom and divers experienced artists who make a livelihood of it , i find it well approved ( as clear and concise ) only the latter were sorry so much was discovered , as detrimental to their practice , particularly about setting off the outjettings , where it 's inconvenient intirely to measure them . the book is small , the price ( though not the worth ) mean , no small encouragements to young students and the vulgar , for whom it was chiefly intended : by which , that they may reap benefit , is the hearty desire of ( a well-willer to the author and them ) john collins . the preface . reader , the title sufficiently informs thee in general of my designs : but i confess i owe thee a a more particular account , not only of that , but several other things which i shall briefly give thee . 1. i have observed that the country aboundeth with such , as by their inclination and interest are prevailed with to take pains in measuring land , that for want of better instruction use ill divided chains and tedious methods of computation , which makes their work intolerable troublesom , if exactness be required . and some for want of skill in the fundamentals of geometry , have imbibed prodigiously false principles , as this for one , viz. that the content of any close , of what figure soever , may be found by squaring a quarter of the perimeter . mathematical-schools , where better things might be learned , are very rare , and an able artist to instruct one in private is hard , and charge able to be procured . excellent books indeed there are in our english tongue , written by our famous rathborn , wing , leybourn , and holwell , to which may be added industrious mr. atwells treatise , and some part of capt. sturmy's : but those i rather esteem fit to be read byan able artist ( towards his perfecting ) than by a new beginner , for in the best of those books he will find the most useful and plain rules so intermixed with others that are less necessary , and more intricate , ( though very excellent for their proper ends ) and so many curiosities touching trigonometry , transmtation of figures , &c. which his business never calls for , that for want of judgment to pick out that which fits his present purpose , and to study higher speculations afterwards , he is apt to be confounded and discouraged ; whereby it accidentally comes to pass that plenty , makes him poor . besides , three of these six books are in folio , another in quarto , and the other two ( though octavo's ) too large for ordinary carrying in a pocket , and in that regard not so convenient for one that hath much occasion to be out of his own house ; to say nothing of their price , which to some poor youths is not the least discouragement . i have therefore made my book so little , that the price can neither much empty the pocket , nor the bulk overfill it . and yet so plain , that i doubt not to be understood by very ordinary capacities . my method is fitted to my design : beginning with the principles of the art , and so proceeding gradatim till i have shewed how all ordinary figures may be measured , protracted , and cast up , without any other instrument of charge but chains , compasses and scales . afterwards for such as desire higher attainments , i have endeavoured to speak so fully ( in a little compass ) of the plain table , and given such hints , applicable not only to it , but also to the peractor , theodolite , and semicircle , as that an ingenious person may make great use of them . but as touching the doctrine of triangles , and transmutation of figures into others equipollent , with the large tables ( referring to the former ) of logarithms of numbers , sines , and tangents , i thought it improper to cumber this small manual , or the unlearned reader with them , having ( as i humbly hope ) sufficiently inform'd him how to find all his sides and angles by instruments , and also the content of any figure without such transmutation , reserving such curiosities and many others touching drawing and painting of maps ; measuring of ways , and rivers , &c. to a second part , which i may perhaps hereafter publish upon due encouragement , but if i do not , the curious may find themselves good store of work in the authors even now quoted . 2. it may seem strange to some , that in referring to the figures , i sometimes use words seeming to imply that the figure i speak of is in that very page , and so it was in my copy , but the printer and gravers have otherwise contrived them for convenience in copper cuts by themselves . and to give them their due they are generally done with great accuracy , and none of them having any such error as is like to beget trouble or mistake to the reader , saving only that fig. 19 hath d instead of o at the center , and the line ol in the margin of fig. 14. should be of the length from l to the uppermost o in the scale , and the figures on the side should be made 1 less than they are , viz. 2 should be 1 , 3 made 2 , &c. and lastly , as to the errata , though i have not been so anxiously careful , as to correct every literal mistake , i have very diligently perused all from p. 1 to p. 224 inclusive , and hope i have sufficiently restored the sense to the places wronged , when thou hast done them right by the pen according to the directions of the errata following next after the contents , and that you continue the line in the margin of p. 34. to the length of the line ol in fig. 14. the contents of the chapters . chapt. 1. of geometrical definitions , divisions , and remarks . p. 1. chapt. 2. of geometrical problems . p. 6. chapt. 3. to find the superficial content of any right lined figure , the lines being given . p. 17. chapt. 4. concerning chains , compasses , and scales . p. 26. chapt. 5. how to cast up the content of a figure , the lines being given in chains and links . p. 35. chapt. 6. how to measure a close , or parcel of land , and to protract it , and give up the content . p. 41. chapt. 7. concerning the measuring of circles and their parts . p. 48. chapt. 8. concerning customary measure , and how it may be reduced to statute measure , & e contra , either by the rule of three , or a more compendious may by multiplication only . p. 52. chapt. 9. how a man may become a ready measurer by practice in his private study , without any ones assistance or observation , till he design to practise abroad . p. 65. chapt. 10. how to measure a piece of land with any chain of what length soever , and howsoever divided ; yea with a cord or cart-rope ; being a good expedient when instruments are not at hand of a more artificial ●ake . p. 67. chapt. 11. concerning dividing of land artificially and ●echanically . p. 70 chapt. 12. concerning the boundaries of land , where the ●ines to be measured must begin and end . p. 80. chapt. 13. containing a description of the plain-table , the ●rotractor , and lines of chords . p. 82. chapt. 14. how to take the true plot of a field by the ●lain-table upon the paper that covers it , at one or ●ore stations . p. 85. chapt. 15. concerning the plotting of many closes together , ●hether the ground be even or uneven . p. 99. chapt. 16. concerning shifting of paper . p. 102. chapt. 17. concerning the plotting of a town field , where 〈◊〉 several lands , buts , or doles , are very crooked : ●●th a note concerning hypothenusual or sloping ●●undaries , common to this and the fifteenth chapter . ● 104. chapt. 18. concerning taking the plot of a piece of ground 〈◊〉 the degrees upon the frame of the plain-table se●●●al ways , and protracting the same . p. 108. chapt. 19. concerning taking inaccessible distances by the ●●ain-table , and accessible altitudes by the protractor . ● 121. chapt. 20. of casting up the content of land by a table . ● 193. errata . page 3 line 16 read trilaterals . p. 4 〈◊〉 geodates . p. 5 l. 29 eneagon . p. 10 l. 6 belong as the other two . p. 16 l. 6 centers at right a●●gles . p. 28 l. 1 forefinger . p. 36 l. 20 poles or r●● p. 47 l. 15 fourth diagonal and the sixth side . p. 〈◊〉 l. 28 as in this figure is abc . p. 56 l. 23 , 〈◊〉 and l. 24 ● . 22 ½ p. 58 l. 11 28. p. 69 l. 5 side 74 l. 25 fg. p. 77 l. 27 138562 , and l. 28 〈◊〉 33 r. 242030. p. 79 l. 33 triangulate . p. 80 l ▪ former . p. 82 l. 24 fitted . p. 86 l. 2 stationary ●●●stances . p. 90 l. 15 chart , or card. p. 95 l. ● park , pond . p. 103 l. 22 line . p. 104. l. 19 〈◊〉 fig. 1. fig. 2. fig. 3. fig. 4. fig. 5. fig. 6. fig. 7. fig. 8. fig. 9. fig. 10. fig. 11. fig. 12. fig. 13. fig. 14 fig. 15. fig. 16. fig. 17. fig. 18. fig. 19. fig. 20. fig. 21. fig. 22. fig. 23. fig. 24. fig. 25. fig. 26. fig. 27. fig. 28. fig. 29. fig. 30. fig. 31. fig. 32. fig. 33. fig. 34. fig. 35. fig. 36. fig. 37. fig. 38. fig. 39. the country survey-book : or , land-meter's vade-mecvm . chap. i. of geometrical definitions , divisions , and remarks . i. a point is that which hath no parts , either of longitude or latitude , but is indivisible , ordinarily expressed with a small prick , like a period at the end of a sentence . ii. a line hath length , but no bredth nor depth , whose limits or extremities are points . this is either right or crooked . iii. a right line lies straight , and equal between its extreme points , being the shortest extension between them ; the crocked or circular not so . iv. a superficies hath length and bredth , but no depth ; of this lines are the limits . v. a plain superficies is that which lieth equally ( or evenly ) between its lines . vi. an angle is the meeting or two lines in one point , so as not to make one straight line , and if drawn on past that point , they will intersect or cross one another . this is vulgar english may be called a corner ; of which there be two sorts , one right , the other oblique . vii . a right angle is that which is made by two right lines , crossing or touching one another perpendicularly , ( or squarely ) like an ordinary cross , or carpenters square . viii . an oblique angle is that which is either greater or less than a right angle , and this is of two sorts , obtuse and acute . ix . an obtuse angle is greater than a right angle , like the left and right corners of a roman x. x. an acute angle is less than a right angle , like the highest and lowest corners of the same letter . xi . a figure is that which is comprehended under one line or many : of this there are two kinds , a circle and a right-lined figure . xii . a circle is a perfect round figure , such as is drawn with a pair of compasses , the one foot being turned round in a point , and the other wheeled about it . the point in the precise middle is called the center ; the round line , the circumference or peripheri ; a line going through the center , and divide the circle into two equal parts , is called the diameter ; half of that line is a somidiameter , or radius ; half the circle is stiled a semicircle ; the quarter , a quadrant ; any portion of it , cut off by a right line not touching the center , is called a segment . xiii . right-lined figures are such as are limited by three right lines or more , and are either triangles or triangulate , that is , such as are compounded of , and resolvable into triangles . xiv . triangles are figures comprehended under three right lines , and ( as ramus thinks for a reason that he gives , lib. 6. pr. 6. ) might be better called trilaterals ; but the name triangle from the number of the angles hath obtained . also from the nature and quantity of their angles these triangles are distinguished into three sorts : 1. rectangled , having one right angle ; 2 obtuse-angled , having one obtuse angle ; and 3. acute-angled ; having all acute angles ; for no triangle can have more right or obtuse angles than one , because by by an old rule ( easie to be demonstrated ) no triangle upon a plain superficies can consist of three greater angles than such , as being jointly taken are equal to two right . these three sorts of triangles may , according to the length and proportion of their sides , be subdistinguished into seven ; for each of them may have either two equal sides or none , and the acute-angled may have all three sides or lines equal : to all which kinds , learned men give distinct greek names , which if mine english reader have a mind to see , they are to be found in 〈…〉 practices , book 1. page . 6. for my present purpose the above-mentioned ●rimembred distinction will abundantly suffice ; for be triangles of what name or kind soever , they are all capable of being exactly measured by one plain rule as hereafter shall fully appear . xv. triangulare figures are such as have more angles ( and consequently more sides or lines ) than three : and these are either quadrangular or multangular . xvi . quadrangular figures are such as have fo●● angles ( and as many side ) and these are either parallellograms or trapezia's . xvii . parallellograms are figures that are bounded with parallel lines , that is , such lines as are every where of the same distance one from another , so as if they were infinitely extended they would never meet , like the upright lines of he roman h. these parallellograms are either rectangular or obliquangular . xviii . rectangular parallellograms are such as have four right angles . viz. the square or quadrat , and the long square , otherwise called the oblong . xix . the square is that figure that hath four right angles , and four equal sides , like any of the six faces of a die. xx. the long square hath also four right angles , and the oposite sides are equal , but the adjoyning sides meeting at each angle differ in length . of this figure is a well printed page in a book , and the superficies of a well cut sheet of paper , or an ordinary pane of glass . xxi . obliquangled parallellograms are such as have oblique angles , viz. two acute , and two obtuse . of these there are two kinds , the rhombus , and the rhomboides . xxii . the rhombus is a figure that hath equal sides , but no right angles , ( like the form of a diamond on the cards , or the most ordinary cut of glass in windows ) whose oposite angles are equal . xxiii . the rhomboides is ( as it were ) a defective rbombus , for if from any side of a rhombus we cut off a part with a parallel line , the remainder will be a rhomboides , which hath neither equal sides nor angles , but yet the opposite sides and angles are equal . xxiv . the trapezium is a figure that is neither parallellogram , nor ( consequently ) hath equal sides or angles , but is irregularly quadrangular , as if drawn at adventure . of this shape most fields prove , that seem to the eye to be squares or oblongs . xxv . multangular figures are such as contain more sides and angles than four , and they are either regular or irregular . xxvi . regular multangulars take their names from their number of angles , so a pentagon , hexagon , heptagon , octogon , encagon , decagon , signifie a multangular figure of five , six , seven , eight , nine , ten , angles , and consequently sides . xxvii . an irregular polygon or multangular figure , is that which hath more angles ( and sides ) than four , the sides ( and angles ) being unequal to one another . chap. ii. of geometrical problems . i. to draw a line parallel to another , at any distance assigned . fig. 1 open your compasses to the distance given and chusing two points conveniently distant in the line given , as here at a and b describe the arches c and d , to whose convixity if you apply a rule , the parallel line is easily drawn . ii. to raise a perpendicular upon a line given , or to cross that line at right angles in a point assigned . fig. 2 suppose the point c in the line ab were assigned for the perpendicular ; open the compasses to a convenient distance , and mark out the two points e and f in the line ab , then opening them some what wider , you may ( by setting one foot in e and f severally ) describe the two arches cutting one another at the point d , from which if you draw a line to the point c , the work is done for the raising of a perpendicular ; but if you be to cross the lines at right angles , you may continue the line from d through c at pleasure . but if the said line ab had been given to be divided in the precise middle , by another line crossing it at right angles , the way were to set one point of the compasses in a and b severally , and having described two arches above the line , intersecting one another as at d , do the like below the line ab from the same points and with the same extent of your compasses , then through the several intersections ( a rule being laid upon them ) a line may be drawn , cutting the given line exactly in the middle at right angles . note , that when one point of your compasses stand in a , you may make both the arches belonging to that center above and below the line , and then removing the compasses to b , you may cross them both . iii. to raise a perpendicular at the end of a line . fig. 3 let or be the line given , then to raise a perpendicular at r , make five little equal divisions , and taking four of them with your compasses , set one foot of your compasses in r , and with the other describe the arch pp ; then take the distance from r to 5 , and placing one foot in 3 , with the other describe the arch bb , intersecting the former in the point s ; then shall the line sr ( being drawn by a straight rule ) be a perpendicular to the line or . iv. to let fall a perpendicular upon a given line from any point assigned . open your compasses so as one foot being set in the assigned point the other may go clear over the line given , and thereby describe an arch cutting the line at two points ; then shall the half distance between those two points be the point to which the perpendicular may be drawn from the point assigned . but if you think it too much pains to find the point of half distance by trial , you may help your self by the second problem : for if you describe two arches intersecting one another on the farther side of the line from the assigned point , placing ( to that purpose ) the foot of your compasses first in one of the intersections of the given line , and then in the other ; you may by laying a rule upon the assigned point , and the intersection of the two arches , draw a perpendicular from the said assigned point , cutting the given line at right angles . note , that all these problems touching perpendiculars , aim at no greater matter , than what may be performed in a mechanical way with exactness enough ( and much more neatly by avoiding unhandsome pricks and arches ) by the help of a small square exactly made , ( or for want thereof a plate quadrant , or broad rule , having a right angle and true sides ) for if you apply one leg of such a square to any line , so as the angle of the square may touch the end of the said line , or any other point where the perpendicular is to be raised , you may by the other leg draw the perpendicular . in like sort to let fall a perpendicular from a point assigned you need only to apply one leg of the square to the line , so as the other may touch ( at the same time ) the assigned point whence you may draw the perpendicular , by that leg that toucheth the point : if the angle of your square be a little blunt either through ill making or long using , you must allow for it when you apply it to the point in a line . and when you are drawing a perpendicular , you must stop before you reach the given line , and then by applying the leg of your square to that part of the perpendicular already drawn , so as part of that leg may pass clearly over the given line , you may draw the rest of your perpendicular as exactly as if the angle had been true . the like course is to be taken when a line is to be crossed by another drawn quite through it at right angles . v. an angle being given , to make another equal to it . fig. 4 the angle xad being given , and a line drawn at pleasure as is the lowest from the point e , open your compasses to any convenient distance , and setting one foot in a describe the arch bc. then with the same extent setting one foot in e , with the other describe the arch gh , long enough to equal or exceed the other . then taking the distance bc between the points of your compasses , set one in g , and with the other mark the point h in the arch gh , through which point h a line being drawn from the point e , will make an angle with the line eg equal to the angle given . note , when we speak of the quantity of angles , their equality , or unequality , we never regard the length of the lines ; for if you extend or contract them at pleasure , the angle is still the same . but that is the greatest angle whose lines are farthest distant from one another , at the same distance from the angular point , or the place where its lines meet . vi. any three lines being given ( equal or unequal ) so as no one of them be longer than the other two joyned together to make a triangle of them . fig. 5 the lines a , b , c , being given , set the line a from d to e ; then with your compasses take the length of the line b , and setting one foot in d describe the arch po. this being done , take with your compasses the length of the line c , and setting one foot in e with the other cross the former arch at f , from which intersection drawing lines by a rule to d and e , the triangle is finished . note , that if all the sides , or two of them , be equal , the method is the same ; but the labour less , because we need not to take the same length twice over with the compasses . vii . to find the perpendicular of the triangle , in order to the measuring of it . fig. 6 let the line ab be accounted the base , and from the angle c let fall a perpendicular as was taught , probl. 4. upon that line at d , which is ready for taking off with compasses and measuring on a scale , of which hereafter in the chapters of measuring the content of figures . but if we have no occasion to draw the perpendicular , but only to know the length of it , ( as it most frequently falls out in measuring ) no more is needful but to set one foot of the compasses in the angular point c , and extend the other to the base ab , so as it may touch it , but not go beyond it ; then have we the perpendicular between the points of the compasses . viii . one side being given , how to make a square . fig. 7 the line cd being given , raise a perpendicular at c of the length ( at the least ) of the given line ; then taking the line cd between the feet of your compasses , set it upon the perpendicular from the angular point c to a : with the same distance setting one foot in d describe the arch op . lastly , with the same distance ( or extent ) set one foot in a , and with the other describe the arch crossing the arch op in n , from which intersection a line drawn by a rule to a , and another to d , finish the geometrical square or quadrant acdn. ix . to make a long square , the length and bredth being given . this is so like the former , that a particular figure is not necessary to conceive of it . suppose each side of the square in the last problem to consist of 8 small equal parts , and you were to make a long square whose length must be equal to a side thereof , viz. 8. and the bredth half so much given in a line thus — 4 ; then when you had drawn the line cd for the length , and raised the perpendicular at c , you must take the shorter line given for the bredth , and set it upon the perpendicular from c upwards to a point , which for distinction we shall call the point e , imagining it so marked : with the same extent of the compasses describe the arch , placing ( to that purpose ) one foot in d. lastly , extending your compasses to the length of the line cd , set one foot in e , and with the other cross the arch aforesaid . then a right line drawn from that intersection to e , and another from the same to d , complete the long square . x. to make a rbombus , the sides being given . fig. 8 if the angles be not limited draw any oblique angle at pleasure , either acute or obtuse , as here the angle bac , which is acute . then let the line op be the length of a side , which being taken with your compasses , set it from the angular point a in both lines to d and e , in which two points place a foot of your compasses successively without altering them , viz. in d to describe the arch fg , and in e to describe the arch hi , crossing one another in the point k , from which , right lines drawn to d and e , finish the rhombus daek . note , if any angle be given , together with the side ; to limit the shape and content , begin with that , and proceed as before : for you must know , that to make a rhombus ( or rhomboides ) like to another for figure , or equal to it in content , it is not sufficient to have the same sides ; for the more oblique the angles 〈◊〉 the farther will the rhombus differ from a 〈◊〉 ( and the rhomboides from a long 〈◊〉 are ) and the less will be the content . but 〈◊〉 must have an angle given , ( which will pro●●●e all the rest ) or else a diagonal line , which 〈◊〉 right line passing through the rhombus ( or ●omboides ) , from one opposite angle to another , and dividing the figure into two equal ●●●angles . if the former ( viz. an angle ) be ●●n , i have shewed what use is to be made 〈◊〉 . if the latter , ( i. e. a diagonal ) toget●●● with the length of the sides , you may by ●●●ng the length of the sides with your com●●es , and setting a foot in the ends of the ●●gonal line , make a triangle on the one side ●he diagonal , by probl. 6. and then another on the other side by the same problem , the ●●gonal being a common base to them both ; this will give the figure exactly . to make a rbomboides , the sides being given . fi. 9 〈◊〉 neither angle nor diagonal be given , 〈◊〉 if either of them be limited , the case is ●●en to in the last problem ) make any angle ●dventures as here abc . then supposing 〈◊〉 lines given to be op and qr , set the 〈◊〉 of the longer upon the line bc from b 〈◊〉 , and the shorter on the line ba to e , 〈◊〉 with the compasses extended from b to e 〈◊〉 one foot in d and describe the arch fg. ●●ewise , with the compasses extended to the 〈◊〉 of the line op , setting one foot in e 〈◊〉 the other describe the arch hi , intersecting fig. 9 the former arch at k , from which intersection lines drawn to d and e finish the rhomboides . xii . to make a trapezium , the diagonal and lines in order being given . fi. 10 let the line hl be the diagonal of a trapezium , whose sides are the lines a , b , c , d , the side a being counted the first , as that which takes its beginning from the point h , and the rest in the order as they are marked alphabetically . then with your compasses set to the length of the line a , place one foot in h , and with the other describe the arch ef. next taking the length of the line b , with the one foot , o● your compasses placed in l , with the other make the arch gi intersecting the former at k , from which point of intersection , lines drawn to h and l make the triangle hkl . then with the extent of the line c , set one of the feet of your compasses at l , and describe the arch op . lastly , setting them to the length of the line d , and placing one foot of your compasses in h , with the other make the arch sr intersecting the former at q ; 〈◊〉 shall lines drawn from q to l and h make u● the triangle lqh , and finish the trapezium hklq . i could have been much briefer in this problem by referring to the sixth ; but this being of very great and frequent use , i desired to be very plain . xiii . to make a regular polygon , otherwise called a regular multangular , or multilateral figure , consisting of many equal sides and angles , viz. above four apiece . being satisfied what shall be the distance between the center and every angle , with that distance describe a circle , which being equally divided into as many parts , as the figure must have angles ( or sides , for they are equal in number ) and lines drawn from the points of division within the circle from point to point , ( ordinarily called chords ) the polygon is finished as in this diagram . fig. 11 suppose an heptagon , or multangular figure of seven sides , and as many angles , be to be described , every angle being designed to be distant from the center a , seven eighths , or three quarters and an half of an inch ; with that distance describe the circle bcdefgh , which being divided into seven equal parts , and lines drawn from point to point , the heptagon bcdefgh will be therein included . i shall rather leave my unlearned reader to find out the points of division by many tryals , than to puzzle him with the geometrical way for finding out chords to that purpose ; nor shall i busie my self to tell him at large how he may divide 360 by the number of his angles or sides , and then finding in his quotient the degrees and parts belonging to every division , set them readily out by a protractor , or ( for want thereof ) by a line of chords ; for i suppose him yet ignorant of such things . i shall therefore only tell him thus much : a line drawn through the circle at the center divides it into two equal parts , which being crossed in the center by another line , the circle will be parted into four equal parts or quadrants , and those by halving them into eight parts . the extent of the compasses whereby the circle is drawn ( usually called the radius or semidiameter ) will divide it into six equal parts ; two whereof must be a third part , and half of one a twelfth part ; and these still easily capable of farther division . xiv . having the sides of the triangles whereof it consisteth , orderly given , to make an irregular multangler , or multilateral figure . this will be more fully handled hereafter , when i come to shew the method of drawing plots of ground : in the interim i will give you a specimen of an irregular pentagon . fi. 12 having the lines of three triangles given , ( which by a rule hereafter to be mentioned are necessary to make up a five figure ) lay down the greatest of the first , viz. 20 , from a to b for a base , and by probl. 6. make a triangle of it and the other lines 16 and 10. viz. the triangle abo . secondly , you find by the number o over the first line of the second triangle that it is the common base to them both , and therefore by the same probl. 6. make the triangle a b p of the lines 20 , 14 , 18. fi. 12 lastly , finding the base of the third triangle to be the same with 18 , one of the sides of the second , make the triangle pbq of the lines 18 , 11 , 12 : so is the quinquangular figure finished . how every line is to be found in its due order in this or any other sort of multangular figures , so as to give a true and exact account , not only of the superficial content , but also of the figure ( or shape ) and situation , is to be taught hereafter in the doctrine and practice of protraction . chap. iii. how to find the superficial content of any right-lined figure , the lines being given . as a foundation to what i shall say upon this subject , there are some few geometrical principles or theorems out of enclid and ramus , which i desire may be remembred ; and because understanding is a mighty help to memory , i design for my country reader a kind of ocular demonstration , which though not so strict and artificial as that which is to be found in the commentators upon euclid in the quoted places , will be more serviceable to him , because more easily understood . theor. 1. every parallellogram being of the same length with the base of a triangle , and of the same height with the perpendicular of that triangle , is double to it , euclid 41. 1. fi. 13 here are two equal oblongs or long squares , abcd and befc , and within them two triangles inscribed , whose bases are of the same length , and their perpendiculars ( op and qr ) of the same height with the oblongs . now each of these triangles being parted into two right-angled triangles by their perpendiculars , then it is plain to the eye ( and from the nature of diagonals , which ever divide a parallellogram into equal parts ) that the two new triangles opd and opc , which make up the first of the given triangles , are equal to the triangles dao and obc , which make up the remainder of the parallellogram abcd. therefore that parallellogram is double to that taiangle , which was to be demonstrated : in like manner it is evident , that the parallellogram befc is double to the triangle cqf , because crq is equal to bqc , and qrf is equal to qef. theor. 2. all triangles having the same base , and lying between the same parallels , are equal . euclid 37. 1. so in our last diagram , the two given triangles having bases of the same length , and lying between the same parallels , are evidently equal , because they are demonstrated to contain each of them the exact half of the parallellograms , wherein they are inscribed ; and the parallellograms being equal , their halves must be equal also . theor. 3. the sides of a triangulate ( that is , one that hath four or more sides ) are ever two more than the triangles of which it is made . ram. lib. 10. prop. 2. fi. 10 , 12. this is plain by inspection , if you view again the figures of the trapezium and irregular pentagon , in the 12th and 14th problems of the second chapter . these theorems being allowed to be found ( as nothing more certain ) the doctrine concerning the superficial content of right-lined figures might be reduced to a narrow compass ; for he that knoweth how to husband these three theorems , may easily take up these corollaries , ordine inverso . 1. any quadrangular figure ( regular or irregular ) may by a diagonal be parted into two triangles ; any five-sided figure by two diagonals into three triangles ; and six-sided figures into four by three diagonals , &c. by theor. 3. 2. 't is no matter of what shape the triangle is , as to the rule for measuring , for whether it be right-angled , acute-angled , or obtuse-angled , and whether it have three , two , or no lines equal ; 't is only the length of the base , and height of the perpendicular , that is considerable ▪ by theor. 2. 3. the true measure or content of any triangle , whether alone , or as part of any triangulate figure of 4 , 5 , 6 , or more sides ( and consequently of the whole figure , by summing up the content of all the several triangles ) is found by multiplying the whele base of the triangle by half the perpendicular , or the whole perpendicular by half the base ; which being a rule of such infinite use in surveying , i desire it may be remembred ; and that it may be understood , i shall give you a plain example . fig. 6 suppose a b the base of the triangle , belonging to the seventh problem of the foregoing chapter , to be 44 , and the perpendicular cd to be 20 : whether you multiply 44 the whole base by 10 the half of the perpendicular , or 20 the whole perpendicular by 22 the half base , the product gives the content 440 , as is here apparent . 44 10 440 20 22 40 40 440 having thus given a general method how all right lined figures may be reduced to triangles , and so their content found out ; i might pass to the next head concerning instruments , and their use ; but because there are nearer ways in measuring particular kinds of triangulate figures proper to those kinds . i shall briefly touch them . i. to find the contents of a square , or long square . multiply the length by the bredth , the product gives the area or content . example of a square 17 inches length . 17 inches bredth . 119 17 289 square inches . example of an oblong 25 feet long . 13 feet broad . 75 25 325 square feet . ii. to find the area or content in measure of a rhombus . let fall a perpendicular from one of the obtuse angles upon the opposite side ; that side multiplied by the perpendicular , gives the area . 20 yards the side . 14 yards the perpendicular . 80 20 80 square yards . iii. to find the area of a rhomboides . divide it into two triangles by a diagonal drawn between either pair of the opposite angles , ( as suppose the acute ) then from either of the other angles ( for instance , the obtuse let fall a perpendicular upon that diagonal then shall that diagonal , being multiplied by that perpendicular , give the area . example . 19 rods the diagonal . 5 rods the perpendicular . 95 square rods the content . iv. to find the content of a trapezium . f. 10 divide it by a diagonal into two parts from angle to angle ; as the trapezium , ch. 2. pr. 12 is divided by the diagonal hl , then from the other two angles ( which in that figure a●● marked with k and q ) let fall perpendicular upon the diagonal , half the sum of those perpendiculars being multiplied by the diagonal ( or common base ) gives the superficial content . example . suppose in the trapezium before mentioned the diagonal is 33 , the perpendicular from 〈◊〉 fi. 10 13 , and that from q15 , the area or superficial content is thus computed : 13 chains the first perpendicular . 15 the second perpendicular 28 the sum of both perpendiculars . 14 their half sum. 33 the diagonal . 42 42 462 square chains the area . v. to find the content of a regular polygonial , or multangular figure , otherwise called multilateral . draw a line from the center to the middle of any side ; half of the perimeter ( or of all the sides ) being multiplied by that line before-mentioned , gives the content . vi. to find the content of an irregular polygon , or many sided figure . divide it into trapezia's and triangles by diagonals , then find their content severally , and sum up all together ; which that you may better apprehend , fi. 12 suppose the polygon belonging to the last problem of the second chapter were given without the diagonals ab and bp ; then by drawing those diagonals , fi. 12 the figure is divided into three triangles , whereof two being upon the same base ab make up a trapezium , whose content may be found , just in the same manner as was taught even now in the fourth rule , having found the perpendiculars from o and p falling upon the line ab . then there remains the triangle bqp , whose content may be found by the general rule concerning triangles , having found the perpendicular falling from q on the line bp ; and then having added the content of that triangle to the content of the trapezium , you have the area of the whole polygonial figure . but now methinks i see ( as it were ) my country student scratching his head , and wishing for an opportunity ) to propound two doubts to me . 1. why i called the numbers correspondent to my lines by divers denominations , as inches , feet , yards , rods ; and sometimes by none at all but propounding the numbers abstractly . 2. how i came to know how many of those measures ( whatever they be ) are represented by the lines given , and perpendiculars found . to the former i answer , i am not yet teaching how to measure lines ( that work is presently to follow ) but what lines of figures are to be measured , and the measures of those lines being known ( or supposed ) how the content upon those real ( or supposed ) grounds may be found , and to this purpose i might call the numbers represented by the lines , inches , feet , yards , or any other measures , at pleasure , provided i called the squares , to which the area is equal , by the same names ; for an inch in length bears the same proportion to a square inch ( having length and bredth ) that a mile in length bears to a square mile . for this reason i profess not in the title of this chapter to teach how to measure figures , ( much less how to measure the lines of such figures ) but how to find the content , the lines being given . and then to take away the second doubt , know that the numbers represented by the lines , were either given by those learned artists from whom i borrowed the figures , or supposed by my self as grounds to go upon ( as in such cases is ordinary ) or , lastly , found out to be agreeable thereto by some scale of small equal parts , which he is yet supposed ignorant of . but now i am going to shew him the nature and use of two or three plain and cheap instruments , by the help whereof he may with much exactness , 1. measure the length of any lines bounding right-lined figures upon the ground . 2. draw lines and figures upon paper proportionable thereunto ( which we call protracting ) . 3. find upon his paper-figures the true length of all the desired perpendiculars , which shall also be proportionable to those on the ground , but much more easie to be obtained . and withal , i intend to give him such farther instructions and cautions for the application of the general and more particular rules of this chapter to his peculiar use , as will render them ( especially some of them ) singularly advantagious . chap. iv. concerning chains , compasses , and scales . 1. amongst the many sorts of chains used for measuring land , three are most famous ▪ bearing the names of their inventors , mr. rathborne , mr. gunter , and mr. wing , all of them ingeniously divided , and useful in their kind● but my brievity will give me leave only to describe one , and that shall be mr. gunter's , being most in use , and easie to be procured . this chain contains in length four statute-poles or perches , each perch containing 1● feet and a half , or 5 yards and a half ; so that the whole chain is 66 feet , or 22 yards long . this whole chain is divided into 100 equal parts or links , whereof 25 are a just pole or perch ; and for ready counting , there is usually a remarkable distinction by some plate or large ring at the end of every 25 links , but especially at the precise middle of the chain , which should differ from the rest in greatness and conspicuousness . also at the end of every tenth link 't is usual to hang a small curtain-ring and if there be at every five links end a piece o● wire made like the bow of a link , with a little shank an inch or less long , ( or some such distinction ) 't is still better . when you are to measure any line by this chain , you need to regard no other denomination but only chains and links , set down with a prick of your pen betwixt them , e. g. if you found the side of a close to be 6 chains and 35 links long , it is thus to be put down 6. 35. but if the links be under 10 , a cypher must be prefixed ; so 7 chains 9 links must be thus set , 7. 09. in the using of this ( or indeed of any ) chain , care must be taken , both to go strait , and to keep a true account ; for which purpose , it is good that he which goeth before carry in his hand a bundle of rods , to stick down one at the end of the chain which leads , having first stretched it well , and that he which follows do not only gather up the rods to keep the accompt , but also at every remove , mark whether he see the leader directly between his eye and the angle , or other mark he aims to measure to ; and if need be , call to the leader to move towards the right or left hand , till he see him in a direct line to it . ii. compasses are so well known , that i need not describe them ; only they should be of brass , with steel points small and neatly wrought , nine or ten inches long from the joint to the points , turning so truly upon the rivet that they may be easily opened ; and yet stand so firmly , that an arch or circle may be without their shrinking described upon a large radius . for the form , i would commend above all , those that have large bows , so contrived , that by pressing them with the hinder part of the hand , they will gently open , and by the thumb and fourth finger be put together ( as others will ) so that they are manageable by one hand , which is a great convenience for one that at the same time should hold his rule with scales in the other . these might also be contrived with a screw to take out one of the points , to place in the room ( upon occasion ) a black-lead pen , or any pen to draw circles , with either black or otherwise coloured . and for a man that would be an artist indeed , it were convenient he were furnished with dividing campasses , beam compasses , and triangular ones , for several uses not here to be mentioned ; but a country surveyor may make a good shift with such a plain pair as i first described ; which mr. wynn , over against the rolls in chancer●-lane , will help him to , with the chain and scales , for a small matter . iii. scales are certain lines divided into equal parts , upon plates or broad rules of brass or box , and they are of two sorts , 1. plain ; 2. diagonal . 1. plain scales are made up of two small lines parallel to one another at a little distance , and these are divided into great equal parts , which signifie tens , and are noted 10 , 20 , 30 , 40 , 50 , &c. according to the length of the lines . they may be of any convenient length , but these great divisions are seldom more than inches , or less than third parts a piece . again , one of the great divisions ( or parts ) is subdivided into ten equal parts by short lines , whereof that in the middle standing for 5 is longer than the rest . according to the numbers of these little parts contained in an inch , the scale is named a scale of 10 , 11 , 12 , 16 , 20 , 24 , 30 , &c. in an inch. fi. 13 that short one which i give you the figure of at a is of 10 in an inch , so noted at the top , according as is usual upon rules , and indices of plain tables . the line marked oq , separates unites and tents ; unites being taken upward from that line , and tens downward ; mixt numbers both ways . as for example . 7 is the extent of the compasses upon the scale a from the line oq to k ; 30 is their extent from the line so marked to oq ; and 27 is their extent from the line 20 , to the short line k aforesaid . here note , that you must not expect to find the letters oq or k upon the scales which you buy , being only marks used at pleasure , to make my meaning plain ; and likewise that this scale of 10 in an inch , and others that are smaller ( all being composed after the same manner ) are usually made for more convenient use , so long as to contain nine or ten ( the more the better ) of the great divisions , signifying tens ▪ though the figure at a being designed for no other use than to help your conceptions , extends but a little beyond 30 , that length being sufficient for my purpose in this place . fi. 14 these plain scales , especially the smaller sorts of them ( such as 24 or 30 in an inch ) are very proper for drawing figures upon paper , where the numbers represented by the lines are not above 100 ( for then every division may be counted as it is upon the scale ) or above upon a long scale . also in the surveying of forests , chases , and great commons , where the lines are vastly long , and the mistake of a few links ( yea , of half a pole ) is not considerable , they may be conveniently used , accounting the tens and unites to signifie so many whole chains , and so estimating the parts of a chain with the compasses upon the small divisions , which a sagacious man may do very near upon one of the larger scales . but it were much better , in my opinion , for ordinary measuring , if the grand divisions on the scale were two inches a piece , as i have one upon the index of my plain table ) for then the smaller divisions being of five in an inch , would be so large as to be subdivided into five apiece , which represents 20 links ; and then the half of one of those smaller divisions signifying 10 links , and the quarter 5 , a very ordinary judgment may come very near to the truth by estimation . 2. but the diagonal scale is so well known to every mathematical instrument-maker , so easie to be procured , and every ways so fitted to gunter's chain , and our countryman's use , that i cannot but highly commend it . of these diagonal scales , there are two sorts , the old and new. fi. 14 by the old one , i mean such as is to be found in mr. leybourn's book , whereof i shall present you with a fragment , with such a description as may enable you to understand the whole . 1. it is made ( as appears by the figure b ) upon eleven parallel lines equidistant , so as to include ten equal spaces , which are all cut at right angles by transwerse lines dividing them all into four equal parts . 2. one of these transverse lines ( viz : pr ) where it toucheth the first and last lines , separates between the hundreds ( or whole chains ) and the tens , ( representing 10 links apiece ) the chains being numbred downwards on the left hand from p only to 3 , but on the instrument it self they may go on to 9 or 10 , ( the rule being a foot long ) but the tens ( or decads ) upward from p to 10. 3. from the points of division into tens upon the first line beginning at p , to the like points beginning at r in the last line , are nine diagonal lines drawn , the first beginning at p , and ending at the first division above r. the second beginning at the first division above p , and ending at the second above r. in a word , they are all drawn from one division less from p , to one more from r ; by which it comes to pass , that every diagonal , by that time it hath passed from the first line to the eleventh is a whole tenth part of an inch ( which answers to ten links of the chain ) farther distant from the line pr , than at the point upon the first line whence it was drawn . fi. 14 4. every one of these diagonals is divided into ten equal parts by the long parallel lines running through the whole scale , and numbred on the top from 1 to 9. whereby it is evident , that the intersection of any of the nine parallel lines that are numbred at the head with any diagonal , must be farther distant from the line pr , than the intersection of the line next before it with the same diagonal by of that is , by which answereth to a single link of your chain . from what hath been said , and inspection of the figure b , these things plainly follow , which as so many clear instances will help you to understand it fully . 1. the distance from pr to the second division below it answereth to two chains . 2. the distance from pr to the eighth division upward being taken ( with compasses ) upon the first line of the eleven from p to 8 , answereth to 80 links . 3. consequently the extent of the compasses from the second grand division below p to the eighth of the less divisions upward , is proportionable to 2 chains 80 links . 4. the distance from pr to the first diagonal being taken upon the parallel line noted with 9 above answereth to 9 links : where note , that the first diagonal is not that which is noted with 1 , but that which is drawn from the point p. 5. the distance upon the same line from pr to the diagonal that is marked with 7 , is answerable to 79 links . fi. 14 6. the extent of the compasses from the bottom of the figure b upon the same line to the same diagonal , answereth to 3 chains 79 links . briefly whole chains may ( by analogy ) be measured upon any line from pr to the grand division noted with the given number , decads alone , or chains and decads upon the first line of the eleven where the diagonals begin . links alone , decads with links , and chains and de●ads with links , always upon that line upon which the number ofodd links stands at the head of the scale . and know , that these directions ( mutatis mutandis ) will as well fit , if half an inch be only allowed for a chain , and consequently all the diagonals drawn within that extent , as it is usual ( and very commodious for longer lines ) upon the other end of the same rule , the grand divisions for chains going the contrary way , ●nd noted with numeral figures in order . it 〈◊〉 good therefore when you furnish your self with scales , to have diagonal scales of both ●imensions on the fore-side of your rule ; and upon the back-side many plain scales of equal parts , with a line of chords ; all which you may have ( by enquiring only for the scales described ●n mr. leybourn's book ) of mr. wynne aforesaid , ●s likewise all other mathematical instruments . having been so large for my plain country-man's sake , i shall not proceed to the description of the new diagonal scale , of which you may have the figure and description in mr. wing's book : for though it be an excellent good one , fi. 14 as i know by experience ; mr. hayes having ( at my desire ) furnished my noble friend si● charles hoghton with an artificial one of that sort , when i had the honour of assisting him in mathematical studies ) yet because 't is pretty cost●● ( if well made ) , and that before described will very well answer its end , i shall at present say no more of it . but my reader may perhaps object to me , th●● though i have instructed him how he may make a line of an exact length , to answer to any number of chains and links ( given or found by measure ) upon the diagonal scales : i have not yet shewed him how to measure a line ( as suppose a perpendicular ) whose length is unknown , upon them . to give him therefore all satisfaction ( though what i have writ already , might help him to find this out ) let us suppose , that in some figure made according to the diagonal scale b of 10● in an inch , we meet in measuring with an unknown perpendicular equal to the line in the margin . taking it between the points of my compasses , i first try whether it be even chains and finding upon the first view that it is not , 〈◊〉 make a second trial , whether it will prove to be even decads , or tens of links ; to which purpose i set one foot at 3 chains in the bottom o● my scale in the first line where the diagonals begin , and the other foot rests in the same line betwixt 6 and 7 ; whereby i am assured the odd links above 3 chains are more than 60 and less than 70. and to find how many above 60 , i remove the compasses from parallel to fi. 14 parallel in order , till one foot in the lowest line resting in the end of a parallel , the other will touch some diagonal at the intersection with that line which falls out to be at l and o in the line marked with 7 , shewing the whole line , being measured by that scale , to signifie 3 chains and 67 links . chap. v. how to cast up the content of a figure , the lines being given in chains and links . having described these plain instruments , and in some measure shewed the use of them in severals , it were very proper in the next place to teach their joynt use in measuring and protracting ; but because i would have my young surveyor , before i take him into a close , able to perform his whole work together , i intend to shew him , 1. how he ought to make his computations ; 2. the grounds or principles that will justifie him in so doing . for the first , take these rules : 1. put down your length and bredth of squares and oblongs , and your base and half perpendicular of triangles directly under one another , expressed by chains and links with a prick betwixt them , as was taught before , chap. 4. 2. if the odd links were under ten , put a cypher before the numeral figure expressing them , ( as there also was shewed ) and if ther● be no odd links , but all even chains , put tw● cyphers after the prick . 3. multiply length by bredth , and base 〈◊〉 the half perpendicular , according to the rul● for finding the content of figures , chap. 3. 4. from their product cut off 5 figures ( accoun●ing cyphers for such ) reckoned from th● right hand backward , with a dash of your 〈◊〉 so shall those to the left hand signifie acres . 5. if those five cut off were not all cypher● multiply them by 4 , and cutting off fiv● towar●● the right hand again , the rest will be roods 〈◊〉 quarters . 6. if amongst these five figures towards the right hand that were cut off at the second multiplication there be any figures besides cyphers multiply all the five by 40 , and cutting off fiv● again by a dash of your pen , those on the left hand signifie square perches , poles , or roods ▪ a few examples will make all plain . quest . 1. what is the content of a square , 〈◊〉 sides are every one of them 7 chains , 25 links ? length 7.25 bredth 7.25 3625 1450 5075 525625 525625 4 102500 40 100000 answ . 5 acres , 1 rood , and 1 perch , as here appears . quest . 2. in a long square , whose length is 14 chains , and the bredth 6 chains 5 links , what is contained ? length 14.00 bredth 6.05 7000 84000 847000 4 188000 40 3520000 answ . 8 acres , 1 rood , and 35 perches , as the work makes it evident . quest . 3. in a triangle , whose base is 3 chains , and half the perpendicular 98 links , what is the content ? the base 3.00 half perpend . 0.98 2400 2700 29400 4 117600 40 704000 answ . 0 acres , 1 rood , 7 perches , as here is plain . there be other ways of computation by scales , tables , &c. but that this is sound and demonstrative , i come now to shew by these following steps . 1. it is evident , that in this way of multiplication the product is square links ; for every chain being 100 links , it is all one to multiply 7.25 by 7.25 , or 725 by 725 without pricks , for the pricks signifie something as to conceptions but nothing at all in operation . the product therefore of the first example was really 525625 links . 2. every chain being 4 perches long , it follows , that 5 chains ( or 20 perches ) in length , and 2 chains ( or 8 perches ) in bredth , make an acre , or 160 square perches ; for 20 being multiplied by 8 , gives 160. 3. from hence it plainly followeth farther , that there are exactly 100000 square links in an acre ; for 5 chains multiplied by 2 , is the same with 500 links by 200 , which makes 100000. and he deserveth not the name of an arithmetician that is ignorant of this old plain rule , when the devisor consists of 1 and cyphers , ( as 10 , 100 , 1000 , 10000 , 100000 , &c. ) cut off from the right hand so many figures of the dividend as the devisor hath cyphers , accounting them the remain ; so shall the rest on the left side be the quotient . it is plain then that 525625 square links make 5 acres , and 25625 square links over . thus i have made it clear to a very ordinary capacity , that as far as concern acres , the rules for computation are good . now for roods and perches , though i might turn off my reader with that known rule in decimal arithmetick : multiplying decimal fractions by known parts , gives those known parts in integers , due regard being had to the separation . i shall proceed in my plain way thus : if 25625 square links , which remain above an acre , do contain any quarter or quarters of an acre ; then if they be multiplned by 4 , and divided by 100000 , ( that is , five cut off from the product ) they will contain so many acres as now they do quarters ( or roods ) , for any number of quarters multiplied by 4 , must needs produce the like number of unites or integers , and the division doth only reduce them into the right denomination . now 25625 being multiplied by 4 , and five figures being cut off from the product , the result is , 1●02500 , that is an acre and above ; which shews it was above a quarter before it was multiplied by 4. and to find how much , ( that is , how many square perches are contained in this last remainder ) you must consider this 2500 , not as square links remaining above the rood or quarter , but as fourth parts or quarters of square links ; or ( which is all one ) as the true number of square links multiplied by 4 , and consequently being multiplied by 40 , ( the fourth part of square perches in an acre ) it must as often contain 100000 square links ( or an acre ) as the quarter of this number 2500 , viz. 625 , signifying square links , containing square perches ; and so it doth , for 100000 divided by 160 ( the number of perches in an acre ) gives 625 as answerable to 1 perch ; and 2500 multiplied by 40 , gives 100000 , or 1 acre ; the five cyphers being cut off as here is manifest . 2500 40 100000 160 ) 100000 ( 625 960 400 320 800 800 0 some may perhaps wonder , that in so small a manual i spend so many words about such ordinary things , as in this and the last chapter ; but i am most afraid , lest i shall not for all my plainness be sufficiently understood by such as i purposely write for , in things of such necessary and frequent use : and i designed not to make this treatise small by being obscurely brief in substantial things , but by leaving out such curiosities as i thought my country friend might well spare . chap. vi. how to measure a close , or parcel of land , and to protract it , and give up the content . hitherto we have been like children learning to spell , now let us set our syllables together . i mean , let us make use of the instructions beforegoing to measure a plece of land , to plot it , and to cast up the content . all closes , or parcels of land , are either such as need not to be plotted for finding out their true measure , but the chain alone doth the work ; or such as cannot be conveniently measured without plotting or protraction . of the first sort are the square and long square , known before-hand to be such , or found so to be by such instruments as i have not yet described , or by measuring all the sides and diagonals . these squares and long squares ( i say ) need no protracting , for you need only to multiply the chains and links of the length , by the chains and links of the bredth , and so proceed as in the first and second examples of the fifth chapter : but all others , whether triangles or triangulate , are to be protracted . i shall give examples therefore in the 3 sorts of figures , triangular , quadrangular , and multangular . but before i proceed to particular instances , let me advise the young practitioner thus : remember , 1. to begin at some notable angle of the field , where there is some house , gate , stile , well , or the like ; or if there be none , then to dig up a clod , drive down a stake ; or at least , to observe what quarter of the heavens it pointeth towards , whether east , west , north , or south , and on your paper mark it with the letter a , or any other . 2. to go parallel to the side of the field , 〈◊〉 pits , bushes , or the like , hinder not , ( and if they do , to allow for it ) accustoming your self to go either cum sole , that is , with your left hand towards the hedges , walls , or pales ; or contra solem , with your right hand towards them ; and when you go contrary to your usual custom , note it on your paper by some mark known to your self . 3. to set down the chains and links of every side as you measure them , and not to trust your memory . a black lead pen will be very proper for this purpose . 4. to take heed ( if you have more scales than one upon your rule ) lest you confound your self by taking lines off of several scales , or measuring perpendiculars upon wrong ones ; for every line of the same figure must be made by the same scale , and the perpendiculars measured by it . 5. to make use of a scale of larger divisions when you measure small closes , and of smaller when you measure great ones . 6. to make your lines and points where angles meet , small , pure , and neat . 7. to set on your chains and links at twice , when any line is too long for your scale . these things being premised , i proceed thus : i. suppose i measure a triangular field with my chain , beginning at the eastern angle a , and find the sides in their order and measures to be severally , thus : ( i going cum sole ) 2.229 , 3.45 , 4.07 . fig. 15 making use of the less diagonal scale , because the other would make the figure too large , otherwise it were more proper for so small a close ) i first with my compasses take off the scale 4 chains and 7 links , and setting them from a to c draw that line for the base , because the longest of the three : then i take 2 chains 29 links off the same scale , and set them in the eastern point a where i began , and turning the loose foot of the compasses above the line a c , because i went cum sole , i describe ( at that distance 2. 29. ) the arch e e. fi. 15 next taking with my compasses upon the same scale the extent of 3 chains 45 links , 〈◊〉 place one foot in the point c , and with the other make the arch ff intersecting the former● in the point b ; and drawing the lines a b and b c , ( as was taught in ch. 2. probl. 6. ) the triangle a b c is the plot of the triangular field measured . but before i can give the content , i must find the length of the perpendicular , which is done by setting one foot of the compasses in b , and extending the other to the base a c , so as 〈◊〉 touch it and pass not over it , ( according to ch. ● ▪ probl. 7. ) for then the length of the perpendicular is between the points of the compasses , and being applied to the same scale by which the triangle a b c was made , it appears to be 1 chain 42 links . with the half whereof i multiply 4.07 the length of the base , and proceeding in my work as was shewed in the last chapter , the content appears to be 0 acres , 1 rood , 6 perches , as it is here evident . the base 4.07 half perpend . 0.71 407 2849 28897 4 115588 115588 40 623520 ii. suppose i were to measure a quadrangular or four-corner'd field , i begin as before at ●ome remarkable angle ; and going round the ●lose cum sole , i find the sides to be 9.04 , 6.72 , ● . 46 , 7.28 , and the diagonal from that remarkable angle to the opposite angle to be 10.02 , i ●●gin therefore to protract it thus . fi. 16 having by the help of my scale and com●asses drawn my diagonal 10. 02 from my remarkable angle a to c the opposite angle , make a triangle of it , and the first and second sides 9.04 and 6.72 . according to ch. 2. probl. 6. ●nd another after the same method of that diagonal , and the third and fourth sides 8.46 and ● . 28 , so have i the trapezium abcd. then by the help of my scale and compasses , 〈◊〉 find the perpendicular of the triangle a b c 〈◊〉 be 6.02 , and of the other , viz. cda 6.01 , which added are 12.03 , whereof the half sum 〈◊〉 6.01 ; by which multiplying the base 10.02 , and proceeding as formerly hath been shewn , i ●nd the content of the field to be 6 acres , 0 roods , 3 perches , as is here apparent . fi. 16 the base10 . 02 half perpend . 6.01 1002 60120 6●02202 4 ●08808 40 3●52320 before i pass any further , let me tell you , 1. any quadrangular close , or parcel ground whatsoever , having right lines , 〈◊〉 be thus measured , protracted , and computed . 2. the odd measure above perches is 〈◊〉 valuable here , nor in the former computatio● being always under a square perch ; but in mu●● angulars where there be many remainders , th●●● must be summed up , and the perches contain● in them added to the content before found . 3. this last , and the following figures ( wh●● i use any scale at all ) are made that they mig●● not be too large , by a scale of 400 in an in●●● i. e. by the less diagonal scale , each chain 〈◊〉 link being counted two . fig. 17 iii. if this multangular figure be conceive to represent a close of seven sides , which is 〈◊〉 be measured , i begin at the remarkable angle 〈◊〉 and going round the close ( with the sun ) find the sides to be in measure 3. 11 , 2. 49 , 2. 4● , 1. 77 , 4. 11 , 2. 29 , 4. 37. fi. 17 then i measure the four diagonals , bd , df , ●b , and bg , in the order that i named them , ●nd i find them to be 3.45 , 4.97 , 4.13 , and 4.36 , ●hich is as short a way as can be taken , to pre●ent unnecessary walks . but when i come to protract by the help of ●●y scale and compasses , i first make the trian●●e bcd of the first diagonal , and the second ●nd third sides . then the triangle def upon 〈◊〉 second diagonal , and fourth and fifth sides , 〈◊〉 upon the same diagonal as a common base , 〈◊〉 triangle bdf of the first , second and third diagonals . next of the same third diagonal , together ●ith the fourth and sixth sides i make the triangle bfg , and upon the fourth diagonal as ●pon a common base with the first and last sides 〈◊〉 triangle abg , so is the whole close ●●otted . and now it stands visibly reduced into two ●rapezia's abfg and bdef , together with ●he triangle bcd , which i shall not now cast 〈◊〉 , having so often shewed how such work is 〈◊〉 be done . but i must acknowledge that this sort of plotting of parcels of land that have many angles , ●equires not only more care and pains , but better skill and memory than to draw diago●als upon paper , when the plot is already taken by the plain table , or other standing instrument . i shall therefore to help my young practitioner in this case , advertize him of two easie ways to help himself , so as to be out of danger of mistakes . one way is to divide the multangular field into two or more parts as the last might have been by the diagonal bf ; then might each pa●● have been measured severally , as if they had been separated by a pale , or were sundry mens land parted by a boundary . another way that much helps both the understanding and memory , is to draw a rude draugh● of the figure of the land you intend to measure , not only as to the sides , but also necessary diagonals . then measuring the lines upo● the ground correspondent to those on the paper ( which by the help of the draught may be easily hit ) set the lines as you measure them upon the lines of the draught , as if it were the true ones , and when you have finished your measuring , protract it truly . such as you see her● ( but it 's better larger ) will do your business for 't is not a pin matter how rude or false the lines or angles be , resemblance being all that is desired . chap. vii . concerning the measuring of circles , and their parts . i have hitherto abstained of purpose from medling with the circle and its parts , that i might lay those things close together without unnecessary mixtures , that are of the greatest use . 't is wonderful rare , if a land-meeter ever have occasion to measure any field or parcel of land , that will prove either circle , semicircle , quadrant , or sector . sometimes indeed there will be a little crook in an old hedge bowing like an arch : but i have never seen any offer to measure it as a segment , but always take it as an angle or angles . yet because it may be expected i should say somewhat of those things , i shall briefly do it . 1. to measere a circle in the more exact way 〈◊〉 to square the diameter , and to multiply that square by . 7854 , so shall the content be in integers and decimals . but the more usual and quick way ( and near enough for any use we shall make of it ) is to multiply the half of the periphery or circumference by the semidiameter . in like manner to find the content of a semicircle , quadrant , or sector made up of semidiameters , and arched lines , multiplying the half arch by the semidiameter , gives the content . fi. 19 but that which falls out most frequently in mensuration ( though seldom much regarded ●ave where a curious exactness is required ) is that particular sort of segment , which we call 〈◊〉 section , less than a semicircle , such as this figure abc . and to find the content of it , the center of the circle whereof this is a section must be first fou●d out , as here at o , from which lines drawn to a and b , make up the sector aobc ; which being measured according to the last rule , and from the content thereof , fi. 19 the content of the triangle aob sub●racted , the difference or residue is the content of the section abc . but two questions may be here demanded : 1. how may the center be found ? 2. how may such a portion of land be truly protracted and computed ? to the first i answer , that the most exact and artificial way is by making a mark any where in the arch. as for example . at the point c ; and then ( by a problem known not only to every surveyor , but to ordinary carpenters and joyners , for finding the center of a circle , whose circumference will pass through 3 given points that are not in a right line as acb ) to find the center o. but if you know not how to do it so , cross the line ab in the middle , as here it is done by the perpendicular oc , so you may by a few trials find both the due extent of your compasses , and the point in the perpendicular that will fit your purpose near enough ; for if a little errour be committed in making up the sector , the most of it goes off again in the substraction of the triangle . ii. for the latter you may take this ready course : measure the length of both your lines , ( the chord and the arch ) and their distance at the middle of them both . then when you come to protract , first take the length of your right line from the scale , and having laid it down , cross it in the middle at right angles with a dry line as in the last figure , so shall it intersect the line ab in the point e ; fig. 19 then from the same scale take the measured distance between the two lines in the middle , and set it upon that dry line from the intersection at e to the point c. then by trials find a due place in the dry line oec , and such a distance with your compasses , that the one foot resting in that line , the other may describe the arch acb , and the section is protracted . these few hints are as much as i thought necessary for my country practitioner concerning circular lines ; but if he think otherwise , there are large treatises enough , and particularly those i mentioned , whose rules ( though ingenious , sound , and fit to be known by every one that intends to plunge deep into mathematical studies ) will not ( i think ) be of that use to him in ordinary measuring , that i should transcend the intended bounds of brevity to transcribe them . chap. viii . concerning customary measure , and how it may be reduced to statute-measure , & è contra , either by the rule of three , or a more compendious way by multiplication only . whereas the statute-perch or pole is 16 feet and a half , and no more , there be poles of larger measure used in many places , as of 18 , 20 , 21 , 24 , and 28 feet , yea in some 22 feet and a half . it were therefore very convenient , that our young surveyor were furnished with a chain fitted to the customary measure of the country where he lives , as i use to make chains for my self and scholars of 21 or 24 feet to the pole for lancashire and cheshire , where those measures most obtain . but because these are too large and cumbersome for small closes , it is very convenient , instead of one chain of 100 links , to make two of 2 poles apiece , each pole divided into 25 links as that of 100 is , which two half chains may in measuring large fields be tied together by the loops with pack-thread , or joyned by a buttoning keyring for more speedy dispatch ; but in smaller we may use the half chain of 50 links , only taking care that we count not half chains for whole ones . and in these cases where the poles are large and the closes small , it were still more convenient if you had a chain of 2 poles only , divided into 100 links : only you must then take notice , that whereas working by whole chains and links , the first multiplication , after five cut off , gives the content in acres and parts . the like work by half chains and half links will give the content in roods or quarters of acres , and parts of such roods . but though it is no hard matter ( for one that can find out the length of a link by dividing the number of feet in a chain by 100 , and provide himself of good iron-wyre , and curtain rings to make it of , and a sharp edged file , and round nosed plyers to make it with ) to be furnished with such a chain ; yet because every one cannot do this , i shall shew you how you may easily and yet very truly reduce statute-measure into customary , that so the chain before described may do your business all england over . know therefore ( for a ground to go upon ) that acres bear proportion to one another , as the squares of their poles ; and therefore if you multiply 33 , the number of half feet in the statute-pole by it self , which gives 1089 , and also multiply the number of half feet contained in a pole of that measure you would reduce into ; in the same manner you may by the rule of three reverse obtain your desire , making to that purpose 1089 the first number , the statute-measure the second , and the squared half-feet of the pole given the third . as for example : 9.33 l. 7.21 b. 933 1866 6531 672693 prod . suppose of a close measured by the statute-pole , the length , breadth , and their product be as here represented in the margin . and it is desired that the content may be cast up according to our large cheshire measure of eight yards or 24 feet to the pole or rood ( as we call it : ) the● before i cut off any figures , i consider that in the statute-pole are 33 half-feet , and in the cheshire-pole 48 , then multiplying 33 by 33 , and 48 by 48 , i have these two square numbers , 1089 and 2304 , which together with the said product may be thus placed : 1089. 672693 ∷ 2304 , and so multiplying 672693 by 1089 , and dividing their product being 732562677 by 2304 , the quotient is 317952 , from which if 5 figures toward the right hand be cut off , and dealt withal as was taught in the fifth chapter , the content by our customary measure of 24 feet to the pole , will be 3 acres , 0 roods , 28 perches as here appears 317952 4 71808 40 2872320 but if the lines on the land had been measured according to our custom here , of 24 feet to the pole , and the content must have been found according to statute measure ; then i must have multiplied the product by 2304 , and have divided that latter product by 1089 ▪ and in the same method you may proceed in all or any of the rest . but the truth is , that though this way be very exact , plain and comprehensive , suting all the customary measures before-mentioned without fractions , which for my learners sake i studiously avoid , and for that reason reduced my poles to half-feet : it is something tedious except he knows how to relieve himself by a large table of logarithms , or at least a set of nepair's-bones , which i cannot stand here to treat of : therefore to contract the work a little , take notice , that all the customary poles before mentioned , ( saving only those of 20 and 28 feet , which i suppose are somewhat rarely used , because i never heard nor read of them ( to my remembrance ) save only in mr. holwel ; all the rest i say , are capable of being divided into half-yards : and therefore if instead of squaring the half-feet you square the half-yards of both poles , and work with them , you will attain the same end without any regardable difference , the small diversity that there is being usually in the useless remainders , not at all affecting the desired quotient that gives the answer near enough for use . as for example . if i had squared 11 , the number of half-yards in the statute-pole , which would make 121 , and also 16 the number of half-yards , in our cheshire-pole , which would make 256 , as appears in the margin , and then multiplied the first product 672693 by 121 , the second product would have been 81319853 , which being divided by 256 , the quotient would have been ( as before ) 317952. and this way is in a manner coincident with mr. holwells first method . 11 11 11 11 121 16 16 96 16 256 take notice also further once for all , that whether you use either of these or the following methods , you need not reduce the particular squares , triangles , or trapezia's severally ; but sum up all their products together , and then reduce all at once . but if you would reduce statute measure into customary by multiplication only , take notice of this present table following . the content by the statute-pole being multiplied by . 84027 gives the content by the pole of 18 feet . . 68062 20 . 61734 21 ½ . 53777 22 . 47265 24 . 34725 28 the use of this table . when you have multiplied lengths by bredths , or bases by half perpendicalars , multiply these products by the decimal fractions answering to the customary-measure into which you would reduce statute-measure , and from that latter product , first cut off five places towards the right-hand as not to be regarded , ( being only parts of a square link ; ) then cutting off 5 more , and proceeding to multiply by 〈◊〉 , and then by 40 , as hath been often shewed , you will have the content by that customary-measure , example . suppose once more the length of a close measured by gunter's chain , and multiplied by the breadth measured also by the same , produced 672693 square links ; and it is desired that the content may be given in cheshire-measure of 24 to the pole : you must multiply 〈◊〉 72693 by .47265 , the decimal fraction answering to 24 feet , and from that product being 31794834645 cut off and cast away 5 places , and the rest being ●17948 , are in the usual way easily ●educible into 3 acres , 0 roods , 28 perches , as here appears , agreeable ●o what it amounted to in the former method . 317948 4 71792 40 2871680 but if you measured by a chain of customary poles , and desire to know what the content 〈◊〉 in statute-measure ; this following table is fo● your purpose . the content measured by the pole of 18 feet . being multiplied by 1. 19008 gives the content by the statute-pole . 20 feet . 1. 46923 21 feet . 1. 61983 22 ½ feet . 1. 85950 24 feet . 2. 11570 26 feet . 2. 87970 to understand which , take this example . suppose the length and breadth of a lo● square being measured by a chain of 24 feet 〈◊〉 the pole , and multiplied together , make the●● product 317952 , le● this be multiplied b● 2.11570 , which answereth to 24 feet , and th● latter product will be 67269104640 , from which if you cut off and cast away 5 places towards the right-hand , the remainder is 672691 , which in the usual way is easily reduced to 6 acres , 2 roods , and 36 perches , as you see here . 67269 29076 4 363056 one thing more and i have done with th● business of reduction : if the content to be r●●duced , be given cast up into acres , roods , and perches , reduce all into perches , and then i● other respects work as before either by th● rule of three , or by this last method of multi●●lication only . so shall you have the content in square perches according to the measure desired , which you may reduce into acres by dividing them by 160 , and if any thing remain , that remainder being divided by 40 , will give you the roods in the quotient , and the latter remainder the number of square perches . for tryal of which rules , mind the answer ●o these two following questions wrought all ●hree ways . quest . 1. how many acres , roods and perches , according to the pole of 18 feet , are contained in 5 acres , 3 roods , and 11 perches , statute-measure ? answ . 4 acres , 3 roods , and 22 perches , as ●●ere appears : i. method . 33 36 5 a : 3 r : 11 p. 33 36 4 — — — 99 216 23 99 108 40 — — — 1089 1296 931 1089 . 931 ∷ 1296 1089 8379 7448 9310 1013859 1296 ) 1013859 ( 782 9072 10665 10368 2979 2592 387 160 ) 782 ( 4 640 40 ) 142 ( 3 120 22 ii. method . 11 11 11 11 121 12 12 24 12 144 121 . 931 ∷ 144 121 931 1862 931 144 ) 112651 ( 782 1008 1185 1152 331 288 43 160 ) 782 ( 4 640 40 ) 142 ( 3 120 22 or thus : 40 ) 782 ( 19 40 382 360 22 4 ) 19 ( 4 16 3 iii. method . 84027 931 84027 252081 756243 782. 291 37 160 ) 782 ( 4 640 40 ) 142 ( 3 120 22 quest . 2. how many acres , roods and perches , of statute-measure are contained in 8 acres , 3 roods ( or quarters ) and 21 perches of 21 feet to the pole ? answ . 14 acres , 1 rood , and 21 perches , as appears by the three following works in the several methods . i. method . 8 a : 3 r : 21 p 4 35 40 1421 42 42 84 168 1764 33 33 99 99 1089 1764 . 1421 ∷ 1089 1764 5684 8526 9947 1421 1089 ) 2506644 ( 2301 2178 3286 3267 1944 1089 855 160 ) 2301 ( 14 160 701 640 40 ) 61 ( 1 40 21 ii. method . 14 14 56 14 196 11 11 11 121 196 . 1421 ∷ 121 196 8526 12789 1421 121 ) 278516 ( 2301 242 365 363 216 121 95 160 ) 2301 ( 14 160 701 640 61 40 ) 61 ( 1 40 21 iii. method . 1.61983 1421 161983 323966 647932 161983 2301.77843 160 ) 2301 ( 14 160 701 640 40 ) 61 ( 1 40 21 chap. ix . how a man may become a ready measurer by practice in his private study , without any ones assistance or observation , till he design to practice abroad . this art above all parts of the mathematicks , is burdened with two inconveniences to the young practitioner : the necessity of having one to assist him in measuring his lines with the chain , as oft as he would practice his skill , or get more , and the exposing of his unreadiness to the view of meddlesom people , while he is yet raw and unexperienced , as every one must needs be at first : both which may in good measure be avoided by this easie knack . take a small packthread , and by knots about half inch asunder divide it into an 100 parts , as gunter's chain is divided ; so shall these small divisions between the knots answer to links ; and if they be not exactly of one length , the matter is not very weighty , but the more equal and short they are , the better . having this string thus prepared , and marked with longer and shorter pieces of thread tied in the knots , so as you may readily see where is the middle , and where your divisions of 25 links , and the smaller divisions of 10 links begin and end ; make all sorts of figures in your study or chamber , by marking places , or sticking knives or bodkins at pleasure for angles , accounting the streight lines betwixt them for sides , and so measure the figures by your knotted string , and cast up the content by a scale . this work you may manage with your own hands in private , and so make your self very quick and ready when you begin to measure for good and all ; as i once made a full experiment , and it was thus : when i first began to instruct youths in mathematical learning in warrington , some of my boys parents desired a sensible demonstration of their sons proficiency in somewhat that they themselves could in some measure understand ; and particularly pitched upon measuring a piece of land : whereupon i took four or five of my scholars to the heath with me , that had only been exercised within the walls of the school , and never saw ( that i know of ) so much as a chain laid on the ground : and to the admiration of the spectators , and especially of a skilful surveyor then living in the town , they went about their work as regularly , and dispatched it with as much expedition and exactness , as if they had been old land-meters . chap. x. how to measure a piece of land with any chain of what length soever and howsoever divided ; yea with a cord or cart-rope , being a good expedient when instruments are not at hand of a more artificial make . if you can procure a chain , and find it is not divided as before hath been shewed , but into feet or quarters of yards , or any such vulgar divisions , make no reckoning of the divisions at all , but measure it as exactly as you can to find out the true length of the whole chain , and if it fit none of those lengths mentioned in the 8th chapter , nor any of their halfs , make it to fit , by taking off a link or two , or piecing it out with a string ; then dividing the length of that chain by 100 , or the half of it by 50 , find the true length of a link according to our artificial division , and having got a long stick or rod , set as many of those link-lengths upon it as it will hold ; then may you measure all the whole chains by your regulated chain , and the odd links of every line by your divided stick or rod , as is manifest in this example following . being far from mine instruments , and requested by a friend to measure him a close , i procure a pair of compasses , an ordinary carpenters rule of two foot , divided into inches and quarters , and meeting also with a piece of an old chain seemingly divided into feet , i measure it by the rule , and finding it to be 45 feet long , and some odd measure , i piece it out with a pretty strong cord that will not stretch much , to 48 feet exactly ; then it will serve me for half a chain of 24 feet to the pole : this 48 i multiply by 12 ( the number of inches in a foot ) and that product being 576 , i divide by 50 , the number of links in half a decimal chain , and the quotient is 1166-50 inches , or 11 inches and an half , and an trifle over : so then dividing a long stick throughout into such parts , each containing 11 inches and an half , besides the breadth of the nicks , i am provided of tools to measure lines to a link with exactness enough . in like manner would i proceed with a cord or rope , having fitted them to some known length or other . and then for protraction it were easie with the compasses to make a plain scale of a large sort , either upon paper , or an even piece of wood ; this for once may serve a mans turn well enough . besides there is a way of measuring the perpendiculars of triangles and trapezia`s upon the ground it self , so as to prevent the necessity of a scale ; for if you have a little square with an hole in it , to turn upon the head of a little stick , which you may fix where you please , as you are measuring the base of a triangle , or the diagonal of a trapezium , you may by a very few trials find the place where the one leg will be just in the line which you are measuring , and the other point at the angle from which the perpendicular falls on it , and then the space between your stick and that angle truly measured , is the perpendicular . if you have not such a square , a square trencher , or any end of a board that hath one right angle , and two true sided , will supply the want of it . and now that i am mentioning this way of measuring , i shall make bold to add , that this is a good way , ( and as such ordinarily used by that general scholar and reverend minister mr. samuel langley of tamworth in staffordshire , whose ancient acquaintance i have long esteemed both mine happiness and honour ) to measure a trapezium thus , though it be protracted afterwards ; for by measuring the perpendiculars as aforesaid , and observing at how many chains and links end the said perpendiculars meet the common base , the whole trapezium may be truly protracted , without going about it ; this little square competently supplying the place of an instrument , which is usually called a cross or square , made up ( as it were ) of two small indices , like those for a plain-table ( but much less ) with fore-sights and back-sights , and cutting one another at right angles , put together , and having an hole at the center , like those things which here in cheshire we call yarndles , being used by country housewives in winding of their yarn . chap. xi . concerning dividing of land artificially and mechanically . were it sutable to my design or humour to be copious or curious , i had here a fait opportunity ; for four or five modern survey-books of the best accompt lying open before me , would tempt me to transcribe abundance of ingenious things ; but for reasons often hinted before , i shall confine my self to a few plain things that will competently do this business . 1. to divide a triangle into any parts required ; divide the base as the demand imports ; then shall lines drawn from the points of division to the opposite angle finish the division of the triangle . example . fi. 20 ac , the base of the triangle abc , being divided into 12 equal parts , a line drawn from the angular point b to the point 6 divides the triangle into two equal parts . 2. lines drawn to 4 and 8 divide it into three equal parts . 3. lines drawn to the points noted with 3 , 6 , and 9 , divide it into four equal parts ; and so lines drawn to 2 , 4 , 6 , 8 , 10 , divide it into six equal parts . also it is very obvious , that if the same triangle were so to be divided , that the one part should be double to the other ; a line drawn from b to 4 or 8 , doth the work . or if it be required to divide it into two parts , so as the one shall be triple to the other , a line drawn from b to 3 or 9 , compleats the work. so also a line from b to 2 or 10 divides it into two parts , whereof the one is quintuple ( or five-fold ) to the other , and a line from b to 1 or 11 , divides it into two parts , whereof the one is 11 times as large as the other . further yet , if it were required this triangle should be so divided , that the two parts should in quantity bear proportion , as 5 and 7 , a line from b to 5 or 7 , doth that feat . but to deal plainly with you , i must confess that sometimes the division will be a little more intricate than thus , yet not such , but that the seeming difficulty may be easily overcome , by observing the method wherein i shall satisfie the following demand . suppose a large triangle of common land be to be divided amongst three tenants a , b , and c , according to the quantity of their tenements , a having 19 acres of land to his tenement , b13 , and c7 , the base of the triangle being found by measure to be 17 chains and 27 links ; and the dem and is , where the points of division must be placed in the base , so as lines drawn from thence to the opposite angle , shall truly limit each mans part ? to answer this , let us add 13 and 07 to 19 , ( as in the margin ) and they give 39 : so is the work plainly reduced to the rule of fellowship ; and therefore to find every mans distinct portion , we need only to multiply the base by his 19 13 07 39 particular number , and divide that product by 39 , the sum of all their numbers as here is plain ▪ a 39 . 17. 27 ∷ 19 19 15543 1727 39 ) 32813 ( 841 14 / 39 312 161 156 53 39 14 b 39 . 17. 27 ∷ 13 13 5181 1727 39 ) 22451 ( 575 2● / 3● 195 295 273 221 195 26 c 39 . 17. 27 ∷ 7 7 39 ) 12089 ( 309 38 / 39 117 389 351 38 from these operations it is plain , that if we set off from the angular point where the base begins , 8 chains 41 links , and a little above the third part of a link upon the base for a , and where that ends , 5 chains and 75 links and 2 / 3 of a link for b , and consequently leave between this second division and the other end of the base 3 chains and almost 10 links for c ; lines drawn from those points of division to the opposite angle , will give each man his due . what i have said touching the division of triangles upon their bases , will with a little variation serve for the dividing of all sorts of parallellograms , whether square , long-squares , rhombus's , or rhomboides's : all the difference is , that in stead of drawing lines from points in the base to the opposite angle , you must draw parallel lines from points in one opposite side to another , as will be sufficiently plain by this one instance . fig. 7 suppose the square figure in the 8th prop. of the second chapter to represent a close of six acres , and i am to cut off an acre at the side ac , having set off the 6th part of the line cd , from c towards d , and also from a towards n , a parallel drawn between those points , takes off exactly a 6th part , or an acre . if it be not thought convenient ( as in some cases it is not ) to cut off a piece so long and narrow , you may by the rule of three find what other length of any greater breadth will limit an equal quantity to it . or you may multiply the breadth by 2 , 3 , or any other , and divide the length by the same number that you multiplied the breadth by . or lastly , if you set out a double proportion that is 2 / 6 or 1 / 3 , from c towards d , and from the point where it falleth , draw a line to the angle a , you will have a triangle equal to 1 / 6 of the square acdn. but to return to triangles , ( the most simple and primitive of all rectilinears , and therefore the most considerable in this case of partition , as giving laws often to the rest : ) it may fall out , that a triangle must be divided ( convenience so requiring ) by a line from some point in a side , so as that line may either be parallel to some other side , or not parallel to any . for the former case take this example following out of mr. wing . lib. 5. prob. 5. fig. 21 let abc be a triangle given , and it is required to cut off 3 / 5 by a line parallel to ab . first , on the line ac , describe the semi-circle , aec , whose diameter ca divide into five equal parts according to the greater term , and upon three of those parts ( the lesser term ) erect the perpendicular de , which cutteth the arch line in e ; then set the line ce from c to f , and from thence draw the line eg parallel to ab ; so will the triangle cgf contain 3 / 5 of the triangle abc , as was required . fig. 22 now for the latter case , when the line of partition goes not parallel with any side , take this example : let abc be a triangle given to be divided into two parts which shall bear proportion to one another , as 3 and 2 , by a line drawn from the point d in the base , or , line ac . from the limited point d , draw a line to the angle b ; then divide the base ac into five equal parts , and from the third point of division draw the line to e , parallel to bd. lastly , from e draw the line ed. so shall the trapezium abed be in content , as 3 to 2 , to the new triangle dec . i have now done with the division of triangles , when i have added these three advertisements . 1. you must be sure to take very exactly the distance of every point , where a dividing line cutteth any side , to one of the ends of the same side , as in this last figure , the distances be and ad , which distances being applied to the scale by which the triangle was protracted , will shew at how many chains and links-end you are to make your dividing line on the field it self . 2. the proportions by which you are to divide , are not always so formally given as in the former examples , but are sometimes to be found out by arithmetical working , as in this case . suppose a triangular field of 6 acres , 2 roods , and 31 perches , must be divided , so as the one of the two parts shall be 4 acres , 3 roods , and 5 perches , and the other ( consequently ) 1 acre , 3 roods , and 26 perches , reduce both measures into perches , and the one will be 765 , and the other 306. their sum is 1071 , which by their common measure being reduced into their lowest terms of proportion in whole numbers , will be 5 , 2 , and 7 , which shews that the triangle being divided into 7 equal parts , the one must have 5 of those 7 parts , and the other 2. and observe , that it will be sufficient to find the common measure between the sum of the terms and either of the terms ; the method whereof is shewed in every arithmetick book for reducing fractions into their lowest terms . but if my unlearned reader cannot skill of that work , he may multiply either of the parts ; ( as suppose 765 ) by the length of the base , which we will suppose to be 8 chains and 75 links , or 875 links : and that product divided by 1071 , ( the content of the whole close in perches ) gives by the rule of three direct , 625 links , or 6 chains and 1 pole , the true distance from either end of the base , that his mind or occasions may direct him to begin with , to the point of division ; for the division must be not only for proportion or quantity , but also as to position or situation of parts upon the paper , as it is required to be on the ground . 3. in these and all other divisions of land , where a strict proportion in quantity is to be observed , you must have respect to the rules hereafter following , concerning measuring of uneven ground , chapter 15. especially if one part prove much more uneven than another : and if there be any useful pond or well to draw your line of division through it ; but if it be an unuseful pond , lake or puddle ; or if there be an boggy or barren ground , that must be cast out in the divisions ; measure that first , and substract it from the content of the whole close , and then lay the just proportion of the remainder on that side that is free from it , that the other may have its just part also , besides that which is useless . what hath been said , with an ordinary measure of discretion , may sufficiently instruct a young artist to divide triangles , parallellograms , and regular polygonials , in an artificial way : but because many closes and open grounds are trapezia's , and many irregular polygons , and even those that are regular enough , may fall under an irregular division , in regard of the quality of the land , woods upon it , or quarries in it : or the conveniences of ways , currents of water , situation in respect of adjacent lands , &c. i shall propose a method , which though it hath somewhat of the mechanick in it , will be singularly useful in such cases . fig. 23 let abcd be a trapezium to be divided betwixt a young heir and his mother , so as his part may be double to hers . having by the diagonal bc divided it into two triangles , i find the content of the triangle abc to be 138550 square links , and the triangle bcd to contain 103468 , in all 242018 square links , which if reduced , as hath been formerly taught , would amount to 2 acres , 1 rood , and 27 perches : ( for which see chap. 5. ) but as to my present work , they are in a better order already . dividing then 242018 into three parts , each of them is 80676 and 2 / 3 , fig. 23 two therefore of those third parts must contain 161353 and 1 / 3 , which 1 / 3 being inconsiderable , i regard not . then resolving to lay out the double part towards the line bd , i strike at adventures the line ef , and measuring the trapezium bounded by that line , and the opposite side bd , together with the interjacent parts of the lines ab and cd , i find it to contain 119140 square links , but because it should have been 161353 , i substract 119140 , out of 161353 , and their difference is 42213 , and perceiving that the lines ab and cd are very near parallel , and finding their distance where they are cut by the line ef , to be 326 links , or 3 chains and 26 links , i divide 42213 by 326 , and the quotient is 129 links and almost half , at which distance i draw the line gh parallel to ef ; so shall the trapezium gbdh be the heirs part . another way whereby this may be preformed , is thus : finding the triangle abc , to contain 138550 square links , substract it out of the heirs part , viz. 161353 , the difference 22803 , shews how many square links must be taken out of the triangle bcd , and added to the triangle abc : which to perform with all necessary exactness ; suppose the side or line bd to be the base , which by measure proves to be 344 links , or 3 chains and 44 links . say by the rule of three direct , if the whole content of the lesser triangle , viz. 103468 , give 344 ; what shall 22803 give ? so will the result be 75 links , and somewhat more than 4 / 5 of a link ; for 22803 multiplied by 344 , gives 7844232 , which being divided by 103468 , the quotient is 75 84132 / ●03468 ; or ( according to decimal division ) 75.8131 , which is ( as i said before ) somewhat more than 75 links and 4 / 5 , wherefore extending your compasses upon the scale to almost ' 76 links , set that distance upon the line bd , from b to i , and draw the line ci : so shall the trapezium abic be double to the triangle icd , within so small a matter as is not worth regarding , though the land were a rich meadow . i hope i need not stand to tell any man of sense , that if he please he may begin with the less part , and take out that : or if there be many partners , he may divide betwixt any one and all the rest , ( putting their parts together ) and then by the same method subdivide amongst them till each hath his due share ; nor to spend many words in telling him he must substract where he hath by a separating line at adventures , or by choosing , out a triangle , taken too much . as i added , when i took too little . nor lastly , that these methods are not only applicable to trapezia's , but to any triangular figure whatsoever , whether regular or irregular . chap. xii . concerning the boundaries of land , where the lines to be measured must begin and end . if there be no agreement between the parties concerned , ( for if there be , that must be observed ) reason and custom are the surveyor's guide . the farmer speaks loudly , that when a piece of arable or meadow-land is let for a year to be sown or mown , no more should be measured nor expected to be paid for , either to the letter or workmen , than the plow or sythe can go over . so also when a parcel of land is let for pasture by measure to a farmer , it seems very reasonable , that all and only so much should be measured as is useful to that purpose . but commons to be enclosed are usually measured ( except it be otherwise agreed ) to the uttermost bounds of every mans particular proportion , without any allowance for ditch or fence ; every man being to make them upon his own of what breadth he pleases : nor is this unreasonable , for 't is as good for one as another , and the rate paid to the lord is usually very little , sometimes nothing . it is also very usual in measuring betwixt lord and tenant , in case of leases for lives , and long terms of years , to extend the lines to the utmost bounds of the tenants claim , taking in the very walls , hedges , and ditches : but this is accounted very hard , and oft proves very unequal among the tenants of a lordship ; some being forced to make much more waste of their ground this way , than others that hold as much or more . but where the custom obtains , the survey or must observe it : for it is others work to appoint what must be measured , and his only to measure truly what is so appointed . a good landlord may ( and will be apt ) to consider it in his rates , and a bad one 't is like will be tenac●●us of a custom to his own advantage . lastly , in case of sale by measure at a rate agreed upon per acre ( no boundaries being specified in the bargain ) the rule ( as i had it from an old famous surveyor many years ago ) is to extend the lines to the quick wood-row , that is , as reason prompts me to understand him , to the place where the quick-wood actually groweth , or where according to custom it ought to be set . i confess these things are trivial , but yet more necessary to be known , than many artificial things much stood upon , for a young artist , whom ignorance of these things may expose to considerable mistakes in practice . chap. xiii . containing a description of the plain-table , the protractor , and lines of chords . though what hath been already said , may competently suffice to instruct my young artist in measuring a close of land , yet to advance him a degree higher in useful knowledge , i shall take occasion to describe unto him the plain-table , which with mr. wing i account the best of all fixed instruments : this instrument consists of several parts . 1. the table it self , which is a parallellogram of wood fourteen inches and an half long , and eleven inches broad , or thereabouts , and for necessity may be made by an ordinary country-workman of one board : but for neatness , convenience of carriage , and freedom from warping , it is usually made of three little boards joyned together side-ways , with a ledge at each end to hold them fast together , and upon the middle board a socket of brass fixed with three screws , and with a fourth to be fastned on the head of a three-legged staff ; of which anon . 2. a frame of wood fixed to it , so as a sheet of paper being laid on the table , the frame being forced down upon it , squeezeth in all the edges , and makes it lie firm and even , so as a plot may be very conveniently drawn upon it : this is usually made with joynts for more easie carriage , but a plain one may suffice . upon one side of this frame should be equal divisions , for drawing parallel lines both longwise and cross-wise ( as occasion may require ) over your paper , and on the other side the 360 degrees of a circle projected from a center of brass conveniently placed in the table . 3. a box with a needle and card , to be fixed with two screws to the table , very useful for placing the instrument in the same position upon every remove . 4. a three-legged staff to support it , the head being made so as to fill the socket of the table , yet so as the table may be easily turned round upon it , when 't is not fixed by the screw . 5. an index , which is a large ruler of wood , ( or rather brass ) at the least sixteen inches long , and two inches broad , and so thick as to make it strong and firm , having a sloaped edge , ( by which we draw the lines ) called usually the fiducial edge , and two sights of one height , ( whereof the one hath a slit above , and a thread below , and the other a thread above and a slit below ) so set in the ruler , as to be perfectly of the same distance from the fiducial edge . upon this index 't is usual to have many scales of equal parts , and there might be a diagonal scale if the instrument-maker please , and lines of chords of sundry lengths : but if you have such a scale as i before described ; you need not to have them here . the protractor is an instrument so well known , and so easie to be made and procured , that i shall be very brief in the description of it . as it is usually made , it consists of two parts , a scale and a semicircle , but the scale is no necessary part of it , but serving ( if you be not otherwise provided ) for other uses before mentioned in the case of plain-scales . but the semicircle is more essential , and it may be made of brass or other metal of any convenient size , as four inches ( more or less ) for the straight sid , this semicircle being bounded as all others are by two lines , the one right or strait , the other circular . the right line is divided in the precise middle by a point which is in the center , upon which the circular boundary is drawn , and two other arches concentrial with it . the center , when the semicircle goes alone without the scale , should be guarded with two little lips , on each side one , or a little loop , for more convenient turning of the instrument about upon a pin fixed in a paper . the arched or circular edge is divided into 180 degrees or equal parts numbred by tens upon the upper concentrick arch , from 0 to 180 , and in the lower from 180 to 360. so that by applying the straight edge of the protractor twice to any line , ( keeping the center right● upon a pin fixed in the line ) that is , with the semicircle first above it , and then below it , or contrarily , you may draw a whole circle by the guidance of the arch , or set out any number of degrees , as will appear more plainly hereafter . a line of chords is a line divided into 90 unequal parts , whereof 60 , and the radius upon which the circle was drawn , are equal , and the divisions upon that line are equal to the next extent in a right line , of so many degrees from the beginning of the quadrant as answer thereunto . when lines of chords are cut upon wood , 't is both usual and necessary that there be two studs of brass , the one at the beginning , and the other at 60 deg. with little holes for the feet of the compasses , when you take the extent of the radius , to preserve the line from being wounded by the compasses ; and being thus fenced , it will for need do the work of a protractor , but not altogether so commodiously . chap. xiv . how to take the true plot of a field by the plain-table , upon the paper that covers it , at one or more stations . there are three ways or methods for doing this work , two more usual and ordinary , the third more unusual and extraordinary , though now pretty well known to most surveyors , and in late books published . the first performs the work by measuring every line from the instrument to every angle , and is a very sure substantial way where it can be done , as it ordinarily may in most closes . the second doth it by measuring only the station or the distances , and is very quick , but not so sure and exact as the other ; yet if managed by a skilful artist , that knows how to plant his instrument , so as to avoid making acute angles unnecessarily , it will come near enough the matter in many cases ; as in measuring for workmen , that take the mowing or reaping of fields by the acre , or when tythes are let at a small value per acre , as in poor barren parishes they usually are . the third is the way of circuition or perambulation , the instrument being oft to be planted , and the plot to be measured about , by which not only difficult closes , but even the thickest woods , yea bogs , meres , and pools of water , may be plotted , which by neither of the other methods can be performed . in all these methods , two things are to be performed : 1. at every angle where there is no perspicuous mark already , as a tree , bush , stile , &c. one must be placed , as a white paper , or such like ; or else some one must go from angle to angle , and remain there as your mark to look at , till you bid him remove to another : only when angles are very near you , this labour may be spared . 2. when ever you have occasion to plant your instrument more than once , ( as it will often fall out in the first method , and ever in in the two latter ) you must be sure it stand just as it did the first time for situation , for which your needle if well touched and hung , will be good direction , but is not thought sufficient without back sight and fore-sight , ( by some practical surveyors : ) i shall therefore in due season shew you that knack . now for the first method . i. when you go about to plot your parcel of land , find such a place in it if possible , from whence you can see all the angles , and in that place plant your instrument covered with a sheet of paper , and turning it about till the needle playing at liberty , hang over the flower-de-luce , ( or any other notable place that you make choice of ) screw it fast . then choosing any convenient place in your paper for a center , and to represent your station ( or place where you fix your instrument ) make a prick with the small point of your compasses , to which prick applying the fiducial edge of the index , ( which is easily done if you keep the point of the compasses resting in it ) direct the index by the sight to all the angles , and when through the slit or long sight , you see the opposite thread cut the mark in the angle , draw a neat dry line along the fiducial edge to or from the center : then measuring from the instrument to every angle , set the measure by a scale and compasses from the center towards the angle , upon the line that points at it , making a prick in the line where the chains and links ( reckoned from the center ) do truly end : then shall lines drawn by a straight rule from prick to prick , give you the perfect plot upon your paper , which you may divide ( as hath been before shewed ) into trapezla's and triangles , and to find the true content . to make which plain , mark this example . fig. 24 suppose abcdefgh to be a field ; having planted my plain-table as before directed at a convenient advantage , so as to see all the angles , ( as at i ) i make a prick to represent my station in the little circle ☉ marked with i , upon which laying the fiducial edge of my index , and directing the sights to all the angles , i draw dry lines toward a , and all the rest of the angles in order from the center ; and then measuring upon the ground from the instrument to the angle a , i find it to be 3. 45 , which i set ( by the help of my scale ) from the center to the point a , and so upon all the rest according to their due measures , and then black lines drawn from point to point , as from a to b , from b to c , &c. limit the true figure of the field according to the scale i used , viz. of 400 in an inch. and now before i pass to further varieties , let my reader take notice of these following things . 1. from henceforth i shall forbear ( for brevities sake ) to take any notice of the measures of lines measured from the instrument to the several angles , having so often shewed how to measure by a scale . 2. when i speak of measuring from or to the instrument , i always mean from or to that part of ground that is perpendicularly under the head of the instrument , where you are to draw your plot , which will ever be enclosed with the three legs of your staff. 3. that it 's usually the quickest way to measure first from the instrument to the first angle , and then back from the second angle to the instrument , and so the rest in order , still one from the instrument , and the other to it . 4. it is no matter at all whether your plain-table be placed towards the middle of a field , as was represented in this figure , or at an angle , as will appear anon . 5. in all workings by this instrument , you must have a care that the instrument be not moved out of its due place , till you have finished the work of the present station ; for which purpose , cast your eye now and then upon your needle , observing whether it continue to hang directly over the same point you set it at when you began your work , and to rectifie your instrument if you see cause . but because all tables have not needles , and where needles are , they are not accounted over-trusty , make use of the following help . when you have planted your instrument , and made a point or prick in your paper , representing your station , set the fiducial edge of your index to it , and turning it softly about till you find one remarkable thing or other upon one side of the close , and another on the opposite side as you look through the sights of your index ( which we call fore-sight and back-sight ) draw a remarkable line with ink , or rather with a black-lead pen quite over your paper , which in this figure is represented by the black line kl : and then if you suspect that by any accidental jog , or other casuality , the instrument is any thing removed , you may easily try and rectifie it , by applying the fiducial edge to the same line , and making use of fore-sights and back-sights again , upon the same marks which you before observed upon the opposite sides of the close . but if there be no convenient place for the placing of your instrument , whence you may see all the angles of the field , more stations must be made use of thus : fig. 25 let abcdefghiklmn be a field whose angles cannot be all seen from any one angle , or other place in it : i plant my instrument at the angle a , and if it have a needle , i mark what degree of the chord it cuts , or turn about the table on the head of the staff , till the needle hang over over some remarkable place ; ( as suppose the flower-de-luce ) and screw it fast ; then setting up a stick with a white paper or cloath on the head of it , where i intend my second sation ( as here at q. ) i make a prick or point in my paper , to signifie the point a upon the paper on the table : to which point i apply the fiducial edge of the index , and when i see the white at q , so as looking through the slit , i see the thread , cut it , i draw the line op quite through my paper with a black-lead pen , and then keeping the fiducial edge still upon the same point , and turning it round by degrees , i look at the angles bcdeflmn , still drawing dry lines with the points of my compasses , and setting on the measures from the station a to every angle measured to or from , as i did in the last example . then i remove the instrument to the place of my second station , having set up a mark at a , and laying the fiducial edge to the line op , i turn about the table upon the head of the staff , till through the slit of the back-sight , i see the thread cutting the mark at a , and then screw it fast , so will my needle , if a good one , hang directly over the same point that it did at the first station ; but however that be , fore-sight and back-sight will do the business ; for which purpose it is good to take back-marks as well as fore-marks at every station , as was taught in the example of a single station , only taking notice that the back-mark when the instrument is planted in an angle , must needs be out of the field ; as suppose here at o. but to proceed . having measured the distance between the first and second station , and finding it to be 7. 10 , i set it upon the line op , from a to q , where i make another point to represent the second station , and turning about my index with the fiducial edge upon that point , and so looking through the sights at the angles ghik , i draw lines towards them on my paper , and having measured between every one of those four angles , and the instrument , i set those measures as i did the other , with my scale and compasses , from q towards every angle upon his proper line : and then having drawn the black bounding-lines from a to b , from b to c and so round about the close , the protraction is finished . but here to make this figure yet more advantageous , let me ( according to my usual method ) add some advertisements . 1. sometimes a station is so taken , that you may measure towards two angles at once , ( as here from q to g and h ) in which case you are to set down the chains and links where the first angle falleth , but still be proceeding to the further angle , causing the remainder of the chains at the fore-end to advance beyond the former angle , so going on with whole chains so far as you can , to which the odd links at the end are to be added . 2. if at any of your stations ( as suppose a ) you can see an angle ( for example e ) to which you cannot measure in a direct line without passing the boundaries of your parcel of land given to be measured ; you may notwithstanding take in that angle by a strait measured line , as i have done , provided it may be lawfully done without trespass , and conveniently without troublesom passing of fences , otherwise it must be taken from another station . 3. i here took one of my stations at an angle , and the other within the body of the field , to shew the variety of working taught by other authors , and that 't is no great matter where you make your stations , so you can see the angles : else it had been full as convenient to have taken my first station also within the body of the field , as suppose at r. 4. though this figure representeth to your eye only two stations , a and q , your fancy may multiply them at pleasure , for suppose the angle h could not have been seen from a or q , how easie had it been to have set up a mark at s , and then to have removed the instrument thither , observing the same directions ●hat were given at the removal from a to q. ii. in the second method the instrument is to be planted twice , or oftener as occasion is , the rules for removal of the instrument fore-sight and back-sight , and measuring the distance of stations , being the same as formerly was ●aught : but instead of measuring to and from ●very angle , we only view each angle through ●he sights from two stations , having applied ●he fiducial edge to the points representing ●hose stations , and having drawn lines with the point of the compasses , or a protracting needle , the interfections represent the angles , from which the boundary-lines may be drawn , so is the field protracted : which that my reader may understand , let him note these three figures . fig. 26 here in these three figures the angles are marked alphabetically , abcdef , &c. and ●he stations by a point in a small circle numbred , 1 , 2 , or 1 , 2 , 3 , according to their number and order . fig. 26 the first of these figures represents the plot●ing of a field at two stations within it , from both which all the angles may be seen . fig. 27 the second , performs the same work by two stations taken without the field , by which 〈◊〉 a close may be measured , though the present possessor will not give us leave to come ●nto it . fig. 28 the third , shews how the work may be performed at three stations or more , when two such places cannot be found whence to view al● the angles ; which last having more of difficulty than the two former , ( though indeed no● very much ) and the explanation of that will sufficiently help to the understanding of them ▪ i shall a little explicate the meaning of it in these particulars . 1. from the first station taken acording to former directions , i see the angles abcd fgk , and acordingly draw lines upon my paper towards them from the point representing that station , by the fiducial edge of my inde● with the point of my compasses . 2. having removed my instrument to the second station , ( and in so doing , observed the rules before given , touching such removals ) i thence see the angles abdefghik ▪ and draw lines upon my paper towards them from the point representing the second station . and now viewing my work , i find upon my paper interfections for the angles abdf gk , but only single lines toward the angles cehi : therefore . 3. removing the instrument regularly as before , to a third station , i thence see those four angles cehi , and drawing lines towards them , i have interfections for them also ; so that having drawn the lines ab , bc , &c. from one interfection to another , i have the field perfectly protracted . for these bounding-lines from angle to angle , do not only signifie the boundaries of a piece of land given to be measured , limiting the figure or shape thereof , ( and are to that purpose given in this and all other survey-books ) but also are the true distance by a scale from angle to angle for the plot upon the paper : i mean by the same scale by which the stationary distances were laid down upon their own lines . and this holds true in all kind of true plotting , whether in this method or any other . iii. the third method is that of circuition , and this hath several varieties , according to these three following cases . 1. when the distance from angle to angle , ( without any exception ) is measured quite round the plot , either within or without . 2. when the distance is taken only between some more notable angles , and the perpendiculars of the rest measured as you pass along their bases , within the plot , proper for plain solid ground . 3. when the like is done without the plot , as in the case of plotting thick woods , meres , pools , bogs , &c. the first of these is very easie , consisting in nothing but planting the instrument at every angle ( either within or without , as necessity and convenience determine it ▪ ) observing the former directions for planting and removing the instrument ; and also for measuring the stationary-lines on the ground , and protracting them on the paper , as is manifest in this example . fig. 29 let abcdef be a park-pond or close to be protracted , i first plant my instrument at a , and direct the sights to a mark in the angle b , drawing a dry line from a convenient poin● on my paper towards b on the ground , and having measured by my chain the distance ab i set it by a scale upon the correspondent line from a to b , drawing a black-line between them with ink or a lead-pen , the extremities whereof are the points a and b on my paper , and the little pricked line that goes beyond b , represents the remainder of the dry line drawn at random ( as to length ) with the point of the compasses . then setting up a mark at a ( if there was none before ) i remove the instrument to b , and laying the fiducial edge to the line ab , i turn about the instrument upon the saff , till through the sight i perceive the thread cutting the mark at a , and my needle ( if i have one ) directly over the same point , that it was when it was planted at a , and so screw it fast . my next work is to lay the fiducial edge to the point b , and direct the sights to c , drawing a dry line towards it , and setting the distance bc measured by the chain from b to c. in this manner i proceed , surrounding the close till i come at last to a , where i began , by planting the instrument at every angle , using the help of back-sight and my needle , as i did at b , and then from the point representing my present station , directing the sight to the next angle , as i did from b to c. in the second case , we do not plant the instrument at every angle , but at the more considerable , taking in the smaller by their perpendiculars from the base as we pass along , of which this following figure may be an instance . fig. 30 let abcdefghikl be a close to be measured ; by planting the instrument only at acf and k , i have the main substance of the close in the trapezium acfk , and for the five small triangles which must be added to the trapezium , they may be easily protracted by the help of such a little square as was mentioned towards the latter end of the tenth chapter ; for thereby finding at how many chains and links distance from a upon the ground , the perpendicular b b falleth upon the line ac ; and having measured the length of that perpendicular , and taken it between my compass-points off my scale , i erect a perpendicular of that length at b , which is the point upon the paper , where so many chains and links determine , as were measured upon the ground , from the angles a , to the place where the perpendicular fell on ac , viz. at b. just in the same manner i raise the other perpendiculars , dd , gg , ii , and ll : and then by the help of the perpendiculars , i draw ( from and to the proper angles ) the boundary-lines ab , bc , cd , de , fg , gh , hi , ik , k l , la ; which together with the line ef between the angles e and f , give the true plot of the field in one large trapezium , and five small triangles ready for casting up . the third case is so like the second , that there needeth no new direction concerning it , but to annex one plain diagram ; all the difference consisting in this , that because we cannot go within it , ( being supposed to be some pool , bog , or thicket ) we must of necessity go on the out-side , and consequently all the triangles made by inward angles , and their lines upon the measured bases , must be excluded by the boundary-lines from being any parts of the plot , as here is manifest . fig. 31 supposing abcdefghiklmn op , to be a great pool , though here be fifteen angles , i plant my table only five times , viz. at aefh and m , and upon the dry lines ae , fh , hm , and ma , i raise their perpendiculars in due places , ( according to measure ) and also of a right height : by which and my five stationary angles , i draw the bounding-lines of the plot , excluding all the triangles as foreign to it , they being no resemblances of any part of the pool , but of land adjacent . where note , 1. that both in this and the former case , such a little square as i mentioned in the second chapter , will be very useful for speedy raising of perdendiculars ; but where the triangles are very small , it needs not be used , not the other mentioned chap. 10. 2. that if by reason of troublesom brush-wood , gorse , or bogs , &c. i could not have measured close to the sides ef , hi , or lm , it would be the same thing if i went parallel to them . and this is a shift that the practical surveyor will oft be put to make use of , in other cases as well as this . chap. xv. concerning the plotting of many closes together , whether the ground be even or uneven . though i design not so high in this manual as to make my reader able to survey lordships and forests , much less to draw maps of countries , but to measure a parcel of land with truth and judgment ; yet i would have him so expert , as not to be puzzled , if any should desire him to draw ( as it were ) a true map of a tenement or small demesn , consisting of several closes ; for which purpose , let him that knows no better observe this method . fig. 32 suppose abcdefghiklm to be a tenement or small demesn divided into fourteen closes , to be measured and protracted according to their several shapes and situation . i first draw the plot of the whole by the method of circuition , planting mine instrument either at every angle , or only the most considerable either within or without , as i find most convenient . this being done , a line from b to m gives the triangle abm from the first close : in the next place , i go round the second close beginning at m , then to b , and so about ( cum scle ) to m again : and then for the third close i plant my table at c and go round to b , ( the line bc being protracted already ) and so of all the rest , still observing which are common lines belonging to several closes ( representing the fences ) that i may avoid the trouble of measuring ●hose lines oftener than once , and lay ever● part of ev●●y close in its due place ; and that i be su●● to keep the instrument throughout the whole work to its true position by needle , fore-sight and back-sight . there are i confess divers other ways of doing this work , but none more sure or plain , especially if the ground be uneven ; for in that case , if you protract according to the length of lines measured from your station to the angles , you will put your closes into unproportionable shapes , except you reduce hypothenusal lines to horizontal , by instruments or otherwise ( which is somewhat troublesom : ) and the like may be said when you plot with the chain only . indeed the method of measuring only the stationary distances were very proper for setting out the figure of each particular close , provided the distance of the stations be large , and taken ( if possible ) upon pretty even ground , ( which sometimes may be done , though most of the close be uneven ) and the work so ordered , as not to make too acute angles : but because this requireth skill and care , i rather advise my young artist to use the circling way , as ordinarily most commodious in my poor judgment , ( but not prejudicing other men's that may differ from me in opinion ) and where need requires let him observe the directions in the 17 chapter . but which way soever you go to work , there is one very necessary rule to be observed . if the ground be uneven considerably , you must not give up the content by measuring the bases and perpendiculars of the triangles on the paper by your scale ; but you must measure the lines correspondent to them on the ground , and cast up the content according to that measure . and if it be desired that you should adjoyn to your plot ( as is usual ) a scale of chains to measure distances by ; you must either by making the forms of hills erect and reverse , or some other note in writing , mark out your uneven ground , lest those that try it by the scale , judge your work erroneous : for though you make that scale exactly correspondent to that you protracted by ( as you ought to do ) the hills and dales in the ground truly measured , may make a considerable alteration . it is convenient when you plant your table that the needle hang just over the north-point of the compass under it in the box ; then may you by the lines overthwart the frame of the table , easily draw two lines quite through the plot , cutting one another at right angles , the one pointing at north and south , and the other at east and west . and if your skill serve you to make the two and thirty points of the compass upon the place where they intersect , and to draw the forms of the houses , woods , and other remarkable things upon the demesn , and the course of brooks and rivers running through it , it will add to your commendation . and so it will also , if you take in such parcels of land bounding it , whether common or peculiar to other men , as will make your plot to look handsomly , like a perfect square or oblong . but however that be , you must be sure to protract truly all lanes going into it , or through it , and all closes of other mens mixed with it ; and also all considerable ponds , ways and outlets , with the names of the closes and quality of the ground , whether meadow , pasture , arable , &c. chap. xvi . concerning shifting of paper . in such work as that of the last chapter , it may sometimes fall out ( through the multitude and largeness of fields ) that one sheet will not hold your whole plot , in which case you may help your self by shifting paper ( as we call it ) thus . fig. 33 let abcd represent our sheet of paper that covereth the table , upon which the plot of the large piece of land efghik should be drawn ; having made my first station at e , and the second at f , i find my paper will not receive the line fg : but however i draw so far as it will go to the edge of the paper , and planting my table again at e , proceed in my circuition the contrary way to k and i , where i find my self again at a loss for my line ih , but draw it also to the edge of the paper ; then with the point of my compasses striking the line po , parallel to the edge of the paper bc , and the line qo parallel to dc , and cutting po in o , i throw aside that paper for a while , covering the instrument with a new one , which i mark with the figure ( 2 ) for my second sheet . fig. 34 upon which second sheet ( the leading part whereof is represented by the three lines meeting in the angular points a and b ) i draw po parallel to ab the leading edge of the paper , and crossing it at right angles in the point o , by a parallel to bc , viz. the line or , being of the same distance from bc , that qo in the former sheet was from dc . then with a rule and a sharp pen-knife i cut off the end of the first sheet at the line po , and applying the edge of it to the line po of the second sheet , so as it may touch that line all along , and the line qo of the former , touch the line or in the latter , so as to make one line with it : i draw the lines pg , being the remainder of the line fg , and the line oh being the remainder of the line ih , and from their extremities the line gh . and if the plot required it , you might proceed on in the second sheet , and annex a third and a fourth , &c. as there is occasion . these sheets may be pieced together with mouth-glew or fine paste , applying the edge of the former ( as you did upon the table ) to the line po of the latter . and note here once for all , that when i speak of applying the edge of the paper to a line , i mean the precise edge cut by the line po ; but when i speak of drawing lines to the edge of the paper upon the table , i hope none will think me so absurd as to mean the edge that is couched under the frame , but that my meaning is , that the lines must be continued on the paper till they touch the frame . chap. xvii . concerning the plotting of a town-field , where the several lands , butts , or doles , are very crooked : vvith a note concerning hypothenusal , or sloaping boundaries , common to this and the fift●enth chapter . fig. 35 suppose abcde divided in the manner of a common field , into seven parts or doles , belonging to seven several men : first plot the whole as before hath been taught , then measuring from a to b upon the land : set one note down ( as you go along ) at how many chains or links ( or both ) the division is between dole and dole , and accordingly mark them out by the help of scale and compasses in the line ab on the paper plot . in the very same manner you must measure and mark out the lines oc and ed ; which being done , take the paper off the instrument , and laying it before you on a table , with the side ae towards you ; the compasses must be so opened and placed ( as by a few tryals they may ) that one foot resting upon the table , the other may pass through the points of division upon all the three lines , viz. ab , oc , and ed , as in this figure they do . if the content of any one or more of these parts , butts or doles , be desired without plotting ; it may easily be done without your plain-table thus : take the breadth by your chain at the head , middle , and lower end , and adding these numbers together , the third part of their sum is the equated breadth : by which multiplying the length measured down the ridge ( or middle ) the product gives the content . but both in this case , and that mentioned in the 15th chapter , the figure of a plot may be somewhat disordered , not only by the unevenness of the ground within , for which i have given due caution already ( that being both the more common and more considerable case ) but also by the great diclivity of the ground where the boundary-lines go , either of the whole plot or particular parcels . for whereas in plotting , every line is presumed to be horizontal ( or level ) that it may pass from angle to angle the shortest way , and that every part may be duly situated , and none thrust another out of its right place : if it be not level , but falling down towards a valley , or rising up hill , or compounded of both ; a line over such ground ( though true for the measure , and for giving up the content ) will be false as to the plot , and therefore must be reduced to a level , and so taken off the scale and protracted . for the doing of this there are several instruments very proper , especially mr. rathbourne's quadrant upon the head of his peractor ( though it were better to have a semicircle than a quadrant so placed ) and divers others . but supposing my country friend to have no other but such as i have already described ; i shall shew him a plain easie way much used by practical surveyors , especially in ireland , as some of themselves have told me , being the very same that he may meet with in mr. leybourn's book , intituled , the compleat surveyor ; i mean the second way by him discovered . fig. 36 suppose abc to be part of an hill falling within my plot , my boundary-line going crookedly from a to b , following the surface of the ground . to find the horizontal line ( equal to ac ; ) i cause one to stand at the point a ( the foot of the hill ) and to hold up the end of the chain to a convenient height , and gently ascending the hill , i draw it level and make a mark where it toucheth the hill , observing the number of links betwixt mine assistant's hand and that place , where he must take his second standing , and hold it up as before , and so i draw it out level again till it touch the place , where he must take his third standing , noting the links as before , and so proceed , till at last from his fifth standing i draw the chain level to the highest point within my plot , viz. the point b. and now as the pricked lines of this figure put together , and evidently equal to the line ac : so are the links noted down at every station , when summed up , equal to the horizontal line of that part of the hill. in the very same manner , only inverting the order , you may find the horizontal line going down-hill , where that is most convenient : and if there be both ascents and descents in one line betwixt two angles , the horizontal lines of both must be found and joyned together in protraction . all this concerning declivities of rising or falling ground , is to be understood when they are considerable , and a very exact plot required : for small ones , especially when much exactness is not expected , are not regardable . chap. xviii . concerning plotting a piece of ground by the degrees upon the frame of the plain-table several ways , and protracting the same . hitherto i have shewed the use of the plain-table as such , and i think my directions have been near as plain as the instrument it self : at which some quarrel for its over-plainness , exposing the art to proud ignorant people , who judging the rest of the surveyors work to be as easie as looking through sights at a mark , and drawing lines by a rule , are apt to undertake to use it , or slight the skill of such as do . others say , ( and that truly ) that for vast things , such as forests , chases , &c. the circumferentor is more proper : and every one must grant , that in wet weather , either that a peractor , a theodolite , or semicircle , must needs be better than the plain-table covered with the paper which cannot endure wet . hence it is that some artists have to good purpose shewed how the box screwed to the index , and that made to turn on the head of the three-legged staff become a circumferentor . and if these thus fixed be turned about upon the center of the table ; they will ( say some with good reason , mr. leybourn for one ) perform the work of the peractor , much better than the peractor it self . others shew , ( as i shall briefly ) that taking the instrument as it is without the charge of further fitting it , or trouble of removing the box , the index turned upon the center will by help of the degrees on the frame , perform the work of the theodolite , to which the semicircle is near of kin . and though i might easily answer all these objections , by saying the first is frivolous ; such foolish arrogance being easily contemned or checkt ( if worth the while ) by putting such conceited fools upon the harder part of the work . the second impertinent to our purpose , who design not to plot such vast parcels of land : and the third concerning only an extraordinary case , and that well provided for otherways , for sure no man that hath not a body of the same metal with his instruments , will ordinarily measure land in continual rain , ( a sudden shower may be fenced against by a cover : ) and if any be so eager upon his work , i have shewed ●how it may be done in the former chapters of this book , without planting any instrument at all , by chain , scale , and compasses alone : yet i shall shew how the plot of a field may be ta●en by the degrees on the frame not every way that i could imagine , nor that i could transcribe , ( for that would be tedious ) but two ways only , whereof the one is proper for an ordinary close , where all the angles may be seen from 〈◊〉 station within it , the other fitting any par●●l of land though much larger , whatever be the figure of it . for the former take this example fig. 37 let abcde represent the figure of field to be plotted by the plain-table in rain weather : i put on the frame without a pap●● the graduated side upwards , and plant it i● some convenient place , whence i can see a●● the angles , as at o ; then placing the index upon th● table , so as the fiducial edge do 〈◊〉 the same time go through the center upon the table , and the lines upon the frame of th● table cutting it perpendicularly at 360 , ( whe●● the degrees begin and end ) and 180 ( the 〈◊〉 act half ) i turn about the table upon the sta●●●head , till through the sights ( the side marke● with 180 being next mine eye ) i see th●● angle a , and then screw it fast , observin● where my needle cutteth , and by back-sigh● causing a mark to be set up in the line cd 〈◊〉 the point f , that the instrument may be ke●● firm from moving ( or be rectified if it be moved ) during the work. and now the li●● aof passing upon the land from the ang●● a , directly under the sights of the instrume●● to the mark at f , is ( as it were ) the pri●● diameter whence the degrees of the angles 〈◊〉 to be numbred , and accordingly i mark th● angle a in my table hereafter to be exempl●●fied with 360 degrees . but to proceed , turning my index with the fiducial edge upon 〈◊〉 center , till i see the thread cutting the ma●●● at b , the said edge cuts upon the frame at 〈◊〉 deg. 15. min. which i note down for that angle : the like work i do , turning the sights to cd and d , ( but not to f , for there is no angle , but only a mark in the boundary ) and i find mine index to cut for every angle as i have marked them within the pricked circle of the last figure , viz. 157 deg. 35 min. for c , 225 deg. 20 min. for d , and 278 deg. and 50 min. for e. then i measure ( or cause to be strictly measured by others ) the distances betwixt the place where the instrument stands , and every angle , and find them to be as i have set them upon the pricked lines in the little circle , viz. a4 chains ●0 links , b4 chains 3 links , c3 ch. 84 li. d5 ch. 35 li. e5 cha. 6 l. and now my table both for lines and angles is thus perfected , and the work is ready for protraction within doors .   d. m. c. l a 360 00 4 20 b 76 15 4 03 c 157 35 3 84 d 225 20 5 35 e 278 50 6 06 your judgment will easily inform you , that in such weather we shall hardly stand to make our table neat and formal , but any thing ( how rude soever ) that we can understand , doth the feat . a welsh slate with a sharp style , ( or for want thereof , a black-lead pen and a smooth end of an hard board like a trencher ) is more convenient at such a season than pen , ink and paper . but of all i would commend for expedition a red-lead pen , whereby you may mark out every angle neatly with one touch upon the table it self , just where it toucheth the frame , by help of the fiducial edge , and close by it the length of the line from the center to that angle : all which may be easily cleared off by a wet sponge or cloath so soon as you have protracted . or if through the sponginess of the wood , the head of the table ( which we use to cover with paper ) were made a little reddish , what great harm were that ? we are forced to do it more real wrong by the points of the compasses in the ordinary way . now to protract our observations : i draw upon a paper the line af at adventures , so it be long enough , and stick a pin in it at pleasure for the center o , upon which i place the center of the protractor , so as the straight side ( or diameter ) of the protractor may just lie upon the line af , the limb or arched-side being upwards towards b , by help whereof i make a prick or point on the paper at 76 deg. 15 min. for b , and at 157 deg. 35 min. for c , according to the numbers nearest to the limb. then turning the protractor about on the pin with the arch or limb down towards d and e , till the diameter lie again just upon the line af , i number downwards from the right hand towards the left , by that rank of figures that are nearer to the center , beginning 190 , 200 , &c. and over against the places where 225 deg. 20 min. and 278 deg. 50 min. fall , i prick the paper at the side of the limb , and through those four points i draw so many several lines , ( having laid aside the protractor ) upon which and also upon the line ao , i mark out by points the true measure of every line ( by a scale ) from the center , and from those points drawing the lines ab , bc , cd , de , and ea , i have the true plot of the field . where note by the way , that we estimate minutes as well as we can both upon the frame of the plain-table , and the protractor , accounting half a degree , 30 minutes ; a third part , ●0 ; a fourth part , 15 , &c. and though by this means it is impossible to avoid small errours , 't is easie to avoid sensible ones ; and the like may be said when we protract by a line of chords , of which i now come to treat . having proceeded in the field as before , and made my table for lines and angles , or done that which is equivolent by a red-lead pen , i draw the line af , and having extended my compasses to the radius ( or 60 degrees ) on a line of chords , i set one foot towards the middle of the line af , and with the other i describe a circle like that in this figure of a five-angled field , but much larger , according to the length of the radius : then extending the compasses from the beginning of the line to 76 deg. 15 min. i set one foot in the intersection of the circle by the line a , and with the other foot make a mark in the circumference of the circle upwards towards the right-hand , and through it draw the dry line bo . in the next place i substract the angle 76. 15 from 157. 35 , where the index cut for the angle c , and there resteth 81 deg. 20 min. which i take off the line as before , and set it upon the circumference from the intersection by bo , towards the end of the diameter marked with f , and through the point were it falleth , draw the dry line co. in like manner i subtract 157 deg. 35 min. from 225 deg. 20 min. and the difference is 67 deg. 45 min. which i set from the intersection by the line co downwards past the prime diameter af , and through the point where it falleth , draw the line do . lastly , having subtracted 225 deg. 20 min. from 278 deg. 50 min. there resteth 53 deg. 30 min. which must be set downward towards the left-hand from the intersection by do , and through the point where that falleth , i draw the line eo . and now when i have set the particular measures upon every line , and drawn the boundary lines , as i must have done if i had used a protractor , the plot is finished . but for better assurance that i have done my work well , i take the measure of the remaining angle aoe upon its proper arch , viz. from the intersection of the circumference by af , to the intersection by eo , and applying it to the line of chords , i find it to be 81 deg. 10 min as it ought to be , for it should be the complement of 276 deg. 50 min. to 360 , and so it is , and for further satisfaction , i sum up the degrees and minutes of all the five angles , which for plainness sake i have noted in every one of them on the outside of the circle in the figure so often referred to , and their sum is 360 , as it ought to be , and as here is evident . 76. 1● 81. 20 67. 4● 53. 3● 81. 1● 360. 00 my reader may now perhaps expect that i teach him how to take a plot at two or more stations , when all the angles cannot be seen from one : but because this is so easie from the grounds already laid , to any that is ingenious , and in part rend●red unnecessary by the method presently following , i shall content my self to give this general hint . when you have from one station taken in all the angles you can see from thence , and then are to remove to your second station , do just as you would do if the table were covered with a paper ; only it is at your choice , whether you would guide your self for back-sight by a line that may be rubbed off , drawn upon the table it self from the center to the degrees on the frame along the fiducial edge , or by noting only what degrees it cuts on either side of the center , the edge passing through it , that by the help thereof and the needle , the instrument may be placed in the same line and situation as before , for taking in the rest of the angles , if it can be , if not , another station must be taken after the same manner . but now to my second method ; fig. 38 let abcde be the figure of a field to be plotted , the weather being bad ▪ i send mine assistants to find the length of every side , measuring it about , cum sole , beginning at a , who return me such an account of every side , in chains , and links , as i have noted them upon the figure and in the table following , viz. ab 3 chains , 73 links , bc 4 chains , 91 links , &c. in the mean season , i make haste to find the angles , and without curiosity plant the instrument at b , and laying the index on the center , i look at c , and find the index cutting 10 deg. 15 min. and looking at a , it cuts 126 deg. 45 min. out of which if i subtract 10 deg. 15. min. there resteth 116 deg 30 min. for the angle a : but because i like not my quarters so well as to subtract there , i set them down thus ; b a 126. 45 c 10. 15. the meaning whereof is , that b notes the angle , and ca the lines meeting there , cutting such degrees on the frame , and the reason why i set a above , is for more ready subtracting afterwards : then removing to the angle c , and thence looking at b and d , i find the index to cut as here expressed , c b 153. 10 c 15. 40. in like manner i find at d thus , d c 96. 05 e 28. 50 at e thus , e d 141. 20 a 11. 45. and lastly , at a i find them thus , a e 98. 30 b. 9. 20 an. d. m sides . ch. l. a 89 10 a b 3 73 b 116 30 b c 4 91 c 137 30 c d 1 88 d 67 15 d e 6 64 e 129 35 e a 2 29 this being done , i hast under covert , and by subtraction find 116 deg. 30 m. for the angle b. 137 deg. 30 m. for c. 67 deg. 15 min. for d. 129 deg. 35 min. for e. and 89. deg. 10 min. for a , as you find them on the figure , and in this table together with the length of the lines . note , that there is a way to find the angles without subtraction , if at every station you lay the fiducial edge over the center , and the divisions 180 and 360 , turning about the head of the instrument upon the staff , till through the sights you see one of the neighbouring angles , for the index turned upon the center to the other angle , will give you the quantity of the angle you are at , but this exact planting at every angle is more tedious than the other , and therefore not so fit for wet weather . but now to protract this plot : first , by my scale , rule , and compass , i draw the line ab in length 3 chains , 73 links , ending at the pont b : then laying the center of my protractor upon the line ab , so as the center of it be upon the point a , and that end of the diameter from which the numbers are reckoned on the arch or limb towards b , i make a point for the angle a at 89 deg. 10 min. by the guidance whereof and the point a , i draw the line ae , which according to my scale , must be 2 chains , 29 links . in like manner placing the diameter upon ae , just as it was upon ab , and the center upon the point e , i mark out by the limb ( for the angle e ) 129 deg. 20 min. by which i draw the line ed , 6 chains , 64 links . in the next place , i bring the center of the protractor to the point d its diameter , lying on the line ed , and its limb towards a , by which i prick out 67 deg. 15 min. for the angle at d and draw the line 1 chain , 88 links . lastly , the center being at c , and the diameter upon the line dc , in such manner as before at other angles , i prick out by the limb or arch 137 deg. 30 min. and draw the line cb , for at b my plot should close , and if rightly done , the angle at b will be 116 deg. 30 min. and the side bc 4 chains 91 links , which by measure i find so to be . but if i plot by a line of chords , i am not bound to this order , but may go from a to b , and so round that way if i please , which i could not so well do with a protractor , without reckoning my numbers backward , yet it must be granted that a line of chords neither doth the work so quickly nor conveniently , for this is the way . when i have drawn the line ab of a right length , i set the compasses to the radius , and placing one foot of the compasses in the point b , and with the other describe an arch of a competent length , beginning at that side of the line ab , that is designed to be the inward-side , and upon this arch , 116 deg. 30 min. must be set , but because my line of chords gives me only 90 , i set them first on from the line ab , and then take off the remainder 26 deg. 30 min. i joyn them to the 90 upon the arch , making a point , through which the line b must be drawn of a due length . in the like manner must i do at ce , but the angles at a and d need no such piecing , being capable of being measured out by a line of chords at once . nor do your angles only give you trouble in this kind of work , but oft-times your lines will be found too short to receive the touch of an arch upon the radius , especially if the line of chords be large and your scale little , and so it may often fall out when you use the protractor upon such short lines as ae and cd of this last figure : in which case a rule must be applied to them , and they must be extended to a due length that the arches may meet them without the figure . and if those extensions of lines and describing of arches spoil the beauty of your plot , the matter is not weighty , 't is so easie to be retrieved , for if you lay it on a clean paper and prick through every angle , lines drawn between those points will give you the plot neat and perfect . one thing more before i close this long chapter ; the artist sometimes loseth his labour of protraction through some error in the field , so as his plot will not close : 't is therefore good to know before we begin that work , whether it will or no ; for which purpose if we take a number less by two than the number of angles in the plot , and thereby-multiply 180 , that product being found to be equal to all the angles , the plot will close , and so it appears by our plot in this present work : the multiplier being 3 , because the angles are 5 , and the multiplier must be two less than the number of angles . 180 3 540 deg. min. 89. 10 116. 30 137. 30 67. 15 129. 35 540   this kind of tryal is grounded upon two principles of euclid and ramus mentioned in the first and third chapters of this book , shewing that in all plain triangles , all the angles taken together , are equal to two right angles , and that the sides ( consequently the angle also ) of every triangulate figure , are more by two than the triangles of which it consisteth : but i think it not proper to be large in such things whereof my young artist is like to make but little use ; for when all is done , i confess with mr. wing in his art of surveying , lib. 6. chap. 15 , that this way of plotting by the degrees , is far more troublesome , tedious , and liable to errour , than the other ways upon a sheet of paper , and therefore not ordinarily to be used , but when necessity compelleth us . chap. xix . concerning taking inaccessible distances by the plain-table , and accessible altitudes by the protractor . fig. 39 the substance of what is to be said for the first of these , is gathered from the instructions given for plotting a field , by measuring only the stationary-distance ; but to make the case more plain to an ordinary capacity : suppose the line ac to be the unknown breadth of a river , over which a bridge of boats is to be laid , and the general ( that he may inform himself what store of boats and planks is necessary to be brought down ) commands me to tell him the true distance from a where he is at present , to c a little boat-house on the other side the water . to satisfie his demand , i plant my table covered with a paper at a , causing one to set me up a mark at b at a good distance from me , along the bank of the river ( the further the better , if distance do not hinder sight : ) then having chosen a point to represent a , and laid the fiducial edge upon it , i direct my sights towards c and b , and strike lines towards them . which done , i set up a mark at a , and from thence measure to b , ( 6 chains , 32 links ) and so plant my instrument at b , laying the fiducial edge to the line ab , and turning about the head of the instrument upon the staff , till through the sights i spy the mark at a , and then screw it fast . in the last place , i take 6 chains 32 links off my scale , and set it on the line ab , from a to b , and laying the fiducial edge to the point b , from thence direct the sights to c , and draw the line bc , meeting or cutting the line ac in c : so shall the space ac measured on the scale ( viz. 8 chains , 29 links be the distance desired : and because the chain is 22 yards long , if i multiply 8. 29 by 22 , the product is 182 yards and 38 / 100 of a yard , which by reduction is some little more than 13 inches and 3 / 5 of an inch. now to take the height of a tree , tower , or steeple by a protractor , without any arithmetical operation , hang a plumet with a fine silk thread at the center of it , and hold it stedfastly with that end to your eye where the numbers begin , then look streight along the diameter , as if you were to shoot in a cross-bow without a sight ( still removing backward and forward as there is occasion ) till you see the top of the tree , tower , or steeple , and the thread at the same time fall upon 45 degrees ; 10 shall the distance from your eye to the tree , tower , or steeple , measured in an horizontal or level line , together with the height of your eye above the bottom of it , be equal to the height thereof . if either for convenience of sight , or any other reason , you think good to set the other end of the diameter to your eye , then the thread for the tryal aforesaid , must fall upon 135 deg ▪ instead of 45. other ways of doing this work by this instrument ( or a quadrant ) with the help of trigonometry , and by other instruments , i forbear at present ( till i write a second part ) considering whose benefit is here intended . chap. xx. of casting up the content of land by a table . to make up the number of my chapters to an even score , i shall add one at the desire of my worthy friend mr. s. l. before mentioned ( to whose experience and communicative●ess i acknowledge my self indebted for the notion of measuring crooked lands or doles at the middle and both ends , marking every where how the divisions fall , as is mentioned in the beginning of chapter 17. ) concerning the use of a table borrowed out of the 46th chapter of mr. leybourns compleat surveyor , second edition , page 271 , which with the use take as followeth . links r. p. 1     00000 4 00 90000 3 24 80000 3 08 70000 2 32 60000 2 16 50000 2 00 40000 1 24 30000 1 08 20000 0 32 10000 0 16 8750 0 14 8125 0 13 7500 0 12 6875 0 11 6250 0 10 5625 0 09 5000 0 08 4375 0 07 3750 0 06 3125 0 05 2500 0 04 1875 0 03 1250 0 02 625 0 01 this table consists of three columns , the first containing links , the second roods ( or quarters of acres ) the third perches : and the use of it is thus : 7. 25 5. 50 36250 3625 3625 3. 98750 suppose a field to be 7 chains and 25 links long , and 5 chains 50 links broad , these by multiplication make 398750 ( as here is evident ) whereof five figures being cut off towards the right-hand , the figure 3 signifies acres , and the rest , viz. 98750 denote parts , and to reduce them into roods and a r p 3 3 24     14 3 3 38 perches , i first subtract from 98750 the greatest number of links in my table that can be subtracted from it , viz. 90000 ( and put down for it 3 roods , 24 perches which i find over against it in the annexed columns ) and the remain being 8750 , i look in the table , and find over against it 14 perches , which by addition makes 3 roods 38 perches : so is the whole content of the field 3 acres , 3 roods , 38 perches . but not here , that if the remainder after the first subtraction cannot be found in the table , you may take the nearest to it , so the error will be but part of a perch . as for example : 7. 35 , being the half perpendicular , and 9. 23 , the base , give for their product 6.78405 . the 6 signifies acres and from the rest 70000 being subducted , ( to which 2 rood , 32 perches answer ) there resteth 8405 , which because i cannot find in my table , i take the nearest , which is 8125 , to which 13 perches answer : so the whole content of that triangular close is 6 acres , 3 roods and 5 square perches , and a little better , a r p 6 2 32     13 6 3 05 but manum de tabula — i am at present taking leave of my country-man , and supposing he brought with him any competent stock of natural capacity , and so much arithm●tick as enabled him to add , subtract , multiply , and divide ; i dare make him ●udge , after he hath as faithfully laboured to understand me , as i to be understood ; whether i have not performed what i undertook in my title or elsewhere . finis . advertisement . the author hereof useth in winter and spring seasons to board young gentlemen and others at his habitation near dun●am in cheshire , and to instruct them in these parts of the mathematicks , viz. arithmetick . vulgar concerning whole numbers . fractions balancing accounts . artificial by decimals logarithms instruments symbols or algebra . geometry and therein the doctrine of plain triangles . measuring superficials , and particularly land , by all usual instruments . measuring of solid bodies . gauging of casks . the doctrine and use of globes and spherical triangle● . the principles of astronomy and navigation . the art of dialling , by logarithms , scales , and geometrical projection , &c. vivat rex . floreat regnum . an appendix containimg xii . problems touching compound interest & annuities . being part of a letter sent by the author to his worthy friend mr. john collins fellow of the royal society . together with a quick and easie method to contract the works of fellowship and alligation alternate . london printed in the year . 1692. xii . problems touching compound interest and annuities , expressed in symbols , to be resolved by logarithms ; first presented in twelve short lines , to the right honourable the lord delamer ; afterwards explained by the inventor adam martindale , and by his consent presented to the royal society by mr. collins , and now applied to pertinent questions in a practical way , to make them more plain and useful . these problems are distinguished into three ranks , whose symbols are thus to be understood . p principal , r rate , viz. 1 l. with its rate , t time , common to all the three ranks . a amount or aggregate , proper to the first rank . s sum of principal and arrearages , proper to the second rank . d difference of principal and worth , proper to the third rank . their capitals stand for the logarithms 〈◊〉 the numbers signified by the small symbolic● letters before mentioned . d. signifies data , q. quaesita , prob. problem res . resolution . the first rank , concerning compound interest for a single sum of money . 1. prob. d p , r , t. q. a ? res . rt + p = ● 2. prob. d. a , r , t. q. p ? res . a − rt = ● 3. prob. d. p , a , t. q. r ? res . a − p / t = ● 4. prob. d. p , a , r. q. t ? res . a − p / r = ● examples relating to the four problems in order . quest . 1. what will 15 l. 10 s. amount to i● 12 yeaps at 6 per cent. compound interest ? answ . 31 l. 3 s. 9 d. 1 q. as appears by the work . r viz. of 1.06 = 0.25306 t = 12 050612 025306 rt = 0.303672 p 15.5 = 1.190332 a 31.188 = 1.494004 quest . 2. what is 31 l. 3 s. 9 d. 1 q. due ●●elve years hence worth in ready money , abating ●●er 6 per cent. compound interest . answ . 15 l. 10 s. as here appears . a 31.182 = 1.494004 r = 0.025306 t 12 050612 025306 rt = 0.303672 a − rt = p = 15.5 = 1.190322 quest . 3. at what rate of compound interest 〈◊〉 15 l. 10 s. amount to 31 l. 3 s. 9 d. 1 q. in ●●elve years ? answ . at 6 per cent. as here . a = 1.494004 p = 1.190382 0.303672 12 ) 0.303672 ( 0.025306 = 1 . 0● 0 quest . 4. in wha● time will 15 l. 10 s. amount to 31 l. 3 s. 9 d. 1 q. at 6 per cent. compound interest . answ . in 12 years . a = 1.494004 p = 1.190332 r. 025306 ) 0.303672 ( 12 = t 0 the second rank , touching annuities in arrear , grounded upon these two axioms . 1. the annuity and rate of interest bein● given , the principal correspondent to that annuity is in effect given also , being easily found by the rule of three , thus ; as the interest of any principal ( ex gr . of 1● 10 , 100 , 1000 , &c. ) is to that principal : s● the annuity of pension , to its principal . 2. the sum of the principal and arrearage● of all the payments being found , the arrearage● alone may be obtained by subtracting the principal from that sum. 1 prob. d. p , r , t : q. s ? res . rt + p = s 2 prob. d. s , r , t. q. p ? res . s − rt = p 3 prob. d. p , s , t. q. r ? res . s − p / t = r 4 prob. d. p , s , r. q. t ? res . s − p / r = t examples suted to the first and last of these four problems . quest . 1. what will 33 l. per annum amount to in 14 years at 6 per cent. compound interest ? answ . 693 l. 10 s. as here . 6 . 100 ∷ 33 33 300 300 6 ) 3300 ( .550 30 30 30 00 r = 0.025306 t = 14 0.101224 0.25306 0.354284 rt = 0.354284 p = 2.740363 s = 3.094647 = 12435 550 6935 quest . 2 in what time will 33 l. per annu●● raise a stock of 693 l. 10 s. at 6 per cent . compound interest ? answ . in 14 years , as here is evident . 6 . 100 ∷ 33 . 550 550 + 693.5 = 1243.5 = s● s = 3.094647 p = 2.740263 25306 ) 0.354285 ( 14 25306 101224 101224 0 the third rank of problems touching annuities anticipated or bought for a sum in hand ( o● that which is equivalent ) at compound interes● discounted , is bottomed upon the former of th●● two axioms above mentioned , and this that followeth : axiom . if the difference of the principal and worth be once found , the worth is easily obtained by subtracting that difference from the principal , which is ever greater , being the worth of the annuity at that rate for ever . 1 prob. d. p , r , t. q. d ? res . p − rt = d 2 prob. d. d , r , t. q. p ? res . d + rt = p 3 prob. d. p , d , t. q. r ? res . p − d / t = r 4 prob. d. p , d , r. q. t ? res . p − / r = t examples fitted to the first and fourth of these problems . quest . 1. what is 17 l. 10 s. per annum to continue for 11 years , worth in present money , at 8 per cent . compound interest allowed to the pur●●aser ? answ . 124 l. 18 s. 8 d. as here is shewed . 8 . 100 ∷ 17.5 ? 17.5 500 700 100 8 ) 1750.0 ( 218.75 0 〈◊〉 r = 0.033424 11 033424 033424 rt = 0.367664 p = 2. 339948 rt = 0.367664 — 21875 d = 1. 972284 = 93817 124933 note , that if in stead of subducting rt from p , i had turned rt into the arithmetical complement 9632335 , and added that to the p 2. 339948 , it would have done the same thing in a more convenient manner , ( save that it is not so suited to the letter of the problems ) as here is evident , 10 being rejected ( as in this case it must ever be ) from the index . 0.033424 11 033424 033424 0.367664 9.632335 2.339948 1.972283 quest . 2. in what time will 17l . 10s . pay off a debt of 124 l. 18 s. 8 d. allowing the creditor after 8 per cent . compound interest ? answ . in 11 years , thus manifest : 8 . 100 ∷ 17.5 . 218.75 = p 124.933 93 817 = d p = 2.339948 d = 1.972284 r = 33424 ) 0.367664 ( 11 0 any one that understands the very elements of algebra , may contract these twelve problems into three ; for the first of any rank will by reduction , application , and transposition , produce the rest . then the work of the second rank may be performed by the first , if one but understand , that instead of the pension , he must take the principal correspondent to it , and work with it till he have found the amount , from which the principal must be subducted when the arrearages of an annuity are sought , and so proportionably in the rest of the problems . my noble lord delamer , only noted down for his own use rt + p = a , and p − rt = d : by which and a small canon of logarithms he will quickly answer any question of this kind . but for the help of young mathematicians , i have set them forth thus explicitely . the only inconvenience of any importance that i can yet discover in this method , is , that in both ranks concerning annuities , the second and third problems are rather for demonstration of the other , and to compleat the rounds than for any other great use , proceeding upon such . data as are seldom given for finding the pensions and rate , ( or if they were , the work would be rendred useless ) yet we are not left without sufficient help to find out pensions or annuities by plain and proper data . for in reference to the second rank , if the arrearages ( or stock to be raised ) with the rate of interest and time , be given for finding out such an annuity , as at such a rate , and in so much time , will raise a given stock by its arrearages ; 't is easily found thus : suppose an annuity at pleasure , and by the first problem of the second rank , find out its arrearages : then say by the rule of three . as the arrearages found , to the supposed annuity : so the arrearages given , to the annuity required . for clearing whereof , let this be the example . quest . what annuity will at 6 per cent . comp . interest , raise a stock of 693 l. 10 s. in fourteen years . answ . 33 l. per annum , as here is manifest . suppose 30 l. then the work goeth on thus : 6 . 100 ∷ 30 30 6 ) 3000 ( 500 30 000. r. 0.025306 14 0.101224 0.25306 rt = 0.354284 2. 698970 s = 3. 053254 = 1130●46 500● 630●46 630.46.30 ∷ 693 . 5● 30 630.46 ) 20805.0 ( 32.999 44046 here we account 32. 999 for 33 , being so much within an inconsiderable trifle . likewise in relation to the third rank , if the worth ( or price ) rate and time be given , and the pension to be purchased be required ; find the worth of any supposed pension by the first problem of the third rank , then the proportion stands thus : as the worth found , to the supposed annuity : so the worth ( or price ) given , to the pension required ; as in the example follow 〈◊〉 : quest . what annuity to continue eleven years will be purchased for 124 l. 18 s. 8 d. at 8 per cent . comp. interest . answ . 17l . 10s . as here . suppose 12 l. then 8 . 100 ∷ 12 ? 12 200 100 8 ) 1200 ( 150 8 40 40 00 r = 0.033424 11 0.033424 0.33424 rt = 0.367664 p = 2. 176091 rt = 0.367664 — 150 1. 808427 = 64332 85668 85.668.12 ∷ 124.933 ? 12 249866 124933 85.668 ) 1499.196 ( 17. 5 60 if the interval betwixt every two payments 〈◊〉 less than a year , consider what part it is ; ●hether ½ ¼ 1 / 12 1 / 13 1 / 32 1 / 365 , &c. and by the ●enominator of the fraction signifying that part , ●ivide the logarithm of 1 l. and its rate of in●rest , ( usually called the logarithm of the rate ) ●en the absolute number answering to that ●●otient , being made less by an unite , will be 〈◊〉 new divisor , whereby dividing the given pen●on so payable , half , yearly , quarterly , &c. the ●orrespondent principal will appear in the quo●ent , with which you may proceed , as if the payments were so many yearly ones ; as this ●ext example shews . quest . 1. what is a quarterly rent of 3 l. 15 s. 〈◊〉 continue thirteen years and one quarter , worth in ●●dy money at 6 per cent . compound interest ? answ . 137 l. 10 s : 1 d : as appears here . r = 4 ) 0.025306 0.006326 = 1●01467 1● ●01467 .01467 ) 3.75000 ( 235.623 1059 1 / 4 r = 0.006326 number of quarters 53 0.018978 0.31630 1 / 4 rt = 0.335278 ar. c. 9●664721 p = 2.407600 — 255623 2.072321 = 118-119 137504 whereas i multiplied the fourth part of the log. of the rate , viz. 0.006326 by 53 ( the number of quarters ) i might as well have multiplied the whole log. of the rate , viz. 0.025306 ▪ by 13.25 , i. e. 13 years and 1 quarter , and it would have been full as exact , or rather more , ( two places being cut off from the logarithm so multiplied towards the right hand : ) i say rather more exact , because there remained 2 when i quartered the log. of the rate . quest . 2. what is 5 s. per week to continue 7 ●ears and three quarters worth in ready money at 8 per cent . compound interest ? answ . 75 l. 17 s. 8 d. 2 q. 52 ) 0.033424 ( 0.000642 = .00148 40 .00148 ) .25000 ( 168.918 136 r = 0.033424 t = 7.75 0 167120 2 33968 2 33268 rt = 0.259036.00 ar. ●9 . 740960 p = 2.227675 — 168918 1.968638 = 913033 75885 here i multiplied ( not by the number of weeks ) but by the number of years and quarters , cutting off two cyphers from the product . and i also took the arithmetical complement of 0.259036 , viz. 9.740963 , and added it to the log. of the principal in stead of substracting the log. 0.259036 from it . lastly , as to the rate of interest , according to the sense of dr. newton , mr. dary , and others , i see not why this method may not b● made use of as well as any other . this universal rule being first understood : in questions belonging to the second rank , the greater rate 〈◊〉 interest , the greater arrearages ; and the less rate the less arrearages . but in questions belonging to the third rank , the greater the rate of interest the less the present worth ( or price ) and the less the rate of interest , the greater the worth , & vice versa . i shall shew this in answering the question following , concerning a yearly payment of 1 l. because that by bare multiplication may easily be applied to any other . a field worth 1 l. per annum clearly , is offered to be let 11 years for 15 l. to be paid at the end of those years : what is the rate of interest demanded for the several payments ? answ . first , i suppose 6 per cent . and trying it by the first problem of the second rank , it find the arrearages to be but 19 l. 19 s. 5 d. which is 6 d. 3 q. too little . then trying what the arrearages will amount to at 6. 2 ( or 6 l. 4 s. ) per cent . i find 15. 13 , or 15 l. 2 s. 7 d. 1 q. perceiving then i have over-shot my mark , i make my third tryal at 6.1 ( or 6 l. 2 s. ) per cent . and the result is 15.05 , or 15 l. 1 s. which is pretty near , being but 〈◊〉 above the truth . but that i may yet bring it nearer , i first subtract the result at 6 per cent . which is 14.971 from the result of the arrearages at 6.1 . viz. 15.05 ( because these are the results that come nearest to the truth ) and their difference is .079 . 2. i subtract the rate 6 from the rate 6.1 , and there resteth . 1. 3. i substract the nearest result to 15 , viz. 14. 971 , from 15 the given arrearages , and their difference is .029 . then working by the rule of three , i find ( as followeth ) .0367 .079 .1 ∷ 029 1 .079 ) .0290 ( .0367 7 which .0367 being added to 6 , gives 6.0367 , or 6 l. 0 s , 8 d. 3 q. per cent . compound interest . and that this rate exactly fitteth , is plain by the following work . 6.0367.100 ∷ 1 1 6.0367 ) 100.0000 ( 16.565 20245 r. 0.025456 11 0.025456 0.25456 0.280016 1.219191 1.499207 = 31 / 565 16 / 565 15 / 000 but perhaps it will be said , that though in this and all other matters foregoing , i agree well enough with the learned authors before mentioned , and others that have writ of these subjects ; yet in my country-almanack for the year 1677 , the fourth problem agrees neither with them , nor what i have here written , but apparently clasheth with them . i confess this charge had been very just , had that problem been designed for the same end , and produced a different effect : ( for in such a case to differ is to contradict . ) but forasmuch as in my very entrance upon it , i began thus . there is a problem in some learned mens works , seemingly of the same importance with this , but indeed much different both in the design and effect : and after in answering objections show wherein the design differs ; i cannot but admire the undertakings of that able artist , who was so much at leisure as to prove with a great deal of pomp , that mine will not attain the end for which i declared it was never designed , as clearly as words can utter it . a sword may be a very good one , yet a very bad instrument to fell trees with : but i hear he is dead , and i shall rather lament the loss of him , and divers other famous mathematicians ( which death hath of late deprived us of ) than unnecessarily to expose the impertinence of his paper to the publick view ; or so much as name him to the prejudice of his memory . but from henceforth i expect from all ingenious persons , that they neither take for granted what i professedly deny and disprove ; nor urge mine objections against my self , without taking notice of mine answers . for understanding of what follows , it were very convenient to have inserted herein the whole discourse in the country-almanack about this business ; but because this little paper cannot afford it room , i shall only point briefly at the design and management ; and answering all the objections i ever met with of any seeming importance , make things as clear as i can in so narrow a compass . the design was to discuss in plain language ( suitable to country-mens understanding ) this practical question , wherein they are oft concerned ; viz. whether it be more advantage for the lender to receive for 100 l. in hand , compound interest at 8 per cent . viz. 71 l. 7 s. 7 d. 3 q. at the end of seven years above the stock of 100 l. supposing it can be legally assured ( as in ireland it may , and in england by equivalence in goods or lands , without mentioning interest ) or to enjoy a farm for seven years in consideration of 100 l. that will clear him just 20 l. per annum ? my answer was , that the former was the better bargain ( and consequently the higher rate of interest for the whole stock during the whole term ) for which i gave in these grounds under the feigned persons of a and b. 1. a is to receive ( as is said ) 171 l. 7 s. 7 d. 3 q. and if b , who takes the farm , receive not equivalent , his rate of interests is lower . 2. b receives only 140 l. by 20 l. per annum ; only he hath the advantage to improve the several payments from the time they grow due , to the end of the term . 3. these must be computed at some certain rate of compound interest : for to compute them at no rate of interests , or at simple interest , or one taken up arbitrarily , will not sute the case . 4. the rate tolerated by the statute , viz. 6 per cent . under which none will take , and above which none dare expresly bind any to give , and at which any responsible man may be fitted , is to be preferred before any other . 5. at this rate the 7 payments will amount but to 167 l. 17 s. 6 d. q. of these 5 pillars , the 132 , and 5 th , were never attempted to be shaken by any that i know of : what assaults have been made against the other two , or design of the whole fabrick , i shall briefly consider ; and i find them ( besides those answered when i first published that problem ) to be these three : 1. ob. the question is not at all , how the receiver improves his payments , but what improvements was made in the debtors hands , and the same rate carried on ? ans . we are agreed that the rate is not to be computed according to what the usurer actually makes of it . if he gives away , loses , or lends freely all the several payments : or if he make new bargains more oppressive than the original one ; the true value of the loan of so much mony for such terms , is one and the same . but i utterly deny that it is to be reckoned , as if the same rate must be carried on , and that for unanswerable reasons ( as i suppose them to be ) laid down in my former discourse , or easily colligible from it . 1. the laws of our nation prohibit upon severe penalties , the taking of more than 6 per cent therefore that is the utmost of the legal worth , which he that exceeds , runs ( as i take it ) the hazard of all , and a great fine . 2. if he can evade the penalty , no responsible man needs to give more than 6 per cent . and few are willing to give more than they need . 3. if he get over both these blocks , and make ●ew oppressive bargains , this is nothing to the question as i propounded it ; for that was , whether a. or b. received the highest interest for his money , by vertue of the above mentioned bargains , not by vertue of occasional after bargains . when the debtor hath paid in a years pension , he hath done with it ; and if he have ●t not ready , he may take it up at ordinary interest , and the proportion is broken off for so much . 2. object . if we regard laws in the case , what need we any rules concerning compound interest , seeing the laws of the land allow only simple interest : ans . 1. the laws are not against compound interest , as it may be managed : that is , the usurer may receive his simple interest at the years end , and put out that as a new stock , and so undeterminately from time to time ; or if you will call this simple interest , it 's the same to the purse . 2. i am told they have ways in london for putting out very small sums to mean traders upon sufficient security ; and then it is both legal and practical , though i say not how lawful before god ; especially as i hear some use it . 3. object . it ought to be a question only o● art , without dependance upon laws and usages ; it being the nature of art in these kind 〈◊〉 questions , not to shew so much what ought 〈◊〉 ●e done , as what is really done . ans . 1. it is one question , what is the natur● of art , and another how far art is concerned that is , whether nothing else save the rules o● art be regardable in the case ; which i deny , because laws and usages have a great influenc● upon it , hindring the continuance of the proportion . 2. i consider not the laws as pinching the u●surers conscience ( as to what is lawful ) but 〈◊〉 tying up his hands , and so obstructing the proportionable increase of his gain . 3. whatsoever may b● said of art ( as art i● the strict notion of it ) the artist must not be such a slave to the rules of it , as not to allow for unavoidable obstructions and irregularities i hope i may be allowed to tell my scholars that learn navigation , that though the direct cours●● from one port to another be upon such a point of the compass ; yet other courses must be steered sometimes in regard of rocks , shallows● crooked chanels , currents , trade-winds 〈◊〉 convenience of harbour , and fresh supplies 〈◊〉 or to avoid pirats , enemies , forts , and places where great customs or payments will be exacted ; and many such things which the experienced sea-man is better acquainted with , than i with their names . and to say to such as learn merchants accompts , that though it were more artificial and rational , that rebates of interest for money paid before ●t be due , should be computed at compound interest ( as certainly it is : ) yet forasmuch as it is usual with merchants to allow no more than simple interest ( as appears by printed accompt-books ) they must submit to the laws of the great tyrant custom . an artist hath not the same liberty of supposition in answering questions ( especially such such as are real and practical ) that he hath in proposing questions , or receiving them from others , when tryal of skill is only or chiefly intended . i may without absurdity in this latter case demand or find the amount or present worth of any single sum of money , or yearly pension for any terms propounded at any rate of interest given , though such as is never likely to come in practice : ( ex . gr . at 2 , 3 , 14 , or per cent . ) but if i be put by the nature of my work , to compute the amount or present worth of payments , no rate of interest being named , i ought prudently to weigh all circumstances , and pitch upon that which is possible and rational . and this is not a work of art , but of discreet judgment , ( wherein great respect is to be had to penal laws , usages , and other obstructions ) after which art takes it own province , in computing after such a rate resolved upon . to make all this plainer ( if possible ) than i made it at the first publication ; let us for once suppose a rare case , viz. that b a mathematician turns usurer , and for 100 l. ready money , takes a farm for 7 years , that he lets to another for 30 l. per annum clearly , knowing before hand he could so let it : and a his familiar friend thus accosts him ; i wonder to bear you are grown such an extortioner , as to receive 20 l. per annum , seven years together for 100 l. b answers , before you find fault with the mote in mine eye , take the beam out of your own : you have bought the reversion of a piece of land after seven years for 100 l. for which i will bona fide give you 172 l. at the time of your entrance upon it ; which i find by the rules of mine art to be 12 s. 4 d. 1 q. above compound interest at 8 per cent . a replies , learned men , say such a bargain as yours will clear 9 l. 3 s. 4 d. per cent . and better . b rejoyns , 't is true they do so , but then they suppose the same rate to be continued , ( for none will say , that if the payments lie by unimproved , or be let out at an under rate , that in such cases that rate of interest can be answered ) and this supposition is really impracticable ; or ( to say the least ) that which a rational man cannot depend upon . i did accidentally meet with this bargain from the hands of a weak man , which yet i durst not have accepted ( the laws are so strict ) if it had been a rent-charge in money . and will you undertake to find me fools that shall at every years end , take off the several payments , yea and all the increase of them as they grow due upon the same terms that i put out the 100 l. upon , and to let me land for it ? if you think you can , i will make you a great bargain , ( because i know you to be a punctual responsible man ) you shall receive the first yearly payment , and at the end of the second year , pay me simple interest for it at 6 per cent . as the statute allows , and i will instantly return it you , together with the second 20 l. which we will joyn into one sum , and you shall take it at the same rate : and thus we will do every year to the end of the term , still adding that years growth to what was before , and so keep up all the accounts to 6 per cent . and if you can make any more profitable use of it , much good may it do you , and i will heartily thank you to boot , for helping me so readily to place out my small parcels without loss . but if you dare not do this , let ingenuity mollifie your charge , and i shall not quarrel with you about your rate of 9 l. 3 s. 4 d. which perhaps you borrowed ( or some one for you : ) from dr. newton , his trigonometria britannica , p. 37. for i acknowledge it is that and somewhat more , though not much ; but i say ( which i desire you to observe ) that i receive no compound interest after that rate , but only simple : and that not for the whole sum during the whole term ( as you do compound interest for all your stock ) but only for the whole 100 l. for the first year : for you know that if at the end of that year 20 l. be subtracted from 109 l. 3 s. 4 d. all the interest is paid , and so much of the stock as brings it down to 89 l. 3 s. 4 d. this 89 l. 3 s. 4 d. being computed at the same rate of interest , 20 l. abated from it , clears the interest again , and brings down the stock much lower : and so year by year the stock is dwindled away , till at last the seventh payment ( if the rate were absolutely exact , as it is near ) clears off 〈◊〉 stock and interest . and this is all i receive , save only the benefit of the severa● yearly payments , which i offer you ( or any other solvent man ) at 6 per cent . as aforesaid 〈◊〉 at which rate ( abating not a farthing for loss of time , but supposing good places ready for eve●ry parcel as it becomes due ) it will but amount● to 167 l. 17 s. 6 d. q. which being the whole aggregate of stock and interest , if we substract from its logarithm , the log. of 100 , and divide their difference by 7 , as we are directed by mr. wingan's 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 , chap 5. prov. 13. the rate of interest will appear to be 7 l. 13 s. 7 d. 2 q. i profess freely , sir , i cannot withstand b's arguments ; but if any other can , i shall neither envy his happiness , nor despise , ( if fairly and ingeniously offered ) his animadversions ; in that case you shall command a sheet from me at any time , in consideration of any thing so objected ; but for such injurious and passionate discourses as are apter to provoke than convince , i confess , 't is such a piece of drudgery to answer them , that ( if i could not ease my self by contempt ) i should think it hard measure that my silence should be interpreted as their victory . sir , you will p●rdon this prolix appendix , when 't is considered that it is not intended for such as your self , but for such to whom nothing can be too plain , by sir , your friend and servant , adam martindale . a compendious method for working out many conclusions in arithmetick , wherein the rule of three is often repeated ; long since invented , practised and taught by the author , but never till now published . in all books of arithmetick that i have had the happiness to peruse , the works of both rules ●f fellowship and alligation alternate are performed by the rule of three , so oft to be repeat●d , as there ere particular proportionable parts ●o be found ; which proving intolerable tedious , when the partners in fellowship , or the parcels 〈◊〉 alligation are many , caused me to think of ●is following course , every way as plain and useful , and much more compendious , which to ●e short is this : the rule . divide that which is usually made the second number in the rule of three , by that which is as ●sually made the first and the common divisor ; that quotient multiplied severally by the respe●●ive third numbers , gives the particular results . ●ut here it will be necessary if you use decimal division ( which i judge most convenient ) that you continue your division till either nothing remain , or you have six places of decimals in the quotient , accounting cyphers ( if there be any ) into the number . and if upon the addition of your parcels , the total amount not just to the sum expected , but an unite short in the integers , & three more figures of 9 immediately following , take it for exact , for so it is within a matter of nothing . all this will be plain by three examples whereof the first shall be wrought ( for plainness ) both in the old and in this newer way ; the other two ( for brevity ) this latter way only . 1. example in fellowship without time . a b c put into the common stock 15 24 33 72 the sum whereof is 72 l. and their gain 63 l. what is each mans part ? the resolution in the old method is thus . a 72.63 ∷ 15 15 315 63 72 ) 945 ( 13.125 or 13l . 2 s. 6 l. b 72.63 ∷ 24 24 252 126 72 ) 1512 ( 21 l. 0 c 72.63 ∷ 33 33 189 189 72 ) 2079 ( 28.875 0 or 28l . 17 s. 6 d. 13.125 21. 28.875 63.000 or thus , 13-02-06 21-00-00 28-17-06 60-00-00 in the new way the work is thus done . 72 ) 63.0 ( .875 a .875 — 15 0 — 4375 875 13.125 b. 875 24 3500 1750 21.000 c. 875 33 2625 2625 8.875 i hope by this time mine intelligent reader is aware , that if the partners had been many ( as in voyages and adventures it oft falls out ) the difference betwixt the two methods would have been yet more signally conspicuous ; for one single division sufficeth , be the partners never so many : though i confess there is yet a nearer way by the help of logarithms ; of which i shall present this specimen . 63 = 1.79934055 72 = 1.85732250 .875 = 1.94201805 .875 = 1.94201805 24 = 1.38021124 21 = 1.32222929 .875 = 1.94201805 15 = 1.17609126 13.125 = 1.11810931 .875 = 1.94201805 33 = 1.51851394 28.875 = 1.46053199 the second example in fellowship with time . a laid in 43 for 8 months they gained 73l . q. each mans part ? b 52 5 c 63 7 the resolution by this new method is thus . a 43 8 344 b 52 5 260 c 63 7 441 344 260 441 1045 1045 ) 73.00 ( .069856 480 a. .069856 344 279424 279424 209568 24.030464 or 24 l. — 0 s. — 7d . — 2 q. b .069856 260 4191360 139712 18.162560 or 18 l. — 3 s. — 3d. — 0 q. c .069856 441 069856 279424 279424 30.806496 l. s. d. q. or 39 l. — 16 s. — 1 d. — 2 q. proof 24.030464 18.162560 30.806469 72.999520 or thus 24 l. — 00 s. — 7 d. — 2 q. 18 l. — 03 s. — 30 d. 30 l. — 16 s. — 1 d. — 2 q. 73 l. — 00 s. — 0 d. — 0 q. the third example in alligation alternate . suppose a mixture of wine of 119 quarts be required , that must be made up of these several prices 7 d. 8 d. 14 d. and 15 d. so as the whole may be afforded at 12 per quart , the parts may be found out in thir method ( without decimals ) thus . having linked 8 to 14 , and 7 to 15 , and counterchanged their differences from the common price 12d , i find the sum of their differences to be 14 , by which dividing 119 the quotient is 8 / 14 or 8 ½ , which for convenience of multiplication we shall change into the improper fraction so ● 2 the resolution● will be thus . 8 2 14 4 7 3 15 5 14 quarts . 17 / 2 x 2 = 34 / 2 = 17 17 / 2 x 4 = 68 / 2 = 34 17 / 2 x 3 = 51 / 2 = 25 ½ 17 / 1 x 5 = 85 / 2 = 42 ½ 119 having our just measure of wine , let us try the prices how they suit our purpose by alligation medial , for considerable errors may be caused by misapplication of prices , when the parts were truly taken ; but here-under it is apparent that each parcel multiplied by its price , the sum of the products is 1428 pence , which divided by 119 give 12 for the common price . 17 8 136 34 14 136 34 476 136 476 178 ½ 637 ½ 1428 25 ½ 7 178 ½ 42 ½ 15 217 ½ 42 637 ½ 119 ) 1428 ( 12 119 238 238 0 this proof by alligation medial i do not account a needless curiosity ; but very useful to be throughly understood , for experience informs me , that young men being defective in skill , care and memory , are apt to mistake in several points , but especially one : that is so as to esteem the several parcels to be of the several prices from which the differences ( by which they are found ) were originally taken , and not ( as the truth is ) of the prices to whom in the counterchange they were annexed . as to that which seems to look like an unnece●●sary affectation of novelty , in linking the pric● and differences by separate couples ; i designed 〈◊〉 no higher thing than to free the printer ( if th●● pass 〈◊〉 hand ) from the trouble of lookin● up his dusty cuts of semilunes intersecting or enclosing one another , as in our usual books of arithmetic●● though the truth is , in such cases as this before us , no linking at all is needful ; but when the common quotient is multiplied severally by all th● differences , any price above the common may b● assigned to any product made by the difference o● riginally belonging to an under price , and contr●●rily , so as true couples be observed . so here 〈◊〉 might have assigned the price 15 to the parcel 3● found out by the difference 4 originally belongi●● to 8 , and the price 14 to the parcel 42 ½ , found b● multiplying the common quotient by 5 the difference of 7 from the common price . but then 〈◊〉 must be sure to do justice , so as to assign the pri●● 8 to the parcel 25 ½ found by 3 the difference o● 15 from the common price , and the price 7 to the parcel 17 arising from 2 the difference of 14● us here is plain . 17 x 7 = 119 25 ½ x 8 = 204 34 x 15 = 510 42 ½ x 14 = 595 1428 119 ) 1428 ( 12 119 238 238 0 finis . notes, typically marginal, from the original text notes for div a52120-e2310 ☞ ☜ ☞ ☞ ☞ ☞ ☜ ☜ ☜ ☜ ☞ ☞ ☜ some considerations of the consequences of the lowering of interest, and raising the value of money in a letter to a member of parliament. locke, john, 1632-1704. 1692 approx. 248 kb of xml-encoded text transcribed from 101 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; 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(eebo-tcp ; phase 1, no. a48895) transcribed from: (early english books online ; image set 56722) images scanned from microfilm: (early english books, 1641-1700 ; 606:9) some considerations of the consequences of the lowering of interest, and raising the value of money in a letter to a member of parliament. locke, john, 1632-1704. [3], 4, [2], 192 p. printed for awnsham and john churchill ..., london : 1692. errata: p. 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ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng money -england. interest -england. 2002-06 tcp assigned for keying and markup 2002-08 spi global keyed and coded from proquest page images 2002-09 john latta sampled and proofread 2002-09 john latta text and markup reviewed and edited 2002-10 pfs batch review (qc) and xml conversion licensed , novemb. 27. 1691. ia. fraser . some considerations of the consequences of the lowering of interest , and raising the value of money . in a letter to a member of parliament . london , printed for awnsham and iohn churchill , at the black-swan in pater-noster-row . 1692. sir , these notions , concerning coinage , having for the main , as you know , been put into writing above twelve months since ; as those other concerning interest , a great deal above so many years : i put them now again into your hands , with a liberty ( since you will have it so ) to communicate them farther , as you please . if , upon a review , you continue your favourable opinion of them , and nothing less than publishing will satisfie you , i must desire to remember , that you must be answerable to the world for the stile ; which is such as a man writes carelesly to his friend , when he seeks truth , not ornament ; and studies only to be in the right , and to be understood . i have , since you saw them last year , met with some new objections in print which i have endeavoured to remove ; and particularly , i have taken into consideration a printed sheet , entituled , remarks upon a paper given in to the lords , &c. because one may naturally suppose , that he that was so much a patron of that cause , would omit nothing that could be said in favour of it . to this i must here add , that i am just now told from holland , that the states , finding themselves abused by coining a vast quantity of their base [ schillings ] money , made of their own ducatoons , and other finer silver , melted down ; have put a stop to the minting of any but fine silver coin , till they should settle their mint upon a new foot. i know the sincere love and concern you have for your country , puts you constantly upon casting about on all hands for any means to serve it ; and will not suffer you to overlook any thing you conceive may be of any the least use , though from the meanest capacities : you could not else have put me upon looking out my old papers concerning the reducing of interest to 4 per cent , which have so long lain by forgotten . upon this new survey of them , i find not my thoughts now to differ from those i had near twenty years since : they have to me still the appearance of truth ; nor should i otherwise venture them so much as to your sight . if my notions are wrong , my intention , i am sure , is right : and whatever i have failed in , i shall at least let you see with what obedience i am , sir , your most humble servant . nov. 7. 1691. errata . page 3. l. 2. read natural ; p. 9. l. 27. r. masters ; p. 12. l. 13. r. natural price ; p. 26. l. 16. r. of 1000 l. l. ult . r. clothing his ; p. 48. l. 25. r. money being ; p. 50. l. 19. r. to their ; p. 52. l. 18. r. be 9 / 10 ; p. 64. l. 13. r. a quality which ; p. 80. l. 14. r. natural ; l. 16. r. natural ; p. 82. l. 27. r. what has ; p. 91. l. ult . r. cheaper ; p. 94. l. 27. r. landholder ; p. 95. l. 6. r. all , as ; ● . 20. r. the yearly ; p. 121. l. 6. r. mortgagee ; p. 122. l. 23 : r. and pay ; p. 123. l. 27. r. other conjurers ; p. 127. l. 11. r. virgula ; p. 129. l. 3. r. this present year 1690. p. 137. l. ult . dele more than is the standard of our other money ; p. ●38 . l. 11. r. these species ; p. 140. l. 18. r. from , it is ; p. 141. l. 8. r. debts , and in ; l. 9. r. rents for ever ; p. 147. l. 18. r. owner ; p. 153. l. ult . r. it to a ; p. 156. l. 29. r. raise the ; p. 168. l. 10. r. rate as readily as any other coin ; l. 28. r. place bringing ; p. 169. l. 8. r. because they ; p. 173. l. 7. r. by the ounce ; p. 174. l. 25. r●ise elsewhere ● p. 182. l. 2. ● . lighter than ; p. 183. l. 12. r. own coin ; p. 186. l. 23. ● . before-hand with those to whom debts are owing . sir , i have so little concern in paying or receiving of interest , that were i in no more danger to be misled by inability and ignorance , than i am to be biassed by interest and inclination , i might hope to give you a very perfect and clear account of the consequences of a law to reduce interest to four per cent. but since you are pleased to ask my opinion , i shall endeavour fairly to state this matter of use with the best of my skill . the first thing to be consider'd , is , whether the price of the hire of money can be regulated by law. and to that i think , generally speaking , one may say , 't is manifest it cannot . for since it is impossible to make a law that shall hinder a man from giving away his money or estate to whom he pleases , it will be impossible , by any contrivance of law , to hinder men , skill'd in the power they have over their own goods , and the ways of conveying them to others , to purchase money to be lent them at what rate soever their occasions shall make it necessary for them to have it . for it is to be remembred , that no man borrows money , or pays use , out of mere pleasure ; 't is the want of money drives men to that trouble and charge of borrowing : and proportionably to this want , so will every one have it , whatever price it cost him . wherein the skilful , i say , will always so manage it , as to avoid the prohibition of your law , and keep out of its penalty , do what you can . what then will be the unavoidable consequences of such a law ? 1. it will make the difficulty of borrowing and lending much greater ; whereby trade ( the foundation of riches ) will be obstructed . 2. it will be a prejudice to none but those who most need assistance and help , i mean widows and orphans , and others uninstructed in the arts and managements of more skilful men ; whose estates lying in money , they will be sure , especially orphans , to have no more profit of their money , than what in●●r●st the law barely allows . 3. it will mightily encrease the advantage of bankers and ●e●●veners , and other such expert brokers ; who skill●d in the arts of putting out money according to the true and nat●●nal value , which the present state of trade , money and debts , shall always raise interest to , they will infallibly get what the true value of interest shall be , above the legal . for men finding the convenience of lodging their money in hands where they can be sure of it at short warning ; the ignorant and lazy will be forwardest to put it into these mens hands who are known willingly to receive it , and where they can readily have the whole , or a part , upon any sudden occasion that may call for it . 4. i fear i may reckon it as one of the probable consequences of such a law , that it is likely to cause great perjury in the nation ; a crime , than which nothing is more carefully to be prevented by law-makers , not only by penalties that shall attend apparent and proved perjury , but by avoiding and lessening , as much as may be , the temptations to it : for where those are strong , ( as they are where men shall swear for their own advantage ) there the fear of penalties to follow will have little restraint ; especially if the crime be hard to be proved . all which i suppose will happen in this case , where ways will be found out to receive money upon oth●r pretences than for use , to evade the rule and rigour of the law : and there will be secret trusts and collusions amongst men , that● though they may be suspected , can never be proved without their own confession . i have heard very sober and observing persons complain of the danger mens lives and properties are in , by the frequency and fashionableness of perjury amongst us . faith and truth , especially in all occasions of attesting it upon the solemn appeal to heaven by an oath , is the great ●ond of society : this it becomes the wisdom of magistrates carefully to support , and render as sacred and ●wful in the minds of the people as they can . but if ever frequency of oaths shall make them be looked on as formalities of law , or the custom of straining of truth ( which mens swearing in their own cases is apt to lead them to ) has once dipt men in perjury , and the guilt with the temptation has spread it self very wide , and made it almost fashionable in some cases , it will ●e impossible for the society ( these bonds being dissolv●d ) to subsist : all must break in pieces● and run to confusion . that swearing in their own cases is apt , by degrees● to lead men into as little regard of such oaths , as they have of their ordinary talk , i think there is reason to suspect , from what has been observed in something of that kind . masters of ships are a sort of men generally industrious and sober , and i suppose may be thought , for their number and rank , to be equally honest to any other sort of men ; and yet , by the discourse i have had with merchants in other countries , i find , that they think in those parts , they take a great liberty in their custom-house oaths , to that degree , that i remember i was once told , in a trading town beyond sea , of a master of a vessel , there esteemed a sober and fair man , who yet could not hold saying , god forbid that a custom-house oath should be a sin. i say not this , to make any reflection upon a sort of men that i think as uncorrupt as any other ; and whom i am sure ought in england to be cherished and esteem'd as the most industrious and most beneficial of any of its subjects . but i could not forbear to give this here as an instance how dangerous a temptation it is , to bring men customarily to swear , where they may have any concernment of their own . and it will always be worthy the care and consideration of law-makers , to keep up the opinion of an oath high and sacred , as it ought to be in the minds of the people ; which can never be done , where frequency of oaths , b●●●sed by interest , has establisht a neglect of them ; and fashion ( which it seldom fails to do ) has given countenance to what profit rewards . but that law cannot keep men from taking more use than you set ( the want of money being that alone which regulates its price ) will perhaps appear , if we consider how hard it is to set a price upon wine or silks , or other unnecessary commodities : but how impossible it is to set a rate upon victuals in a time of famine ! for money being an universal commodity , and as necessary to trade , as food is to life , every body must have it at what rate they can get it , and unavoidably pay dear when it is scarce , and debts , no less than trade , have made borrowing in fashion . the bankers are a clear instance of this : for some years since the scarcity of money having made it in england worth really more than six per cent. most of those that had not the skill to let it for more than six per cent. and secure themselves from the penalty of the law , put it in the bankers hands , where it was ready at their call , when they had an opportunity of greater improvement , so that the rate you set , profits not the lenders , and very few of the borrowers , who are fain to pay the price for money , that commodity would bear , were it left free ; and the gain is only to the banker . and should you lessen the use to four per cent. the merchant , or tradesman , that borrows , would not have it one jot cheaper than he has now ; but probably these two ill effects would follow . first , that he would pay dearer ; and secondly , that there would be less money left in the country to drive the trade . for the bankers paying at most but four per cent. and receiving from six to ten per cent. or more , at that low rate could be content to have more money lye dead by them , than now when it is higher . by which means there would be less money stirring in trade . and a greater scarcity ; which would raise it upon the borrower by this monop●ly . and what a part of our treasure their skill and management , joyned with others laziness or want of skill , is apt to draw into their hands , is to be known by those vast sums of money they were found to owe at the shutting up of the exchequer . and though it be very true , yet it is almost beyond belief , that one private goldsmith of london should have credit , upon his single security , ( being usually nothing but a note under one of his servants hands ) for above 〈…〉 at once . the same reasons i suppose will still keep on the same trade : and when you have taken it down by law to that rate , no body will think of having more than four per cent. of the banker , though those who have need of money , to employ it in trade , will not then , any more than now , get it under five or six , or as some pay , seven or eight . and if they had then , when the law permitted men to make more profit of their money , so large a proportion of the cash of the nation in their hands , who can think but that by this law it should be more driven into lombard-street now ? there being many now who lend them at four or five per cent. who will not lend to others at six . it would therefore perhaps bring down the rate of money to the borrower , and certainly distribute it better to the advantage of trade in the country , if the legal use we●e kept pretty near to the natural ; ( by na●ur●l u●e , i mean that rate of money which the present scarcity of it makes it naturally at , upon an equal distribution of it ) for then men being licensed by the law to take near the full natural use , will not be forward to carry it to london , to put it into the bankers hands ; but will lend it to their neighbours in the country , where it is convenient for trade it should be . but if you lessen the rate of use , the lender , whose interest it is to keep up the rate of money , will rather lend it to the banker , at the legal interest , than to the tradesman or gentleman , who when the law is broken , shall be sure to pay the full natural interest , or more ; because of the ingrossing by the banker , as well as the risque in transgressing the law : whereas were the natural use suppose seven per cent. and the legal six ; first , the owner would not venture the penalty of the law for the gaining 1 / ● part , that being the utmost his money would yeild . nor would the banker venture to borrow , where his gains would be but one per cent. nor the money'd man lend him what he could make better profit of legally at home . all the danger lies in this , that if your being behind hand has made the natural use so high , that your tradesman cannot live upon his labour , but that your rich neighbours will so undersell you , that the return you make will not amount to pay the use and afford a livelihood , there is no way to recover from this but by a general frugality and industry , or being masters of the trade of some commodity , which the world must have from you at your rate , and cannot be other where supplied . now i think the natural interest of money is raised two ways : first , when the money of a country is but little in proportition to the debts of the inhabitants one amongst another ; for suppose 10000 l. were sufficient to manage the trade of bermudas , and that the ten first planters carried over 20000 l. which they lent to the several tradesmen and inhabitants of the country , who living above their gains , had spent 10000 l. of this money , and it wer● gone out of the island : 't is evident , that should all the creditors at once call in their money , there would be a great scarcity of money when that employ'd in trade must be taken out of the tradesmens hands to pay debts ; or else the debtors want money and be exposed to their creditors , 〈…〉 interest will be high . but this sel 〈…〉 ing , that all , or the greatest 〈…〉 creditors do at once call for 〈…〉 unless it be in some great and 〈…〉 is less and seldomer seit 〈…〉 unless where the debts 〈…〉 own to a greater pro 〈…〉 causing more 〈…〉 leade●s , will 〈…〉 high secondly . that which con 〈…〉 raises the 〈…〉 of money , is , when 〈…〉 to the trade of a country ; for in trade every body calls for money according as he wants it , and this disproportion is always felt . for if englishmen owed in all but one million , and there were a million of money in england , the money would be well enough proportionable to the debts , yet if two millions were necessary to carry on the trade , there would be a million wanting , and the price of money would be raised as it is of any other commodity in a market , where the merchandize will not serve half the customers , and there are two buyers for one seller . 't is in vain therefore to go about effectually to reduce the price of interest by a law ; and you may as rationally hope to set a fixt rate upon the hire of houses , or ships , as of money ; he that wants a vessel , rather than lose his market , will not stick to have it at the market rate , and find ways to do it , with security to the owner , though the rate were limited by a law ; and he that wants money , rather than lose his voyage , or his trade , will pay the natural interest for it , and submit to such ways of conveyance as shall keep the lender out of the reach of the law. so that your act , at ●est , will serve only to increase the arts of lending , but not at all lessen the charge of the borrower ; he 't is likely shall with more trouble , and going farther about , pay also the more for his money , unless you intend to break in only upon mortgages and contracts already made , and ( which is not to be supposed ) by a law , post factum , void bargains lawfully made , and give to richard what is peters due , for no other reason but because one was borrower and the other lender . but supposing the law reach'd the intention of the promoters of it ; and that this act be so contrived , that it forced the national price of money , and hindred its being by any body lent at a higher use than 4 l. per. cent. which is plain it cannot . let us in the next place see what will be the consequences of it . 1. it will be a loss to widows , orphans , and all those who have their estate in money , one third of their estates , which will be a very hard case upon a great number of people ; and it is warily to be consider'd by the wisdom of the nation , whether they will thus at one blow , fine and impoverish a great and innocent pa●t of the people , who having their estat●● in money , have as much right to make a● much of their money , as it is worth , ( for more they cannot ) as the landlord ha● to let his ●and for as much as it will yield , and to ●ine men one third of their estates without any crime or offence committed , seems very hard . 2. as it will be a considerable loss and injury to them , so it will be no advantage at all to the kingdom ; for so trade be not cramp'd , and the exportation of our native commodities and manufactures not hindred , it will be no matter to the kingdom , who amongst our selves gets or loses , only common charity teaches , those should be most taken care of by the law , who are least capable of taking care for themselves . 3. it will be a gain to the borrowing merchant ; for if he borrow at four per cent , and his returns be twelve per cent. he will have eight per cent. and the lender four , whereas now they divide the profit equally at six per cent. but this neither gets nor loses the kingdom in your trade , supposing the merchant and lender to be both englishmen ; only it will as i have said , transfer a third part of the monied mans estate , who has nothing else to live on , into the merchants pocket , and that without any merit in the one , or trangression in the other , and that to the prejudice of trade : since it will discourage lending at such a disproportion of profit , to risque , as we shall see more by and by , when we come to consider of what consequence it is to encourage lending , that so none of the money of the nation may lie dead , and thereby prejudice trade . 4. it will hinder trade , for there being a certain proportion of money necessary for driving such a proportion of trade , so much money of this as lies still , lessens so much of the trade : now it cannot be rationally expected , but that where the venture is great , and the gains small , ( as it is in lending in england upon low interest ) many will choose rather to hoard up their money than venture it abroad on such terms . this will be a loss to the kingdom , and such a loss as here in england ought chiefly to be looked after ; for we having no mines , nor any other way of getting or keeping of riches amongst us but by trade , so much of our trade as is lost , so much of our riches must necessarily go with it ; and the over-ballancing of trade between us and our neighbours , must inevitably carry away our money , and quickly leave us poor and exposed . in a country not furnish●d by nature with mines of gold and silver , ( and those too , as far as i can observe , are generally poor enough , the digging and resining of those metals , taking up the labour , and wasting the number of the people ; for which reason , the wise policy of the chineses will not suffer those mines they have to be wrought ) there are but two ways of growing rich , ( i. e. of bringing more riches , and consequently more plenty of all the conveniencies of life , than what falls to the share of neighbouring kingdoms and states ) and those two ways of growing rich , are either conquest or commerce . by the first , the romans made themselves masters of the riches of the world , but i think that in our present circumstances , no body is vain enough to entertain a thought of our reaping the profits of the world by our swords , and making the spoil and tribute of vanquish'd nations , the fund for the supply of the charges of the government , with an over-plus for the wants , and equally craving luxury , and fashionable vanity of the people . commerce therefore is the only way left to us , either for riches or subsistence , for this t●e advantages of our situation , as well as the industry and inc●ination of our people , bold and skil●ful at sea , do naturally fit us ; by this the nation of england ha● been hitherto supported , and trade left almost to it self , and assisted only by the natural advantages above-mentioned , brought us in plenty and riches , and always set this kingdom in a rank equal , if not superior to any of its neighbours , and would no doubt without any difficulty have continued it so , if the more enlarged , and better understood interest of trade , since the improvement of navigation had not raised us many rivals ; and the amazing politicks of some late reigns , let in other competitors with us for the sea , who will be sure to seize to themselves whatever parts of trade our mismanagement , or want of money , shall let slip out of our hands ; and when it is once lost , 't will be too late to hope , by a mistim'd care , easily to retrieve it again . for the currents of trade , like those of waters , make themselves channels , out of which they are afterwards as hard to be diverted , as rivers that have worn themselves deep within their banks . trade then is necessary to the producing of riches , and money necessary to the carrying on of trade : this is principally to be looked after and taken care of ; for if this be neglected , we shall in vain , by contrivances amongst our selves , and shu●tling the little money we have from one anothers hands , endeavour to prevent our wants : decay of trade will quickly waste all the remainder ; and then the landed man , who thinks perhaps by the fall of interest to raise the value of his land , will find himself cruelly mistaken , when the money being gone , ( as it will be if our trade be not kept up ) he can get neither farmer to rent , nor purchaser to buy his land. whatsoever therefore hinders the lending of money , injures trade : and so the reducing of money to four per cent. which will discourage men from lending , will be a loss to the kingdom , in stopping so much of the current of money , which turns the wheels of trade . but all this upon a supposition that the lender and borrower are both english men . if the lender be a foreigner , by lessening interest from six to four you get to the kingdom ⅓ of the interest we pay yearly to foreigners ; which let any one if he please think considerable . but then upon lessening interest to four per cent. it is likely one of these things will happen . that either you fall the price of your native commodities ; or lessen your trade ; or else prevent not the high use as you intended . for at the time of lessening your interest , you want money , or you do not : if you do not , there is no need to prevent borrowing at a high rate of your neighbours ; for there can be no money borrowed , but in order to trade ; for what is not employ'd in trade lyes still , and no body borrows for that . for borrowing of one to pay what we owe to another may be generally accounted to be for trade ; it being very seldom people call in their money to let it lye still . and if you do want money , necessity will still make you borrow of them , and at the rates your necessity , not your laws , shall set : or else , if there be fearcity of money , it must hinder the merchant's buying and exportation , and the artisan's manufacture . now the kingdom gets or loses by this ( for no question the merchant by low 〈◊〉 gets all the while ) only propo●tionably ( allowing the consumption of foreign commodities to be still the s●me ) as the paying of use to foreigners carries away more or less of our money , than want of money and stopping our trade keeps us from bringing in , by hindring our gains ; which can be only estimated by those who know how much money we borrow of foreigners , and at what rate ; and too , what profit in trade we make of that money : though perhaps it will appear true upon examination , that our growing rich or poor depends not at all upon our borrowing upon 〈◊〉 or not ; but only which is greater o● less , our importation or exportation of consumable commodities . for supposing two millions of money will drive the trade of england , and that we have money enough of our own to do it ; if we consume o● our own product and manufacture , and what we purchase by it of foreign commodities , one million , but of the other million consume nothing , but make a return of ten per cent. per an. we must then every year be 100000 l. richer , and our stock be so much encreast : but if we import more consumable commodities than we export , our money must go out to pay for them , and we grow poorer . suppose therefore ill husbandry hath brought us to one million stock , and we borrow the other million ( as we must , or lose half our trade ) at six per cent. if we consume one moyety , and make still ten per cent. per an. return of the other million , the kingdom gets 40000 l. per an. though it pay 60000 l. per an. use. so that if the merchant's return be more than his use , ( which 't is certain it is , or else he will not trade ) and all that is so traded for on borrowed money be but the ov●●ballance of our exportation to our importation , the kingdom gets by this borrowing so much as whatsoever the merchant's gain is above his use. but if we borrow only for our own expences , we grow doubly poor , by paying money for the commodity we consume , and use for that money ; though the merchant gets all this while , by making returns greater than his use. and therefore borrowing of foreigners in it self makes not the kingdom rich or poor ; for it may do either ; but spending more than our fruits or manufactures will pay for , brings in poverty , and poverty borrowing . for money , as necessary to trade , may be doubly considered ; first , as in his hands that pays the labourer and land-holder , ( for here its motion terminates , and through whose hands soever it passes between these , he is but a broker ) and if this man want money , ( as for example , the clothier ) the manufacture is not made ; and so the trade stops , and is lost . or secondly , money may be considered as in the hands of the consumer , under which name i here reckon the merchant who buys the commodity , when made , to export ; and if he want money , the value of the commodity , when made is lessened , and so the kingdom loses in the price . if therefore use he lessened● and you cannot tye foreigners to your terms , then the ill effects fall only upon your own landholders and artisans : if foreigners can be forc'd by your law to lend you money only at your own rate , or not lend at all , is it not more likely they will rather take it home , and think it safer in their own country at four per c●nt than abroad ; nor can their over-plus of money bring them to lend to you , on your terms ; for when your merchants want of money , shall have sunk the price of your market , a dutchman will find it more gains to buy your commodity himself , than lend his money at four per cent. to an english merchant to trade with : nor will the act of navigation hinder their coming , by making them come empty , since even al-already there are those who think , that many who go for english merchants , are but dutch factors , and trade for others in their own names : the kingdom therefore will lose by it if it makes foreigners withdraw any of their money , as well as if it hinders any of your people from lending theirs , where trade has need of it . in a treatise writ on purpose for the bringing down of interest , i find this argument of foreigners calling away their money to the prejudice of our trade , thus answer'd , that the money of foreigners is not brought into the land by read , 〈◊〉 bullion , but by goods or bills of exchange ; and when it is paid must be returned by goods or bills of exchange , and there will not be the less money in the land. i could not but wonder to see a man , who undertook to write of money and interest , talk so directly besides the matter in the business of trade ; foreigners money , he says , is not brought into the land by ready coin or bullion , but by goods , or bills of exchange . how then do we come by pullion or money ? for gold grows not that i know in our country , and silver so little , that one hundred thousandth part of the silver we have now in england , was not drawn out of any mines in this island . if he means that the monied man in holland , who puts out his money at interest here , did not send it over in pullion or specie hither , that may be true or false ; but either way helps not that authors purpose . for if he paid his money to a merchant his neighbour , and took his pills for it here in england , he did the same thing as if he had sent over that money , since he does but make that merchant 〈◊〉 in england , the money which ●e has due to him there , and otherwise would carry away : 〈◊〉 , says our author . 〈…〉 ; i must not be paid and exported in ready money , so says our law indeed , but that is a law to hedge in the cookoe , and serves to no purpose ; for if we export not goods , for which our merchants have money due to them in holland , how can it be paid by bills of exchange ? and for g●ods , 100 l. worth of goods can no where pay 200 l. in money , this being that which i find many men deceive themselves with in trade : it may be worth while to make it a little plainer . let us suppose england peopled as it is now , and its woollen manufacture in the same state and perfection that it is at present , and that we , having no money at all , trade with this our woollen manufacture for the value of 200000 l. yearly to spain , where there actually is a million in money ; let us suppose that we bring back from spain , yearly in oyl , wine , and fruit , to the value of 100000 l. and continue to do this ten years together ; 't is plain we have had for our two millions value in woollen manufacture carried thither , one million return'd in wine , oyl , and fruit , but what is become of ● other million ? will the merchants be content to lose it ? that you may be sure they would not , nor have traded on , if they had not every year returns made answering their exportation . how then were the returns made ? in money it is evident . for the spaniards having in such a trade , no debts , nor the possibility of any debts in england , cannot pay one farthing of that other million by bills of exchange ; and having no commodities that we will take off above the value of 100000 l. per annum , they cannot pay us in commodities . from whence it necessarily follows , that the 100000 l. per annum , wherein we over-ballance them in trade , must be paid us in money ; and so at the ten years end , their million of money , ( though their law make it death to export it ) will be all brought into engl●nd , as in truth , by this over-ballance of trade , the greatest part of our money hath been brought into england out of spain . let us suppose our selves now possessed of this million of money ; and exporting yearly out of england , to the several parts of the world● consumable commodities to the value of a million , but importing yearly in commodities , which we consume amongst us to the value of 1100000 l. if such a t●●de as this be managed amongst us , and continue ten y●●●s it is evident , that our million of money will at the end of the ten years be inevitably all gone from us to them , by the same way that it came to us ; that is , by their over-ballance of trade . for we importing every year 100000 l. worth of commodities more than we export , and there being no foreigners that will give us 100000 l. every year for nothing , it is unavoidable , that 100000 l. of our money must go out every year to pay for that over-plus , which our commodities do not pay for ; and 't is ridiculous to say , that bills of exchange shall pay our debts abroad ; that cannot be till scrips of paper can be made current coin. the eng●ish merchant , who has no money owing him abroad , cannot expect to have his bills paid there ; or if he has credit enough with a correspondent , to have his bills answer'd ; this pays none of the debt of england , but only changes the creditor : and if upon the general ballance of trade , english merchants owe to foreigners 100000 l. or 1000000 , if commodities do not , our money must go out to pay , or else our credit be lost , and our trade stop , and be lost too . a kingdom grows rich or poor just as a farmer doth , and no otherwise : let us suppose the whole isle of portland one farm , and that the owner , besides what serves his family , carries to market to weymouth and dorchester , &c. cattle , corn , butter , cheese , wooll , or cloath , lead and tin , all commodities produced and wrought within his farm of portland , to the value of 1000 l. yearly ; and for this , brings home in salt , wine , oyl , spice , linnen and silks , to the value of 900 l. and the remaining 100 l. in money : 't is evident he grows every year 100 l. richer , and so at the end of the ten years will have clearly got 1000 l. if the owner be a better husband , and contenting himself with his native commodities , buy less wine , spice and silk , at market , and so bring home 500 l. in money yearly , instead of 100 l. at the end of ten years he will have 5000 l. by him , and be so much richer . he dies , and his son succeeds , a fashionable young gentleman , that cannot dine without champane and burgundy , nor sleep but in a damask bed ; whose wife must spread a long train of brocard , and his children be always in the newest french cut and stuff : he being come to the estate , keeps on a very busie family ; the markets are weekly frequented , and the commodities of his farm carried out , and sold , as formerly , but the returns are made something different ; the fashionable way of eating , drinking , and clothing 〈◊〉 his wife , children and family , requires more sugar and spice , wine and fruit , silk and ribons , than in his fathers time ; so that instead of 900 l. per annum , he now brings home of consumable commodities , to the value of 1100 l. yearly . what comes of this ? he lives in splendor , 't is true , but this unavoidably carries away the money his father got , and he is every year 100 l. poorer . to his expences , beyond his income , add debauchery , idleness , and quarrels , amongst his servants , whereby his manufactures are disturbed , and his business neglected , and a general disorder and confusion through his whole family and farm ; this will tumble him down the hill the faller , and the stock , the industry , frugality , and good order of his father had laid up● will be quickly brought to an end , and he fast in prison . a farm and a kingdom in this respect di●●er no more than as greater and less . we may trade , and be busie , and grow poor by it , unless we regulate our expenses ; if to this we are idle , negligent , di●honest , malitious , and disturb the sober and industrious in their business , let it be upon what pretence it will , we shall ruine the faster . so that whatever this author , or any one else may say , money is brought into england by nothing but spending here less of foreign commodities , than what we carry to market can pay for ; nor can debts we owe to foreigners be paid by bills of exchange , till our commodities exported , and sold beyond sea , have produced money or debts due there , to some of our merchants ; for nothing will pay debts but money or moneys worth , which three or four lines writ in paper cannot be ; for if they have an intrinsick value , and can serve instead of money , why do we not send them to market instead of our cloth , lead and tin ? and at an easier rate purchase the commodities we want . all that a bill of exchange can do , is to direct to whom money due , or taken up upon credit in a foreign country , shall be paid ; and if we trace it , what is due already , we shall find , became so , for commodities , or money , carried from hence ; and if it be taken up upon credit , it must ●et the debt be shif●●d from one creditor to another as often as you will ) at last be paid by money or goods , carried from hence , or else the merchant here must turn bankrupt . we have seen how riches and money are got , kept , or lost , in any country ; and that is by consuming less of foreign commodities than what , by commodities or labour is paid for . this is in the ordinary course of things : but where great armies and alliances are to be maintain'd abroad by supplies sent out of any country , there often , by a shorter and more sensible way , the treasure is diminished . but this , since the holy war , or at least since the improvement of navigation and trade , seldom happening to england , whose princes have found the enlarging their power by sea , and the securing our navigation and trade , more the interest of this kingdom than wars or conquests on the continent ; expences in arms beyond sea have had little influence on our riches or poverty . the next thing to be considered , is , how money is necessary to trade . the necessity of a certain proportion of money to trade , ( i conceive ) lyes in this , that money in its circulation driving the several wheels of trade , whilst it keeps in that channel ( for some of it will unavoidably be dreined into standing pools ) is all shared between the land-holder , whose land a●●ords the materials ; the labourer , who works them ; the broker , ( i. e. ) merchant and shop keeper , who distributes them to those that want them : and the consumer , who spends them . now money is necessary to all these sorts of men , as serving both for counters and for pledges , and so carrying with it even reckoning and security that he that receives it shall have the same value for it again , of other things that he wants , whenever he pleases . the one of these it does by its stamp and denomination ; the other by its intrinsick value , which is nothing else but its durableness , scarcity , and not being apt to be counterfeited . which intrinsick value , though it be not natural , but is only in the opinion of men consenting to it , yet being universal , has generally , but not always , ( for we see that in a siege or man of war silver may not be of equal value to gunpowder , and in a famine gold not be worth its weight in bran ) the same effect as if it were natural the necessity therefore of a proportion of money to trade , depends on money , not as counters for the reckoning may be kept or transferred by writing , but on money as a pledge . for since the bill , bond , or other note of debt , i receive from one man , will not be accepted as security by another , he not knowing that the bill or bond is true or legal , or that the man bound to me is honest or responsible ; and so is not valuable enough to become a current pledge , nor can by publick authority be well made so , as in the case of assigning of bills ; because a law cannot give to bills that intrinsick value , which the universal consent of mankind has annexed to silver and gold. and hence foreigners can never be brought to take your bills or writings for any part of payment , though perhaps they might pass as valuable considerations among your own people , did not this very much hinder it , viz. that they are liable to unavoidable doubt , dispute and counterfeiting , and require other proofs to assure us they are true and good security , than our eyes or a touchstone . and at best this course , if practicable , will not hinder us from being poor ; but may be suspected to help to make us so , by keeping us from feeling our poverty , which in distress will be sure to find us with greater disadvantage . though it be certain it is better than letting any part of our trade fall for want of current pledges ; and better too than borrowing money of our neighbours upon use , if this way of assigning bills can be made so easie , safe and universal at home , as to hinder it . to return to the business in hand , and shew the necessity of a proportion of money to trade : every man therefore must have at least so much money , or so timely recruits , as may in hand , or in a short distance of time , satisfie the man who supplies him with the necessaries of life , or of his trade . for no body has any longer these necessary supplies than he has money or credit , which is nothing else but an assurance of money in some short time . so that it is requisite to trade there should be so much money as to keep up the landholders , labourers and brokers credit ; and therefore ready money must be constantly exchang'd for wares and labour , or follow within a short time after . this shews the necessity of some proportion of money to trade ; but what proportion that is , is hard to determine , because it depends not barely on the quantity of money , but the quickness of its circulation ; which since it cannot be easily traced , for the very same shilling may at one time pay 20 men in 20 days , at another , rest in the same hands 100 days together ; to make some probable guess , we are to consider how much money it is necessary to suppose must rest constantly in each man's hands , as requisite to the carrying on of trade . first therefore the labourers , living generally but from hand to mouth , and indeed , considered as labourers in order to trade , may well enough carry on their part , if they have but money enough to buy victuals , cloaths , and tools ; all which may very well be provided , without any great sum of money lying still in their hands . the labourers therefore being usually paid once a week , ( if the times of payment be seldomer , there must be more money for the carrying on this part of trade ) we may suppose there is constantly amongst them , one with another , or those who are to pay them , always one weeks wages in ready money . for it cannot be thought that all or most of the labourers pay away all their wages constantly as soon as they receive it , and live upon trust till next pay day . this the farmer and tradesman could not well bear , were it every labourer's case , and every one to be trusted ; and therefore they must of necessity keep some money in their hands to go to market for victuals , and to other tradesmen , as poor as themselves , for tools ; and lay up money too to buy cloaths , or pay for those they bought upon credit : which money thus necessarily resting in their hands , we cannot imagine to be one with another much less than a weeks wages , that must be in their pockets , or ready in the farmer 's hands . for he who employs a labourer at 1 s. per day , and pays him on saturday nights , cannot be supposed constantly to receive that 6 s. just the same saturday ; it must ordinarily be in his hand● one time with another , if not a whole week , yet several days before . this was the ordinary course , whil'st we had money running in the several channels o● commerce : but that now very much failing , and the farmer not having money to pay the labourer , supplies him with corn , which in this great plenty the labourer will have at his own rate , or else not take it off his hands for wages and as for the workmen who are employed in our manufacture , especially the woollen one , these the clothier not having ready money to pay , furnishes with the necessaries of life , and so truck commodities for work , which , such as they are , good or bad , the workman must take at his master's rate , or sit still and starve , whil'st by this means this new sort of ing●oners or ●oresta●lers , having the feeding and supplying this numerous body of workmen out of their warehouses , ( for they have now magazines of all sorts of wares ) set the price upon the poor landholder . so that the markets now being destroyed , and the farmer not finding vent there for his butter , cheese , bacon and corn , &c. for which he was wont to bring home ready money , must sell it to these ingrossers , on their own terms of time and rate , and allow it to their own day-labourers under the true market-price ; which what kind of influence it is like to have upon land , and how this way rents are like to be paid at quarter-day , is easie to apprehend ; and 't is no wonder to hear every day of farmers breaking and running away ; for if they cannot receive money for their goods at market , 't will be impossible for them to pay their landlord's rent : and if any one doubt whether this be so , i desire him to enquire how many farmers in the west are broke and gone since michaelmas last . want of money being to this degree , works both ways upon the landholder . for first , the ingrossing forestaller lets not the money come to market ; but supplying the workman , who is employed by him in manufacture , with necessaries , imposes his price and forbearance on the farmer , who cannot sell to the others . and the labourer , who is employed by the landholder in husbandry , imposes also his rate on him for the commodities he takes . for there being a want of day-labourers in the country , they must be humoured , or else they will neither work for you , nor take your commodities for their labour . secondly , as for the landholder , since his tenants cannot coin their rent just at quarter-day , but must gather it up by degrees , and lodge it with them till pay-day , or borrow it of those who have it lying by them , or do gather it up by degrees , which is the same thing , and must be necessarily so much money for some time lying still ; for all that is paid in great sums must somewhere be gathered up by the retail incomes of a trade , or else lye still too in great sums , which is the same stop of money , or a greater . add to this , that to pay the creditor that lent him his rent , he must gather up money by degrees , as the sale of his commodities shall bring it in , and so makes a greater stop and greater want of money , since the borrowed money that paid the landholder the 25th of march , must be supposed to lye still some time in the creditor's hand , before he lent it the tenant ; and the money that pays the creditor three months after must lye still some time in the tenant's . nor does the landlord pay away his rent usually as soon as he receives it , but by degrees , as his occasions call for it ; we cannot but suppose that between the landlord and tenant there must necessarily be at least ¼ of the yearly revenue of the land constantly in their hands . indeed considering that most part of the rents of england being paid at our lady-day and michaelmas , and that the same money which pays me my rent from my tenant the 25th of march , or thereabouts , cannot pay my next neighbour his rent from his tenant at the same time , much less one more remote in another country ; it might seem requisite to suppose half the yearly revenue of the land to be necessarily employed in paying of rent . for to say that some tenants break and pay not their rent at all , and others pay not till two , three , four , five , six , &c. months after quarter-day , and so the rent is not all paid at one time , is no more than to say , that there is money wanting to the trade : for if the tenant fail the landlord , he must fail his creditor , and he his , and so on , till somebody break , and so trade decay for want of money . but since a considerable part of the land of england is in the owners hands , who neither pay nor receive great sums for it at a certain day ; and because too , ( which is the chief reason ) we are not to consider here how much money is in any one man's , or any one sort of mens hands at any one time ; for that at other t●mes may be distributed into other hands , and serve other parts of trade ; but how much money is necessary to be in each man's hands all the year round , taking one time with another , ( i. e. ) having 200 l. in his hand one month , is to be reckon●d as 100 l. in his hand three months , and so proportionably ) i think we may well suppose ¼ of the yearly revenue to be constantly in the landlords or tenants hands ; where● by the by , we may observe , that it were better for trade , and consequent●y for every body , ( ●or more money wo●●d be stirring , and less would do t●e business ) if rents were paid by 〈◊〉 in●●rvals than six months . for su●●●sing i let a farm at 52 l. per an. i● my rent be paid half yearly , there is re●●●●ed 26 l. to be employed in the payment of it in ●ne entire sum. ( if it ●e paid well , and if it be not paid well , 〈◊〉 ●●nt of so 〈◊〉 money to be spared to that purpose , there is so much want of money , and trade is still endamag'd by it ) a great part whereof must necessarily lie still before it come out of my tenants chest to my hands : if it be paid once a quarter 13 l. alone will do it , and less money is laid up for it , and stop'd a less while in its course ; but should it be paid every week , one single 20 s. will pay the rent of 52 l. per annum , whence would follow this double benefit ; first , that a great deal less money would serve for the trade of a country ; and secondly , that less of the money would lie still , the contrary whereof must needs happen where growing debts are to be paid at larger distances , and in greater sums . thirdly , as for the brokers , since they too must lay up the money coming in by retail , either to go to market , and buy wares , or to pay at the day appointed , which is often six months ; for those wares they have already , we cannot suppose them to have less by them , one with another , than one twentieth part of their yearly returns , whether the money be their own , or they be indebted so much or more it matters not , if it be nece●sary they should have constantly by them , comparing one time with another , at least one twentieth part of their yearly return : indeed in some great towns , where the bankers are ready at hand to buy bills , or any other way to lend money , for short time at great interest , there perhaps the merchant is not forced to keep so much money by him , as in other places , where they have not such a supply . but if you consider , what money to do this must necessarily be constantly lodg'd in the bankers hands ; to which , if you add , what part of the money of a country scholars of all sorts , women , gamesters , and great mens menial servants , and all such that do not contribute at all to trade , either as landholders , labourers , or brokers , will unavoidably have constantly in their hands , it cannot well be thought , that less than one fiftieth part of the labourers wages , one fourth part of the landholders yearly revenue , and one twentieth part of the brokers yearly returns in ready money , will be enough to drive the trade of any country . at least to put it beyond exception low enough ; it cannot be imagin'd that less than one moiety of this , i. e. less than one hunderd part of the labourers yearly wages , one eighth part of the landholders yearly revenue , and one fortieth part of the brokers yearly returns , in ready money , can be enough to move the several wheels of trade , and keep up commeree in that life and thriving posture it should be ; and how much the ready cash of any country is short of this proportion , so much must the trade be impair'd and hindred for want of money ; but however these measures may be mistaken , this is evident , that the multiplying of brokers hinders the trade of any country by making the circulation , the money goes larger , and in that circuit more stops , so that the returns must necessarily be flower and ●cantier , to the prejudice of trade : besides that , they eat up too great a share of the gains of trade , by that means starving the labourer , and impoverishing the landholder , whose interest is chiefly to be taken care of , it being a settled unmoveable concernment in the commonwealth ; and therefore it would be convenient to hinder , as much as is possible , any one from selling any of our native commodities but he that makes it ; shopkeepers in this being worse than gamesters ; for they do not only keep so much of the money of a country constantly in their hands , but also make the publick pay them for their keeping of it ; though gaming too , upon the account of trade , ( as well as other reasons ) may well deserve to be restrain'd , since gamesters , in order to their play , keep great sums of money by them , which there lies dead ; for though gamesters money shift masters oftner than any , and is tumbled up and down with every cast of a die , yet as to the publick lies perfectly still , and no more of it comes into trade than they spend in lating or wearing . here too we may observe , how much manufacture deserves to be incourag'd , since that part of trade , though the most considerable , is driven with the least money , especially if the workmanship be more worth than the materials ; for to the trade that is driven by labour and handicrafts men , one two and fiftieth part of the yearly money paid them will be sufficient ; but to a trade of commodities of our bare native growth , much greater proportion of money is requir'd . perhaps it will be wondered , why having given some estimate ( how wide i know not ) of the money necessary in the hands of the landholder , labourer , and br●ker , to carry on trade , i have said nothing of the consumer , whom i had mentioned before ; but to this i answer , there are so few consumers , who are not either labourers , brokers , or landholders : ( for those who immediately depend on the landholder , as his children and servants , come in under that title , being maintained by the rent of his land , and so of the rest ) that they make a very inconsiderable part in the account . by what has been said , we may see what injury the lowering of interest is like to do us by hindering trade , when it shall either make the foreigner call home his money , or your own people backward to lend , the reward not being judged proportionable to the risque . there is another seeming consequence , of the reducing of money to a low price , which at first sight has such an appearance of truth in it , that i have known it impose upon very able men , and i guess has no small influence at this time in the promoting this alteration a●d that is , that the lowering of interest will raise the value of all other things in proportion . for money being the c●unter-ballance to all other things purchasable by it and lying , at it were , in the opposite scale of commerce , it looks like a natural consequence , that as much as you take off from the value of money 〈◊〉 much you add to the price of other things which are exchanged for it ; the raising of the price of any thing being no more but the addition to its value in respect of money , or , which is all one , lessening the value of money . for example : should the value of gold be brought down to that of silver , 100 guineas would purchase little more corn , wool , or land , than 100 shillings , and so the value of money being brought lower , say they , the price of other things will rise ; and the falling of interest from 6 to 4 per cent. is taking away so much of the price of money and so consequently the lessening its value . the mistake of this plausible way of reasoning will be easily discovered , when we consider that the measure of the value of money , in proportion to any thing purchasable by it , is the quantity of the ready money we have in comparison with the quantity of that thing and its vent ; ( which vent depends upon its necessity or usefulness , as convenience of life or opinion , guided by fansie or fashion , shall determine ) or which amounts to the same thing , the price of any commodity rises or falls by the proportion of the number of buyers and sellers ● whereby the vent comes to be increased or decreased , as a greater part of the money we have is designed to be laid out by several people , at the same time , rather in one thing than another , as we see in the change of fashions ; this rule holds universally in all things that are to be bought and sold , bateing now and then an extravagant phancy of some particular person , which never amounts to so considerable a part of trade as to make any thing in the account worthy to be thought an exception to this rule . i shall begin first with the necessaries or conveniencies of life , and the consumable commodities subservient thereunto ; and shew , that the value of money in respect of those depends only on the plenty or scarcity of money in proportion to the plenty and scarcity of those things , and not on what interest shall be by necessity , law or contract at that time laid on the borrowing of money : and then afterwards i shall shew that the same holds in land. there is nothing more confirmed by daily experience , than that men give any portion of money for whatsoever is absolutely necessary , rather than go without it : and in such things , the scarcity of them alone makes their prices . as for example : let us suppose 1 / ● ounce of silver , or half a crown now in england , is worth a bushel of wheat ; but should there be next year a great scarcity of wheat in england , and a proportionab●e want of all other food , five ounces of siver would perhaps in exchange purchase but one bushel of wheat , so that money would be then 9 / 10 less worth in respect o● food , though at the same value it was before , in respect of other things that kept their former proportion in their quantity and consumption . by the like proportions of increase and decrease , does the value of things more or less convenient rise and fall in respect of money , only with this difference , that things absolutely necessary for life must be had at any rate ; but things convenient will be had only as they stand in preference with other conveniencies ; and therefore in any one of these commodities , the value rises only as its quantity is less , and vent greater , which depends upon its being p●eferr'd to other things in its consumption ; for supposing that at the same time that there is a g●●at scarcity of wh●●t , and other grain , there were a considerable quantity of o●●s , men no question would give far more for wheat than oats , as being the healthier , pleasanter , and more convenient food ; but since oats would serve to supply that absolute necessity of sustaining life , men would not rob themselves of all other conveniencies of life , by paying all their money for wheat , when oats that are cheaper , though with some inconvenience , would supply that defect . it may then so happen at the same time , that half an ounce of silver , that the year before would buy one bushel of wheat , will this year buy but 1 / 10 of a bushel : half an ounce of silver , that the year before would have bought three bushels of oats , will this year still buy one bushel ; and at the same time half an ounce of silver , that would the year before have bought 15 pounds of lead , will still buy the same quantity . so that at the same time silver , in respect of wheat , is 9 / 10 less worth than it was , in respect of oats ⅔ less worth , and in respect of lead , as much worth as before . the fall therefore or rise of interest , making neither more or less land , money , or any sort of commodity in england , than there was before ; immediately by its change alters not at all the value of money , in reference to commodities ; because the measure of that is only the quantity and vent which are not immediately chang'd by the change of interest , but only as the change of interest in trade conduces to the bringing in or carrying out money or commodity , and so in time varying their proportion here in england from what it was before , which is not in this place to be considered . this is perfectly the value of money in respect of consumable commodities : but the better to understand it in its full latitude , in respect both of consumable commodities , and land too , we must consider , first , that the value of land consists in this , that by its constant production of saleable commodities it brings in a certain yearly income . secondly , the value of commodities consists in this , that as portable and useful things , they , by their exchange or consumption , supply the necessaries or conveniencies of life . thirdly , in m●r●y there is a double value , answering to both of these first , as it is capable by its interest to yield us such an yearly income ; and in this it has the nature of land , the income of one being called ren● , of the other , use ; only with this difference , that the land in its soil being different , as some fertile , some barren , and the products of it very various , both in their sorts , and value too , according as their quantity and vent , varies ; but money● constantly the same , and by its interest giving the same sort of product through the whole country , is capable of having a sixed yearly rate set upon it by the magistrate ; but ●and is not . but though in the uniformity of its legal worth , 100 l. of lawful money being all through england equal in its current value to any other 100 l. of lawful money , ( because by vertue of the law it will every where pass for as much ware or debt , as any other hundred pounds ) is capable to have its yearly hire valued better than land : yet in respect of the varying need , and necessity of money , ( which changes with the encrease or decay of money or trade in a country ) it is as little capable to have its yearly hire fixed by law , as land it self . for were all the land in rumney-marsh , acre for acre , equally good , that is , did constantly produce the same quantity of equally good hay or grass , one as another , the rent of it , under that consideration of every acre being of an equal worth , would be capable of being regulated by law ; and one might as well enact , that no acre of land in rumney-marsh shall be let for above 40 s. per an. as that no 100 l. shall be let for above 4 l. per an. but no body can think it fit ( since by reason of the equal value of that land it can ) that therefore the rent of the land in rumney-marsh should be regulated by law. for supposing all the land in rumney-marsh , or in england , were all of so equal a worth , that any one acre , compar'd at the same time to any one other , were equally good in respect of its product , yet the same acre , compar'd with it self in different times , would not in respect of rent be of equal value ; and therefore it would have been an unreasonable thing , if in the time of henry ● the rent of land in rumney-marsh had been settled by a law , according to the judg'd value of it at that time , and the same law , limiting the rent perhaps to 5 s. per acre , have continued still . the absurdity and impracticableness of this every one sees at the first proposal , and readily concludes within himself , that things must be left to find their own price● and it is impossible in this their constan● mutability for human foresight to se● rules and bounds to th● constantly-varying proportion and use , which will alway● regulate their value . they who consider things beyond their names , will find , that money , as well as all other commodities , is liable to the same changes and inequalities : nay in this respect of the variety of its value brought in by time in the succession of affairs , the rate of money is less capable of being regulated by a law in any country than the rent of land ; because of the quick changes that happen in trade this too must be added , that money may be brought in or carried out of the kingdom , which land cannot ; and so that be truly worth 6 or 8 per cent. this year , which would yield but 4 the last . 2. money has a value , as it is capable by exchange to procure us the necessaries or conveniencies of life ; and in this it has the nature of a commodity , only with this difference , that it serves us commonly by its exchange , never almost by its consumption ; but has not at all a more standing settled value in exchange with any other thing , than any other commodity has , but a more known one , and better sixed by name , number and weight , to enable us to reckon what the proportion of scarcity and vent of one commodity is to another . for supposing , as before , that half an ounce of silver would last year exchange for one bushel of wheat , or for 15 l. weight of lead ; if this year wheat be 10 times scarcer , and lead in the same quantity to its vent as it was , is it not evident that half an ounce of silver will still exchange for 15 l. of lead , though it will exchange but for one tenth of a bushel of wheat ; and he that has use of lead will as soon take 15 l. weight of lead , as ● ounce of silver , for one tenth of a bushel of wheat , and no more ; so that if you say that money now is 9 / 10 less worth than it was the former year , you must say so of lead too , and all other things that keep the same proportion to money they were in before ; only this variation is first observed in money , because it is the measure by which people reckon . for calling that half ounce of silver half a crown , they are understood better when they say , half a crown , or two shilling● and six pence , will now but 1 / 10 of a bushel of wheat , but do not say , that 15 l. of lead will now but 1 / 10 of a bushe● of wheat , because it is not generally used to this sort of reckoning ; nor do the● say lead is less worth than it was , though in respect of wheat lead be 〈…〉 worse than it was , as well as silver ; only by the tale of shillings we are better enabled to judge of it . this i suppose is the true value of m●●ney when it passes from one to anothe● in buying and selling ; where it runs the same changes of higher and lower , as an● other commodity doth ; for one equ●● quantity whereof you shall receive more or less of another commodity at on● time than you do at another in exchange for a farmer that carries a bushel ● wheat to market , and a labourer th●● carries half a crown , shall find that the money of one , as well as corn of the other , shall at some times purchase him more or less leather or salt , according as they are in greater plenty and scarcity one to another . so that in exchange of coin'd silver for any other commodity , which is buying and selling , the same measure governs the proportion you receive , as if you exchang'd lead or wheat , or any other commodity , which is nothing else but their quantity in proportion to their vent . if then change of use makes not your silver more in sp●ci● , or your wheat or other commodities less , it will not have any influence at all to make it exchange for less of wheat , or any other commodity , than it will have on lead , to make it exchange for less wheat , or any other commodity . money therefore in buying and selling being perfectly in the same condition with other commodities , and subject to all the same laws of value , let us next see how it comes to be of the same nature with land , by yielding a certain yearly income , which we call use or interest . for land produces naturally something new and profitable , and of value to mankind ; but money is a barren thing , and produces nothing , but by compact transfers that profit that was the reward of one man's labour into another man's pocket . that which occasions this , is the unequal distribution of money ; which inequality has the same effect too upon land that it has upon money . for my having more money in my hand than i can , or am dispos'd to use in buying and selling , makes me able to lend ; and another's want of so much money as he could employ in trade , makes him willing to borrow . but why then , and for what consideration doth he pay use ? for the same reason , and upon as good consideration , as the tenant pays rent for your land. for as the unequal distribution of land , ( you having more than you can or will manure , and another less ) brings you a tenant for your land ; and the same unequal distribution of money , ( i having more than i can or will employ , and another less ) brings me a tenant for my money : so my money is apt in trade , by the industry of the borrower , to produce more than 6 per cent. to the borrower , as well a● your land , by the labour of the tenant , is apt to produce more fruits than his rent comes to ; and therefore deserves to be paid for , as well as land , by an yearly rent . for though the usurer's money would bring in no yearly profit , if he did not lend it , ( suppo●ing he employ it not himself ) and so his six per cent. may seem to be the fruit of another mans labour , yet he shares not near so much of the profit of anothers mans labour , as he that lets land to a tenant ; for without the tenants industry ( supposing as before , the owner would not manage it himself ) his land would yield him little or no profit ; so that the rent he receives is a greater portion of the fruit of his tenants labour than the use is at 6 per cent , for generally he that borrows 1000 l. at six per cent. and so pays 60 l. per a●num use , gets more above his use in one year , by his industry , than he that rents a farm of 60 l. per annum gets in two above his rent , though his labour be harder . it being evident therefore that he that has skill in traffick , but has not money enough to exercise it , has not only reason to borrow money to drive his trade , and get a livelyhood , but as much reason to pay use for that money , as he that not having land of his own , yet has skill in husbandry , has not only reason to rent land , but to pay money for the use of it ; it follows , that borrowing money upon use is not only by the necessity of affairs , and the constitution of humane society● unavoidable to some men , but that also to receive profit for the loan of money , is as equitable and lawful , as receiving rent for land , and more tolerable to the borrower , notwithstanding the opinion of some over-scrupulous men. this being so , one would expect , that the rate of interest should be the measure of the value of land in number of years purchase , for which the fee is sold ; for 100 l. per annum being equal to 100 l. per annum , and so to perpetuity . and 100 l. per annum being the product● of 1000 l. when interest is at 10 per cent. of 1250 l. when interest is at 8 per cent. of 1666 l. or thereabouts , when interest is at 6 per cent. of 2000 l. when money is at 5 per cent. of 2500 l. when money is at 4 per cent. one would conclude , i say , that land should sell in proportion to use , according to these following rates , viz. when money is at 10 per cent. for 10 years purchase . when money is at 8 per cent. for 12 1 / ● years purchase . when money is at 6 per cent. for 16 ● / ● years purchase . when money is at 5 per cent. for 20 years purchase . when money is at 4 per cent. for 25 years purchase . but experience tells us , that neither in queen elizabeth , nor king iames the first reigns , when interest was at ten per cent. was land sold for ten ; or when it was at eighth per cent , for 12 ½ years purchase , or any thing near the low rate that high use requir'd ( if it were true , that the rate of interest govern'd the price of land ) any more than land , now yields 25 years purchase , because a great part of the monied men will now lett their money upon good security at four per cent. thus we see in fact how little this rule has held at home ; and he that will look into holland , will find that the purchase of land was not raised there when their interest fell . this is certain , and past doubt , that the legal interest can never regulate the price of land , since it is plain , that the price of land has never changed with it in the several changes have been made in the rate of interest by law , nor now that the rate of interest is by law the same through all england , is the price of land every where the same , it being in some parts constantly sold for 4 or 5 years purchase more than in others . whether you or i can tell the reason of this , it matters not to the question in hand , but it being really so , this is plain demonstration against those who pretend to advance and regulate the price of land by a law , concerning the interest of money . but yet i will give you some of my guesses , why the price of land is not regulated ( as at first sight it seems it should be ) by the interest of money . why it is not regulated by the legal use is manifest , because the rate of money does not follow the standard of the law , but the price of the market ; and men not observing the legal and forced , but the natural and current interest of money , regulate their affairs by that ; but why the rate of land does not follow the current interest of money requires a farther consideration . all things that are bought and sold , raise and fall their price in proportion , as there are more buyers or sellers : where are a great many sellers to a few buyers , there use what art you will , the thing to be sold will be cheap ; on the other side , turn the tables , and raise up a great many buyers for a few sellers , and the same thing will immediately grow dear ; this rule holds in land as well as all other commodities , and is the reason , why in england at the same time , that land in some places is at seventeen or eighteen years purchase , it is about others , where there are pro●itable manu●actures at two or three and twenty years purchase ; because there ( men thriving and getting money by their industry , and willing to leave their estates to their children in land , as the surest , and most lasting provision , and not so liable to casualties as money in untrading or unskillful hands ) there are many buyers ready always to purchase , but few sellers , for the land thereabout being already possessed by that sort of industrious and thriving men , they have neither need , nor will , to sell : in such places of manufacture , the riches o● the one not arising from the squandring and waste of another , ( as it doth in other places where men live lazily upon the product of the land ) the industry of the people bringing in increase of wealth from remote parts , makes plenty of money there without the impoverishing of their neighbours . and when the thriving tradesman has got more than he can well employ in trade , his next thoughts are to look out for a purchase , but it must be a purchase in the neighbourhood , where the estate may be under his eye , and within convenient distance , that the care and pleasure of his farm may not take him off from the engagements of his calling , nor remove his children too far from him , or the trade he breeds them up in ; and this seems to me the reason , why in places wherein thriving manufactures have erected themselves , land has been observed to sell quicker , and for more years purchase than in others , as about hallifax in the north , taunton and exeter in the west . this is that then which makes land as well as other things dear ; plenty of buyers , and but few sellers ; and so by the rule of contraries , plenty of sellers and few buyers makes land cheap . he that will justly estimate the value of any thing , must consider its quantity , in proportion to its vent , for this alone regulates the price ; for the value of any thing , compar'd with its self , or with a standing measure , is greater , as its quantity is less in proportion to its vent ; but in comparing it , or exchanging it with any other thing , the quantity and vent too of that must be allowed for in the computation of their value . but because the desire of money is constantly , almost every where the same , its vent varies very little ; but as its greater scarcity enhanses its price , and increases the scramble , there being nothing else that does easily supply the want of it the le●sening its quantity , therefore , always increase● its price , and makes an equal portion of it exchange for a greater of any other thing . thus it comes to pass , that there is no manner of settled proportion between the value of an ounce of silver , and any other commodity ; for either varying its quantity in that country , or the commodity changing its quantity in proportion to its vent , their respective values change , i. e. less of one will barter for more of the other ; though in the ordinary way of speaking , 't is only said , that the price of the commodity , not of the money is changed . for example , half an ounce of silver in england , will exchange sometimes for a bushel of wheat , sometimes for ½ , sometimes but ¼ , &c. and this it does equally , whether by use it be apt to bring in to the owner 6 / 100 of its own weight per annum , or nothing at all ; it being only the change of the quantity of wheat to its vent , supposing we have still the same summ of money in the kingdom ; or else the change of the quantity of our money in the kingdom , supposing the quantity of wheat , in respect to its vent be the same too , that makes the change in the price of wheat ; for if you alter the quantity or vent on either side , you presently alter the price , but no other way in the world. for it is not the being , adding , increasing or diminishing of any good quality in any commodity that makes its price greater or less , but only as it makes its quantity or vent greater or less , in proportion one to another . this will easily appear by two or three instances . 1. the being of any good and useful quality in any thing , neither increases its price , nor indeed makes it have any price at all , but only as it lessens its quantity or increases its vent , each of these in proportion to one another . what more useful or necessary things are there to the being or well-being of men , than air and water , and yet these have generally no price at all , nor yield any money , because their quantity is immensly greater than their vent in most places of the world ; but , as soon as ever water ( for air still offers its self every where , without restraint or inclosure , and therefore is no where of any price ) comes any where to be reduced into any proportion to its consumption , it begins presently to have a price , and is sometimes sold dearer than wine ; and hence it is , that the best and most useful things are commonly the cheapest , because , though their consumption be great , yet the bounty of providence has made their production large and suitable to it . 2. nor does the adding an excellency to any commodity , raise its price , unless it increase its consumption . for suppose there should be taught a way ( which should be published to the knowledge of every one ) to make a medicine of wheat alone , that should infallibly cure the stone , 't is certain the discovery of this quality in that grain , would give it an excellency very considerable ; and yet this would not increase the price of it one farthing in twenty bushels , because its quantity or vent would not hereby , to any sensible degree , be alter'd . 3. neither does the increasing of any good quality , in any sort of things make it yield more ; for though teasels be much better this year than they were last , they are not one jot dearer , unless they be fewer too , or the consumption of them greater . 4. nor does the lessening the good qualities of any sort of commodity lessen its price ; which is evident in hops , that are usually dearest those years they are worst . but if it happen to be a species of commodity , whose defects may be supplyed by some other , the making of it worse does lessen its price , because it hinders its vent ; for if rye should any year prove generally smutty or grown , no question it would yield less money than otherwise , because the deficiency of that might be , in some measure , made up by wheat and other grain ; but if it be a sort of commodity whose use no other known thing can supply , 't is not its being better or worse , but its quantity and vent is that alone which regulates and determines its value . to apply this now to money as capable of different rates of interest , considering money in its proper use , as a commodity passing in exchange from one to another , all that is done by interest is but adding to money by agreement or publick authority , which naturally it hath not , viz. a faculty of increasing every year six per cent ; now if publick authority sink use to four per cent. 't is certain it diminishes this good quality in money 1 / ● but yet this making the money of england not one farthing more than it was , it alters not the measures upon which all changeable commodities increase or sink their price , and so makes not money exchange for less of any commodity than it would without this alteration of its interest ; but rather if lessening use to four per cent. does at all alter the quantity of money and makes it less ; it makes money as it has the nature of a commodity dearer , i. e. a less quantity of money will exchange for a greater quantity of another commodity than it would before . this perhaps will appear a little plainer by these following particulars . 1. that the intrinsick natural worth of any thing , consists in this , that it is apt to be serviceable to the necessities or conveniencies of human life , and it is naturally more worth , as the necessity or conveniency it supplies is greater ; but yet , 2. that there is no such intrinsick natural settled value in any thing , as to make any assigned quantity of it , constantly worth any assigned quantity of another . 3. the value of any assigned quantities of two or more commodities , are pro hic & nunc , equal , when they will exchange one for another ; as supposing one bushel of wheat , two bushels of barley , 30 l. of lead , and one ounce of silver , will now in the market be taken one for another , they are then of equal worth , and our coin being that which englishmen reckon by ; an englishman would say , that now one bushel of wheat , two bushels of barley , 30 l. of lead , one ounce of silver , were equally worth five shillings . 4. the altering of this value , two things in respect of one another , or any one standing common measure , is not the altering of any intrinsick value or quality in the commodity , ( for musty and smutty corn will sell dearer at one time than the clean and sweet at another ) but the alteration of some proportion , the commodity bears to something else . 5. this proportion in all commodities , whereof money is one , is the proportion of their quantity to the vent , which vent is nothing else but the passing of commodities from one owner to another in exchange , and is then called quicker , when a greater quantity of any species of commodity is taken off from the owners of it in an equal space of time . 6. this vent is regulated , i. e. made quicker or slower , as greater or less quantities of any saleable commodity are removed out of the way , and course of trade ; separated from publick commerce ; and no longer lie within the reach of exchange . for though any commodity should shift hands never so fast , and be exchanged from one man to another ; yet if they were not thereby exempted from trade and sale , and did not cease to be any longer traffick , this would not at all make , or quicken their vent ; but this seldom or never happening , makes very little or no alteration : and thus the vent is altered three ways ; 1. by consumption , when the commodity in its use is destroy'd , as meat , drink , and cloths , &c. all that is so consumed is quite gone out of the trade of the world. 2. exportation ; and all that is so carried away , is gone out of the trade of england , and concerns englishmen no more in the price of their commodities among themselves , than if it were out of the world. 3. buying and laying up for a mans private use. for what is by any of these ways shut out of the market , and no longer moveable by the hand of commerce , makes no longer any part of merchantable ware , and so in respect of trade , and the quantity of any commodity , is not more considerable than if it were not in being . all these three terminating at last in consumption of all commodities , ( excepting only jewels and plate , and some few others which wear out but insensibly ) may properly enough pass under that name . ingrossing too has some influence on the present vent , but this inclosing some considerable part of any commodity ( for if the ingrossing be of all the commodity , and it be of general use , the price is at the will of the ingrosser ) out of the free common of trade only for some time , and afterwards returning again to sale , makes not usually so sensible and general an alteration in the vent as the others do , but yet influences the price , and the vent more according as it extends its self to a larger portion of the commodity , and hoards it up longer . 7. most other portable commodities ( excepting jewels , plate , &c. ) decaying quickly in their use , but money being less consumed or increased , i. e. by slower degrees removed from , or brought into the free commerce of any country , than the greatest part of other merchandize ; and so the proportion between its quantity and vent , altering slower than in most other commodities , it is commonly look'd on as a standing measure to judge of the value of all things , especially being adapted to it by its weight and denomination in coinage . 8. money , whilst the same quantity of it is passing up and down the kingdom in trade , is really a standing measure of the falling and rising value of other things in reference to one another : and the alteration of price is truely in them only . but if you increase or lessen the quantity of money current in traffick in any place , then the alteration of value is in the money ; and if at the same time wheat keep its proportion of vent to quantity , money to speak truly alters its worth , and wheat does not , though it sell for a greater or less price than it did before ; for money being look'd upon as the standing measure of other commodities , men consider and speak of it still as if it were a standing measure , though when it has varied its quantity , 't is plain it is not . 9. but the value or price of all commodities , amongst which money passing in trade is truly one , consisting in proportion , you alter this , as you do all other proportions , whether you increase one or lessen the other . in all other commodities , the owners when they design them for traffick , endeavour as much as they can to have them vented and gone , i. e. removed out of the reach of commerce and exchange , by consumption , exportation , or laying up , which vent is sometimes slower , and sometimes quicker , but money never lying upon peoples hands , or wanting vent , ( for any one may part with it in exchange when he pleases ; ) the endeavour of the publick , and almost every body , is to keep it from venting or consuming , i. e. exportation or hoarding up , which is its proper consumption . the vent of money therefore being always sufficient , or more than enough , its quantity alone is enough to regulate and determine its value , without considering any proportion between its quantity and vent , as in other commodities . 10. therefore lessening of use , not bringing one penny of money more into the trade or exchange of any country , but rather drawing it away from trade , and so making it less , does not at all sink its value , and make it buy less of any commodity , but rather more . 11. that which raises the natural interest of money , is the same that raises the rent of land , ( i. e. ) its aptness to bring in yearly to him that manages it , a greater overplus of income above his rent , as a reward to his labour . that which causes this in land is the greater quantity of its product , in proportion to the same vent of that particular fruit , or the same quantity of product , in proportion to a greater vent of that single commodity ; but that which causes encrease of profit to the borrower of money , is the less quantity of money , in proportion to trade , or to the vent of all commodities , taken together , & vice versa . 12. the natural value of money , as it is apt to yield such an yearly income by interest , depends on the whole quantity of the then passing money of the kingdom , in proportion to the whole trade of the kingdom , ( i. e. ) the general vent of all the commodities . but the natural value of money , in exchanging for any one commodity , is the quantity of the trading money of the kingdom , designed for that commodity , in proportion to that single commodity and its vent . for though any single man's necessity and want , either of money , or any species of commodity , being known , may make him pay dearer for money , or that commodity ; yet this is but a particular case , that does not at the same time alter this constant and general rule . 13. that supposing wheat a standing measure , that is , that there is constantly the same quantity of it in proportion to its vent , we shall find money to run the same variety of changes in its value , as all other commodities do . now that wheat in england does come nearest to a standing measure , is evident , by comparing wheat with other commodities , money , and the yearly income of land in hen. 7. time and now . for supposing 1 hen. 7. n. let 100 acres of land to a. for 6 d. per an. per acre , rack-rent● and to b. another 100 acres of land , o● the same soil and yearly worth with the former , for a bushel of wheat per acre● rack-rent , ( a bushel of wheat about that time being probably sold for about 6 d. it was then an equal rent . if therefore these leases were for years yet to come 't is certain that he that paid 6 d. per acre . would pay now 50 s. per an. and he that paid a bushel of wheat per acre , would pay about 25 l. per an. which would be ne●r about the yearly value of the land● were it to be let now . the reason where of is this , that there being ten times a● much silver now in the world , ( the discovery of the w●st-indi●s having made the plenty ) as there was then , it is 9 / 1● less worth now than it was at that time ; that is , it will exchange for 9 / 1● less of any commodity now , which bears the same proportion to its vent as it did 200 years since ; which , of all other commodities● wheat is likeliest to do . for in england , and this part of the world , wheat being th● constant and most general food , not altering with the fashion , not growing by chance ; but as the farmers sow more or less of it , which they endeavour to proportion , as near as can be guessed , to the consumption , abstracting the over-plus of the precedent year in their provision for the next ; and vice versâ , it must needs fall out that it keeps the nearest proportion to its consumption , ( which is more studied and designed in this than other commodities ) of any thing , if you take it for 7 or 20 years together ; though perhaps the plenty or scarcity of one year , caused by the accidents of the season , may very much vary it from the immediately precedent , or the following . wheat therefore , in this part of the world , ( and that grain which is the constant general food of any other country ) is the fittest measure to judge of the alter'd value of things in any long tract of time : and therefore wheat here , rice in turkey , &c. is the fittest thing to reserve a rent in , which is designed to be constantly the same for all future ages . but money is the best measure of the alter'd value of things in a few years ; because its vent is the same , and its quantity alters slowly . but wheat , or any other grain , cannot serve instead of money● because of its bulkiness and too quick change of its quantity : for had i a bond , to pay me 100 bushels of wheat next year , it might be ¾ loss or gain to me ; too great an inequality and uncertainty to be ventur'd in trade , besides the different goodness of several parcels of wheat in the same year . 14. that supposing any island separate from the commerce of the rest of mankind , if gold and silver , or whatever else , ( so it be lasting ) be their money , if they have but a certain quantity of it , and can get no more , that will be a steady standing measure of the value of all other things . 15. that if in any country they use for money any lasting material , whereof there is not any more to be got , and so cannot be encreas'd , or being of no other use , the rest of the world does not value it , and so it is not like to be diminished ; this also would be a steady standing measure of the value of other commodities . 16. that in a country where they had such a standing measure , any quantity of that money ( if it were but so much that every body might have some ) would serve to drive any proportion of trade , whether more or less , there being counters enough to reckon by , and the value of the pledges being still sufficient , as constantly encreasing with the plenty of the commodity . but these three last , being built on suppositions that are not like to be found in the practice of mankind , since navigation and commerce have brought all parts acquainted with one another , and introduced the use of gold and silver money into all trading parts of the world ; they serve rather to give us some light into the nature of money , than to teach here a new measure of traffick , though it be certain , that that part of the world , which bred most of our gold and silver , used least of it in exchange , and used it not for money . 17. that therefore in any country that hath commerce with the rest of the world , it is almost impossible now to be without the use of silver coin , and having money of that , and accounts kept in such money , it is impossible to have any standing , unalterable measure of the value of things ; for whil'st the mines supply to mankind more than wastes and consumes in its use , the quantity of it will daily grow greater in respect of other commodities , and its value less . 18. that in a country that hath open commerce with the rest of the world , and uses money made of the same materials with their neighbours , any quantity of that money will not serve to drive any quantity of trade , but that there must be a certain proportion between money and trade : the reason whereof is this , because to keep your trade going without loss , your comodities amongst you , must keep an equal , or , at least , near the price of the same species of commodities in the neighbour countries , which they cannot do , if your money be far less than in other countries ; for then , either your commodities must be sold very cheap , or a great part of your trade must stand still ; there not being money enough in the country to pay for them ( in their shifting of hands ) at that high price which the plenty , and consequently low value of money makes them at in another country ; for the value of money in general is the quantity of all the money in the world , in proportion to all the trade ; but the value of money in any one country , is the present quantity of the current money in that country , in proportion to the present trade : supposing then , that we had now in england but half as much money as we had seven years ago , and yet had still as much yearly product of commodities , as many hands to work them , and as many brokers to disperse th●m as before , and that the rest of the world we trade with , had as much money as they had before ( for 't is likely they should have more by our moiety shared amongst them ) 't is certain , that either half our rents should not be paid , half our commodities not vented , and half our labourers not imployed , and so half the trade be clearly lost , or else that every one of these must receive but half the money for their commodities and labour they did before , and but half so much as our neighbours do receive for the same labour , and same natural product at the same time , which , though it will make no scarcity of our native commodities amongst us , yet it will have these ill consequences . 1. it will make our native commodities vent very cheap . 2. it will make all foreign commodities very dear , both which will keep us poor : for the merchant making silver and gold his measure , and considering what the foreign commodity costs him ( i. e. how many ounces of silver ) in the country where money is more plenty , i. e. cheaper , and considering too how many ounces of silver it will yield him in another country , will not part with it here , but for the same quantity of silver , or as much as that silver will buy here of our commodity , which will be a great deal more than in another place ; so that in all our exchange of native for foreign commodities , we pay double the value that any other country does , where money is in greater plenty : this indeed will make a dearness , and , in time , a scarcity of foreign commodities ; which is not the worst inconveniency that it brings upon us , supposing them not absolutely necessary : but 3. it endangers the drawing away our people , both handicrafts , mariners , and soldiers , who are apt to go where their pay is best ; which will always be where there is greatest plenty of money , and , in time of war , must needs bring great distress . 19. upon this measure too it is , that the variation of exchange of money , between several countries , does somewhat depend ; for it is certain , that one ounce of silver is always of equal value to another ounce of silver considered in its intrinsick worth , or in reference to the universal trade of the world ; but 't is not of the same value at the same time , in several parts of the world , but is of most worth in that country where there is the least money , in proportion to its trade ; and therefore men may afford to give 20 ounces of silver in one place , to receive 18 or 19 ounces of silver in another : but this is not all to this then , ( to find out the alteration of the exchange ) the over-ballance of the trade must be taken into consideration ; and these two together regulate the exchange in all the commerce of the world , and , in both the increase of the exchange ( i. e. receiving a greater quantity of silver ( for that is the measure , let the coin or the denomination be what it will ) in one country for a less quantity of silver paid in another country ) depends upon one and the same thing , viz. the greater plenty of money in one country than in the other , only with this difference , that where the over-ballance of trade raises the exchange above the par , there it is the plenty of money which private merchants have in one country , which they desire to remove into another : but where the riches of the country raises the exchange above the par , there it is the plenty of the money in the whole country . in one , the merchant has more money ( or debts , which is all one ) in a foreign country than his trade there will imploy , and so is willing to allow upon exchange to him abroad , that shall pay him ready money at home , 1 , 2 , 3 , &c. per cent. more or less , proportionably as his or his countrymens plenty of ready money abroad , the danger of leaving it there , or the difficulty of bringing it home in specie , and his present need of money at home is greater or lesi . in the other , the whole country has more money than can well be imploy'd in the trade thereof , or at least , the proportion of the money to the trade is greater than in the neighbouring country , where the exchange is below the par. for , supposing the ballance of trade to be equal between england and holland , but that there be in holland a greater plenty of money than in england , ( which will appear by the lowness of the national use in holland , and the heighth of the national use in england ; and also by the dearness of food and labour in general in holland , and the cheapness of it in england . ) if n. has 10000 l. in holland , which the greater advantage he could make of it in england , either by use or purchase , tempts him to transfer into england , 't is probable he will give as much to a merchant in holland to pay him 10000 l. in england , as the ensurance of that time between holland and england is worth ; which , if it be in a country where the exportation of bullion is prohibited , he must pay the more , because his venture , if he carry it in specie , will be greater ; and , upon this ground , perhaps the prohibiting the exportation of money out of england , under penalties , may be of some use , by making the rate of the exchange greater upon those countries who import upon us more than they export in commodities , and so retain some part of the money which their over-ballance of trade would carry away from us , though , after all , if we are over-ballanc'd in trade it must go . but , since the holland merchant cannot receive n — 's 10000 l. in money in holland , and pay him 10000 l. in england , unless his over-ballance of trade make english-men indebted to him 10000 l. in money , which he is not like to take in commodity . i think the over-ballance of trade is that which chiefly raises the exchange in any country , and that plenty of money in any country does it only for so much of the money as is transfer'd either to be let out to use , or to be spent there ; and though lending to foreigners , upon use , doth not at all alter the ballance of trade between those countries , yet it does alter the exchange between those countries for so much as is lent upon use , by not calling away the money that should follow the over-ballance of trade , but letting it rest there , as if it were accounted for ; all one as if the ballance of trade were for so much altered : but this being not much in comparison of the gener●● traffick between two nations , or at lea●● varying slower , the merchant too regulating the exchange , and not the usurer i suppose it is the present ballance of trade , on which the exchange immedi●ately and chiefly depends , unless some accident shall make a great deal of money be remitted at the same time , from one place to another , which will for the timeraise the exchange all one as an ove●-ballance of trade ; and indeed , when examin'd is generally very little different from it● to be able to estimate the par with the rise and fall of the exchange , it is necessary to know the intrinsick value , i● how much silver is in the coins of th● two countries , by which you reckon and charge the bill of exchange . sir , if i have been led a little too f●● from one thing to another , in the considerat●●on of money , i beg your pardon , h● pu●●● that these particulars will afford some lig●● to our present subject . to return to the price of land , by which has been abovesaid , it is evident that the years purchase of land do not increase with the fall of interest , and the abating that good quality in money of yielding yearly six p●r cen● . to four , does not presently so sink its value , in respect of land , that 1 / ● part more is requir'd in exchange : that is , that falling of interest from six to four , will not raise land from twenty to thirty years purchase . the raising and falling of the price of land , as of other things , depends much on the quantity of land , set to sale , compar'd with the quantity of money design'd for that traffick , or which amounts to the same thing , upon the number of buyers and sellers , for where there are many sellers and few purchasers , though interest be lessened , land will be cheap , as i have already shew'd . at least , this is certain , that making a law to reduce interest , will not raise the price of lands : it will only , by driving it more into the bankers hands , leave the country barer of money , whereby , if the price of land about london , should be accidently raised , that of remoter countries would thereby have fewer purchasers , and at lower rates . this being so , that the low rate of land depends much on the great number of sellers in proportion to purchasers , the next thing to be inquir'd into , is , what makes plenty of sellers ? and to that the answer is obvious , general ill husbandry ; and the consequence of it debts . if a neglect of government and religion , ill examples , and depraved education , have introduced debauchery ; and art or chance has made it fashionable for men to live beyond their estates , debts will increase and multiply , and draw with them a necessity on men , first of incumbring , and then selling their estates ; this is generally the cause why men part with their land : and i think there is scarce one of an hundred that thinks of selling his patrimony till mortgages have pretty well eat into the freehold ; and the weight of growing debts force a man , whether he will or no , out of his possessions . when almost is there ever a clear and unincumbred estate set to sale ? 't is seldom a thriving man turns his land into money to make the greater advantage . the examples of it are so rare , that they are scarce of any consideration in the number of sellers . this i think may be the reason , why in queen elizabeth's days ( when sobriety , frugality , and industry , brought in dai●y increase , to the growing wealth of the kingdom ) ●and kept up its price , and sold for more years purchase than corresponded to the interest of money , then busily imploy●d in a thriving trade , which made the natural interest much higher than it is now , as well as the parliament then set it higher by law. on the contrary side , what makes scarcity of purchasers ; 1. the same reason , ill husbandry ; when the tradesman lives up to the height of his income , and the vanity of expences either drains the merchants coffers , or keeps them from over-flowing , he seldom thinks of purchasing : buying of land is the result of a full and satiated gain , and men in trade seldom think of laying out their money upon land , till their profit has brought them in more than their trade can well employ , and their idle bags cumbring their counting houses , put them upon emptying them on a purchase . 2. another thing that makes a scarcity of buyers of land , are doubtful and ill titles , where these are frequent and fatal , one can no more expect , that men who have money , should be forward to purchase , than ships richly laden to venture themselves amongst roc●s and quicksands . 't is no wonder such seas should not be much frequented where the examples , and remains of daily wrecks , shew the ●olly and hazard of the venture , in the number of those who have miscarried . 3. a general decay of trade discourages men from purchasing● for this threatens an universal poverty , which is sure to fall first and heaviest upon land. the merchant who furnishes the improvident landholder , will not fail to have money for his wares with gain , whether the kingdom get by his trade or no , and he will keep his money rather employ'd in trade , which brings him in profit , ( for the merchant may get by a trade that makes the kingdom poor ) than lay it out in land , whose rents he sees sinking , and foresees by the course of trade , is likely to continue on to do so . when a nation is running to decay and ruine , the merchant and monied man , do what you can , will be sure to starve last : observe it where you will , the decays that come upon , and bring to ruine any country , do constantly first fall upon the land ; and though the country gentleman , ( who u●ually securely relies upon so much a year as was given in at his marriage settlement , and thinks his land an unmoveable fund for such an income ) be not very forward to think so ; yet this neverthe●ess is an undoubted truth , that he is more concern'd in trade and ou●ht to take a greater care that it be w●ll manag'd and preserved than even the merchant himself ; for he will certainly find● that when a decay of trade has carried away one part of our money out of the kingdom , and the other is kept in the merchant and tradesmans hands , that no laws he can make , nor any little arts of shifting property amongst our selves , will bring it back to him again : but his rents will fall , and his income every day lessen , till general industry , and frugality , join'd to a well order'd trade , shall restore to the kingdom the riches and wealth it had formerly . this by the way , if well consider'd , might let us see , that taxes , however contrived , and out of whose hand soever immediately taken , do in a country , where their great fund is in land , for the most part terminate upon land. whatsoever the people is chiefly maintain●d by , that the government supports it self on : nay , perhaps it will be found , that those taxes which seem least to affect land , will most surely of all other , ●a● the rents ; which is an evil the hardest to be recovered , for rents once f●●len are not e●sily raised again . a tax laid upon land seems hard to the landholder , because it is so much money going visibly out of his pocket ; and 〈…〉 ease to ●imself , the landholder i●●●●●ys fo●ward to lay it upon commodities : but 〈…〉 through●y consid●● it , and 〈◊〉 the effects , he will find he buys this seeming ease at a very dear rate , and though he pays not this tax immediately out of his own purse , yet there will be more wanting there at the end of the year than that comes to , with the lessening of his rents , which is a settled and lasting evil , that will stick upon him beyond the present payment . to make this clear , let us suppose in the present state of affairs in england , that the rents of england are twelve millions , and that the charge and necessities of the government requires a supply of three millions from the parliament , which is laid on land ; here is one fourth part of his yearly income goes immediately out of the landlords and landholders pocket : this is a burthen very apt to be felt , he readily perceives what goes thus out of his estate , who actually pays the money out of his pocket , or finds it deducted out of his rent at quarter-day for taxes ; but though this be a quarter of his yearly income , and out of an estate of four hundred pounds a year , the publick tax now openly takes away one hundred ; yet this influences not at all the yearly rent of the land , which the rack-renter or under tenant pays ; it being the same thing to him , whether he pays all his rent to the king or his landlord , or ½ or ¼ or none at all to the king ; the case is all one to him what hand receives his rent , when due ; so trade flourishes , and his commodities go off well , he will be able to pay his rent on . this lessens not any more the value of his farm , than an high or a low chief rent does , paid out of it to the lord of the fee ; and the tenant's bargain and profit is the same , whether the land be charg'd or not charg'd with an annuity payable to another man. we see this in college leases , where though the college tenant pays for it to the college some years five times as much as he does others , upon the varying rate of corn , yet the under tenant feels not this alteration in the least , nor finds a reason to have his rent abated , because a greater part of it is diverted from his landlord . all this is but changing the hand that receives the rent , without any influence at all upon the yearly value of the estate ; which will not be let for one penny more or less to the renter , however , or amongst whomsoever , the rent he pays , be divided . from hence it is evident , that taxes laid on land do not in the least make rents fall . but suppose , to shift off the burthen from the land , some country gentlemen should think fit to raise these three millions upon commodities , to let the land go free . first , it is to be considered , that since the publick wants require three millions , ( for that we suppos'd for argument sake ; let it be three millions , or one million , that 's all one ; ) and so much must go into the king's coffers ; or else the necessities of the government will not be supplied ; that for raising these three millions on commodities , and bringing so much into the exch●quer , there must go a great deal more than three millions out of the subj●cts pockets : for a tax of that nature cannot be levied by officers , to watch every little rivulet of trade , without a great cha●ge , especially at first trial . but supposing no more charge in raising it , than of a land tax , and that there are only ● millions to be paid , t is evident that to do this out of commodities , they must to the co●●umer b● raised ¼ in their price ; so that every t●●●g , to him that uses it , must be ¼ d●●●er . ●et us see now who at long run 〈◊〉 pay this ¼ and where it will light . 't is p●ain , the merchant and broker , neither will nor c●n ; for if he pays 1 / ● more for commodities than he did , he will sell them at a price proportionably raised . the poor labourer and handicraftsman cannot ; for he just lives from hand to mouth already , and all his food , cloathing and utensils , costing ¼ more than they did before ; either his wages must rise with the price of things , to make him live , or else , not being able to maintain himself and family by his labour , he comes to the parish ; and then the land bears the burthen a heavier way . if the labourer's wages be rais'd in proportion to the encreas'd rates of things , the farmer , who pays ¼ more for wages , as well as all other things , whil'st he sells his corn and wool , either at the same rate , or lower , at the market , ( since the tax laid upon it makes people less forward to buy ) must either have his rent abated , or else break and run away in his landlord's debt ; and so the yearly value of the land is brought down , and who then pays the tax at the years end , but the landlord ; when the tenant , not able to raise his rent by his commodities , either runs away in his landlords debt , or cannot be cotinued in the farm without abatement of rent ? for when the yearly charge in his farm is greater by the increase of the labourers wages , and yet his product sells ●ea●er by reason of the tax laid on his commodities ; how will the farmer be able to make up his rent at quarter day ? for this may be worth our notice , that any tax laid on foreign commodities in england , raises its price , and makes the importer get more for his commodity ; but on the contrary , a tax laid on your native product , and home made commodities , lessens their price , and makes them yield less to the first seller . the reason whereof is plain . for the merchant importing no commodity but what the necessity , or fashionable wantonness of your people gives him vent for , will not only proportion his gain , to the cost and risque he has been at before landing , but will expect profit of his money paid here , for any tax laid on it ; and take advantage from thence to raise his price above what his tax comes to ; and if he cannot do that , he will trade no more in that commodity . for it being not the product of his farm , he is not tied to bring it to market , if he finds its price not answer his expectation there , but turns himself to other wares , which he finds your markets take off better . a merchant will never continue to trade in wares , which the change of fashion , or humour amongst your people , have made less vendible , though he may be sometimes caught by a sudden alteration . but that seldom happens in the course of trade , so as to influence the great bulk of it : for things of necessity must still be had , and things of fashion will be had as long as men have money or credit , whatever rates they cost , and the rather because they are dear ; for it being vanity not use that makes the expensive fashions of your people , the emulation is , who shall have the finest , that is the dearest things , not the most convenient or useful . how many things do we value and buy , because they come at dear rates from iapan and china , which if they were our own manufacture or product , to be had common and for a little money , would be contemned and neglected ? have not several of our own commodities offered to sale at reasonable rates been despised , and the very same eagerly bought and brag'd of when sold for french at a double price ? you must not think therefore that the raising their price will lessen the vent of fashionable foreign commodities amongst you , as long as men have any way to purchase them , but rather increase it . french wine is become a modi●h drink amongst us , and a man is asham'd to entertain his friend , or almost to dine himself without it . the price is in the memory of man rais'd from 6 d. to 2 s. and does this hinder the drinking of it ? no , the quite contrary , a man's way of living is commended , because he will give any rate for it ; and a man will give any rate rather than pass for a poor wretch , or penurious curmudgeon that is not able or knows not how to live well nor use his friends civilly . fashion is for the most part nothing but the ostentation of riches , and therefore the high price of what serves to that , rather increases than lessens its vent : the contest and glory is in the expence , not the usefulness of it , and people are then thought and said to live well , when they can make a shew of rare and foreign things , and such as their neighbours cannot go to the price of . thus we see how foreign commodities fall not in their price by taxes laid on them , because the merchant is not necessitated to bring to your market any but fashionable commodities , and those go off the better for their high rate : but on the contrary your land 〈◊〉 being forced to bring his commodities to market , such as his land and industry affords them , common and known things , must sell them there at such price as he can get . this the buyer knows ; and these home-bred commodities being seldom the favourites of your people , or any farther acceptable than as great conveniency recommends them to the vulgar or downright necessity to all , as soon as a tax is laid on them , every one makes as sparing a use of them as he can , that he may save his money for other necessary or creditable expences , whereby the price they yield the first seller is mightily abated , and so the yearly value of the land which produces them lessen'd too . if therefore the laying of taxes upon commodities does , as it is evident , affect the land that is out at rack-rent , it is plain it does equally affect all the other land in england too , and the gent● will , but the worst way , increase their own charges ; that is by lessening thei● yearly value of their estates , if they hope to ease their land by charging commodities . it is in vain in a country whose great fund is land● to hope to lay the publick charge of the government on any thing else , there at last it will terminate . the merchant ( do what you can ) will not bear it : the labourer cannot , and therefore the landholder must ; and whether he were best do it , by laying it directly where it will at last settle , or by letting it come to him by the sinking of his rents , which when they are once fallen every one knows are not easily raised again , let him consider . holland is brought as an instance of laying the charge of the publique upon trade , and 't is possible ( excepting some few small free towns ) the only place in the world that could be brought to favour this way . but yet when examin'd will be found to shew the quite contrary , and be a clear proof , that lay the taxes how you will , land every where in proportion bears the greater share of the burthen . the publick charge of the government , is , 't is said in the united provinces , laid on trade , i grant it is , the greatest part of it ; but is the land excus'd or eas'd by it ? by no means , but on the contrary so loaded , that in many places ½ , in others ¼ , in others 1 / ● of the yearly value does not come in to the owners pocket : and if i have not been misinformed , the land in some places will not pay the taxes ; so that we may say , that the charge of the government came not upon commodities till the land could not bear it . the burthen unavoidably settles upon the land first , and when it has pressed it so that it can yield no more , trade must be brought in aid to help to support the government rather than let all sink : but the first stress is always upon land , and as far as that will reach it is unavoidably carried , lay your taxes how you will. 't is known what a share of the publick charges of the government is supported by the trade of amsterdam alone , as i remember the 36 / 100 ; but are the lands of guelderland eas'd by it ? let any one see in that country of land more than trade , what they make clear of their revenues , and whether the country genttlemen there grow rich on their land , whilst the merchant having the taxes laid on his commerce is impoverish'd ? on the contrary guelderland is so low and out of cash , that amsterdam has been fain for many years to lay down the taxes for them , which is , in effect , to pay the taxes of guelderland too . struggle and contrive as you will , lay your taxes as you please , the merchants and traders will shift it off from their own gain , bear the least part of it , and grow poor last . in holland it self , where trade is so loaded , who , i pray , grows richest the land-holder or the trader ? which of them is pinch'd , and wants money most ? a country may thrive , the country gentleman grow rich , and his rents increase ( for so it has been here ) whilst the land is taxed . but i challenge any one to shew me a country wherein there is any considerable publick charge raised , where the land does not most sensibly feel it , and in proportion bear much the greater part of it . we must not therefore impute the fal●ling of the rents , or price of land to high interest : nor if i●l husbandry has wasted our riches hope by such kind of laws to raise them to their former value , i humbly conceive we shall in vain endeavour it by the fall of interest . the number of buyers must be increased and sellers lessen'd , which must be done by other ways than regulating of interest , or else the landed man will neither find chapmen for his land , nor for the corn that grow on it at the rate he desires . but could an act of parliament , bring down interest to 4 per cent. and the lowering of that immediately raise the purchasers fine from 20 to 25 years purchase ; yet it may be doubted , whethe● this be sit to be made into a law , becaus● it would be of no advantage to the king●dom . for what profit would it b● to the nation to make a law , that 〈◊〉 who sells land should instead of 4 hav● 5 hundred pounds of the purcharser . thi● indeed a little alters the distribution of th● money we have amongst us englishma● here at home , but neither helps to continue what we have , nor brings in more from abroad ; which being the only concernment of the kingdom , in reference to its wealth , is apt to be supposed by us without doors to be the only care of a parliament : for it matters not so it be here amongst us , whether it be in thomas or richards hands , provided it be so ordered , that whoever has it may be encouraged to let it go into the current of trade , for the improvement of the general stock and wealth of the nation . as this increase of the fine in the purchase of land is not an advantage to the kingdom , so neither is it to the land-holder , who is the person that bearing the greatest part of the burthens of the kingdom , ought , i think , to have the greatest care taken of him , and enjoy as many privileges and as much wealth , as the ●avour of the law can ( with regard to the publick-weal ) confer upon him . but pray consider , to raise the years purchase in buying of land gives the advantage not to the landholder , but to him that ceases to be so . he that has no longer the land has the more money , and he who has the land is the poorer . the true advantage of the landholder is , that his ●orn , flesh , and wool , sell better , and yield a greater price ; this indeed is a profit that benefits the owner of the land and goes along with it ; it is this alone raises the rent and makes the possessor richer ; and this can only be done by increasing our wealth , and drawing more money into england , which the falling of interest , and thereby ( if it could effect it ) raising the purchase of land is so far from doing , that it does visibly and directly one way hinder our increase of wealth , that is , by hindering foreigners to come here and buy land , and settle amongst us . whereby we have this double loss ; first we lose their persons , increase of people being the increase both of strength and riches : secondly we lose so much money . for though whatever an englishman gives to another for land , though raised to 40 years purchase , be not one farthing advantage to the kingdom , yet whatever a foreigner , who purchases land here , gives for it , is so much every farthing clear gain to the nation , for the money comes clear in , without carrying out any thing for it● and is all one as if it drop'd down from the clouds . but farther , if consideration be to be had only of sellers of land , the lowering of interest to 4 per cent will not be in their favour , unless , by it , you can raise land to thirty years purchase , which is not at all likely ; and i think no body by falling of interest to four per cent , hopes to get chapmen for their land at that rate ; and whatsoever they have less , if law can regulate interest , they lose of their value of land , money being thus abased . so that the landedman will scarce find his account neither , by this law when it comes to trial . and at last i imagine this will be the result of all such attempts , that experience will shew , that the price of things will not be regulated by laws , though the endeavours after it will be sure to prejudice and inconvenience trade , and put your affairs out of order . if this be thus , that interest cannot be regulated by law , or that if it could , yet the reducing of it to four per cent. would do more harm than good ; what then should there ( will you say ) be no law at all to regulate interest ? i say not so , for , 1. it is necessary that there should be a stated rate of interest , that in debts and forbearances , where contract has not setled it between the parties , the law might give a rule , and courts of judicature might know what damages to allow : this may , and therefore should , be regulated . 2. that in the present current of running cash , which now takes its course almost all to london , and is ingrossed by a very few hands in comparison , young men , and those in want , might not too easily be exposed to extortion and oppression ; and the dextrous and combining money jobbers not have too great and unbounded a power , to prey upon their ignorance or necessity , there would not be much danger of this , if money were more equally distributed into the several quarters of england , and into a greater number of hands according to the exigences of trade . if money were to be hired , as land is , or to be had as corn , or wooll , from the owner himself , and known good security be given for it , it might then probably be had at the market ( which is the true ) rate , and would be a constant gauge of your trade and wealth ; but when a kind of monopoly , by consent , has put this general commodity into a few hands , it may need regulation , though what the stated rate of interest should be in the constant change of affairs , and ●lux of money , is hard to determine . possibly it may be allowed as a reasonable proposal that it should be within such bounds 〈…〉 quite l●t up the merchants and tradesmans profit , and discourage their industry ; nor on the other hand so low , as should hinder men from risquing their money in other mens hands , and so rather chuse to keep it out of trade , than venture it upon so small profit . when it is too high , it so hinders the merchants gain , that he will not borrow ; when too low , it so hinders the monied mans profit , that he will not lend ; and both these ways it is a hindrance to trade . but this being perhaps too general and loose a rule , let me add , that if one would consider money and land alone , in relation one to another , perhaps it is now at six per cent. in as good a proportion as is possible , six per cent. being a little higher than land at twenty years purchase , which is the rate pretty near that land has generally carried in england , it never being much over nor under . for supposing 100 l. in money , and land of 5 l. per annum , be of equal value , which is land at twenty years purchase : 't is necessary for the making their value truly equal , that they should produce an equal income , which the 100 l. at 5 l. per cent. interest is not likely to do . 1. because of the many , and sometimes long intervals of barrenness , which happen to money more than land. money at use , when return'd into the hands of the owner , usually lies dead there , till he gets a new tenant for it , and can put it out again ; and all this time it produces nothing . but this happens not to land , the growing product whereof turns to account to the owner , even when it is in his hands , or is allow'd for by the tenant , antecedently to his entring upon the farm. for though a man who borrows money at midsummer , never begins to pay his interest from our lady-day , or one moment backwards , yet he who rents a farm at midsummer , may have as much reason to begin his rent from our lady-day , as if he had then entred upon it . besides the dead intervals of ceasing profit , which happen to money more than land , there is another reason why the profit and income of money let out , should be a little higher than that of land ; and that is , because money out at interest ●●●s a greater risque than land does ; the ●o●●ower may break and run away with the money , and then not only the 〈◊〉 due , but all the future profit , with the principal , is lost forever ; but in land a man can lose but the rent due , for which usually too the stock upon the land is sufficient security ; and if a tenant run away in arrear of some rent , the land remains , that cannot be carried away or lost . should a man purchase good land in middlesex of 5 l. per annum , at twenty years purchase , and other land in rumney-marsh , or elsewhere of the same yearly value , but so situated , that it were in danger to be swallowed of the sea , and be utterly lost , it would not be unreasonable he should expect to have it under twenty years purchase ; suppose 16 ½ . this is to bring it to just the case of land at twenty years purchase , and money at six per cent. where the uncertainty of securing ones money may well be allowed that advantage of greater profit ; and therefore perhaps the legal interest now in england at six per cent , is as reasonable and convenient a rate as can well be set by a standing rule , especially if we consider that the law requires not a man to pay six per cent , but ties up the lender from taking more ; so that if ever it falls of it self , the monied man is sure to find it , and his interest will be brought down to it . high interest is thought by some a prejudice to trade ; but if we will look back , we shall find that england never throve so well , nor was there ever brought into england so great an increase of wealth since , as in queen elizabeth's and king iames i. and king charles i. time . when money was at 10 and 8 per cent. . i will not say high interest was the cause of it ; for i rather think that our thriving trade was the cause of high interest , every one craving money to employ in a profitable commerce . but this i think i may reasonably infer from it , that lowering of interest is not a sure way to improve either our trade or wealth . to this i hear some say , that the dutch , skilful in all arts of promoting trade , to out do us in this as well as all other advancements of it , have observed this rule , that when we fell interest in england from 10 to 8. they presently sunk interest in holland to 4 per cent. and again , when we lower'd it to 6 , they fell it to 3 per cent. thereby to keep the advantage which the lowness of interest gives to trade . from whence these men readily conclude , that the falling of interest will a●●ance trade in england . to which i answer , 1. that this looks like an argument , rather made for the present occasion , to mislead those who are cred●lous enough to swallow it , than arising from 〈◊〉 reason and matter of fact. for if lowering interest were so advantageous to trade , why did the dutch so constantly take their measures only by us , and not as well by some other of their neighbours , with whom they have as great or greater commerce than with us ? this is enough at first sight to make one suspect this to be dust only rais'd to throw in peoples eyes , and a suggestion made to serve a purpose . for , 2. it will not be found true , that when we abated interest here in england to 8. the dutch sunk it in holland to 4 per cent. by law ; or that there was any law made in holland to limit the rate of interest to 3 per cent. when we reduced it in england to 6. it is true , iohn de witt , when he managed the affairs of holland , setting himself to lessen the publick debt , and having actually paid some , and getting money in a readiness to pay others , sent notice to all the creditors , that those who would not take 4 per cent. should come and receive their money . the creditors finding him in earnest , and knowing not how otherwise to employ their money , accepted his terms , and changed their obligations into 4 per cent. whereas before they were at 5. and so ( the great loans of the country being to the state ) it might be said in this sense , that the rate of interest was reduced lower at that time ; but that it was done by a law , forbidding to take higher interest that 4 per cent. that i deny , and require any one to shew . indeed upon good security one might lately have borrowed money in holland at 3 , and 3 ½ per cent. but not by vertue of any law , but the natural rate of interest . and i appeal to the men learned in the law of holland , whether last year ( and i doubt not but it is so still ) a man might not lawfully lend his money for what interest he could get ; and whether in the courts he should not recover the interest he contracted for , if it were 10 per cent. so that if money be to be borrowed by honest and responsible men , at 3 , or 3 ½ per cent. it is not by the force of statutes and edicts , but the natural course of things , which will always bring interest upon good security low , where there is a great deal of money to be lent , and little good security in proportion to be had . holland is a country where the land makes a very little part of the stock of the country . trade is their great fund ; and their estates lie generally in money ; so that all who are not traders , generally speaking , are lenders : of which there are so many whose income depends upon interest , that if the states were not mightily in debt , but paid every one their principal , instead of the 4 per cent. use , which they give , there would be so much more money than could be used , or would be ventured in trade , that money there would be at 2 per cent. or under , unless they found a way to put it out in foreign countries . interest , i grant these men , is low in holland ; but not as an effect of law , nor the politick contrivance of the government , to promote trade ; but as the consequence of great plenty of ready money , when their interest first fell , i say when it first fell : for being once brought low , and the publick having borrowed a great part of private mens money , and continuing in debt , it must continue so , though the plenty of money , which first brought interest low , were very much decayed , and a great part of their wealth were really gone . for the debt of the state affording to the creditors a constant yearly income , that is looked on as a safe revenue , and accounted as valuable as if it were in land ; ( and accordingly they buy it one of another ; and whether there be any money in the publick coffers or no , he who has 10000 l. owing him from the states may sell it every day in the week , and have ready money for it ) this credit is so great an advantage to private men , who know not else what to do with their stocks , that were the states now in a condition to begin to pay their debts , the creditors , rather than take their money out to lie dead by them , would let it stay in at lower interest , as they did some years since , when they were call'd on to come and receive their money . this is the state of interest in holland ; their plenty of money , and paying their publique debts , some time since lowered their interest , but it was not by law , nor in consequence of our reducing it here by law to 6 per cent. for i deny that there is any law there yet , to forbid lending of money for above 3 , or 6 , or 10 per cent. what ever some here suggest , every one there may hire out his money as freely as he does any thing else , for what rate he can get ; and the bargain being made , the law will inforce the borrower to pay it . i grant low interest , where all men consent to it is an advantage to trade , if merchants will regulate their gains accordingly , and men be perswaded to lend to them ; but can it be expected , when the publique gives 7 , 8 , or 10 per cent. that private men , whose security is certainly no better , shall have it for 4 ? and can there be any thing stranger , than that the same men who look on , and therefore allow high use as an encouragement to lending to the chequer , should think low use should bring money into trade ? the states of holland some few years since , paid but 4 l. per cent. for the money they owed ; if you propose them for an example , and interest be to be regulated by a law , try whether you can do so here , and bring men to lend it to the publique at that rate , this would be a benefit to the kingdom , and abate a great part of our publique charge : if you cannot , confess , that 't is not the law in holland has brought the interest there so low , but something else , and that which will make the states , or any body else pay dearer now , if either their credit be less , or money there scarcer . an infallible sign of your decay of wealth , is the falling of rent● , and the raising of them would be worth the nations care ; for in that , and not in the falling of interest lies the true advantage of the landed man , and with him of the publick . it may be therefore not besides our present business , to enquire into the cause of the falling of rents in england . 1. either the land is grown barrenner , and so the product is less , and consequently the money to be receiv'd for that product is less ; for it is evident that he whose land was wont to produce 100 bushels of wheat communibus annis , if by long tillage and bad husbandry it will now produce but 50 bushels , the rent will be abated half . but this cannot be suppos'd general . 2. or the rent of that land is lessen'd . 1. because the use of the commodity ceases : as the rents must fall in virginia , were taking of tobacco forbid in england . 2. or because something else supplies the room of that product : as the rate of copis-lands will fall upon the discovery of coal mines . 3. or , because the markets are supplied with the same commodity , cheaper from another place . as the breeding countries of england must needs fall their rents , by the importation of irish cattle . 4. or , because a tax laid on your native commodities , makes what the farmer sells , cheaper , and labour , and what he buys dearer . 3. or , the money in the country is less . for the exigencies and uses of money not lessening with its quantity , and it being in the same proportion to be imploy'd and distributed still in all the parts of its circulation , so much as its quantity is lesse●'d , so much must the share of every one that has a right to this money be the less ; whether he be landholder , for his goods ; or labourer , for his hire ; or merchant , for his brokage . though the land-holder usually finds it first . because money failing , and falling short , people have not so much money as formerly to lay out , and so less money is brought to market , by which the price of things must necessarily fall . the labourer feels it next . for when the landholder's rent falls , he must either bate the labourer's wages , or not imploy , or not pay him ; which either way makes him feel the want of money . the merchant feels it last . for though he sell less , and at a lower rate , he buys also our native commodities , which he exports , at a lower rate too ; and will be sure to leave our native commodities unbought , upon the hands of the farmer , or manufacturer , rather than export them to a market , which will not afford him returns with profit . if one third of the money imploy'd 〈◊〉 trade were locked up , or gone out of england , must not the land-holders necessarily receive ⅓ less for their goods , and consequently their rents fall ; a less quantity of money by ⅓ being to be distributed amongst an equal number of receivers ? indeed , people not perceiving the money to be gone , are apt to be jealous one of another● and each suspecting anothers inequality of gain to rob him of his share , every one will be imploying his skill and power the best he can to retrieve it again , and to bring money into his pocket in the same plenty as formerly● but this is but scrambling amongst 〈◊〉 selves , and helps no more against 〈◊〉 want , than the pulling off a short cover let will , amongst children that lye toge●ther , preserve them all from the col●● some will starve , unless the father of th●●amily provide better , and enlarge 〈◊〉 scanty garments . this pulling and con●●● is usually between the landed man ar● the merchant . for the labourer's share , b●●ing seldom more than a bare subsistenc● never allows that body of men time 〈◊〉 opportunity to raise their thoughts abo●● that , or 〈◊〉 with the richer 〈◊〉 theirs● ( as one common interest , ) unle●● when some common and great distre●● uniting them in one universal ferme● makes them forget respect , and emb●●dens them to carve to their wants 〈◊〉 armed force : and then sometimes the break in upon the rich , and sweep ● like a deluge . but this rarely happens 〈◊〉 in the mal-administration of neglected mis-manag'd government . the usual struggle and contest , as i said before , in the decays of wealth and riches , is between the landed man and the merchant , with whom i may here joyn the money'd man. the landed man finds himself aggrieved , by the falling of his rents , and the streightning of his fortune ; and thinking the merchant ( whom he sees flourish and thrive ) eats up his profit , and builds up a fortune upon his ruines ; he therefore endeavours , by laws , to keep up the value of lands , which he suspects lessened by the others excess of profit : but all in vain . the cause is mistaken , and the remedy too . 't is not the merchants nor mon●y'd man's gains that makes land fall ; but the loss of the kingdom , in our decay of trade , which the land always first feels . if the landed gentleman will have , and by his example , make it fashionable to have more claret , spi●● , silk , and other foreign consumable wares , than our . exportation of commodities does exchange for ; money must unavoidably follow to ballance the account , and pay the debt . and therefore i fear that another proposal , i hear talked of , to hinder the exportation of m●ney and bullion , will shew more our need of care to keep our money from going from us , than a way and method how to preserve it here . 't is death in spain to export money : and yet they , who furnish all the world with gold and silver , have least of it amongst themselves . trade fetches it away from that lazy and indigent people , notwithstanding all their artificial and forced contrivances to keep it there . it follows trade against the rigour of their laws ; and their want of foreign commodities makes it openly be carried out at noon-day . nature has bestow'd mines on several parts of the world : but their riches are only for the industrious and frugal . whomever else they visit , 't is with the diligent and sober only they stay . and if the vertue , and provident way of living of our ancestors ( content with our native conveniences of life , without the costly itch after the materials of pride and luxury from abroad ) were brought in fashion and countenance again amongst us ; this alone would do more to keep increase our wealth , and inrich our land , than all our paper helps about interest , money , bulli●n , &c. which , however eagerly we may catch at , will not , i fear , without better husbandry , keep us from sinking , whatever contrivances we may have recourse to . 't is with a kingdom , as with a family . spending less than our own commodities will pay for , is the sure and only way for the nation to grow rich. and when that begins once seriously to be consider'd , and our faces and steps are in earnest turn'd that way , we may hope to have our rents rise , and the publick stock thrive again . till then , we in vain , i fear , endeavour with noise , and weapons of law , to drive the wolf from our own to one anothers doors . the breed ought to be extirpated out of the island . for want , brought in by ill management , and nursed up by expensive vanity , will make the nation poor , and spare no body . if three millions were necessary for the carrying on the trade of england , whereof one million were for the land-holder , to maintain him ; another were for the payment of the labourer and handicraftsman ; and the third were the share of the brokers , coming to them for their care and pains in distributing ; if one million of this money were gone out of the kingdom , must not there be ⅓ part less to be shared amongst them for the product of their land , their labour and their distribution ? i do not say they will feel it at the same time . but the landholder having nothing but what the product of his land will yield ; and the buyer , according to the plenty or scarcity of money he has , always setting the price upon what is offered to sale ; the land-holder must be content to take the market-rate for what he brings thither , which always following the scarcity or plenty of money , if any part of our money be gone , he is sure first to find it in the price of his commodities . for the broker and merchant , though he sell cheaper , yet he buys cheaper too ; and he will be sure to get by his returns , or let alone a commodity which will not produce him gains ; and whatsoever is so let alone , and left upon hands , always turns to the land-holders loss . supposing that of our woollen manufacture , foreign markets took off one half , and the other half were consumed amongst our selves ; if a sensible part , ( as ⅓ of our money ) were gone , and so men had equally ⅓ less than they had ( for , 't is certain , it must be tantamount ; and what i 'scape of ⅓ less , another must make up ) it would follow , that they would have less to lay out in cloaths , as well as other things , and so would either wear them longer , or pay less for them . if a clothier finds a want of vent , he must either sell cheaper or not at all : if he sells cheaper , he must also pay less , both for wool and labour : and if the labourer hath less wages , he must also pay less for corn , butter , cheese , flesh , or else forbear some of these quite . in all which cases , the price of wool , corn , flesh , and the other products of land are brought down , and the land bears the greatest part of the loss . for where-ever the consumption or vent of any commodity is stopt , there the stop continues on till it comes to the land-holder . and where-ever the price of any commodity begins to fall , how many hands soever there be between that and the land-holder , they all take reprisals one upon another , till at last it comes to the land-holder ; and there the abatement of price , of any of his commodities , lessens his income , and is a clear loss . the owner of land , which produces the commodity , and the last buyer , who consumes it , are the two extreams in commerce . and though the falling of any sort of commodity in the land-holder's hand , does not prove so to the last consumer , the arts of intervening brokers and ingrossers keeping up the price to their own advantage ; yet whenever want of money , or want of desire in the consumer , make the price low , that immediately reaches the first producer ; no body between having any interest to keep it up . now , as to the two first causes of falling of rents , falling of interest has no influence at all . in the latter , ●it has a great part : because it makes the money of england less , by making both english-men and foreigners withdraw or withhold their money . for that which is not let loose into trade , is all one whil'st hoarded up , as if it were not in being . i have heard it brought for a reason , why interest should be reduced to four per cent ; that thereby the landholder , who bears the burthen of the publick charge , may ●e , in some degr●e , eased by falling of interest . this argument will be put right , if you 〈◊〉 it will case the forrower , and say the less on the lender ; but it concern not the land in general , unless you will suppose all land-holders in debt . 〈…〉 we may yet think that men in ●●gland , who have land , have money too ; and that landed men , as well a● others , by their providence and good husbandry , accommodating their expences to their income , keep themselves from going backwards in the world. that which is urged , as most deserving consideration and remedy in the case , is , that it is hard and unreasonable , that one , who has mortgaged half his land , should yet pay taxes for the whole , whil'st the mortgage goes away with the clear profit of an high interest . to this i answer , 1. that if any man has run himself in debt , for the service of his country , 't is fit the publick should reimburse him , and set him free . this is a care that becomes the publick justice ; that men , if they receive no rewards , should , at least , be kept from suffering , in having served their country . but i do not remember the polity of any nation , who altered their constitution , in favour of those whose mismanagement had brought them behind-hand ; possibly , as thinking the publick little beholding to those who had misimploy'd the stock of their country , in the excess of their private expences , and , by their example , spread a fashion that carries ruine with it : mens paying taxes of mortgaged lands , is a punishment for ill-husbandry , which ought to be discouraged ; but it concerns very little the frugal and the thrifty . 2. another thing to be said in reply to this , is , that it is with gentlemen in the country , as with tradesmen in the city . if they will own titles to greater estates than really they have , it is their own faults , and there is no way left to help them from paying for them . the remedy is in their own hands , to discharge themselves when they please . and when they have once sold their land , and paid their debts , they will no longer pay taxes for what they own , without being really theirs . there is another way also , whereby they may be relieved , as well as a great many other inconveniencies remedied ; and that is by a registry : for if mortgages were registred , i and taxes might reach them , and order the lender to pay his proportion . i have met with patrons of four per cent , who ( amongst many other fine things they tell us of ) affirm , that if interest were reduc'd to four per cent , then s●me men would , borrowing money at this low rate , pay their debts ; others would borrow more than they now do , and improve their land ; others would borrow more , and imploy it in trade and manufacture . gilded words indeed , were there any thing substantial in them ! these men talk as if they meant to shew us , not only the wisdom but riches of solomon , and make gold and silver as common as the stones in the street ; but at last , i fear , 't will be but wit without money ; and , i wish it amount to that . 't is without question , that could the country-man and the trades-man take up money cheaper than now they do , every man would be forward to borrow , and desire that he might have other mens money to imploy to his advantage ; and therefore , i confess , those who contend for four per cent , have found out a way to set mens months a watering for money at that rate , and to increase the number of the borrowers in england ; if any body can imagine it would be an advantage to increase them . but to answer all their fine projects , i have but this one short question to ask them : will four per cent increase the number of the lenders ? if it will not , as any man at the very first hearing , will shrewdly suspect it will not , then all the plenty of money these conjurers bestow upon us for improvement of land , paying of debts , and advancement of trade , is but like the gold and silver which old women believe others conjurers , bestow sometimes by whole lapfuls , on poor credulous girls , which , when they bring to the light , is found to be nothing but wither'd leaves , and the possessors of it are still as much in want of money as ever . indeed i grant it would be well for england , and i wish it were so , that the plenty of money were so great amongst us , that every man could borrow as much as he could use in trade , for four per cent ; nay , that men could borrow as much as they could imploy for six per cent. but even at that rate , the borrowers already are far more than the lenders . why else doth the merchant upon occasion , pay six per cent , and often above that rate for brokage ? and why doth the country gentleman of 1000 l. per annum find it so difficult , with all the security he can bring to take up 1000 l ? all which proceeds from the scarcity of money , and bad security ; two causes which will not be less powerful to hinder borrowing , after the lowering of 〈◊〉 ; and i do not see how any one can imagine how reducing use to four per cent , should abate their force ; or how lessening the reward of the lender , without diminishing his risque , should make him more forward and ready to lend . so that these m●n , whilst they talk , that at four 〈…〉 m●n would take up , and ●mploy more money to the publick advantage , do but 〈◊〉 to multip●y the number of borrowers among us , of which it is certain we have too many already . whilst they thus set men a longing for the golden days of four per cent , methinks they use the poor indigent debtor , and needy tradesman , as i have seen pratling jack-daws do sometimes their young , who kawing and fluttering about the nest , set all their young ones a gaping , but having nothing in their empty mouths but noise and air , leave them as hungry as before . 't is true these men have found out by a cunning project , how by the restraint of law to make the price of money ⅓ cheaper , and then they tell iohn a nokes , that he shall have 10000 l. of it to employ in merchandise , or cloathing ; and iohn a stiles shall have 20000 l. more to pay his debts ; and so distribute this money as freely as dego did his legacies , which they are to have even where they can get it . but till these men can instruct the forward borrowers where they shall be furnished , they have perhaps done something to increase mens desire , but not made money one jot easier to come by . and till they do that , all this sweet gingling of money in their discourses , goes just to the tune of , if all the world were oatmeal . methinks these undertakers , whilst they hav● put men in hopes of borrowing more plentifully at easier rates , for the supply of their wants and trades , had done better to have bethought themselves of a way , how men need not borrow upon use at all ; for this would be much more advantageous , and altogether as feisible . for i am sure , 't is as easie to contrive in a country that wants money in proportion to its trade , how every man shall be supplied with as much money as he needs , ( i. e. can employ in improvement of land , paying his debts , and return of trade ) for nothing , as for four per cent ; as it is as easie to distribute twenty pair of shooes amongst thirty men , if they pay nothing for them at all , as if they paid 4 s. a pair . ten of them ( notwithstanding the statute rate should be reduced from 6 s. to 4 s. a pair ) will be necessitated to sit still barefoot , as much as if they were to pay nothing for shooes at all . either we have already more money than the owners will lend , or we have not . if part of the money , which is now in england , will not be lent at the rate interest is at present at , will men be more ready to lend , and borrowers be furnished for all those brave purposes more plentifully , when money is brought to four per cent ? if people do already lend all the money they have , above their own occasions , whence are those who will borrow more at 4 per cent , to be supplied ? or is there such plenty of money , and scarcity of borrowers , that there needs the reducing of interest to 4 per cent , to bring men to take it ? all the imaginable ways of increasing money in any country , are these two : either to dig it in mines of our own , or get it from our neighbors . that 4 per cent , is not of the nature of the de●sing-rod , or virgila divina , able to discover mines of gold and silver , i believe will easily be granted me . the way of getting from foreigners , is either by force , borrowing , or trade . and whatever otherways besides these men may fansie or propose , for increasing of money , ( except they intend to set up for the philosophers stone ) would be much the same with a destracted man's device , that i knew , who , in the beginning of his distemper first discover'd himself to be out of his wits , by getting together , and boiling a great number of groats , with a design , as he said , to make them plim , and grow thicker . that 4 per cent , will raise armies , discipline soldiers , and make men valiant , and fitter to conquer countries , and enrich themselves with the spoils , i think was never pretended . and that it will not bring in more of our neighbours money upon loan , than we have at present among us , is so visible in it self , that it will not need any proof ; the contenders for 4 per cent looking upon it as an undeniable truth , and making use of it as an argument to shew the advantage it will be to the nation , by lessening the use paid to foreigners , who upon falling of use will take home their money . and for the last way of increasing our money , by promoting of trade , how much lowering of interest is the way to that , i have , i suppose , shew'd you already . having lately met with a little tract intituled a letter to a friend concerning usury , printed in the year 1690 ; which gives in short , the arguments of some treatises printed many years since , for the lowering of interest ; it may not be amiss , briefly to consider them . 1. a high interest decays trade . the advantage from interest is greater than the profit from trade , which makes the rich merchants give over , and put out their stock to interest , and the lesser merchants break. answ. this was printed in 1621 , when interest was at 10 per cent. and whether england had ever a more flourishing trade than at that time , must be left to the judgment of those who have consider'd the growing strength and riches of this kingdom in q. e. and king i. the 1st reigns : not that i impute it to high interest , but to other causes i have mention●d , wherein usury had nothing to do . but if this be thought an argument , now in 1690 , when the legal interest is 6 per cent ; i desire those who think fit to make use of it , to name those rich merchants who have given over and put out their stocks to interest . 2. interest being at 10 per cent , and in holland at 6 ; our neighbor merchants undersell us . answ. the legal interest being here now at 6 per cent , and in holland not limited by law ; our neighbor merchants under-sell us , because they live more frugally , and are content with less profit . 3. interest being lower in holland than in england , their contributions to war , works of piety , and all charges of the state , are cheaper to them than to us . answ. this needs a little explication . contributions greater or less , i understand : but contributions cheaper or dear●r , i confess i do not . if they manage their wars and charges cheaper than we , the blame is not to be laid on high or low interest . 4. interest being so high , prevents the building of shipping , which is the strength and safety of our island , m●st merchant ships being built in holland . answ. though this argument be now gone , such ships being prohibited by a law , i will help the author to one as good . the du●ch buy our rape-seed , make it into oil , bring it back to us , and sell it with advantage . this may be as well said to be from high interest here , and low there . but the truth is , the industry and frugality of that people , makes them content to work cheaper , and sell at less profit than their neighbours , and so get the trade from them . 5. the high r●te of usury makes land sell so cheap , being n●t worth more than 14 or 15 years purcha●● ; whereas in holland , where interest is at 6 , it is worth above 25. so that a low interest raises the price of land. where money is dear land is cheap . ans. this argument plainly confesses , that there is something else regulates the price of land , besides the rate of interest ; else when money was at 10 per cent here , land should have been at 10 years purchase ; whereas he confesses it then to have been at 14 or 15. one may suppose , to favour his hypothesis , he was not forward to speak the most of it . and interest , as he says , being at 6 per cent in holland . land there should have sold by that rule for 16 ● / ● years purchase , whereas he says it was worth about 25. and mr. manly says , ( p. 33. ) that 〈◊〉 in france being at 7 per cent , noble 〈…〉 4 and 35 years purchase , and 〈◊〉 land for 25. so that the true 〈…〉 from hence is not what our 〈…〉 that 't is not the legal 〈…〉 something else , that governs the 〈◊〉 of land. i grant his position , that 〈…〉 . but it must be so by the natural , not legal interest . for where money will be lent on good security at 4 or 5 per cent , 't is a demonstration that there is more than will be ventured on ordinary credit in trade . and when this plenty becomes general , 't is a sign there is more money than can be employed in trade ; which cannot but put many upon seeking purchases , to lay it out in land , and so raise the price of land , by making more buyers than sellers . 6. 't is not probable lenders will call in their money , when they cannot make greater interest any where . besides , their security upon l●nd will be better . answ. some unskilful and timorous men will call in their money ; others put it into the banker's hands . but the bankers and skilful will keep it up , and not lend it , but at the natural vse , as we have shewn . but how securities will be●ne e●d●d by lowering of interest , is i confess beyond my comprehension . of raising our coin. being now upon the consideration of interest and money , give me leave to say one word more on this occasion , which may not be wholly unseasonable at this time . i hear a talk up and down of raising our money , as a means to retain our wealth , and keep our money from being carried away . i wish those that use the phrase of raising our money , had some clear notion annex'd to it ; and that then they would examine , whether , that being true , it would at all serve to those ends , for which it is propos'd . the raising of m●n●y then signifies one of these two things ; either raising the value of our money , or raising the denomination of our coin. the raising of the value of money , or any thing else , is nothing but the making a less quantity of it exchange for any oth●r thing , than would have been taken for it before . v. g. if 5 s. will exchange for , or ( as we call it ) buy a bushel of wheat ; if you can make 4 s. buy another bushel of the same wheat , it is plain the value of your money is raised , in respect of wheat , ⅕ . but thus nothing can raise or fall the value of your money , but the proportion of its plenty or scarcity , in proportion to the plenty , scarcity , or vent of any other commodity , with which you compare it , or for which you would exchange it . and thus silver , which makes the in●●ntick value of money , compar'd with it self , under any stamp or denomination of the same or different countries , cannot be raised . for an ounce of silver , whether in p●ne● , g●o●●● ● or cr●wn pieces , stivers or du●●t●●ns , or in bullion , is and always eternally will be of equal value to any other ounce of si●ver , under what stamp or denomination soever ; unless it can be shewn that any stamp can add any new and better 〈…〉 parc●l of silver , which 〈…〉 of silver 〈◊〉 . 〈◊〉 therefore 〈…〉 of equal value to silver , 〈…〉 coin , com 〈◊〉 with 〈…〉 less , or equal , 〈…〉 or equal silve● 〈◊〉 and 〈…〉 can by no 〈…〉 your money . 〈…〉 of the world , 〈…〉 being a●oy●d , 〈…〉 so much silver alloy'd , or mixed with baser metals : because , besides the weight of the silver , those who have need of fine ( i. e. unmixed silver ; as gilders , wyre-drawers , &c. ) must according to their need , besides an equal weight of silver mixed with other metals , give an overplus to reward the refiner's skill and pains . and in this case , fine silver and alloy'd or mixed silver are considered as two distinct commodities . but no money being coin'd of pure fine silver , this concerns not the value of money at all ; wherein an equal quantity of silver is always the same value with an equal quantity of silver , let the stamp or denomination be what it will. all then that can be done in this great mystery of raising money , is only to alter 〈…〉 , and call that a crown now , which before by the law was but a part of a crown . for example : supposing , according to the standard of our law , 5 ● . or a crown , were to weigh an ounce , ( as it does now , wanting 18 grains ) whereof , ● ½ were copper , and 11 / 12 silver , ( for there abouts it is ) 't is plain here 't is the quantity of silver gives the value to it . for let another piece be coined of the same weight , wherein half the silver is taken out , and copper or other alloy put into the place , every one knows it will be worth but half as much . for the value of the alloy is so inconsiderable as not to be reckon'd . this crown now must be raised● and from henceforth our crown pieces coined 1 / 20 lighter than an ounce ; which is nothing but changing the denomination , calling that a crown now , which yesterday was but a part , viz. 19 / 20 of a crown ; whereby you have only raised 19 parts to the denomination formerly given to 20. for i think no body can be so senseless , as to imagine that 19 grains or ounces of silver can be raised to the value of 20 ; or that 19 gr. or ounces of silver shall at the same time exchange for or buy as much corn , oyl , or wine , as 20 ; which is to raise it to the value of 20. for if 19 ounces of silver can be worth 20 ounces of silver , or pay for as much of any other commodity , then 18 , 1● , or ● ounce may do the same . for if the abating 1 / 20 of the quantity of silver of any coin , does not lessen its value , the abating 1● / 20 of the quantity of the silver of any coin , will not abate its value . and so a single three-pence , or a single penny , being call'd a crown , will buy as much spice , or silk , or any other commodity , as a crown-piece , which contains 20 or 60 times as much silver ; which is an absurdity so great , that i think no body will want eyes to see , and sense to disown . now , this raising your money , or giving a less quantity of silver the stamp and denomination of a greater , may be done two ways . 1. by raising one species of your money . 2. by raising all your silver coin at once , proportionably ; which is the thing i suppos'd , now propos'd . 1. the raising of one species of your coin , beyond its intrinsick value , is done by coining any one species , ( which in account bears such a proportion to the other species of your coin ) with less silver in it than is required by that value it bears in your money . for example , a crown with us goes for 60 pence , a shilling for 12 pence , a t●ster for 6 pence , and a groat for 4 pence : and accordingly , the proportion of silver in each of them , ought to be as 60. 12. 6. and 4. now , if in the mint there should be coin'd groats , or testers , that being of the same alloy with our other money , had but 2 / ● of the weight that those species are coin'd at now ; or else , being of the same weight , were alloy'd with ⅓ of copper 〈…〉 〈…〉 ; and should thus , by law , be made current ; ( the rest of your silver money being kept to the present standard in weight and fineness ) 't is plain those species would be raised ⅓ part ; that passing for 6 d which had but the silver of 4 d in it ; and would be all one as if a groat should by law be made current for 6 d ; and every 6 d in payment pass for 9 d. this is truly raising the species : but is no more in effect , than if the mine should coin clip'd money . and has , besides the cheat that is put , by such base or light money , on every particular man that receives it , that he wants ⅓ of that real value which the publick ought to secure him , in the money it obliges him to receive as lawful and current ; it has● i say , this great and unavoidable inconvenience to the publick , that , besides the opportunities it gives to domestick coin●●● to cheat you with lawful money , it p●●● it into the hands of foreigners to 〈◊〉 away your money without any commodities for it● for if they find that two-penny we●ght of silver , marked with a certain impression , shall ●●re in e●gland be equivalent to 3 d weight marked with anoth●r impression ; they will not fail to 〈◊〉 pieces of that fashion ; and so importing that base and low coin , will , here in england , receive 3 d for 2 d , and quickly carry away your silver in exchange for copper , or barely the charge of coynage . this is unavoidable in all countries where any one species of their money is disproportionate in its intrinsick value , ( i. e. in its due proportion of silver to the rest of the money of that country ) which the king of france could not avoid , with all his watchfulness . for though , by edict , he made his 4 s●ls pieces , whereof 15 were to pass for ● french crown , though 20 of them had not so much silver in them , as was in a french crown piece ) pass in the inland parts of his kingdom , 15 for a crown , in all payments ; yet he durst not make them current in his sea-port towns , for fear that should give an opportunity to their importation . but yet this caution served not the turn . they were still imported ; and , by this means , a great loss and damage brought upon his country . so that he was forced to cry them down , and sink them to near their intrinsick value ; whereby a great many particular men , who had quantities of that species in their hands , lost a great part of their estates ; and every one that had any , lost proportionably by it . if we had groats or six-pences current by law , amongst us , that wanted ⅓ of the silver they now have by the standard , to make them of equal value to our other species of money ; who can imagine that our neighbours would not presently pour in quantity of such money upon us , to the great loss and prejudice of the kingdom ? the quantity of silver that is in each piece or species of coin , being that which makes its real and intrinsick value , the due proportions of silver ought to be kept in each species , according to the respective rate set on each of them by law. and when this is ever varied from , it is but a trick to serve some present occasion ; but is alway● with loss to the country where the trick is play'd . 2. the other way of raising m●ny is by raising all your silver coin at once ; the proportion of a crown , a shilling , and a penny , in reference to one another , being still kept , ( viz. that a shilling shall weigh 1 / ● of a crown piece , and a penny weigh 1 / 12 of a shilling , in standard silver ) but out of every one of these , you abate 1 / 20 of the silver they were wont to have in them . if all the species of money , be , as 't is call'd , rais'd by making each of them to have 1 / 2● less of silver in them than formerly ; and so your whole money be lighter than it was : these following will be some of the consequences of it . 1. it will rob all creditors and landlords of 1 / 20 ( or 5 per cent ) of their debts , in their 〈◊〉 rents , for ever ; and all other rents , as far as their former contracts reach , of 5 per cent of their yearly income ; and this without any advantage to the debtor or farmer : for he receiving no more pounds sterling for his land or commodities , in this new lighter coin , than he should have done of your old and weightier money , gets nothing by it . if you say yes , he will receive more crown , half-crown , and shilling pieces , for what he now sells for new money , than he should have done if the money of the old standard had continued ; you confess your money is not raised in value , but in denomination ; since what your new pieces want in weight , must now be made up in their number . but which way ever this falls , 't is certain , the publick ( which most men think , ought to be the only reason of changing a settled law , and disturbing the common current course of things ) receives not the least profit by it ; nay , as we shall see by and by , it will be a great charge and loss to the kingdom . but this , at first sight , is visible ; that in all payments to be received upon precedent contracts , if your money be in effect raised , the receiver will lose 5 per cent. for money having been lent , and leases and other bargains made , when money was of the same weight and fineness that it is now , upon confidence that under the same names of pounds , sh●l . and pence , they should receive the same value , ( i. e. the same quantity of silver ) by giving the denomination now to less quantities of silver by 1 / 20 , you take from them 5 per cent of their due . when men go to market to buy any other commodities with their new , but lighter money , they will find 20 s. of their new money will buy no more of any commodity than 19 would before . for it not being the denomination but the quantity of silver , that gives the value to any coin , 19 grains or parts of silver , however denominated or marked● will no more be worth , or pass for , or buy so much of any other commodity as 20 grains of silver will , than 19 s. will pass for 20 s. if any one thinks a shilling or a crown in name has its value from the denomination , and not from the quantity of silver in it , let it be tried ; and hereafter let a penny be called a shilling or a shilling be called a crown . i believe no body would be content to receive his debts or rents in such money ; which though the law should raise thus , yet he foresees he should lose 11 / 12 by the one , and by the other ⅘ of the value he received ; and would find his new shilling , which had no more silver in it than 1 / 12 of what a shilling had before , would buy him of corn , cloth , or wine but 1 / 12 of what an old shilling would . this is as plainly so in the raising , as you call it , your crowns to 5 s. and 3 d. or ( which is the same thing ) making your crown 1 / 2● lighter in silver ; the only difference being that in one the loss is so great , ( it being 11 / 12 ) every body sees and abhors it at first proposal ; but in the other ( it being but 1 / 20 , and covered with the deceitful name of raising our money ) people do not so readily observed it . if it be good to raise the crown-piece this way 1 / 20 this week , i suppose it will be as good and profitable to raise it as much again the next week . for there is no reason why it will not be as good to raise it again another 1 / 20 the next week , and so on ; wherein , if you proceed but 10 weeks successively , you will by new-years-day next have every half-crown raised to a crown , to the loss of ½ of peoples debts and rents , and the king's revenue , besides the confusion of all your affairs : and if you please to go on in this beneficial way of raising your money , you may by the same art bring a penny-weight of silver to be a crown . silver , i. e. the quantity of pure silver separable from the alloy , makes the real value of money . if it does not , coin copper with the same stamp and denomination , and see whether it will be of the same value . i suspect your stamp will make it of no more worth than the copper-money of ireland is , which is its weight in copper and no more . that money lost so much to ireland as it passed for above the rate of copper . but yet i think no body suffered so much by it as he by whose authority it was made current . if silver give the value , you will say what need is there then of the charge of coinage . may not men exchange silver by weight , for other things ; make their bargains , and keep their accounts in silver by weight ? this might be done , but it has these inconveniencies . 1. the weighing of silver to every one we had occasion to pay it to , would be very troublesome , for every one must carry about scales in his pocket . 2. scales would not do the business . for , in the next place , every one cannot distinguish between fine and mix'd silver : so that though he received the full weight , he was not sure he received the full weight of silver ; since there might be a mixture of some of the baser metalls , which he was not able to discern . those who have had the care and government of politick societies , introduced coinage as a remedy to those two inconveniencies . the stamp was a warranty of the publick , that under ●●ch a denomination they should receive a piece of such a weight and such a ●iness ; 〈◊〉 is , they should receive so much silver . and this is the reason why the counter●iting the stamp is made the highest crime , and has the weight of treason ●aid upon it ; because the stamp 〈…〉 of the intrins●ck value . the royal authority gives the 〈…〉 the law ●●lows and confirms the denomination , and both together give as it were the pub●●●k faith , as a secu●ity that 〈◊〉 of money 〈◊〉 for 〈…〉 , be of such a 〈…〉 have 〈◊〉 them so much silver . for 〈◊〉 si●ver ●nd not names that pay deb●● and pur●●ase commodities . if therefore i have contracted for twenty crowns , and the law then has required that each of those crowns should have an ounce of silver ; 't is certain my bargain is not made good , i am defrauded ( and whether the publick faith be not broken with me , i leave to be considered ) if , paying me 20 crowns , the law allows them to be such as have but 19 / 2● of the silver they ought to have , and really had in them , when i made my contract . 2. it diminishes all the kings revenue 5 per cent. for though the same number of pounds , shillings , and pence are paid into the exchequer as were wont , yet these names being given to coin that have each of them 1 / 20 less of silver in them ; and that being not a secret conceal'd from strangers , no more than from his own subjects , they will sell the king no more pitch , ●arr , or hemp , for 20 shillings , after the raising your money , than they would before for 19 : or to speak in the ordinary phrase , they will raise their commodities 5 per cent , as you have rais'd your money 5 per cent : and 't is well if they stop there . for usually in such changes , an out-cry being made of your lessening your coin , those who you have to deal with you , taking the advantage of the allarm to secure themselves from any loss by your new trick , raise their price even beyond the par of your lessening your coin. i hear of two inconveniencies complain'd of , which 't is proposed by this project to remedy . the one is , the melting down of our coin ; the other , the carrying away of our bullion . these are both inconveniencies i fear we lie under , but neither of them will be in the least removed or prevented by the proposed alteration of our money . 1. it is past doubt , that our money is melted down ; the reason whereof is evidently the cheapness of coinage for a tax on coin , paying the coinage , the particular owners pay nothing for it . so that 100 ounces of silver coined , comes to the owner at the same rate , as 100 ounces of the standard silver in bullion . for delivering into the mint his silver in bars , he has the same quantity of silver deliver'd out to him again in coin , without any charges to him . whereby if at any time he has occasion for bullion , 't is the same thing to melt down our mi●'d money as to buy bullion from abroad , or take it in exchange for other commodities . thus our mint to the only advantage of our officers , but at the publick cost , la●●urs in vain , as will be found . but yet this makes you not have one jot less money in england , than you would have otherwise ; but only makes you coin that which otherwise would not have been coin'd , nor perhaps been brought hither ; and being not brought hither by an over-ballance of your exportation , cannot stay when it is here . it is not any sort of coinage , does or can keep your money here . that wholly and only depends upon the ballance of your trade . and had all the money in king charles the ii. and king iames the ii. time , been minted according to this new proposal , this raised money would have been gone as well as the other , and the remainder been no more , nor no less than it is now ; though i doubt not but the mint would have coined as much of it as it has of our present mil●'d money . the short is this ; an over-ballance of trade with spain brings you in bullion ; cheap coinage , when it is here , carries it into the mint , and money is made of it ; but if your exportation will not ballance your importation in the other parts of your trade , away must your silver go again , whether monied or not monied . for where goods do not , silver must pay for the commodities you spend . that this is so will appear by the books of the mint , where may be seen how much mill'd money has been coin'd in the two last reigns . and in a paper i have now in my hands , ( supposed written by a man not wholly ignorant in the mint ) 't is confessed , that whereas 1 / ● of the current payments were some time since of mil●'d money , there is not now 1 / ●● gone then it is . but let not any one mistake and think it gone , because in our present coinage , an ounce wanting ●8 grains is denominated a crown● or that ( as is now proposed ) an 〈…〉 about 40 grains , being 〈…〉 denominated a 〈…〉 it , or will ( if our money be 〈…〉 for the future fix it here . coin what quantity of silver you please , in one peice bigger or less , and give it the denomination of a crown ; when your money is to go to pay your foreign debts , ( or else it will not go out at all ) your heavy money , ( i. e. that which is weight according to its denomination , by the standard of the mint ) will be that which will be melted down , or carried away in coin by the exporter , whether the pieces of each species be by the law greater or less . for whilst coinage is whol●y paid for by a tax , whatever your size of money be , he that has need of bullion to send beyond sea , or of silver to make plate , need but take mill'd money , and melt it down and he has it as cheap as if it were in pieces of eight , or other silver coming from abroad ; the stamp , which so well secures the weight and fineness of the mill'd money , costing nothing at all . to this perhaps will be said , that if this be the effect of milled money , that it is so apt to be melted down , it were better to return to the old way of coining by the hammer ; to which i answer by no means . for , 1. that way of coinage less secures you from having a great part of your money melted down . for in that way there being a greater inequality in the weight of the pieces , some being too heavy and some too light , those who know how to make their advantage of it , cull out the heavy pieces , melt them down , and make a benefit of the over-weight . 2. coinage by the hammer exposes you much more to the danger of false coin. because the tools are easily made and concealed , and the work carried on with fewer hands , and less noise than a mill ; whereby false coiners are less liable to discovery . 3. the pieces not being so round , even , and fairly stamp'd , nor marked on the edges are expos'd to clipping , which mill'd money is not . mill'd-money is therefore certainly best for the publique . but whatever be the cause of melting down our mill'd-money , i do not see how raising our money ( as they call it ) will at all hinder its being melted down . for if our crown-pieces should be coin'd 1 / 20 lighter ; why should that hinder them from being melted down more than now . the intrinsique value of the silver is not alter'd , as we have shewn already : therefore that temptation to melt them down remains the same as before . but they are lighter by 1 / 20. that cannot hinder them from being melted down . for half crowns are lighter by half , and yet that preserves them not . but they are of less weight , under the same denomination , and therefore they will not be melted down . that is true , if any of these present crowns that are 1 / ●0 heavier , are current for crowns at the same time . for then they will no more melt down the new light crowns , than they will the old clipp'd ones , which are more worth in coin , and tale , than in weight and bullion . but it cannot be suppos'd that men will part with their old and heavier money , at the same rate that the lighter new coin goes at ; and pay away their old crowns for 5 s. in tale , when at the mint they will yield them 5 s. 3 d. and then if an old mill'd crown goes for 5 s. 3 d. and a new mill'd crown ( being so much lighter ) go for a crown , what i pray will be the odds of melting down the one or the other ? the one has 1 / 20 less silver in it , and goes for 1 / 20 less , and so being weight , they are melted down upon equal terms . if it be a convenience to melt one , it will , be as much a convenience to melt the other ; just as it is the same convenience , to melt mi●l'd half crowns as mill'd crowns ; the one having with half the quantity of silver , half the value . when the money is all brought to the new rate , i. e. to be ● / 20 lighter , and commodities raised as they will proportionably ; what shall hinder the melting down of your money then more than now , i would fain know ? if it be coin'd then as it is now g●●tis , a crown piece , ( let it be of what weight soever ) will be as it is now , just worth it s own weight in bullion , of the same fineness for the coinage , which is the manufactury about it , and makes all the difference , ●●●●ing nothing ; what can make the difference of value ? and therefore , whoever wants bullion , will as cheaply melt down these new crowns , as buy bullion with them . the raising of your money cannot then ( the act for free coinage standing ) hinder its being meltted down . nor , in the next place , much less can it , as is pretended , hinder the exportation of our bullion . any denomination or stamp we shall give to silver here , will neither give silver a higher value in england , nor make it less prized abroad . so much silver will always be worth ( as we have already shew'd ) so much silver given in exchange one for another . nor will it , when in your mint a less quantity of it is raised to a higher denomination ( as when 19 / 20 of an ounce has now the denomination of a crown , which formerly belong'd only to the whole 20 ) be one jot raised , in respect of any other commodity . you have rais'd the denomination of your stamped silver 1 / 20 , or which is all one 5 per cent. and men will presently raise their commodities 5 per cent. so that if yesterday 20 crowns would exchange for 20 bushels of wheat , or 20 yards of a certain sort of cloth , if you will to day coin current crowns 1 / 20 lighter , and make them the standard , you will find 20 crowns will exchange for but 19 bushels of wheat , or 19 yards of that cloth , which will be just as much silver for a bushel , as yesterday . so that silver being of no more real value , by your changing your denomination , and giving it a less quantity ; this will no more bring in , or keep your bullion here , than if you had done nothing . if this were otherwise , you would be beholden ( as some people foolishly imagin ) to the clippers for keeping in your money . for if keeping the old denomination to a less quantity of silver , be raising your money ( as in effect it is all that is or can be done in it by this project of making your coin lighter ) the clippers have sufficiently done that ; and if their trade go on a little while longer , at the rate it has of late , and your mi●l'd-money be melted down and carried away , and no more coin'd ; your money will , without the charge of new coinage , be , by that sort of artificers , raised above 5 per cent , when all your current money shall be clipp'd , and made above 1 / ●0 lighter than the standard , preserving still its former denomination . it will possibly be here objected to me , that we see 100 l. of clipt money , above 5 per cent lighter than the standard , will buy as much corn , cloth , or wine , as 100 l. in mill'd mon●y , which is 1 / 20 heavier ; whereby it is evident that my rule fails , that it is not the quantity of silver that gives the value to money , but its stamp and denomination . to which i answer , that men make their estimate and contracts according to the standard , upon supposition they shall receive good and lawful money ; which is that of full weight ; and so in effect they do , whil'st they receive the current money of the country . for since 100 l. of clipt money will pay a debt of 100 l. as well as the weightiest mill'd money , and a new crown out of the mint will pay for no more flesh , fruit , or cloth , than five clipt shillings ; 't is evident that they are equivalent as to the purchase of any thing here at home , whil'st no body scruples to take five clipt shillings in exchange for a weighty mill'd crown . but this will be quite otherwise as soon as you change your coin , and● to raise it , as you call it ) make your money 1 / ●0 lighter in the mint ; for then no body will any more give an old crown of the former standard for one of the new , than he will now give you 5 s. and 3 d. for a crown ; for so much then his old crown will yield him at the mint . clipt and unclipt money will always buy an equal quantity of any thing else , as long as they will without scrup●e change one for another . and this makes that the foreign merchant , that comes to fell his goods to you , always counts upon the value of your money by the silver that is in it , and estimates the quantity of silver by the standard of your mint ; though perhaps by reason of clipt money , any sum that is ordinarily received is much lighter than the standard , and so has less silver in it than what is in a like sum new coin'd in the mint . but whilst clipt and weighty will equally change one for another , it is all one to him whether he receive his money in clipt money or no , so it be but current . for if he buy other commodities here with his money , whatever sum he contracts for , clipt as well as weighty money equally pays for it . if he would carry away the price of his commodity in ready cash , 't is easily chang'd into weighty money ; and then he has not only the sum in tale that he contracted for , but the quantity of silver he expected for his commodities , according to the standard of our mint . if the quantity of your clipt money be once grown so great , that the foreign merchant cannot ( if he has a mind to it ) easily get weighty money for it , but having sold his merchandise , and received clip'd money , finds a difficulty to procure what is weight for it ; he will , in selling his goods , either contract to be paid in w●ighty money , or else raise● the price of his commodities , according to the diminish'd quantities of silver in your current coin. in holland , ( ducatoons being the best money of the country , as well as the largest coin ) men , in payments , received and paid those indifferently , with the other money of the country , till of late the coining of other species of money , of baser alloy , and in greater quantities , having made the ducatoons , either by melting down , or exportation , scarcer than formerly , it became difficult to change the baser money into ducatoons ; and since that no body will pay a debt in ducatoons , unless he be allowed ½ per cent , more than they were coin'd for . to understand this , we must take notice , that guilders is the denomination that in holland they usually compute by , and make their contracts in . a ducatoon formerly passed at three guilders , and three stuyvers , or 63 stuyvers . there were then ( some years since ) began to be coin'd another piece , which was call'd a three guilders piece , and was order'd to pass for three guilders , or sixty stuyvers . but 21 three guilders pieces , which were to pass for 63 guilders , not having so much silver in them as 20 ducatoons , which passed for the same summ of 63 guilders , the ducatoon● were either melted down in their mints , for the making of these 〈…〉 , or yet baser money , with profit ; or were carried away by foreign merchants ; who when they carried back the product of their sale in money , would be sure to receive their payment of the number of guilders they contracted for in ducatoons , or change the money they received into ducatoons ; whereby they carried home more silver than if they had taken thei payment in three guilder pi●ces , or any other species . thus ducatoons became scarce . so that now he that will be paid in ducatoons must allow ½ per cent , for them . and therefore the merchants , when they sell any thing now , either make their bargain to be paid in ducatoons , or if they contract for guilders in general , ( which will be sure to be paid them in the baser money of the country ) they raise the price of their commodities accordingly . by this example in a neighbour country , we may see how our new mill'd money goes away . when foreign trade imports more than our commodities will pay for ; 't is certain , we must contract debts beyond sea , and those must be paid with money , when either we cannot furnish , or they will not take our goods to discharge them to have money beyond sea to pay our debts , when our commodities do not raise it , there is no other way but to send it thither . and since a weighty crown costs no more here than a light one ; and our coin beyond sea , is valued no otherwise than according to the quantity of silver it has in it ; whether we send it in specie , or whether we melt it down here , to send it in bullion ( which is the safest way , as being not prohibited ) the weightiest is sure to go . but when so great a quantity of your money is clip'd , or so great a part of your weighty money is carried away , that the foreign merchant , or his factor here , cannot have his price paid in weighty money , or such as will easily be changed into it , then every one will see , ( when men will no longer take five clip'd shillings for a mill'd or weighty crown ) that it is the quantity of silver that buys commodities and pays debts , and not the stamp and denomination which is put upon it . and then too it will be seen what a robbery is committed on the publick , by clipping . every grain diminished from the just weight of our money , is so much loss to the nation ; which will , one time or other , be sensibly felt ; and which , if it be not taken care of , and speedily stop'd , will , in that enormous course it is now in , quickly , i fear , break out into open ill effects ; and , at one blow , deprive us of a great part , ( perhaps , near ¼ ) of our money . for that will be really the case , when the increase of clip'd money makes it hard to get weighty , and men begin to put a difference of value between that which is weighty , and light money , and will not sell their commodities but for money that is weight , and will accordingly make their bargains . let the country gentleman , when it comes to that pass , consider what the decay of his estate will be , when receiving his rent in the tale of clip'd shillings● according to his bargain , he cannot get them to pass at market for more than their weight . and he that sells him salt or silk , will bargain for 5 s. such a quantity , if he pays him in fair weighty coin , but in clip'd money he will not take under 5 s. 3 d. here you see you have your money without this new trick of coinage , raised 5 per cent. but whether to any advantage of the kingdom i leave every one to judge . hitherto we have only consider'd the r●isi●g of silver c●in , and that has been only by coining it with les● silver in it , under the same denomination . there is another way yet of raising money , which has something more of reality , though as little good as the former in it : which now , that we are upon the chapter of raising of money , it may not be amiss to mention ; and that is , when either of the two richer metals , ( which money is usually made of ) is by law raised above its natural value , in respect of the other . gold and silver , have , in almost all ages and parts of the world ( where money was used ) generally been thought the fittest materials to make it of . but there being a great disproportion in the plenty of these metals in the world , one has always been valued much higher than the other ; so that one ounce of gold has exchanged for several ounces of silver : as at present , our guinea passing for 21 s. 6 d. in silver , gold is now about 15 ½ times more worth than silver ; there being about 15 ½ times more silver in 21 s. 6 d. than there is gold in a guinea . this being now the market rate of gold to silver ; if by an established law the rate of guinea's should be set higher , ( as to 22 s. and 6 d. ) they would be raised indeed , but to the loss of the kingdom . for by this law gold being raised , 5 per cent above its natural true value , foreigners would find it worth while to send their gold hither , and so fetch away your silver at 5 per cent profit , and so much loss to you . for when so much gold as would purchase but 100 ounces of silver any where else , will in england purchase the merchant 105 ounces , what shall hinder him from bringing his gold to so good a market ; and ( ei●her selling it at the mint , where it will yield so much , or having it coin'd into guinea's ) either go with them to market , with that advantage of 5 per cent in the very sort of his money , or change them into silver , and carry that away with him ? on the other side , if by a law you would raise your silver money and make 4 crowns or 20 s. in silver , equal to a guinea , at which rate i suppose it was first coin'd ; so that by your law a guinea should pass but for 20 s. the same inconvenience would follow . for then strangers would bring in silver , and carry away your gold , which was to be had here at a lower rate than any where else . if you say , that this inconvenience is not to be fear'd ; for that as soon as people found that gold began to grow scarce , or that it was more worth than the law set upon it , they would not then part with it at the statute-rate ; as we see the broad pieces that were coin'd in k. iames i. time for 20 s. no body will now part with under 23 s. or more , according to the market value ; this i grant is true ; and it does plainly confess the foolishness of making a law which cannot produce the effect it is made for ; as indeed it will not , when you would raise the price of silver in respect of gold , above its natural market value : for then , as we see in our gold , the price of it will raise its self . but on the other side , if you should by a law set the value of gold above its 〈◊〉 then peopl● would be bound to receive it at that high rate , and so part with their silver at an under value . but supposing that having a mind to raise your silver in re●pect of 〈◊〉 ( for when you would raise the value of money , fansie what you will 't is but in respect of something you 〈…〉 it for , and is only 〈…〉 make a less quantity of the 〈…〉 money is made of change 〈…〉 quantity of that thing 〈…〉 to ) you make a law 〈…〉 of that ? if your law 〈…〉 that as much as you 〈…〉 gold ( for they are 〈…〉 things pu● in 〈…〉 the one 〈…〉 clear loss to the kingdom as you raise silver and debase gold by your law , below their natural value . if you raise gold in proportion to silver the same effect follows . the effect and ill consequence indeed is not so easily observed in the one as in the other : because your accounts being kept , and your reckonings all made in pounds , shillings , and pence , which are denominations of silver coins or numbers of them ; if gold be made current at a rate above the free and market value of those two metals , every one will easily perceive the inconvenience . but there being a law for it , you cannot refuse the gold in payment for so much . and all the money or bullion people will carry beyond sea from you will be in silver , and the money or bullion brought in , will be in gold and the same just will happen when your silver is raised and gold debased in respect of one another , beyond their true and natural proportion : ( natural proportion or value i call that respective rate they find any where without the prescription of law ) for then silver will be that which is brought in , and gold will be carried out ; and that still with loss to the kingdom , answerable to the over-value , set by the law. only as soon as the mischief is felt , people will ( do what you can ) raise their gold to its natural value . for your accounts and bargains being made in the denomination of silver-money ; if , when gold is raised above its proportion , by the law , you cannot refuse it in payment , ( as if the law should make a guinea current at 22 s. and 6 d. you are bound to take it at that rate in payment ; but if the law should make guineas current at 20 s. he that has them is not bound to pay them away at that rate , but may keep them if he pleases , or get more for them if he can : yet from such a law , one of these 3 things follow . either 1st , the law forces them to go at 20 s. and then being found passing at that rate , foreigners make their advantage of it ; or 2 ly , people keep them up and will not part with them at the legal rate , understanding them really to be worth more , and then all your gold lies dead , and is of no more use to trade than if it were all gone out of the kingdom ; or 3 ly , it passes for more than the law allows , and then your law signifies nothing , and had been better let alone . which way ever it succeeds it proves either prejudicial or ineffectual . if the design of your law take place , the kingdom loses by it ; if the inconvenience be felt and avoided , your law is eluded . mo●ny is measure of commerce , and of the rate of every thing , and therefore ought to be kept ( as all other measures ) as steady and unvariable as may be . but this cannot be● if your money be made of two me●●l● , whose proportion , and consequently whose price , constantly varies in respect of one another . silver , for many reasons is the 〈◊〉 of all metals to be this measure , and therefore generally made use of for money . but then it is very unfit and inconvenient , that gold , or any other met●l should be made current legal money● at a standing settled rate . this i● to do by law , what justly cannot be done ; set a rate upon the varying value of things ; and is● a● i have shew'd , as far 〈◊〉 it 〈◊〉 , a constant damage and prej●dice to the country where it is prac●ised . suppose fifteen to one be now the exact p●r between g●ld and si●ver ; 〈…〉 make it lasting , and establish it so tha● next year , or twenty years 〈…〉 just value of gold to silver● and that one ounce of gold shall be 〈…〉 ounces of silver , neither more nor les● ? ●tis possible , the 〈…〉 trade sweeping away great 〈◊〉 of gold , may make it scarcer in 〈◊〉 . pe●haps the guinea trade , and mines of peru , affording it in a greater abundance , may make it more plentiful ; and so its value in respect of silver , come on the one side to be as sixteen , or on the other as fourteen to one . and can any law you shall make alter this proportion here , when it is so every where else round about you ? if your law set it at fifteen , when it is at the free market rate , in the neighbouring countries , as sixteen to one ; will they not send hither their silver to fetch away your gold at 1 / 16 loss to you ? or if you will keep its rate to silver , as fifteen to one , when in holland , france , and spain , its market value is but fourteen ; will they not send hither their gold● and fetch away your silver at 1 / 1● loss to you ? this is unavoidable , if you will make money of both gold and silver at the same time , and set rates upon them by law in respect of one another . what then ? ( will you be ready to say ) would you have gold kept out of engl●nd ? or being here , would you have it useless to trade , and must there be no money made of it ? i answer , quite the contrary . 't is sit the kingdom should make use of the treasure it has . 't is necessary your gold should be coin'd , and have the kings stamp upon it to secure men in receiving it , that there is so much gold in each piece . but 't is not necessary that it should have a fixed value set on it by publick authority . 't is not convenient that it should in its varying proportion have a settled price . let gold , as other commodities , find its own rate . and when , by the kings image and inscription , it carries with it a publick assurance of its weight and fineness ; the gold money so coin'd will never fail to pass at the known market rates ; as readily as any other twenty 〈◊〉 , though designed at first for 20 l , go now as current for 21 l. 10 s. as any other money , and sometimes for more , as the rate varies . the value or price of any thing being only the respective estimate it bears to some other , which it comes in competition with , can only be known by the quantity of the one which will exchange for a certain quantity of the other . there being no two things in nature , whose proportion and use does not vary , 't is impossible to set a standing regular price between them . the growing plenty or scarcity of either in the market ; ( whereby i mean the ordinary places , where they are to be had in tra●fick ) the real use , or changing fashion of the place bringing either of them more into demand than formerly ; presently varies the respective value of any two things . you will as fruitlesly endeavour to keep two different things steadily at the same price one with another , as to keep two things in an aequilibrium , where their varying weights depend on different causes . put a piece of spunge in one scale , and an exact counterpoise of silver in the other , you will be mightily mistaken if you imagine , that because th●t they are to day equal they shall always remain so . the weight of the spunge varying with every change of moisture in the air , the silver in the opposite scale will sometimes rise and sometimes fall. this is just the state of silver and gold in regard of their mutual value . their proportion , or use , may , nay constantly does vary , and with it their price . for being estimated one in reference to the other , they are as it were put in opposite scales , and as the one rises the other falls , and so on the contrary . farthings made of a baser metal , may on this account too deserve your consideration . for whatsoever coin you make current , above the intrinsick value , will always be dammage to the publick , whoever get by it . but of this i shall not at present enter into a more particular enquiry . only this i will confidently affirm , that it is the interest of every country , that all the current . money of it should be of one and the same metal ; that the several species should be all of the same alloy , and none of a baser mixture : and that the standard once thus settled , should be inviolably and immutably kept to perpetuity . for whenever that is alter'd upon what pretence soever , the publick will lose by it . since then it will neither bring us in more money , bullion , nor trade ; nor keep that we have here ; nor hinder our weighty money of what denomination soever from being melted ; to what purpose should the kingdom be at the charge of coining all our money a-new ? for i do not suppose any body can propose , that we should have two sorts of money at the same time , one heavier , and the other lighter , as it comes from the mint . that is very absurd to imagine . so that if all your old money must be coin'd over again , it will indeed be some advantage , and that a very considerable one , to the officers of the mint . for they being allow'd 3 s. 6 d. for the coinage of every pound troy , which is very near 5 ½ per cent ; if our money be six millions , and must be coin'd all over again , it will cost the nation to the mint 330000 l. if the c●ipt money must scape , because it is already as light as your new standard ; do you not own that this design of new coinage is just of the nature of c●ipping ? this business of money and coinage is by some men , and amongst them some very ingenious persons , thought a great mystery , and very hard to be understood . not that truly in it self it is so : but because interessed people that treat of it , wrap up the secret they make advantage of in mystical , obscure , and unintelligible ways of talking ; which men , from a preconceiv'd opinion of the difficulty of the subject , taking for sense , in a matter not easie to be penetrated but by the men of art , let pass for current without examination . whereas , would they look into those discourses , enquire what meaning their words have , they would find , for the most part , either their positions to be false ; their deductions to be wrong ; or ( which often happens ) their words to have no distinct meaning at all . where none of these be ; there , their plain , true● honest sense , would prove very easie and intelligible , if express'd in ordinary and direct language . that this is so , i shall shew , by examining a printed sheet on this subject , intituled , remarks on a paper given in to the lords , &c. remarks . 't is certain , that what place soever will give most for silver by weight , it will thither be carried and sold : and if of the money which now passes in england , there can be 5 s. 5 d. the ounce , given for standard silver at the mint ; when but 5 s. 4 d. of the very same money can be given elsewhere for it ; it will be certainly brought to the mint ; and when coined , cannot be sold , ( having one penny over-value set upon it by the ounce ) for the same that other plate may be bought for , so will be left unmelted ; at least , 't will be the interest of any exporters , to buy plate to send out , before money ; whereas now 't is his interest to buy money to send out before plate . answ. the author would do well to make it intelligible , how , of the money that now passes in england , at the mint can be given 5 s. 5 d. the ounce for standard silver , when but 5 s. 4 d. of the same money can be given elsewhere for it . next , how it has one penny over-value set upon it by the ounce ; so that , when coin'd it cannot be sold. this , to an ordinary reader , looks very mysterious ; and , i fear , is so ; as either signifying nothing at all , or nothing that will hold . for , 1. i ask who is it at the mint , that can give 5 s. 5 d. per ounce , for standard silver , when no body else can give above 5 s. 4 d ? is it the king , or is it the master worker , or any of the officers ? for to give 5 s. 5 d. for what will yield but 5 s. 4 d. to any body else , is to give 1 / ●5 part more than it is worth . for so much every thing is worth , as it will yield . and i do not see how this can turn to account to the king , or be born by any body else . 2. i ask , how a penny over-value can be set upon it by the o●ne● ; so that it cannot be sold ? this is so mysterious , that i think it near impossible . for an equal quantity of standard silver will always be just worth an equal quantity of standard silver . and it is utterly impossible to make 64 parts of standard silver equal to , or worth 65 parts of the same standard silver ; which is meant by setting a penny over-value upon it by the ounce , if that has any meaning at all . indeed , by the workmanship of it , 64 ounces of standard silver may be made not only worth 65 ounces , but 70 or 80. but the coinage , which is all the workmanship here , being paid for by a tax , i do not see how that can be reckon'd at all : or if it be , it must raise every 5 s and 4 d coin'd , to above 5 s. 5 d. if i carry 64 ounces of standard silver in bullion to the mint , to be coin'd ; shall i not have just 64 ounces back again for it in coin ? and if so , can these 64 ounces of coin'd standard silver , be possibly made worth 65 ounces of the same standard silver uncoin'd ; when they cost me no more , and i can , for barely going to the mint , have 64 ounces of standard silver in bullion turn'd into coin ? cheapness of coinage in england , where it costs nothing , will , indeed , make money be sooner brought to the mint , than any where else ; because there i have the convenience of having it made into mony for nothing . but this will no more keep it in england , than if it were perfect bullion . nor will it hinder it from being melted down ; because it cost no more in coin than in bullion : and this equally , whether your pieces , of the same denomination , be lighter , heavier , or just as they were before . this being explain'd , 't will be easie to see , whether the other things , said in the same paragraph , be true or false ; and particularly , whether 't will be the interest of every exporter , to buy plate to send out before money . remark . 't is only barely asserted , that 〈◊〉 silver be raised at the mint , that 't will ●●ise elsewhere above it ; but can never be known till it be tried . answ. the author tells us in the last paragraph , that si●v●r th●t is worth but 5 s. 2 d. per ounce at the 〈◊〉 is w●●th 5 s. 4 d. elsewhere . this how true or what inconvenience it 〈…〉 not here examine . but be the inconvenience of it what it will , this raising the money he proposes as a remedy : and to those who say , upon raising our money silver will rise too , he makes this answer , that it can never be known , whether it will or no , till it be tried . to which i reply , that it may be known as certainly , without trial , as it can , that two pieces of silver that weighed equally yesterday , will weigh equally again to morrow in the same scales . there is silver , ( says our author ) whereof an ounce ( i. e. 480 grains ) will change for 5 s. 4 d. ( i. e. 496 grains ) of our standard silver coin'd . to morrow you coin your money lighter ; so that then 5 s. 4 d. will have but 472 grains of coin'd standard silver in it . can it not then be known , without trial , whether that ounce of silver , which to day will change for 496 grains of standard silver coin'd , will change to morrow but for 472 grains of the same standard silver coin'd ? or can any one imagine that 480 grains of the same silver , which to day are worth 496 grains of our coin'd silver , will to morrow be worth but 472 grains of the same silver , a little differently coin'd ? he that can have a doubt about this till it be tried , may as well demand a trial to be made , to prove , that the same thing is aequiponderent , or aequivalent to it self . for i think it is as clear , that 472 grains of silver are aequiponderent to 496 grains of silver , as that an ounce of silver , that is to day worth 496 grains of standard silver , should to morrow be worth but 472 gr. of the same standard silver ; all circumstances remaining the same , but the different weight of the pieces stamp'd : which is that our author asserts , when he says , that 't is only barely asserted , &c. what has been said to this , may serve also for an answer to the next parapraph . only i desire it may be taken notice of , that the author seems to insinuate that silver goes not in england , as in foreign parts , by weight ; which is a very dangerous as well as false position ; and which , if allowed , may let into our mint what corruption and debasing of our money one pleases . remark . that our trade hath heretofore furnished us with an overplus , brought home in gold and silver , is true : but that we bring home from any place more goods than we now export to it , i do not conceive to be so . and more goods might be sent to those parts ; but by reason of the great value of silver in this part of the world , more money is to be got by exporting silver , than by any other thing that can be sent ; and that is the reason of it . and for its being melted down , and sent out , because it is so heavy , is not by their paper denied . answ. that we bring home from any place more goods than we now export , ( the author tells us ) he doth not conceive . would he had told us a reason for his conceit . but since the money of any country is not presently to be changed , upon any private man's groundless conceit , i suppose this argument will not be of much weight with many men. i make bold to call it a groundless conceit ; for if the author please to remember the great sums of money are carried every year to the east-indies , for which we bring home consumable commodities ; ( though i must own that it pays us again with advantage . ) or if he will examine how much only two commodities , wholly consumed here , cost us yearly in money , ( i mean canary wine and currants ) more than we pay for with goods exported to the canaries and zant ; besides the over-ballance of trade upon us in several other places ; he will have little reason to say , he doth not conceive we bring home from any place more goods than we ●ow export to it . as to what he says concerning the melting down and exporting our money , because it is heavy ; if by heavy , he means , because our crown-pieces ( and the rest of our sp●cies of money in proportion ) are 23 or 24 grains heavier than he would have them coin'd . this , whoever grants it , i deny ; upon grounds which i suppose , when examined , will be found clear and evident . indeed when your debts beyond sea , to answer the over-ballance of foreign importations , call for your money ; 't is certain the heavy money , that is that which has the standard weight , will be melted down and carried away ; because foreigners value not your stamp , but your silver . he would do well to tell us what he means by the great value of silver in this part of the world. for he speaks of it as a cause that draws away our money more now than formerly ; or else it might as well have been omitted as mentioned in this place : and if he mean , by this part of the world , england ; 't is scarce sense to say . that the great value of silver in england should draw silver out of england . if he means the neighbouring countreys to england , he should have said it , and not doubtfully this part of the world. but let him● by this part of the world , mean what he will , i dare say every one will agree , that silver is not more valued in this , than any other part of the world ; nor in this age , more than in our grandfathers days . i am sorry if it be true , what he tells us , that more money is to be got by exportation of silver , than by any other thing that can be sent . this is an evidence , that we bring home more goods than we export : for till that happens , and has brought us in debt beyond sea , silver will not be exported ; but the overplus of peoples gain , being generally laid up in silver , it will be brought home in silver ; and so our people will value it as much as any other , in this part of the world. the truth of the case in short is this . whenever we , by a losing trade , contract debts with our neighbours ; they will put a great value on our silver , and more money will be got by transporting silver than any thing can be sent : which comes about thus . suppose that , by an over-ballance of their trade ( whether by a sale of pepper , spices , and other east-india commodities , it matters not ) we have received great quantities of goods , within these two or three months , from h●lland , and sent but little thither ; so that the accounts ballanced between the inhabitants of england and the united provinces , we of england were a million in their debt ; what would follow from hence ? this : that these dutch creditors , desiring to have what is due to them , give order to their factors and correspondents here , to return it them . for enquiring , as we do , what are the effects of an over-ballance of trade , we must not suppose they invest their debts in commodities , and return their effects that way . a million then being to be returned from england to holland in money , every one seeks bills of exchange : but englishmen not having debts in holland to answer this million , or any the least part of it , bills are not to be got . this presently makes the exchange very high ; upon which the bankers , &c. who have the command of great quantities of money and bullion , send that away to holland in specie , and so take money here to pay it again there upon their bills at such a rate of exchange as gives them five , ten , fifteen , &c. per cent. profit ; and thus sometimes a 5 s. piece of our mill'd money may truely be said to be worth 5 s. 3 d. 4 d. 6 d. 9 d. in holland . and if this be the great value of silver in this part of the world , i easily grant it him . but this great value is to be remedied , not by the alteration of our mint , but by the regulation and ballance of our trade . for be your coin what it will , our neighbours , if they over-ballance us in trade , will not only have a great value for our silver , but get it too ; and there will be more to be got by exporting silver to them , than by any other thing can be sent . remarks . the alteration of the coins in spain and portugal are no way at all like this . for there they alter'd in denomination near half , to deceive those they paid , with paying those to whom they owed one ounce of silver , but half an ounce for it . but in the alteration here designed , to whoever an ounce of silver was owing , an ounce will be paid in this money ; it being here only designed , that an ounce of money should equal an ounce of silver in value , at home , as well as abroad , which now it does not . answer . in this paragraph the author confesses the alteration of the coin in spain and portugal was a cheat ; but the alteration here design'd , he says , is not : but the reason he gives for it is admirable ; viz. because they there alter'd in denomination near half , and here the denomination is alter'd but 5 per cent ; for so in truth it is , whatever be designed . as if 50 per cent were a cheat , but 5 per cent were not ; because perhaps less perceiveable . for the two things that are pretended to be done here by this new coinage , i fear will both fail , viz. 1. that to whom 〈◊〉 an ounce of silver is owing , an ounce 〈◊〉 silver shall be paid in this money . for when an ounce of silver is coin'd , as is proposed , into 5 s. 5 d. ( which is to make our money 5 per cent. higher than it is now ) i that am to receive an 100 l. per annum , fee farm rent ; shall i in this new money receive 105 l. or barely 100 l. ? the first i think will not be said . for if by law you have made it 100 l. 't is certain the tenant will pay me no more . if you do not mean that 400 crowns , or 2000 shillings of your new coin shall be an 100 l. but there must be 5 per cent , in tale , added to every 100 , you are at the charge of new coinage to no other purpose but to breed confusion . if i must receive 100 l , by tale , of this new money for my fee farm rent , 't is demonstration that i lose five ounces per cent of the silver was due to me . this a little lower he confesses in these words , that where a man has a rent-sec , that can never be more , this may somewhat affect it , but so very little , that it will scarce ever at all be perceived . this very little is 5 per cent. and if a man be cheated of that , so he perceives it not , it goes for nothing . but this loss will not affect only such rents as can never be more , but all payments whatsoever that are contracted for before this alteration of our money . 2. if it be true , what he affirms , that an ounce of money doth equal an ounce of silver in value abroad , but not at home ; then this part of the undertaking will also fail . for i deny that the stamp on our money does any more debase it here at home than abroad , or make the silver in our money not equal in value to the same weight of silver every where . the author would have done well to have made it out , and not left so great a paradox only to the credit of a single assertion . remarks . and for what is said in this bill to prevent exportation , relates only to the keeping in our coin , and bullion , and leaves all foreign to be exported still . answer . what the author means by our own and foreign bullion , will need some explication . remarks . there is now no such thing as payments made in weighty and mill'd money . answer . i believe there are very few in town , who do not very often receive a mill'd crown for 5 s. and a mill'd half crown for 2 s. 6 d. but he means i suppose in great and entire sums of mill'd money . but i ask , if all the clipp'd money were call'd in , whether then all the payments would not be in weighty money ; and that not being call'd in , whether if it be lighter than your new mill'd money , the new mill'd money will not be melted down as much as the old ; which i think the author there confesses , or else i understand him not . remark . nor will this any way interrupt trade ; for trade will find its own course ; the denomination of money in any country no way concerning that . answ. the denomination to a certain weight of money , in all countries , concerns trade ; and the alteration of that necessarily brings disturbance to it . remark . for if so be it occasions the coining more money , answ. he talks as if it would be the occasion of coining more money . out of what ? out of money already coin'd , or out of bullion ? for i would be glad to know where it is . remarks . it may be some gain to those that will venture to melt down the coin , but very small loss ( if any ) to those that shall be paid in the new : 't is not to be denied , but that where any man has a rent-sec , that can never be more , this may somewhat affect it ; but so very little , 't will scarce ever at all be perceived . ans. as much as it will be gain to melt down their coin , so much loss will it ●e to those who are paid in the new : 〈◊〉 5 per cent ● which , i suppose , is more than the author would be willing to lose , unless he get by it another way . rem . and if the alteration designed should have the effect of making our native commodities any way dearer , ans. here the author confesses , that proportionably as your money is raised , the price of other things will be raised too . but to make amends , he says , rem . it does at the same time make the land which produces them , of more than so much more in value . ans. this more than so much more in value , is more than our author , or any body else for him , will ever be able to make out . the price of things will always be estimated by the quantity of silver is given in exchange for them . and if you make your money less in weight , it must be made up in tale. this is all this great mystery of raising money , and raising land. for example , the mannor of blackacre would yesterday have yielded 100000 crowns , which , let us suppose , numero re●und● , to be ounces a piece of standard silver . to day your new coin comes in play , which is 5 per cent lighter . there 's your money raised . the land now at sale yields 105000 crowns , which is just the same 100000 ounces of standard silver . there 's the land raised . and is not this an admirable invention , for which the publick ought to be at charges for new coinage , and all your commerce put in disorder ? and then to recommend this invention , you are told , as a great secret , that , had not money , from time to time , been raised in its denomination , lands had not so risen too : which is to say , had not your money been made lighter , fewer pieces of it would have bought as much land as a greater number does now . rem . the loss of payments therespoken of , will , in no sort , be so great as if the parties to whom these debts are owing , were now bound to receive them in the money now passes , and then to melt the same down ; so at this they will have no cause to complain . ans. a very good argument ! the clippers have rob'd the publick of a good part of their money ( which men will , some time or other , find in the payments they receive ) and 't is desired the mint may have a liberty to be before-hand in it . they are told they will have no reason to complain at it , who suffer this loss ; because it is not so great as the other . the damage is already done to the publick , by clipping . where at last it will light , i cannot tell . but men who receive clip'd money , not being forced to melt it down , do not yet receive any loss by it . when clip'd money will no longer change for weighty , than those who have clip'd money in their hands , will find the loss of it . rem . 't will make the customs better paid , because there will be more money . ans. that there will be more money in tale , 't is possible : that there will be more money in weight and worth , the author ought to shew . and then , what-ever becomes of the customs , ( which i do not hear are unpaid now ) the king will lose in the excise above 30000 l. per annum . for in all taxes where so many pounds , shillings , or pence are determin'd by the law to be paid , there the king will lose 5 per cent. the author here , as in other places , gives a good reason for it . for , his majesty being to pay away this money by tale , as he received it , it will be to him no loss at all . as if my receiving my rents in full tale , but in money of undervalue 5 per cent , were not so much loss to me , because i was to pay it away again by tale. try it at 50 per cent. the odds only is , that one being greater than the other , would make more noise . but our author 's great refuge in this is , that it will not be perceived . remark . if all foreign commodities were to be purchased with this new species of money sent out ; we agree , that with 100 l. of it there could not be so much silver or other commodities bought , as with 100 l. in crown pieces as now coined ; because they would be heavier ; and all coin in any kingdom , but where 't is coined , only goes by weight ; and for the same weight of silver , the same every where still will be bought ; and so there will , with the same quantity of goods . and if those goods should cost 5 per cent more here in england than heretofore , an● yield but the same money ( we mean by the ounce abroad ) the same money brought ho●●●nd coined , will yield the importer 5 per cent more at the mint than it heretofore could do , and so no damage to the trader at all . answ. here truth forces from the author a confession of two things , which demonstrate the vanity and usele●nes● of the project . 1. that upon this c●ange of your coin , foreign goods will be raised . 2. your own goods will 〈◊〉 more 5 per cent. so that goods of all kind● being thereupon raised ; wherein con●●● the raising of your money , when an 〈◊〉 of standard silver , however 〈◊〉 ●tamped , or denominated , will buy 〈◊〉 more commodities than it did before ? this confession also shews the falshood of that dangerous supposition , that money , in the kingdom where it is coin'd , goes not by weight , i. e. is not valued by its weight . rem . 't is true , the owners of silver will find a good market for it , and no others will be damaged ; but , on the contrary , the making plenty of money will be an advantage to all . answ. i grant it true , that if your money were really raised , 5 per cent , the owners of silver would get so much by it , by bringing it to the mint to be coin'd . but since , as is confessed , commodities will ( upon this raising your money ) be raised to 5 per cent , this alteration will be an advantage to no body but the officers of the mint . rem . when standard silver was last raised at the mint , ( which it was , from 5 s to 5 s and 2 d the ounce , in the 43 d of eliz. ) and , for above forty years after , silver uncoin'd was not worth above 4 s 10 d the ounce , which occasioned much coining ; and of money , none in those days was exported : whereas silver now is worth but the very same 5 s and 2 d the ounce still at the mint , and is worth 5 s 4 d elsewhere . so that if this bill now with the lords does not happen to pass , there can never any silver be ever more coined at the mint ; and all the mill'd money will in a very little time more be destroyed . answ. the reason of so much money coin'd in queen elizabeth's time , and afterwards , was not the lessening your crown pieces from 480 to 462 gr . and so proportionably all the rest of your money , ( which is that the author calls , raising standard silver from 5 s to 5 s 2 d the ounce ) but from the over-ballance of your trade , bringing then in plenty of bullion , and keeping it here . how standard silver ( for if the author speaks of other silver , it is a fallacy ) should be worth it s own weight in standard silver at the mint , ( i. e. 5 s 2 d the ounce ) and be worth more than its own weight in standard silver , ( i. e. 5 s 4 d the ounce ) in lombard-street , is a paradox that no body , i think , will be able to comprehend , till it be better explain'd . it is time to give off coining , if the value of standard silver be lessened by it ; as really it is , if an ounce of coin'd standard silver will not exchange for an ounce of uncoin'd standard silver , but an ounce of coin'd standard silver will not exchange for an ounce of uncoin'd standard silver , unless you add 15 or 16 grains overplus to it : which is what the author would have taken upon his word , when he says , silver is worth five shillings four pence elsewhere . five shillings four pence of money coin'd at the mint , the author must allow to be at least 495 grains . an ounce is but 480 grains . how then an ounce of uncoin'd standard silver can be worth five shillings four pence , ( i. e. how 480 grains of uncoin'd standard silver can be worth 495 grains of the same standard silver , coin'd into money ) is unintelligible ; unless the coinage of our mint lessens the value of standard silver . sir , coin and interest are two things of so great moment to the publick , and of so great concernment in trade , that they ought , very accurately to be examin'd into , and very nicely weigh'd , upon any proposal of an alteration to be made in them . i pretend not to have treated of them here as they deserve . that must be the work of an abler hand . i have said something on th●se subjects , because you required it . and , i hope , the readiness of my obedience will excuse , to you , the faults i have committed , and assure you that i am , sir , your most humble servant . finis . interest mistaken, or, the holy cheat proving from the undeniable practises and positions of the presbyterians, that the design of that party is to enslave both king and people under the masque of religion : by way of observation upon a treatise, intitutled, the interest of england in the matter of religion, &c. / by roger l'estrange. l'estrange, roger, sir, 1616-1704. 1661 approx. 285 kb of xml-encoded text transcribed from 96 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2005-10 (eebo-tcp phase 1). a47873 wing l1262 estc r41427 31355330 ocm 31355330 110404 this keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the early english books online text creation partnership. this phase i text is available for reuse, according to the terms of creative commons 0 1.0 universal . the text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission. early english books online. (eebo-tcp ; phase 1, no. a47873) transcribed from: (early english books online ; image set 110404) images scanned from microfilm: (early english books, 1641-1700 ; 1744:15) interest mistaken, or, the holy cheat proving from the undeniable practises and positions of the presbyterians, that the design of that party is to enslave both king and people under the masque of religion : by way of observation upon a treatise, intitutled, the interest of england in the matter of religion, &c. / by roger l'estrange. l'estrange, roger, sir, 1616-1704. the second impression. [16], 173, [2] p. printed for henry brome ..., london : 1661. advertisement: p. [1]-[2] at end. imperfect: print show-through. reproduction of original in the british library. created by converting tcp files to tei p5 using tcp2tei.xsl, tei @ oxford. re-processed by university of nebraska-lincoln and northwestern, with changes to facilitate morpho-syntactic tagging. gap elements of known extent have been transformed into placeholder characters or elements to simplify the filling in of gaps by user contributors. eebo-tcp is a partnership between the universities of michigan and oxford and the publisher proquest to create accurately transcribed and encoded texts based on the image sets published by proquest via their early english books online (eebo) database (http://eebo.chadwyck.com). the general aim of eebo-tcp is to encode one copy (usually the first edition) of every monographic english-language title published between 1473 and 1700 available in eebo. eebo-tcp aimed to produce large quantities of textual data within the usual project restraints of time and funding, and therefore chose to create diplomatic transcriptions (as opposed to critical editions) with light-touch, mainly structural encoding based on the text encoding initiative (http://www.tei-c.org). the eebo-tcp project was divided into two phases. the 25,363 texts created during phase 1 of the project have been released into the public domain as of 1 january 2015. anyone can now take and use these texts for their own purposes, but we respectfully request that due credit and attribution is given to their original source. users should be aware of the process of creating the tcp texts, and therefore of any assumptions that can be made about the data. text selection was based on the new cambridge bibliography of english literature (ncbel). if an author (or for an anonymous work, the title) appears in ncbel, then their works are eligible for inclusion. selection was intended to range over a wide variety of subject areas, to reflect the true nature of the print record of the period. in general, first editions of a works in english were prioritized, although there are a number of works in other languages, notably latin and welsh, included and sometimes a second or later edition of a work was chosen if there was a compelling reason to do so. image sets were sent to external keying companies for transcription and basic encoding. quality assurance was then carried out by editorial teams in oxford and michigan. 5% (or 5 pages, whichever is the greater) of each text was proofread for accuracy and those which did not meet qa standards were returned to the keyers to be redone. after proofreading, the encoding was enhanced and/or corrected and characters marked as illegible were corrected where possible up to a limit of 100 instances per text. any remaining illegibles were encoded as <gap>s. understanding these processes should make clear that, while the overall quality of tcp data is very good, some errors will remain and some readable characters will be marked as illegible. users should bear in mind that in all likelihood such instances will never have been looked at by a tcp editor. the texts were encoded and linked to page images in accordance with level 4 of the tei in libraries guidelines. copies of the texts have been issued variously as sgml (tcp schema; ascii text with mnemonic sdata character entities); displayable xml (tcp schema; characters represented either as utf-8 unicode or text strings within braces); or lossless xml (tei p5, characters represented either as utf-8 unicode or tei g elements). keying and markup guidelines are available at the text creation partnership web site . eng corbet, john, 1620-1680. -interest of england in the matter of religion. interest of england in the matter of religion. presbyterianism -controversial literature. church and state -england. great britain -politics and government -1660-1688. 2003-11 tcp assigned for keying and markup 2003-12 spi global keyed and coded from proquest page images 2005-01 rachel losh sampled and proofread 2005-01 rachel losh text and markup reviewed and edited 2005-04 pfs batch review (qc) and xml conversion interest mistaken , or the holy cheat ; proving from the undeniable practises and positions of the presbyterians , that the design of that party is to enslave both king and people under the masque of religion . by way of observation upon a treatise , intituled , the interest of england in the matter of religion , &c. by roger l'estrange . the second impression . aug. de civ . dei. nullo modo his artibus placatur divina majestas , quibus humana dignitas inquinatur . london , printed for henry brome at the gun in ivy-lane . 1661. to the honourable hovse of commons assembled in parliament . most honourable , to begg your pardon , or protection , were to suppose a fault , or hazzard , but in this dedication finding neither , i shall waive that formality : humbly submitting what i have to say ; my reasons , and my self , to your authority , and wisdom , without more prologue , or apology . there is a faction which under the note of presbyterian , seems much concerned to stickle against bishops , & church-rites , on the behalf of tender consciences . their writings and opinions , are with great freedom , craft , and diligence , dispers'd throughout the nation ; to the great scandal of the true church , and the encouragement of those of the revolt . but this is yet the least part of the mischief , or in effect of their design : their ayme being to tumultuate the people , and make a partie against the civil power . indeed their pamphlets wear the face of church-disputes , and modells ; but he that reads them through , and marques them narrowly , shall find the king's authority the question . that the late war against the king was lawfull ; is a position common to them all , and this they publiquely maintain , as the main basis of the cause . by which assertion , they cast the bloud , and guilt upon his majestie ; make his adhaerents traitors : place the supreme authoritie in the two houses : subject the law to an ordinance : the government , to a faction : and animate the schismatiques to serve his majestie in beeing as they did his father . this is the drift of their seditious libells , and of their projects too ; if any judgement may be made upon their strict conformity of argument , and methode , to those that first embroyl'd us . how farr this matter may require your care , becomes not me to meddle : i thought it might be worth your honours knowledge , and led by an opinion of my duty , this state of the affair , ( such as it is ) i doe most humbly lay before you . his majesty had no sooner set foot upon english ground , but swarms of pestilent papers were in a readiness to enterteyn him . some of the sharpest of them , i delivered to several members of that session , with the stationers name for whom they were printed , ( smith , at the bible in cornhill , croftons agent ) but all too little to suppress them . one passage is this that follows ; speaking of the limited power of kings — this may serve to justify the proceedings of this kingdom against the late king , who in a hostile way set himself to overthrow religion , parliaments , lawes and liberties . hand in hand with this pamphlet , came forth smectymnuus ; reviv'd , and recommended by mr. manton : and since that time , some hundreds more of the same stamp , whose common business 't is , by affronting of the law , and flattering of the rabble to cast all back into confusi●n . among the many other actours of religion , i find not any man playes his part better , then the author of that treatise which hath extorted this : who indeed , abuses the people in very good terms . some hasty observations i have pass'd upon him , in favour of the easie , and deceivable vulgar ; which prailties i submit to your honours charity ; but the main equitie of the cause , i hope , will stand the test of your severest justice : for doubtlesse much is due to the late king's honour , as well as to his blood. and somewhat ( with submission to your wisdoms ) may be allow'd to his partie : at least sufficient to protect them from popular contempt , and the infamous lash of every daring libell . i dare not trust my self further with my own thoughts , and yet i take them to be such as very well consist with the duty of your honours most obedient and humble servant , roger l'estrange . to the good people of england . the cm mon good is the common pretence of all seditious combinations : and it is no new thing for a crafty faction to impose upon a simple multitude , empty appearances , for truths and reason . but our reformers scorn to stop at this dull , general method of confusion . the law of god must be subjected as well as that of the nation ; we must call treason , loyalty , and commit murther as a point of conscience . no lesse than this is hinted in the presbyterians justification of the scotish league and quarrel : nor have they any other aim , than by procuring an allowance of that war , to make way to another . to this end , they disperse their poysonous infusions into all quarters of the kingdom , under those very forms of piety , and tenderness , by which they first betrayed us : and by those very means do they now prosecute afresh their first intentions . that is , they labour to promote the cause , by scandalous and rank invectives , against the church , and stirring up of tumults to reform it : by a loud pharisaical ostentation of their own holyness , & a sour churlish censure of all others : by sharp and sawcie aspersions upon the royal party , and by reflections yet more bitter and audacious , upon his sacred majesty , and his murtherd father . to see these libells passe with freedom , and impunitie , as if they were authorized : and to observe what foul mistakes are grounded upon these grosse allowances , to the kings disadvantage , and all without controll or confutation . this , and no other reason ( so god blesse me ) that is ; of private passion , or animosity of temper ) hath drawn this honest folly from me . i reckon it my duty to my prince and country , to my own honour , and to the oath i have taken , where ever i find a publique enemy to discover him : and being thus commissioned , both by authority and conscience , i proceed . the benefit of this treatise is directed to the people , and the design of it is onely to lay open the presbyterian juggle , that in one age they be not twice deluded by the same imposture . my arguments are drawn from their own practises , and positions : from presidents of former times ; ( cartwright and his disciples ) from what hath passed within our own experience ; from what these very men have done , and from the very logique of their own writings , what they professe , they do intend to doe . as the delusion is apparent , so is the justice of discoursing it . can it be thought , that by the act of pardon , his majestie ever meant to subject all the sober and legal interests of the nation , to be worried by a faction ? who of the royal party charges them ? or if they did , what has the law done to offend them ? or say the law be sharp against them , his majesties unparalell'd mercy has by his royal grace taken off the edge of it ; hazzarding himself to preserve these unthankfull people , which are now practising upon that authoritie , that saved them . and i beseech you what is the goodly subject of the controversie ? the presbyterian discipline forsooth ; and ceremonies of mystical and humane institution . touching the former ; st. augustine tells us , that aërius turn'd heretique upon the misse of a bishopprick . ( the first assertor of church-parity ) i am affraid some of our reverend clergy are sick of his disease ; for their design is not so much to convert bishops into presbyters , as to make every presbyter a bishop . and then for ceremonies ; they teaz and chafe the common-people into a pettish scruple , that would be well and quiet enough without them . they make their consciences like skittish jades , that boggle at their own shadowes , and start into a precipice to avoid a feather . they tell us too of number , and press their importunities in the name of many thousands of the good people of the nation ; so did the kings insolent judges , and with as much truth the one as the other . let it be further noted , that in this case , the factious and schismatical clergy are but ( with reverence ) bawds to a state-faction . a tumult for religion , is within one step of rebellion . nor do they only shape their loose opinions to their lewd purposes , but by all secret arts and practises , they form their parties . but here i am confin'd . — all i design is only a fit caution to all well-meaning subjects , not to believe their eares against their reason . if they can adde one syllable , of weight , to what they have already promised , and broken , i 'le give my self up to the partie . this is not yet to cast a general blot upon all persons of that judgement , nor to excite any unquiet thoughts toward the rest : but only to present a modest , and an usefull warning to the people . so far am i from a desire to move any distemper , that i do positively affirm , should the king ( which is impossible ) pick out of all his subjects those very persons , who upon twentie years experience , have proved through all extremities how much they love his cause and person , above their lives and fortunes : should , i say , these be pick'd out by his majestie , and marqu'd for slaves to those that with an equal zeal and steadynesse have opposed him ; our dutie were the same yet . severitie , and kindnesse may move us as men , but not as subjects : obedience to kings being a divine precept , and not subjected to those accidents which work upon our passions . nor shall this sense of my own clearness betray me yet to a surprize ; for i fore-see a thousand mischiefs may befall me , and all which either private malice , or open and bold prejudice can cast upon me ; i am provided for . to those of the presbyterian perswasion that truly love the king , i bear a more then ordinarie respect , because it is a more then ordinarie virtue , and for the rest , i care not . i am not now to learn the temper of the rigid presbyterians . they did me once the honour to condemn me , almost at mid-night , by a pack'd committee , and without a hearing ; well-nigh four years they kept me in newgate upon that account . this was a pretty tast of their good nature . i do not now complain , but i confesse , it would have pleas'd me as well if the bishop that christens still by the directory , had chosen some other chancellour , instead of my judge advocate : — but i desire only to make a sober use of these mistakes ; the king knowes nothing of them . god preserve his majesty , convert his enemies , & comfort his friends . farewell . the holy cheat : proving , from the undeniable practices and positions of the presbyterians , that the design of that party is to enslave both king and people , under the masque of religion , &c. if the authour of the interest of england , &c. had meant fairly to the question , he would as well have told us the good of bishops , and the ill of presbyters , as he hath done the contrary , and never have concluded for , or against either , from the best actions of the one , and the worst of the other . at least , a man would think this partiality of method , might content him without the further service of those little arts he uses , to aid , and recommend his undertaking . the present state of things , he represents quite other then it is : and raises thence a political expedience of doing this , or that , — of linking interests , — never considering , that he himself creates that interest , and gives affairs the face of that expedience . page the 16. he laies his ground-work , in these following words . among the various dis-agreeing parties within this kingdom , which seem to render it an indigested mass of people ; two main ones appear above the rest , of so large an interest , that if by any means they might become no more twain , but one ; they would take in , and carry along the whole stream and strength of the nation . and these two are the episcopal and presbyterian parties , each of them highly laying claim to the protestant religion . and undoubtedly whilst these two remain divided , the kingdom of england , and the protestant religion is divided against it self . this dis-union is removed , either by the abolition of one party , or by the coalition of both into one . the former , if supposed possible , cannot be accomplished , but by violent & perillous ways and means . the latter is brought to pass by accommodation , or mutual yielding . moreover , there is a third way imaginable , toleration indulged to the weaker side . in which of these ways lies the true interest of the king and kingdom , is the greatcase of the time , and the subject of this discourse , which presumes not to inform his majesty , but in subordination unto his declared moderation and condescention , endeavours , by shewing things as they are , to convince and perswade interessed persons , that the pacification begun for this interim may be entire and perfect , and fully setled for perpetual unity . observation let it be here observed , first , what the difference is ; next , betwixt whom ; in the third place , the danger of it ; and lastly , the expedient to remove it . it seems , the episcopal , and presbyterian parties , united in religion , cannot agree yet about discipline : and while these two remain divided , the publick is in danger . from hence results the interest of mutual yielding — ( his coalition of both parties into one ) upon which hinge moves the whole frame of his design ; and in two pages , he gives the presbyter possession of his claim , deciding with exceeding ease , the case of king and kingdom . opinion is a great mistress : for that which he so magisterially lays down and challenges , appears to me mis-stated , and worse managed . i must confess , his reduction of all other interests under episcopal and presbyterian , is , in some sense , no ill dichotomy , that is , intended of the two main parties , whereof , the one's against the law , the other for it : but why the single presbyterian should be esteemed the ballance of the nation , i cannot comprehend . if they are so , they should do well to cast their cause upon a popular vote , and try the issue by the poll. for quiet sake , no matter , many or few , there may be equity where there wants number . we 'l rather see in point of right what 't is they insist upon : which , if exemption from episcopal authority , in things indifferent , and of humane institution . we must plead judgment of discretion too , as well as they : a freedom , and capacity to distinguish betwixt a scandal given and taken ; betwixt a dis-conformity proceeding from conscience , and from passion ; where the dissent proceeds from conscience , a toleration clears that scruple : but our good peoples liberty consists in burthening others , as well as freeing themselves , and that 's intolerable . how many strange indecencies are here , one upon the neck of another i first , here 's the minor part imposing upon the major : secondly , a novel , and vulgar imagination , bearing down an apostolical institution : thirdly , a private opinion , contesting with a solemn , and publike sanction : and finally , the subject of all this earnestnesse , in their own phrase , is but a very accommodable difference . from what i have said , i am perswaded that severity to the pertinacious presbyter , is the true interest of this nation , allowing yet indulgence to the conscientious . well , but our authour tells us , that abolition if possible , is perillous , and toleration only an imaginary remedy . is not this to intimate that the party makes less conscience of a tumult , than of a ceremony : and to argue the necessity of complying , from the danger of refusing ? what would these people do if they had power , that are so bold without it ! and yet our politician makes it the kings interest to close with them . he means perchance , according to the covenant : the coalition , there , of all schisms , and heresies into one interest , was of great reason , and important service to the commune work : but we are now advising how to settle not to disjoynt a government , and to incorporate dis-agreements , were to begin upon a principle of confusion . as the case stands with us , in my weak judgement , persons should rather be indulg'd , than parties . my reason is this , some individuals of that perswasion , have done his majesty some service , but ( to the best of my remembrance ) the entire party , never any . yet one reflexion more . allow these people all their askings , in what concerns their discipline , will they rest quiet there , without a further hankering after more ? ( the legislative power perhaps ; the militia ; — or some such trifle ) i am the more suspitious , because i do not well remember , where ever that party was satisfied with less than all. nor need i look far back for instances to justifie my fears ; but having in some measure hitherto discovered his foundation , we 'l forward now , and see what work he makes upon this sandy bottom , taking his title-page in my way , for , to my thinking , he stumbles at the threshold . — it runs thus . the interest of england in the matter of religion , unfolded in the solution of these three questions . i. qu. vvhether the presbyterian party should in justice or reason of state be rejected and depressed , or protected and encouraged . ii. qu. vvhether the presbyterian party may be protected and encouraged , and the episcopal not deserted nor disobliged . iii. qu. whether the upholding of both parties by a just and equal accommodation , be not in it self more desirable and more agreeable to the state of england , then the absolute exalting of the one party , and the total subversion of the other . written by j. c. observation i would fain know what is meant by , the matter of religion , as it stands here related to civil interest ? doctrine it cannot be , for that were to advise a yielding upon a principle of policy , in opposition to a rule of conscience : subjecting interest of religion , which is eternal happiness , to reason of state , which regards but temporal convenience . if it be discipline , what 's that to the interest of england ? our settlement depends upon a due obedience to the establish'd law ; not the encouraging of froward humors , by an audacious and mis-govern'd zeal , under pretext of conscience to affront it . let authority reform , and private persons either obey , or suffer ; we are to answer for our own faults , not those of the government . and in fine , if the hill will not come to mahomet , let mahomet go to the hill. after a pleasant breviate of the story of our late troubles , handsomely penn'd indeed ) in his tenth page he takes his biass . at length ( says he ) a full tide of concurring accidents carries him ( the duke of albemarle , then general ) to a closure with the sober part of the parliamentary party , who from first to last intended onely a reformation , and due regulation of things in church and state , but abhorred the thought of destroying the king , or changing the fundamental laws of the kingdom . observation i thought the act of pardon and oblivion had quieted all animosities , and silenc'd all discourses of this quality ; but 't is , it seems , the interest of england in the matter of religion , to keep the quarrel waking ; and by asserting the proceedings of the two houses in the late war , to engage this king within the danger of his fathers president . to be as free with the authour , as he is with his majesty , i 'le put his meaning in a little plainer english. beside the grand division of the nation into a royal and a popular party ; that party which he here calls parliamentary , is again split ; and under this subdivision are comprised , those which did actually destroy the king ; and those which by good fortune , did it not . ( presbyterians , and independents . ) the sober part , ( meaning the presbyterian ) he justifies from first to last , even to their very intentions . ( i must tread warily , for i am here upon a narrow and a slippery path . ) not to dispute the gentlemans intuitive knowledge ; we 'l rather modestly believe that they mistook their way , then he , their meaning : for certainly , the murther of the king , was not the onely unlawful violence acted upon that sacred person , and he that stops there , does as much as nothing . i would not touch upon this subject , were i not bound by oath , and duty , to discharge my soul , in what concerns the honor , and the safety of my prince . can the first cause asserted by both houses , in opposition to his late majesty , be justifi'd , and not the king condemn'd ? and is not the honor and safety of his majesty that now is , concern'd in these indignities upon his murther'd father ? what was then lawful , is so still : and he that but implicitly charges the last king , strikes at this. the text will bear no other sense without a torture . but i shall by-and-by , compare him with himself . in the mean while we may explain one presbyterian by another . douglas , in 1651. preach'd the kings coronation-sermon . which since his majesties return , is over and over again reprinted . a king ( says he ) abusing his power , to the overthrow of religion , laws , and liberties , which are the very fundamentals of this contract and covenant , may be controlled and opposed ; and if he set himself to overthrow all these by arms , then they who have power , as the estates of a land , may and ought to resist by arms ; because he doth , by that opposition , break the very bonds , and overthroweth all the essentials of this contract and covenant . this may ☜ serve to justifie the proceedings of this kingdom against the late king , who in an hostile way set himself to overthrow religion , parliaments , laws and liberties . i think this needs no comment , — about the same time , smectymnuus was revived by mr. manton , ( a most auspicious welcome doubtless to his majesty ) wherein five champions of the cause take up the cudgels against one bishop , on the behalf of scandalous pamphlets , and tumultuary petitions against episcopacy . this is the naked truth , what ever the jolly priest may tell the reader , of the * faction against which they dealt . five orthodox divines , he says , were the authors . four of the five i shall not mention , the fifth was marshal , of whose divinity , a taste ; that by the sweet agreement , we may the better judge of mr. manton's . in a letter printed 1643. arguing for the authority of the two houses , page 14. thus. let every soul in england be subject to king and parliament , for they are the higher powers ordained unto you of god ; whosoever therefore resisteth king and parliament , resisteth the ordinance of god ; and they that resist shall receive to themselves damnation . the man was no conjurer , yet he had wit enough , when presbytery went down , to court the rising interest ; and ' though the common-prayer was an abomination , to marry his daughter by it , for fear of after-claps . but i suppose 't was huddl'd up , as 't is in mr. manton's church , that no man might be able to make oath 't was not the directory . if the case had been concerning * the allowance of christian burial to a gentleman that was quartered for his loyalty . or to determine in the great point of the late kings death , ( upon an anniversary fast ) whether or no 't was murther : truly considering the potent arguments brought on both sides , 't is possible that mr. marshal would have contented himself ( as well as his neighbours ) barely to put the case , and leave the point at last undecided to his auditory . not to spend time , and paper needlesly , the whole stream of the disciplinarians runs this way : onely perhaps more or less bold , and open , according to the present strength , or weakness of the faction . but to return : can any thing be more gentle , then a reformation , and due regulation of things in church and state ? ( words smoother than oyle , yet are they very swords . ) first , to reform , and regulate , belongs to the supreme magistrate ; if they intended that , they were to blame . now to take it in a qualifi'd and softer sense ; 't was a due regulation they intended . to put this general notion in more intelligible terms ; upon this point depends no less then all that 's dear to every honest man. the dignity of the king , the liberty of the subject , the freedome of parliaments , and the honor of the nation . god knows my thoughts , i do not envy any man , either the benefit of his majesty's mercy , or the blessing of his favour , that hath the grace at last not to abuse it . i look upon his royal act of pardon with reverence ; and upon every soul within that pale as in a sanctuary . but yet i do not understand a pardon for one rebellion , to be a dispensation for another ; nor how the argument lies from fact to right . under these two words , due regulation ; thus much is comprehended , ( waiving less differences and greater . ) 1. the transferring of the power of chusing great officers , and ministers of state ; from the king to the two houses . 2. all matters of state in the interval of parliaments must be debated , and concluded by a counsel so chosen , and in number not above twenty five , nor under fifteen ; and no publick act esteemed of any validity , as proceeding from the royal authority , unless it be done by the advice and consent of the major part of that counsel ; attested under their hands . and these too sworn to the sense of both houses . 3. the lords and commons must be intrusted with the militia . 4. his majesty may appoint , but the two houses , or the counsel ( in such manner as aforesaid ) must approve of all governors of forts , and castles . lastly , no peers hereafter made , must sit , or vote in parliament , unless admitted thereunto by the consent of both houses . upon these terms ; his majesty shall be supported , in honor , and plenty ; by his most humble and faithful subjects , who have in their thoughts and desires nothing more precious , ( next to the honor and immediate service of god ) than their just , and faithful performance of their duty to the king , and kingdom . this is the due regulation they intended : ( for sure they meant what they proposed , to our late soveraign . i speak not this , of persons , but of the gross of the party ; nor to reproach that neither , but to remove a scandal from the ashes of that blessed martyr , and to direct a reverence towards his successor . what provocation have these restless people , now to revive this question : but an unruly impotency of passion against the government ? this is their way . in generals , they justifie from first to last , the presbyterians cause . the multitude , they look into particulars : and from those injuries which the late king suffered , draw inferences dis-honourable , and dangerous to this . in the next periode , me-thinks he falls upon a non-sequitur . the re-admission of the secluded members , ( he says ) did necessarily draw after it , the restoring of king , lords , and commons , according to the antient constitution . not necessarily ( under favour ) according to the antient constitution : ( i will not say nor probably : but ) there were two shrewd blocks cast in the way . the first , in the militia ; where no commissionated officer was to act , that should not first acknowledge in these words , viz. i do acknowledge and declare , that the warre undertaken by both houses of parliament in their defence against the forces raised in the name of the late king , was just and lawful ; and that magistracy and ministery , are the ordinances of god. the second , was in the exclusion of the royal party from the next choice , as followeth . resolved , that all and every person who have advised , or voluntarily aided , abeited , or assisted , in any war against the parliament ( since the first day of january 1641. ) his or their sons , unless he or they have since manifested their good affections to this parliament , shall be uncapable to be elected to serve as members of the next parliament . now how a choice thus limited in the house , and principled in the field , should necessarily set us right , does not to me appear ? perhaps it was the most the time would bear : but god forbid , that declaration charging the guilt , and blood of the late war upon the king , should stand upon record to future generations . who ever affirms that war was lawful , does beyond question meditate another ; not to say more than needs , it blasts the memory of the late king , and upon the king that now is , it reflects many mischiefs , subjecting both his dignity and person , to his fathers hazards . it administers argument for a new war ; and shakes the very foundation of royalty . grant that , the act of oblivion is on the wrong side ; if the king was in fault , the presbyterians must grant the pardon . from the clear reason of the matter in it self , and from the obvious consequences ; beside that justice which both king and people owe to the ashes of a father and a soveraign , it seems to me of high concern , to counter-state that declaration , and place the militia of this nation now in such hands , as will acknowledge the late kings quarrel was defensive . i am the bolder in this particular , because i find the faction pressing beyond both modesty and reason , upon this bottom . where majesty it self is affronted , it were a second injury to allow the servant better quarter than the master . but they are very exact and careful in this particular : as will appear in what follows . after a dreadful earthquake , shaking all the powers of the kingdom , and over-turning the very foundations , and after a new frame of things erected standing for divers years , and seemingly stated for perpetuity , the regal family and government is raised up again , not by the power or policy of that party , who fought under the banner of his late majesty in the wars , between him and both houses of parliament ; but by the restless desire of the nation , and the vigorous actings of the city of london , with the concurrence of the secluded members of the long parliament , in conjunction with that renowned person , who then held the power of the sword. let it be noted here , that ( by his confession ) the war was between the king and both houses of parliament . now to that party who fought under the banner of his late majesty . ( whom he might have spared for the general 's sake . ) truly , considering what havock hath been made of them , by slaughters , extrajudicial sentences , plunders , sequestrations , imprisonments , banishments ; shipping them away into plantations , &c. — and this for twenty years continuance . 't is no great wonder to find some abatement of their power . but to affirm that they contributed nothing to his majesties restauration , is very unkind , and something rash. the nation did , ( he says ) the city of london , and the secluded members of the long parliament ; but not that party . ( a pleasant and phantastical dis-junction . ) this way of barely affirming , and denying ; crying one party up , and the other down , and proving nothing , is neither mannerly , nor prudent . how comes this man of metaphysical inspection , that reads the very thoughts of the presbyterians , and seems so well enformed in all the actings of the royal party : how comes he by this wondrous insight and intelligence ? does he not find that all he says is nothing , unless he can see things invisible , and prove negatives ? is this the work of the spirit of pacification ? or will he tell us , in the holy dialect , that 't is the enmity betwixt the seed of the woman , and the seed of the serpent ? so far were we , ( for i write my self of that party ) from this unfriendly and unchristian temper of dis-uniting , that we declared unanimously against it , binding our selves by all that 's sacred , to an eternal union with all parties , in order to the restauration of his majesty , all differences apart ; of what degree or quality soever . in this , we had an eye to the king's interest , and to the nation 's ; for it referred both to his majesty's return , and to a lasting peace ; the former being facilitated by that conjunction of interests ; and the latter , provided for by a conciliation of affections , to be wrought by suppressing all motions toward revenge in the one party , and the fears of it in the other . it had been good manners to have met us half way ; but truly high discretion , as well as common equity , to close with us , and entertain the offer . but far from this , we do not onely get not one good word , but many a bad one : such , as those people that will never leave the king , are to expect from such as do not love him. our adversary talks much of the gospel . is it a gospel-precept , to render evil for good ▪ what i have shewed already , that the kings party did , amounts to somewhat more than nothing . we 'l see a little further , allowing yet to all that acted in that work their share of glory . the duke of albemarle was the leading card , then in the head of an army , better dispos'd to his command , than design : and to him the honest part of the city and nation were no ill seconds . but till he had tasted and tri'd them , he did well to walk warily : and rather take the middle and safer way , of gratifying all interests then on foot , than the more positive , and hazardous , of disobliging any two parties , in favour of the third . for there were then three several interests in play : the king 's , the presbyterian's , and the phanatique's : the royal party press'd for a free choice and convention , without prelimination . the presbyterians urg'd a re-admission of the secluded members . the phanatiques , they were for filling up the house , according to such qualifications as the rump should resolve upon . the course the general steer'd was this ; — the rump continued ; the secluded members returned ; and the royallists were satisfied with the assurance of a new choice soon after . his excellence acting in this affair rather as a conciliator , than a party , and in order to a settlement , giving things the best consistency they would then bear . but had the antient stock of royallists no hand at all in this procurement ? it never came to blows , so that the matter rests upon the effects of policy and counsel ; whereof our undertaker cannot give any absolute account ; nor shall we in our just apology , exalt our selves , and cry , we brought the king in . that 's presbyterian language . we did not drive him out , we 'l say ; and that we joyn'd with many thousands , as honest as our selves , in duty to restore him . whether there was place for action , and to do the king a service that way , we never articled for offices or rewards , but without further care of interest , persu'd our duties . in fine the loyal part of the nation was animated by the same soul , joyn'd stocks , and counsels : and many thousands of brave fellows that never saw the king , were forward and ambitious to die for him . i could say what was undertaken by the old royal party , particularly , in hewson's scuffle , ( and indeed where not ) but that it casts a slur upon some of his majesty's new friends . this however , those lads of the city , that would have done the work without more ado , had they not been muzzl'd by some of their mungrel magistrates , that din'd with the mayor , and supp'd with the committee of safety : those honest people will , if need be , bear witness for us , and in like manner the whole nation , that by action , counsel , writing , we did all that was possible in the business . neither does what i have delivered in defence of the royal party , disagree with his majesty's testimony of the other , in his gracious speech to the house of peers for hastning the act of indempnity : which yet our author cites against us . my lords , if you do not joyn with me in extinguishing those fears , which keep mens hearts awake , and apprehensive of safety and security , you keep me from performing my promise , which if i had not made , i am perswaded that neither i nor you had been now here : i pray you let vs not deceive those who brought vs , or permitted vs to come together . observation the king does not there say so much who brought him in , as who permitted his restoring ; implying , that he was fain to condition for that too ; but withal , a great earnestness to perform his promise . had but this gentleman considered as well what the king said at the passing of the indempnity , as at the hastning of it , this wrangle would have been saved ; i 'l do him the service to mind him of it . i do very willingly pardon all that is pardoned by this act of indempnity , to that time which is mentioned in the bill . nay , i will tell you , that from that time to this day , i will not use great severity , except in such cases where the malice is notorious , and the publick peace exceedingly concern'd . but for the time to come , the same discretion and conscience which disposed me to the clemency i have express'd , which is most agreeable to my nature , will oblige me to all rigour and severity , how contrary soever it be to my nature , towards those who shall not now acquiesce , but continue to manifest their sedition and dislike of the government , either in actions or words . and i must conjure you all ( my lords and gentlemen ) to concur with me in this just and necessary severity ; and that you will in your several stations , be so jealous of the publick peace , and of my particular honor , that you will cause exemplary justice to be done upon those who are guilty of seditious speeches or writings , as well as those ☜ who break out into seditious actions : and that you will believe those who delight in reproaching and traducing my person , not to be well affected to you and the publick peace . never king valued himself more upon the affections of his people , than i do ; nor do i know a better way to make my self sure of your affections , than by being just and kind to you all ; and whilst i am so , i pray let the world see , that i am possessed of your affections . thus far the ground-work , now the goodly structure . his majesty thus brought back to a willing and free-spirited people , by their own act , beholds his undoubted interest set forth to his hand , and made plain before him ; which is no other , than a well-tempered and composed state of affairs , both religious and civil , in all his dominions , by the abolishing of former differences , and the reconciling of all reconcileable parties ; and especially of those grand parties , which ( if made one ) do upon the matter carry the whole nation . and this his majesties wisdom hath already observed , in that excellent proclamation against vitious , debauched , and prophane persons , in these words , [ that the reconciliation and union of hearts and affections , can onely , with god's blessing , make us rejoyce in each other , and keep our enemies from rejoycing . ] and this is the earnest expectation and hope of the religious , and well affected to the publick tranquillity , that the king , our supreme head and governor , whose gracious disposition doth not suffer him to cleave to any divided part of his subjects , and to reject others that are alike loyal , will , as a common father , protect and cherish all those that are found capable and worthy , and become our great moderator by his authority and wisdom , to lessen differences , and allay animosities , between dissenting brethren , which already agree in the main points of religion . having hitherto asserted , that those who fought under the late king's banner , were not his majesty's friends ; and that those who fought against it , ever were ; he proceeds now to a conclusion suitable to his premises , and states the interest of the king in favour of that voluntary mistake : directing an accord betwixt all reconcilable parties , and an indulgence toward all those that are found capable , and worthy . in both ( and in all ) cases , the presbyterian himself must be the judge : and then we know what will become of royallists and bishops . the kings friends have ever had the honor to be divided ( by these people ) into persons popishly affected , evil counsellors , and loose livers ; and it is evident , that they design , under these limitations of reconcilable , capable , and worthy , to cast all such as conscientiously , and frankly adhere to monarchy , and episcopacy , out of the terms of their pretended pacification . all those that they find capable and worthy , and esteem reconcilable , shall be admitted . now to the question . 1. quest. whether in justice or reason of state the presbyterian party should be rejected and depressed , or protected and encouraged ? observation it would be first agreed what 's meant by the presbyterian party : we 'l weigh the justice and reason of the proposition after . his own remarque upon it is not amiss . as concerning their true character , the notation of the name whereby they are called , is both too shallow , and too narrow for it . the word presbyterian hath not sufficient depth to go to the root of the matter , nor breadth sufficient to comprehend this sort of men . that form of ecclesiastical government by parochial and classical presbyteries , provincial and national assemblies , is remote enough from their main cause , and those firm bonds that make them eternally one , in respect whereof many that approve a regulated episcopacy , will be found of their number . observation 't is truly and well said . their cause is not the form , but the exercise of government : for they like well enough to have that power themselves , which they condemn in others . nor do i doubt but that many of them approve a regulated episcopacy ; that is , a presbyter in a bishop's seat , where the office appears regulated by the person , as 't is in a regulated monarchy ; where the king 's subject to the law , and the law to the two houses . but i condemn not all , that wear that character . the wise , and honest few of that denomination , who keep themselves within the terms of duty , and the question ; such as can talk of the church , without disturbing the state ; and debate their private opinions , without giving publick scandal : for these , i have much charity , and reverence , and wish as great a tenderness toward them , as they themselves desire . but where i see a bold seditious faction , bidding defiance to the civil magistrate under the churches colours : i find not any thing so sacred in the name of presbyterian , as to protect a turbulent party assuming that appellation . it will be urg'd , that they do as little justifie the seditious , as i condemn the sober presbyterian . but to agree that point , i 'l prove , that the same party , for whom they plead , and against whom i engage , are no less enemies to the king , and people , than to bishops : and , which is more , from their own practises and positions , i 'l make it good . yet one would hardly guess this from their following character . as concerning their main and rooted principles , they admire and magnifie the holy scriptures , and take them for the absolute perfect rule of faith and life , without the supplement of ecclesiastical tradition ; yet they deny not due respect and reverence to venerable antiquity . they assert the study and knowledge of the scriptures , to be the duty and priviledge of all christians , that according to their several capacities , being skilful in the word of righteousness , they may discern between good and evil , and being filled with all goodness , may be able to exhort and admonish one another : yet they acknowledge the necessity of a standing gospel-ministery , and receive the directive authority of the church , not with implicite faith , but the judgment of discretion : they hold the teaching of the spirit necessary , to the saving knowledge of christ : yet they do not hold that the spirit bringeth new revelations , but that he opens the eyes of the understanding to discern what is of old revealed in the written word : they exalt divine ordinances , but debase humane inventions in gods worship , particularly ceremonies properly religious , and of instituted mystical signification : yet they allow the natural expressions of reverence and devotion , as kneeling , and lifting up of the hands and eyes in prayer ; as also of those meer circumstances of decency and order , the omission whereof would make the service of god either undecent , or less decent . as they worship god in the spirit , according to the simplicity of gospel institutions , so they rejoyce in christ jesus , having no confidence in a legal righteousness , but desire to be found in him , who is made unto us rigteousness by gracious imputation : yet withal they affirm constantly , that good works of piety towards god , and of justice and charity towards men , are necessary to salvation . their doctrine bears full conformity with that of the reformed churches , held forth in their publick confessions , and particularly with that of the church of england , in the nine and thirty articles , onely one or two passages peradventure excepted , so far as they may import the asserting of prelacy , and human mystical ceremonies . they insist much on the necessity of regeneration , and therein lay the ground-work for the practise of godliness . they press upon themselves and others the severe exercise , not of a popish , outside , formal , but a spiritual and real mortification , and self-denyal , according to the power of christianity . they are strict observers of the lords day , and constant in family prayer . they abstain from oathes , yea , petty oathes , and the irreverent usage of gods name in common discourse ; and , in a word , they are sober , just , and circumspect in their whole behaviour . such is the temper and constitution of this party , which in its full latitude lies in the middle between those that affect a ceremonial worship , and the heighth of hierarchical government on the one hand , and those that reject an ordained ministery , and setled church-order , and regular vnity on the other hand . observation here is much said , and little proved ; onely a pharisaical story , of what they are not , and what they are ; that they are not as other men are , and their bare word for all . the tale is well enough told to catch the silly vulgar , that look no further then appearances : but to a serious person , how gross , and palpable is the imposture ! in the main points of doctrine they fully agree with the nine and thirty articles : and 't is but peradventure , that they differ , in one or two passages , so far as they may import the asserting of prelacy , and humane mystical ceremonies . ] behold the mighty subject of an holy war ; the goodly idol , to which we have sacrific'd so much christian blood . can any man imagine this the true and conscientious reason of the quarrel ? or that the middle way our presbyter steers , betwixt phanaticism and popery , is the just measure of the case : but hear him on , and he 'l tell ye , the party is numerous as well as godly . vvithin these extensive limits the presbyterian party contains several thousands of learned , godly , orthodox ministers , being diligent and profitable preachers of the word , and exemplary in their conversation ; among whom there are not a few that excel in polimical and practical divinity , also of the judicious , sober , serious part of the people , ( in whose affections his majesty is most concern'd ) they are not the lesser number . by means of a practical ministery , this way , like the leaven in the gospel-parable , hath spread and season'd the more considerate and teachable sort in all parts of the kingdom , and especially in the more civiliz'd places , as cities and towns. observation it had been well our undertaker had put his orthodox , and learned thousands upon the list ▪ for that party is a little given to false musters . how many forg'd petitions and remonstrances ; what out-eries from the press and pulpit , in the name of the people , when yet the forti'th part of them were never privy to their own askings ! of * ninety and seven ministers within the walls of london , fourscore and five were driven from their churches , and houses , at the beginning of our troubles . and notwithstanding the monstrous clamours , which occasion'd the conference at hampton-court in 1603. * arch-bishop spotswood tells us , that [ of above nine thousand ministers , but forty nine appeared upon the roll , that stood out , and were deposed for disconformity . such a noise will a few disturbers cause in any society , where they are tollerated . ] touching his practical ministery ; i 'l grant , the cause is much beholden to the pulpit , and that , without the aid of seditious lectures , i do believe the strife had never come to blood : but yet these preachments did not the whole business . do not we know what craft and violence hath been used to cheat and force the people ; what protestations , covenants , and negative oathes have been imposed , upon pain of imprisonment , banishment , sequestration ? have not all schools , and nurceries of piety and learning , been subjected to the presbyterian mode , and many thousands of godly , and reverend divines , reduced to beg their bread , because they would not covenant : yet all too little to procure either a general kindess , or submission to their principles ? for the reasons afore-going , the infringement of due liberties in these matters , would perpetuate most unhappy controversies in the church from age to age. let the former times come in , and give good evidence . as touching ceremonies , the contest began early , even in king edward's reign , between hooper and other bishops . the consecration of hooper , elect bishop of glocester being stayed , because he refused to wear certain garments used by popish bishops , he obtained letters from the king and from the earl of warwick , to the arch-bishop of canterbury and others , that he might not be burthened with certain rites and ceremonies , and an oath common●y used in the consecration of bishops , which were offensive to his conscience . nevertheless he found but harsh dealing from his fellow-bishops , whereof some were afterwards his fellow-martyrs , and ridley among others , who afterwards thus wrote unto him , when they were both prisoners for the gospel . [ however in time past in certain circumstances and by-matters of religion , your wisdom , and my simplicity ( i grant ) hath a little jarred , each of us following the abundance of his own sense and judgment : now be assured , that even with my whole heart , in the bowels of christ , i love you in the truth , and for the truth's sake which abideth in us . ] some godly martyrs in queen mary's days disliked the ceremonies , and none of them died in the defence of ceremonies , liturgy , and prelacy , in opposition to all other ecclesiastical government and order . it was the protestant verity which they witnessed , and sealed in blood , in opposition to popery ; especially the prodigious opinion of transubstantiation , and the abomination of the romish mass or sacrifice . in the same bloody days , certain english protestants being fled for refuge into germany , and setled at frankford , were divided amongst themselves about the service-book , even with scandalous breach of charity and in the issue , the congregation was sadly broken and dissipated . what is intended by due liberty , might be a doubt , did not the coherence explain it to be a freedom of acting to all intents and purposes at pleasure , ( whether without law , or against it , no matter ) according to such presidents of former times , as our resolver refers unto , and justifies . he tells us , the contest about ceremonies began early ; and so in truth it did : for in the time of king edward , there was a wambling toward the geneva discipline ; but neither very earnest , nor very popular : and that ( so far as i can learn ) procured even by the author of that platform , calvin himself . concerning godly martyrs in queen mary's days ; some suffered that disliked the ceremonies , others , that liked them . that none died in defence of them , is a remarque might have been spared ; for the question was matter of faith , not discipline . the frankford breach indeed was a sad story , but yet , considering the dividers , of no great honor , or authority to our friends purpose . knox and whittingham were the prime ring-leaders in this disorder , who upon some disputes started about the service-book , joyning with others of the consistorian stamp , drew such an extract of it , as they thought fit , and sent it to calvin , requesting his opinion of it . such was the answer they received , as blew the whole congregation into a flame ; from whence arose that scandalous breach ensuing . viz. the english service being established , whitingham , gilby , goodman , with some others , divided , and went to geneva , whence , both by letters and discourses , they tampered the ministers and people of england and scotland into a revolt , encouraging them to set up their new discipline , in despite of all opposers whatsoever . the gospel returning under queen elizabeth , these differences were revived and held up by disputes , writings , and addresses to several parliaments ; and there were great thoughts of heart for these divisions . observation why this is english yet : it is but turning now to queen elizabeth's reign to understand these people , and unriddle the due liberty they plead for . ( but of this , in its proper place ) having drawn down the quarrel from edward the sixth , to the blessed restauration of charls the second , ( whom god protect ) he proceeds to descant upon the present . the greatest part of the ministers named puritans , yielded conformity to those controverted rites and forms , that were by law or canons established , as to things burdensome not desirable , in their nature supposed indifferent , but in their use many ways offensive ; and groaning more and more under the yoke of bondage , ( as they conceived ) they waited for deliverance , and were in the main , of one soul and spirit with the nonconformists . and even then the way called puritanism , did not give , but get ground . but now the tenents of this way are rooted more than ever ; and those things formerly imposed , are no● by many , if not by the most of this way , accounted not onely burdensome , but unlawful . observation but is it so , that matters by law established , in themselves indifferent , and onely burthensome to day , ( rebu●sic stantibus ) may become vnlawful to morrow ? by the same rule , kings may be taken away as well as bishops ; all dignities and powers being alike submitted to a popular level : for if the people shall think fit to say , the magistrate is unlawful , as well as the ceremony , by the same reason he may destroy one with the other ; and virtually he does it . we know , the rites and forms of worshipping , are not of the essence of religion , and the huge bustle about discipline , is onely an appeal to ignorance and tumult . the church must be reformed . by whom ? not by the rabble . what means this application then of so many factious sermons , and libels to the people ? they are not judges of the controversie . but in a cause more capable of force than argument , they do well to negotiate , where clamour , and pretence , weigh more than modesty and reason . if a man asks , by what commission act these zelots ? they answer readily : 't is god's cause , and better obey god than man. he that said , give not credit to every spirit ; i suppose knew as much of gods mind , as our illuminates . is not mistaken , or perverted scripture , the ground of all schism and heresie ? counsels may erre , they say , and cannot presbyterians ? how comes this party to be more infallible than their neighbours ? if they are not , let but all other people of different judgments take the same freedom they do , of out-cries against any thing , under pretext of conscience ; let any man imagine the confusion . for , where every man is his own judge , all men shall dispute , till each particular condemns himself ; so that the strife is endless , and the event restlesness , and confusion . this comes of not submitting to some final , and over-ruling decision . upon this pinch at a dead lift , they fly to their judgment of discretion : which leaves them still at liberty to shape their duty to their profit . they tell us ; they 'l be tryed by the word of god : not heeding , how that is again to be tri'd by them : so that in issue , their private interpretation of the scriptures must pass for the law paramount , to which both king and people are equally , and indispensably subjected . undoubtedly , what god commands , we ought to do , and not to do what he forbids . this , in few words , comprises the duty of reasonable nature , without distinction either of offices or persons . but these inviolable fundamentals apart , the accidents of worship , the modes of doing this or that ; the how , when , where , &c. are left various , and variable , according to the several requiries of manners , times , and places , at the discretion of those rulers whom god sets over us . where we find matters of this middle nature orderly setled , and dispos'd , we are commanded to submit to these humane ordinances for the lords sake ; and not to obtrude upon the word for conscience , such disagreements , as effectually arise from peevishness , or want of due enquiry . but why do i talk to those that stop their ears ? their minds are fix'd in this opinion , after a long time of search and practice , and are not like to be reduc'd to the practice of former times . this is but martin junior revived , who says , that it will be very dangerous to our state , to maintain two contrary factions ; that the magistrates are then bound , even for the quieting of our state , to put down the one ; that those that stand for the discipline , neither can nor will give it over , ( so as they will not be put down ) and that the said magistrates cannot maintain the corruption of our church , namely , arch-bishops and bishops , without the discontentment of their subjects . me-thinks the man of peace grows peremptory . will not this argument from search and practice , absolve them from obedience to the king , as well as to the church ? has not the regal power been scann'd and sifted , as well as the ecclesiastick ? or have their practises been more favourable to his majesty , than to the clergy ? but ( their minds are fix'd , and not to be reduc'd . ) this is to say , that if the law and they cannot agree , they 'l tug for 't , upon this supposition , thus he concludes . that ( in all reason , the imposing of such matters of controversie , as by so many are held unlawful , and by those that have a zeal for them judged indifferent , not necessary , cannot procure the peace of church and kingdom . ) observation i say on the contrary , that the peace of church and kingdom cannot be preserved , where every private and licentious spirit shall dare to question the authority of either . in fine , admit the scruple truly conscientious . it would be well yet , that such as fault the present government , would frame another , that should be liable to no exceptions , before they alter this. if that cannot be done , let us rest here ; for if we are bound to change till all are pleas'd , never must we expect to be at quiet . some consciences will have no magistrates at all ; others will govern those they have , or quarrel with them . to reconcile these two in any end of settlement , is as impossible , as 't is unsafe to put much power into the hands of people , so dangerously principled ; ( but to destroy a government none agree better , and this we speak upon experience . ) from hence to his 40th . page , i find little but rapture , in commendation of the presbyterians , with now and then a snap at the late prelates , which is beside my purpose . see now his complement to the king. blessed be god for our gracious soveraign , who makes it his care and study to allay distempers , and compose differences by his just and gracious concessions already published concerning ecclesiastical affairs . observation for fear his majesty's concessions should be taken for a pure act of grace , they are epitheted , just , as well as gracious , to lessen the favour , by intimating the duty ; what return gives the presbyterian party for this indulgence ? are they not troublesome as ever both in their writings and contrivements ? that declaration was no sooner publique , but a petition was exhibited from divers ministers in and about london , for more liberty , with some formalities indeed of gratitude for that . how many bold and scandalous invectives since that time , both from the press and pulpit , against the rites of the church , and the episcopal clergy : nay , and against the sacred majesty of that very person , to whose incomparable clemency they owe their heads and fortunes ? one observation here , to shew , that onely severity can work upon this faction ; * the single imprisonment of crofton hath quieted that party more , than all the multiply'd , and transcendent mercies of his majesty . that worthy gentleman , in his epistle dedicatory to the liturgical considerator , tells us , that [ the common-prayer-book hath been expell'd by a lawful authority , ] ( referring to an ordinance of january 3. 1644. ) if this be not treason , then scot and peters were no traitors . the considerator further assures us , page 34. [ that very few christians that know the power of godliness , care for medling with the liturgy . ] i hope his majesty may pass for one of those few . a great assertor of his principles is the authour of the covenanters plea , although in some respects more plausibly couch'd ; in others bolder ; treating his majesty with a most unpardonable insolence , and with a suitable regard all his episcopal friends as they fall in his way . i should exceedingly wonder how he scap'd a lash from the last convention , especially dedicating that reverend piece to the commons then assembled , did i not consider , that those very pamphlets , whereof his majesty complains in his declaration , touching ecclesiastical affairs , were by my self , at their first comming forth , delivered to several members of that session , which notwithstanding , they were still sold in the hall ; all the interest i had being too little to get them suppressed . but now return we to our author , who complains , that the presbyterians are loaded with many calumnies ; as , that they are against the interest of civil magistracy , especially of monarchy ; that they are giddy , factious , schismatical , domineering , and what not ? but no such matter he assures us ; for , they yield unto the supreme magistrate a supreme political power in all spiritual matters ; but they do not yield that he is the fountain of spiritual power , there being a spiritual power belonging to the church , if there were no christian magistrate in the world . they assert onely a spiritual power over the conscience , as intrinsecally belonging to the church ; and acknowledge , that no decree nor canon of the church , can be a binding law to the subjects of any kingdom under temporal penalties , till it be ratified by the legislative power of that kingdom . and they do not claim for the convocation , or any other ecclesiastical convention , an independency on parliaments ; if they did , surely the parliament of england would resent such a claim . neither are they antimonarchical . did the english or scotish presbyters ever go about to dissolve monarchy , and to erect some other kind of government ? in no wise : for in the solemn league and covenant , they bound themselves to endeavour the preservation of the king's person and authority , and declared they had no intent to diminish his majesty's just power and greatness . observation how far their principles comport with the interest of civil magistracy or monarchy , shall have a place by it self : yet i might very well content my self with what arises from his own words , as they lie here before us ; to prove what he denies ; for in the same breath he both starts the question and resolves it . did not the english and scotch presbyters go about to dissolve monarchy ? what is the analysis of monarchy , but a government by a single person ? ( and , as i take it , the injur'd father of our present soveraign was that person , to whom of right the regal dignity belonged . ) did not these presbyters he talks of , place the supreme power in the two houses , and under their commission , seize the king's towns , and forts ; levy arms ; tax the people ; plunder , and kill their fellow-subjects ; impose oathes ; share his majesty's revenues ; persue , and jewishly sell and betray his sacred person ? if to do all this , not onely without , but expresly against the king's commission , be not to go about to dissolve monarchy , i know not what is . or if the gentleman had rather dispute the royal prerogative , than confess his own mistake in this particular , we 'l look a little that way too : but i doubt the prospect will be none of the pleasantest . upon the trial of cook and peters , this was delivered for law. see the narrative , page 182 and 183. it is the law of this nation , that no one house , nor both houses of parliament , have any coercive power over the king : — that the imprisoning of the king is treason . and a little further , thus , the king of england is one of those princes who hath an imperial crown : what 's that ? it is not to do what he will ; no , but it is , that he shall not be punished in his own person , if he doth that which is in it selfe unlawful . this is a short and clear decision of the case : nor will it serve the good man's turn to argue their integrity , from what they were bound to by their covenant and declarations . it matters not what they profess'd , but what they did. if this be all they have to say ; some heads are now upon the city-gates that said as much . what was the covenant , but a popular sacrament of religious disobedience , a mark of discrimination , who were against the king , and who were for him ? and this the marquis of montross soon found , who being at first unwarily engaged in it , with the kirk-party , quickly perceived his error , and retired ; living and dying the honor of his nation , and of the royal cause . mark this , * his loyalty was charged upon him at his death , for breach of covenant . the presbyterian casuists would fain perswade the nation , to think themselves obliged by that engagement . who vnderstands it first ? ( and certainly we cannot be bound to do we know not what ) next , 't is impossible either to keep , or break it : 't is made up of so many contradictions . but once for all ; there is a nullity in the institution . no man can oblige himself in things wherein he is subject , without leave from his superior . and again ; the oath of one who is under the power of another , without the others consent , is neither lawful nor obligatory . thus the reverend , and learned bishop sanderson . now to my presbyterian again . after the violent change of government , they came slowest , and entred latest into those new engagements imposed by the vsurped powers , and some utterly refused , even to the forfeiture of their preferments , and the hazzard of their livelyhoods , when the nation in general submitted to the yoke ; and many of those who thus object against them , did in temporizing run with the foremost . the truth is , the generality of conscientious presbyterians never ran with the current of those times . some more eminent among them , ministers and others , hazzarded their lives , and others lost their lives , in combining to bring our soveraign that now is to the rightful possession of this his kingdom . and those in scotland adventured no more then all to uphold him ; and when he lost the day , they lost their liberty ; and when he fell , it was said by the adversary , presbytery was fallen . where i must either leave the story foul on the kings side , or prove it so on the other , my choice is pardonable : but otherwise i shall be very tender of engaging the honest presbyterians , with the guilty . that many of them lov'd his majesty , and suffer'd for him , i will not question ; and that they all submitted most unwillingly , to that violent change here mention'd , i do as little doubt . but i must needs say , the action had been nobler , and the loyalty much clearer , had they consulted the kings security , before they lost their own . this does not yet oblige me to the same charity for the scotish party ; who first , during a treaty with his majesty , basely and brutishly murthered montrose , and after that , treated the king himself , liker a prisoner , than a prince . he urges , that [ the presbyterians first divided , and then dissipated the sectarian party , and so made way for his majesties return in peace . ] lambert , and his nine worthies did as much . i do believe him too , [ that the sense of the covenant quickned many men's consciences in their allegiance to the king. ] so did the cock-crowing mind st. peter of the denial of his master . but he went out , and wept bitterly ; so does not every body . alas , alas , the saints have no faults ; what should they weep for ? it may be peradventure said , the presbyterians would enervate monarchy ; but surely ( says our discourser ) i cannot find the rise of this objection , unless from hence , that they were not willing to come under any yoke , but that of the law of the realm , or to pay arbitrary taxes , levied without consent of parliament . observation from hence these two deductions ; first , that the subjects free from that which binds the king , namely , the yoke of law. suppose he breaks that law , by what law can we question him ? at best , 't is but to punish one transgression by another . the second hint is dis-ingenuous : as if arbitrary taxes had been the subject of the difference . all the world knows , before a blow was strook , the king had stript himself to his honour , and his conscience , to gratifie his people . but 't was the government they aim'd at , and that they fought for . here is yet another gentle slip : what are taxes to presbytery ? but this is a devil that will hardly be kept within his circle . just so in their practices do they reduce all civil actions , under the cognizance of their courts of conscience , as he brings here by head and shoulders , arbitrary taxes to matter of religion . i confess ( says he ) there are none that more reverence their liberties , and value the native-happiness of the free-born subjects of england . and verily their true knowledge and sense of the nature of christian religion , makes a due freedom exceeding precious : for this religion is not variable , according to the will of man , but grounded upon an unchangeable and eternal truth , and doth indispensably bind every soul , high and low , to one divine law and rule , perpetual and unalterable . and therefore doth strongly plead the expedience of a due civil liberty on the behalf of its professors ; yet such a liberty as will not enfeeble monarchy , nor the legal power of the kings of england . observation truly i think i have not seen words so well put together , that signifie so little . because religion is not variable , but grounded upon an unchangeable and eternal truth , &c. — therefore the professors of it must have a due civil liberty , &c. is not a due liberty , due to all people ? again , what is civil liberty to matter of salvation ? and yet again . why should the presbyterians challenge that liberty to themselves , which they refuse to others , upon the very same plea : and not rather submit their discipline to the law , then stoop the law to their discipline ? there is a liberty which is a cloak for maliciousness : and i am afraid , theirs and that are much a-kinn . one thing is very notable ; they never state what they would have , their terms are general , and indefinite , hard to be understood , because they are resolv'd not to be satisfi'd . a due freedom , a due civil liberty , the legal power ; — what means all this , but any thing they shall be pleased to make of it ? a king ruling a free people , hath a power much more noble and more free , than he that ruleth over perfect vassals , that have no propriety . the power is more noble , because it hath a more noble subject of government ; it is more honorable to rule men than beasts , and freemen than slaves . likewise the power is more free : for whatsoever prince hath not his power limited by his people's legal freedom , he will be bound up some other way , either by the potency of subordinate princes and great lords within the realm , or by a veterane army , as the turkish emperor by his janizaries , and the roman caesars by the pretorian bands and the legions . vpon which account , to be a powerful monarch over a free people , is the freedome and glory of our soveraign lord , above all the potentates on earth . observation a king ruling a free people , is a kind of presbyterianism , and sounds better in the mouth of a lawyer , than of a divine . the correlate to rule , is subjection : nor will their title to a propriety , yet justifie the common usage of the term. 't is of a dangerous intimation , and seems to give the people more than comes to their share . ( i speak with reverence to the benignity of our english laws , and the indubitable right which every subject hath to the benefits thereof . ) that it is more honorable to rule free-men than slaves , is but a complement for i can make those slaves , free , when i please , whereas the other way of my power 's confin'd ; that is , in equity , a prince is bound to observe the law , as his own act : and if he fails , the people may compel him to it , if they can shew a law for 't . to end this point ; what prince soever shall suffer every bubling brain to controvert the bounds of king and subject ; the royal authority , and the peoples freedom ; that prince , i say , runs a great hazzard of his soveraignty . the very moving of the question , is to prophane the sacredness of majesty ; and by degrees begets irreverend and sawcy habits in the people . but rebellion ( he tells us ) and disobedience , is the loud out-cry of some against this party . and this were a crying sin indeed . but let not sober minds be hurried into prejudice by such exclamations and out-cries . it were to be wished , for common peace and amity , that the late publick discords were eternally forgotten . but seeing some in these times of expected reconciliation , will not cease to implead and condemn the honest minded , and render them odious to the higher powers , a necessity is laid upon us to speak something apologetical , at least to mitigate the business , and remove prejudice . observation sure this loud out-cry of rebellion aad disobedience , comes from within himself ; for truly i have a little watch'd the press , and since his majesty's return , ( nay , a good while before ) upon my conscience i have not met with one syllable of bitterness against that party , but defensive : yet i dare undertake to produce forty presbyterian pamplets , and discourses , of fresh date , exceeding foul against the king , and his adherents . it really makes me blush and tremble , to consider how great a mercy they abuse , how sad a vengeance they provoke . had but these people the least spark of natural affection and remorse , the venerable ruines of a glorious chuch and state would work upon them ; or now and then a thought how matters stand betwixt god and their souls : but their great care of others make them neglect themselves , and become true anathemaes for a pretended publick good . however they do well to cry whore first ; and call that a necessitated apology , which seems to me a palpable and causeless slander . we have heard much and often of the presbyterians loyalty and religion ; we 'l look a little now into their law , which very fairly gives us to understand , that the vnbishopping of timothy and titus , will not do their trick . they are at work already upon the two main props of royalty ; the king 's negative voice , and the power of the sword. a blessed age the while , when the pulpit shall pretend to dispose of the crown ; kerve out the government ; and every scribling priest vent his seditious and crude politiques to the people . but now it works . the presbyterian party in england never engaged under a less authority than that of both houses of parliament . i have read , that the parliament of england hath several capacities , and among the rest , these two ; first , that it represents the people as subjects , and so it can do nothing but manifest their grievances , and petition for relief . secondly , that by the constitution it hath part in the soveraignty , and so it hath part in the legislative power , and in the final judgment . now when as a part of the legislative power resides in the two houses , as also a power to redress grievances , and to call into question all ministers of state and justice , and all subjects of whatsoever degree in case of delinquency , it might be thought , that a part of the supreme power doth reside in them , though they have not the honorary title . observation me-thinks we should do well to leave calling the two houses , the parliament of england , having already paid so dear for that mistake . concerning the power of the parliament of england . 't is beyond doubt , onely inferiour to the fountain of all power , even god himself . but then an agreement is imply'd ; neither king , lords , nor commons , nor any two of them , can pretend to a parliamentary authority , without the third . this is not to suppose co-ordination neither . the two houses are still subjects : their office being onely consultive , or preparatory ▪ the character of power rests in the final sanction , and that 's the king's : so that effectually , the passing of a bill , is but the granting of a request . so much for parliaments , in propriety of speaking . now to the power of the two houses , by my antagonist mis-call'd , the parliament of england , upon which bottom stands the presbyterian fabrick . he tell us , they act in two capacities . as subjects , or petitioners , first : and then , as sharers of the soveraignty : as if he said , they are sent to ask what they list , and take what they please . the petitioning capacity is not for the presbyterians purpose ; wherefore he waves that , and sticks to the other . what their power is , will best appear from the king 's writ of summons , which both commands and limits them , pro quibusdam arduis , & urgentibus negotiis , &c. — ordinavimus , &c. — he states it otherwise , and places a part of the legislative power in the two houses , which is not doctor-like . for the legislative power is totally the king 's . they do but make the bill , he makes the law ; 't is the stamp , not the matter , makes it current . nor do i comprehend what he can mean by part of the legislative power : to my thinking , he might as well have said , part of an indivisible point . this will come to a pretty fraction , two thirds of a parliament , shall make two thirds of a law. is it not enough that the king can do nothing without the two houses , unless they may do every thing without the king ? grant this , and of all people living we are the greatest slaves , as of all constitutions ours is the most ridiculous . touching the power of the two houses , to redress grievances , and question all ministers of state and justice , ] the power they have is either from prescription or commission . to the former , i think , few will pretend ; and to the latter , none . never was the house of commons , at any hand reputed a court of justice . they cannot give an oath , impose a fine : not indeed exercise any empire but over their own members . 't is true , the lords house hath in some cases a right of judicature ; but claiming by prescription , they are likewise limited by custom . further , both houses are no court of judicature , and ( with due reverence to his majesty ) the king himself in parliament , joyn'd with the three estates , claim not a right of judication , but very rarely , and with great tenderness . it is the proper business of a parliament to make laws , alter , or repeal them , not to interpret them , unless in matters of very great importance . that 's left to the judges ; and to determine of their validity . for acts of parliament , either repugnant in themselves , or of impossible supposition , or against common right , are deem'd not binding . the common , and most specious shift of all the rest , is , that the government of this nation is in king , lords , and commons . this must be swallowed with great wariness , or 't will choak half the nation . by the king , architectonicè ; and by the other two , organicè , ( as walker distinguishes it ) the king , as the architect ; and the two houses , as his instruments . if there were neither practice , law , nor interest in the case , me-thinks the very odds of honor in the deputation , should be enough to carry it . the king is god's representative , they are but the peoples . say i should now admit them all they challenge , ( as delegated by the people ) so tickle is the point yet , that if any one single person of the number , should be illegally debarr'd the freedom of his vote ; that nicety avoids , and nulls the whole proceeding . i can hardly think any thing clearer , than the error of placing part of the supreme power in the two houses . it implies a contradiction : a part of a thing ( with leave ) impartible . ( but drowning men will catch at straws ) however , i perceive , that his majesty's best friends , and the church's ( as they style themselves ) are resolved to serve both king and bishops alike . that is ; just as the bishop is to rule in consociation with his presbyters , so shall his majesty with his fellow-princes , the presbyterian members . it cannot but exceedingly dispose the king , to grant these people all due liberty , that will give him so much . crowns are but troublesome ; and government sits heavy upon the shoulders of a single person ; they 'l ease him of that care and weight : and for the honor of their prince , and their country's good , divide the glorious load among themselves . this being past , ( which heaven avert ) we may ( says the late king ) be waited on bare-headed , we may have our hand kiss'd , the style of majesty continued to us , and the king's authority , declared by both houses of parliament , may be still the style of your commands ; we may have swords and maces carried before us , and please our self with sight of a crown and scepter . ] — but soft , the man relents , and tells us , ( though the law says , the king can do no wrong ) [ that this part of the supreme power , is indeed capable of doing wrong , yet how it might be guilty of rebellion , is more difficult to conceive . ] observation put case the two houses should take up arms against the king , because he will not banish the one half of his friends , and hang up the rest : would not that be rebellion ? i could start twenty suppo●itions more ; but i 'll stop here , and the rather , because our author professes , that [ in this high and tender point , it belongs not to him to determine . ] yet he goes on , and certainly believes , that the world is divided into fools and presbyterians : he would not otherwise have thrust upon us so gross a juggle , as that which i am now about to examine . touching the much debated point of resisting the higher powers , without passing any judgment in the great case of england , i shall onely make rehearsal of the words of grotius , a man of renown , and known to be neither anti-monarchical , nor anti-prelatical , which are found in his book , de jure belli & pacis , by himself dedicated to the french king. ( si rex partem habeat summi imperii , partem alteram populus aut senatus , regi in partem non suam involanti , vis justa opponi poterit , quia eatenus imperium non habet . quod locum habere censeo , etiamfi dictum sit , belli potestatem penes regem fore . id enim de bello externo intelligendum est , cum alioqui quisquis imperii summi partem habeat , non possit non jus habere eam partem tuendi . ) lib. 1. c. 4. s. 13. observation here we find grotius cited , to justifie , that the lords and commons may make war against the king , to defend their title to the supreme power . ( pythagoras his opinion concerning wild-foul , had been as much to the purpose ) for the english reader 's sake i 'l turn it ; and in this point desire a more than ordinary attention . where the supremacy is in the king , in some cases ; in others , in the people , or senate . that king invading the others right , may be lawfully resisted ; for his power reaches not so far . and this i think will stand good , although i have already placed the right of making war , in the king ; for that must be understood of a forreign war : since whosoever hath a part of the supreme power , hath consequently a right of maintaining such part as he hath . ] there is one line yet remaining , which our author hath very prudently kept for a reserve , till the presbyterians shall have gotten the better of the king. quod ubi fit , potest rex etiam suam imperii partem belli jure amittere ; that is , where thus it happens , the king's encroachment upon the peoples right , may fairly amount to a forfeiture of his own . is it not pity that people of these milde , and complying principles , should be charg'd with disobedience ? if this be the case of england , the question is no longer , the presbyterians liberty , but the king's title to his crown . that chapter of grotius , whence he takes his quotation , treats de bello subitorum , in superiores ; where , and where not , subjects may take up arms against their superiors . this learned man , among other cases , tells us , in this they may , and the reason is evident ; : for where the soveraignty is thus dispos'd ; half to the king , half to the people , that prince is but a subject to some purposes , a king to others . so that in any point of soveraignty , formally vested in the people ; he is not their superior , but they his . how finely he hath match'd the case of england , where kings have no restraint , but what they put upon themselves , for the laws are their proper acts ! but mark the process of his reasonings : and how ( in his own phrase ) he feels his way step by step . the presbyterians were ever in the right ; he says . why , if he would be quiet , who says the contrary ? but then the king was in the wrong . to bring the case up to grotius his determination : we must admit first , that by the constitution of england , the soveraignty is shared betwixt the king and the two houses : and next , that the late king did actually invade the popular prerogative : from whence arises the lawfulness of resistance ; and after that , potest rex etiam suam imperii partem belli jure amittere . they have at last the same right to the crown , they had at first to the quarrel . he that peruses the first eight sections of the fore-mentioned chapter , will find grotius no favourer of his opinions that quotes him . be the prince what he will , he tells us , summum imperium tenentibus resisti jure non posse . bodin yet more expresly , that england and scotland are absolute monarchies : that the supreme power is onely in the king ; ( iura majestatis , ac imper●i summam , in unius prinoipis arbitria versari . further , in senatu nullum est imperium ; nor onely so , but whoever urges the contrary , meditates a commotion , isti qui imperium senatui tribuunt , reipublicae interitum , ac status eversionem moliuntur . as to the point of loyalty now in question , the subversion of the fundamental government of this kingdom could not be effected , till those members of parliament that were presbyterian , were many of them imprisoned , others forcibly secluded by the violence of the army , and the rest thereupon withdrew from the house of commons . observation then it seems till that violence by the army , upon the presbyterians , there was none acted by the presbyterians upon the king. to seize his towns and magazines ; hunt , and assault his royal person ; part his revenues ; hang up his friends : all this is justifi'd , in case his majesty refuses to be rul'd by his two houses . alas , the fundamental government was safe , ( i warrant ye ) so long as the rights of soveraignty were exercis'd , first by the assembly in scotland , and then by a pack'd party , in a close committee : and the presbyterians never the less honest men for selling the king first ; then voting him a prisoner ; and after that , for pinching him even upon the very point of presbytery . surely they are much to blame that charge these innocents with disloyalty . if the presbyterian members had not been forced , ( they say ) all had been well . truly it may be so ; yet if i mistake not , there was a time when the episcopal members were forced too ; and had that violence been spared , it had never come to this. but i suppose , the city-tumults against bishops : the outcries of the rabble at white-hall : the multitudes that baul'd for reformation : posting up such and such for straffordians , as honestly opposed the torrent of the people . this in the vvell-affected , passes for christian liberty . but our author follows his opinion with a proof . for they ( says he , meaning the presbyterians ) had voted the king's concessions a ground sufficient for the houses to proceed to settle the nation , and were willing to cast , whatever they contended for , upon a legal security . observation waving their former vote of non-addresses , and that foul declaration of their reasons for it : we will in charity believe , they were over-aw'd , and that it was extorted by the army . but what excuse for the matter of the propositions ? that they were actuated by a presbyterian spirit , appears in this , that they demanded a settlement of a presbyterian government . it remains now onely from hence , to gather the fair equivalence , of this gentleman's doctrine , and to discover what 't is the presbyterian faction calls a legal security . they hold , that if the king of england will not comply with the two houses , the people may chase , sequester , and imprison him : and when they have him in distress , they may without disloyalty press him to these , or the like conditions for his liberty . 1. by a publick act to justifie that violence , and condemn himself . 2 ly . to renounce and abolish episcopacy , although bound by oath and judgment to defend it . 3 ly . to transfer the right of levying men and monies , to the two houses ; by them to be raised and disposed of at pleasure , without rendring any accompt to his majesty . 4 ly . to deliver up the lives , liberties , and fortunes of all that served him , to the mercy of that party . 5 ly . to grant , that all offices of trust may be disposed of by the appointment of both houses . this is a short , and modest accompt of presbyterian loyalty , the due liberty they contend for : which being setled upon a legal security , with such further concessions , as their modesty shall vouchsafe to require , puts an end to the dispute . his late majesty observes ( upon uxbridge treaty ) that it was a grand maxim with them , always to ask something , which in reason and honor must be denyed , that they might have some colour to refuse all that was in other things granted . ] and so we find it . but what 's the reason of this peevishness ? is there any thing in the nature of prelacy that frames the mind to obedience and loyalty ? or is there any thing in presbytery , that inclines to rebellion and disobedience ? observation truly i think there is . prelacy holds a better proportion in the scale of order , as a more regular subordination of duties and relations . nature and providence do not move by leaps , but by insensible and soft degrees , which give stability and beauty to the universe . is not the world compos'd of disagreements , hot and cold , heavy and light ? — and yet we see those oppositions are by the means of middle , and conciliating mixtures wrought into a compliance ? 't is the same case in subject and superior : higher and lower , betwixt top and bottom , are but as several links of one providential chain , where every individual , by vertue of this mutual dependency , contributes to the peace and benefit of the whole . some are below me ; and this sweetens the thought that i am below others : by which libration are prevented those distempers which arise either from the affectation of more power , or the shame of having none at all . as these degrees of mean and noble , are beyond doubt of absolute necessity to political concord ; so possibly the closer the remove , the better yet , as to the point of social expedience ; provided , that the distances be such as to avoid confusion , and preserve distinct offices , and powers from enterfering . nor is this gradual method onely suited to humane interest , as being most accommodate to publick quiet , and to defend the sacredness of majesty from popular distempers : but 't is the very rule which god himself imposes upon the whole creation : making of the same lump , one vessel to honor , and another to dishonor . subjecting by the law of his own will , this to that : that to what 's next above it : both to a further power , all to himself . and here we rest : as at the fountain of authority . from god , kings reign ; they appoint their substitutes , and so on to inferior delegations ; all powers derive from a divine original . this orderly gradation , which we find in prelacy , must needs beget a reverence to authority ; the hierarchy it self depending upon a principle of obedience ; whereas our utopian presbytery advances it self upon a level of confusion . it is a kind of negative faction , united to dissolve a laudable and setled frame of government , that they may afterward set up they know not what . we may have learn'd thus much from late and sad experience . let him that would know more of it , read the survey of pretended holy discipline . i think it would be hard to shew one eminent presbyterian , that stickles not for an aristocracy in the state , as well as in the church : and he that said , no bishop , no king , gave a shrewd judgment ; not as implying a princes absolute dependance upon bishops , but in effect the king's authority is wounded through the church ; the reformation of what is amiss , belonging to the ruler , not to the people . i do not yet condemn all presbyters , nor justifie all prelates . we are told , that in antient times , and for a series of many ages , the kings of england have had tedious conflicts with prelates , in their dominions . ] 't is right , and the same cause is now espoused by our more than ordinary papal presbyterians ; to wit , ecclesiastical jurisdiction over the civil power . but we are further question'd . if presbytery and rebellion be connatural , how comes it to pass , that those states or kingdoms where it hath been established or tollerated , have for any time been free from broils and commotions . observation it is as true , that those places have been quietest , where presbytery hath gain'd footing , as 't is , that presbyterians have never disclaimed or abandoned their lawful prince : that they have never ceased to solicite , and supplicate his regards and favours , even when their power hath been at the highest , and his sunk lowest . this is something which in good manners wants a name . how far the presbyterians have abandon'd their prince , i shall not press , but rather refer the reader to examine how far , and in what manner they have solicited him . ( cujus contrarium . ) his late majesty , after forty messages for peace , and a personal treaty , finding himself most barbarously laid aside ; in a declaration from carisbrook castle , dated janu. 18. 1647. expostulates the matter in these termes . now would i know , what it is that is desired : is it peace ? i have shewed the way ( being both willing and desirous to perform my part in it ) which is , a just compliance with all chief interests . is it plenty and happiness ? they are the inseparable effects of peace . is it security ? i , who wish that all men would forgive and forget like me , have offered the militia for my time . is it liberty of conscience ? he who wants it , is most ready to give it . is it the right administration of justice ? officers of trust are committed to the choice of my two houses of parliament . is it frequent parliaments ? i have legally , fully concurr'd therewith . is it the arriers of the army ? upon settlement , they will certainly be paid , with much ease ; but before , there will be found much difficulty , if not impossibility in it . thus all the world cannot but see my real , and unwearied endeavours for peace , the which ( by the grace of god ) i shall neither repent me of , nor ever be slackned in : notwithstanding my past , present , or future sufferings . but , if i may not be heard , let every one judge , who it is that obstructs , the good i would do , or might do . where the right lies , a presbyterian may better determine , than a royallist question . — magno se judice quisque tuetur . here 's the testimony of a pedant , in ballance against the authority of a prince . he tells us by and by , that prophaneness , intemperance , revellings , out-rages , and filthy lewdness were not at any time in the memory of the present age , held under more . restraint , than in the late distracted times , by means of a practical ministery . observation these generals spell nothing , and to name particulars were not so candid ; i could else make up scot and peters , at least a score , even out of the select tribe of the reformers , ( and these i think are not as yet canoniz'd for saints . ) 't is no prophaneness ( is it ? ) to play the hocus pocus in a pulpit , with rings and bodkins ; to talk treason by inspiration ; and entitle the holy ghost to murther and rebellion . to appoint mock-fasts , and thank god for victories he never gave them . to swear for , and against the king , in the same breath . to convert churches into stables , and for fear of superstition to commit sacrilege . nor is it out-rage sure , or intemperance to seize the patrimony of the church , the king's revenues ; pillage and kill their fellow-subjects . to set up ordinances against setled laws , and subject the ten commandements to the superior vote of a committee . to justifie tumults against authority , and suffer the most damnable heresies to scape without reproof . but what if there were disorders ; by whom were they caused ? it is most unreasonable to object , that the late wild postures , extravagancies , and incongruities in government , were the works of presbytery , or presbyterians . the nation had never proof of presbytery , for it was never setled , but rather decry'd , and expos'd to prejudice by those that were in sway , and that in the more early times of the late wars . observation i must confess indeed , that presbytery was never setled , nor ever likely to be , so much did the whole nation stomach it ; but yet how this agrees with his former reasoning , pag. 29. i do not understand . there he pretends , that by * long practise mens minds are fix'd in this opinion : and that the party is numerous . here he contents himself to acknowledge , that the presbyterians lost their power early , and that they never recovered it since . this will not serve his turn , to acquit the faction ( so denominated ) of our late miseries . our soveraign ( of blessed memory ) brings the contest down , to his surprisal at holmby , and the distractions in the two houses , the army , and the city , ensuing upon it . these ( says that excellent prince ) are but the struglings of those twins , which lately one womb enclosed , the younger striving to prevail against the elder . * what the presbyterians have hunted after , the independents now seek to catch for themselves . ] in fine ; one finish'd what the other began ; for the king died at last , but of those wounds which he at first received in his authority . his majesty , upon his leaving oxford , and going to the scots , clears this yet further : where he calls it , adventuring upon their loyalty , who first began his troubles . the truth of this matter ( says he ) is cleared by a passage of our late soveraign , in a let-to his majesty that now is . [ all the lesser factions were at first officious servants to presbytery their great master , till time and military success discovering to each other their particular advantages , invited them to part stakes , and leaving the joynt stock of uniform religion , pretended each to drive for their party the trade of profits and preferments , to the breaking and undoing not onely of the church and state , but of presbytery it self . — ( it follows ) which seem'd and hop'd at first to have engross'd all . observation the last line is as true as any of the rest ; but all truths are not to be spoken . indeed this slip is somewhat with the grossest . not to trouble my self with their formal fopperies , of deacons , elders , and their parish-meetings ; those are but popular amusements : we 'll pass to what 's more pertinent , and see how he acquits his friends of joyning with the independents . the truth is , sectarianism grew up in a mystery of iniquity and state-policy , and it was not well discerned , till it became almost triumphant by military successes . observation 't is a strange thing the presbyterians should not see what they themselves contrived ; what all others took notice of ; and what the late king offered to prove , [ in his declaration of august the 12th 1642. ] the insolence of sectaries being not onely wink'd at , but publickly avow'd ; and the law thwarted to protect them . see what one says ( no stranger to their practises ) to prove , and evidence the combination . the leading-men , or grandees , first divided themselves into two factions or juncto's , presbyterians and independents : seeming to look onely at the church , but they involv'd the interests of the common-wealth . — these having seemingly divided themselves , and having really divided the houses , and captivated their respective parties judgments . — teaching them by an implicite faith , jurare in verba magistri , to pin their opinions upon their sleeves : they begin to advance their projects of monopolizing the profits , preferments , and power of the kingdom in themselves . to which purpose , though the leaders of each party seem to maintain a hot opposition , yet when any profit or preferment is to be reach'd at , it is observ'd , that a powerful independent especially , moves for a leading presbyterian , or a leading presbyterian for an independent : and seldom doth one oppose or speak against another , in such cases , unless somewhat of particular spleene or competition come between : which causeth them to break the common-rule . by this means , the grandees of each faction , seldom miss their mark , since an independent moving for a presbyterian , his reputation carries the business clear with the independent party : and the presbyterians will not oppose a leading man of their own side . i find we are not like to agree , for these people cannot see their own faults , nor we their virtues . i would take a good journey to meet any man stiff in that way , that would but confess he was ever in any error . of all the prejudices and scandals taken against this way , there is none greater than this , that it is represented as tyrannical and domineering , and that those who live under it , must ( like issachar ) crouch under the burdens . we do indeed account the presbyterian discipline very tyrannical , and by and by we 'l give our reasons for it . not because this discipline censures scandalous disorders ] ( as he insinuates ) but for that it subjects all civil matters to a consistorian cognisance , and rapt by an impulse of passion , calls many things scandalous , which measured by the rule of piety and reason , are found praise-worthy , and of laudable example . the usage of the common-prayer book is to them , scandalous , though setled by the law : but to eject a minister for reading it , though both without law , and against it , that , they esteem no scandal ; we , the contrary . i have now brought the gentleman to his first stage , where i might very fairly leave him , for having already done my business ; what i do more , is but for company . so far as i can judge , i have not scap'd one syllable material to his purpose : nor have i either broken his periods , or unlink'd his reasonings , to puzzle , or avoid his meaning . how fairly i have dealt with what i have expos'd : whether in matter of fact , deduction , or good manners , ( the subject of the difference duely weighed ) that i submit to the reader , and where the reason lies betwixt us . i have indeed omitted a great part of the debate , as not at all related to my design , nor ( to speak freely ) much to the point in question . his frequent and rhetorical raptures , extolling to the heavens , the wisdom and sanctity of the presbyterians ; ( but above all , the legions of the saints ) what does this florid vanity ●ignifie more than the putting of his own name to a fair picture , when yet , for ought he proves , and for ought we discern , there 's not one line betwixt them of agreement . the contrary course he takes with the prelatick party . they ( forsooth ) are not so and so : and from his generals , there he is pleased to enter into prohibited particulars , taxing in special manner the excesses of some of our late prelates : but without any instances of good in the other party , which does but spitefully and weakly imply , that bishops have more faults , than presbyterians have virtues . it will not be now expected , that we that differ in the premises , should agree in the conclusion . but for that we 'll take our fortunes . vpen the whole matter aforegoing , we firmly build this position : that the presbyterian party ought not in justice or reason of state , to be rejected and depressed , but ought to be protected and encouraged . ( this is but one doctor 's opinion ; we think otherwise . ) nevertheless ( says he ) there being a seeming complication in this business , and an other ample party appearing in competition , a difficulty remains , and the matter falls into a further deliberation . and thereupon we are fallen upon the second main enquiry . ii. quest. whether the presbyterian party may be protected and encouraged , and the episcopal not deserted nor disobliged . observation 't is a particular grace , that the bishops party may yet be admitted into the competition , and that the man of the short robe will vouchsafe to enquire into the consistence of episcopacy and presbytery : yet it was boldly ventur'd to determine what ought to be done before he had examin'd , whether the thing was fesible or no. i shall not spend my time to controvert idea's , and wrangle about governments in the air : we are for plain and practicable contrivements , such as authority , good order , and long experience have recommended to us . i suppose the agreeing of both parties in such middle terms as he proposes , a thing not utterly impossible . many things may be fair enough in notion , yet of exceeding hazzard to be put in practice ; especially 't is dangerous to try tricks with politick constitutions . great alterations are scarce safe , even where they are lawful , and wrought with good intention : much less are those so , which are promoted by a disorderly , and popular earnestness , and with seditious meaning . for this i dare lay down as a position : never did any private party band against a publick settlement , with an intent to mend it . but what have we to do with the imaginary coalition of the two church-parties ; when the kirk-discipline affronts the civil sanction , and actually invades the kings authority ? let them first bring their principles to their duties , treating like subjects , and submitting as christians . can any man believe those people friends to the church , that are enemies to the state ▪ or that the god of order can be pleased with the promoters of confusion ? were there no other reason to deny the thing they ask , than their bare manner of asking ; it ought not to be granted . what signifies their talk of number , power , resolution , but a false muster of the faction , to make a party with the rabble ? when yet , god knows , they 're inconsiderable : let every man but over-look his neighbour , and count , he 'l find the disproportion . undoubtedly the most insufferable of all their arguments is that of danger ; there 's but one step between that word and violence . first , it implies a seditious complication . they move for such as they believe will tumult : if not , where lies the hazzard ? besides , those subjects that dare tell their prince , 't is dangerous to deny their askings , do by that insolence render his concessions much more hazzardous . persons of that audacious temper , will hardly make a sober use of an extorted bounty . so far as presbyterian , and episcopal , purely refer to the church , i shall not much concern my self in our resolvers second main enquiry : ( equal to all the world is the incomparable hooker , upon that subject ) but where these terms are in a greater latitude , applyed to civil matters , i shall be bold to pass some further observations . the dissenting side oppose not all liturgy , but desire that the present onm may be changd , or reformed . observation that 's but a modest motion . but now suppose his majesty , the law , and forty for one of the nation , should desire the continuance of it as it is : what equity have the dissenters to the change ; or what would be the benefit if granted ? not the tenth part even of the presbyterians , would be contented with it . some of them are against all set-forms of common-prayer whatever ; others ( more moderate forsooth ) do not oppose a prescript form , so it be not enjoyn'd . a third sort , will vouchsafe to permit the english liturgy , provided they may have the purgeing of it themselves . and when all 's done , the sectaries may claim as much right to abolish that , as they to alter this. and now for ceremonies . they oppose not any circumstance of decency and order , but desire , that mystical ceremonies of humane institution , may be abolished or not enjoyned . first , the dissenters are not the judges of decency and order ; and for mystical ceremonies of humane institution ; ( as scaliger says of the sepia ) caliginem effundit , & evadit ; he troubles the water , and escapes in the dark . multiformity in religion ( says our reconciler , pleading for accommodation ) publickly profess'd , doth not well comport with the spirit of this nation , which is free , eager , jealous , apt to animosities and jealousies , besides that it hath ever had a strong propension to vniformity . observation had this fallen from a common pen , i could have better born the disproportion of his character of the english temper , — free , eager , jealous , and yet propense to vniforformity . this seems to me a mixture incompossible . but the good man means well , and writes so , when he lists . his drift is , to perswade us , that to comply with the presbytery , is to comport with the spirit of this nation : which being free and eager , seems to cry , beware . how blessedly would these free-spirited worthies order their subjects , if they were once in power , that thus presume from their own level , to menace and control authority . if toleration might compose the difference , there were some hope ; but that , alas , is more than they can afford the government , and much less will they accept it for themselves . the temper of this kingdom ( says he ) does not well accord with extremes on either hand ; ] and to see the fortune of it , the presbyterians are just in the middle . toleration being not the daughter of amity , but of enmity , ( at least ) in some degree supposeth the party tolerated to be a burden , especially if conceived dangerous to the way established , and commonly holds no longer than meer necessity compels ; and consequently neither party take themselves to be safe , the one always fearing to lose its authority , and the other its liberty . observation behold a learned expostulation , and a dutiful . [ where the party toelrated appears dangerous to the way established : the one fears to lose its authority , and the other its liberty . ] there 's no great depth in the discovery , that from an opinion of mutual danger , arises mutual jealousie . but what 's this case to the subject of our debate ? by toleration is not meant an imprudential yielding to an untractable , and churlish faction : but a discreet and pious application of tenderness toward such as by their fair comportment in the main of order , and good manners , appear to merit it . true it is , god himself is the onely searcher of hearts , who sees our thoughts , even in the bed of their conception . yet where we find an inconformity of practise to profession : people that strein at a gnat , and swallow a camel , we may without offence to charity , rank those incongruous christians amongst hypocrites : and with great justice hold them to the law , that strive to bring the law down to their humors . by the same rule ought we to judge in favour of their scruples , whose lives are squar'd by a conform severity and strictness . it is most true , that such proposals may suffice for peace , which will not satisfie humor and faction , and carnal interest . ] why do we not apply our selves then to the onely umpire of the controversie , the setled law , which without either passion or design , lays down our duty , and our interest ? these wranglings about trifles do but enflame the difference , and start new animosities , instead of quieting the old. the great pretence of scandal ( forsooth ) is this. the presbyterians stick at ceremonies properly sacred , and significant by humane institution , which they conceive to be more than meer circumstances , even parts of worship ; and whatsoever instituted worship is not ordained of god , they hold unlawful . this passage lies a little out of my rode , but however , i 'le make it my way . it is much easier to call our ceremonies sacred , and parts of worship , than to prove them such ; or that we understand them so . is the manner of doing any thing , part of the thing done ? and for significant by humane institution ] the exception is as frivolous . because that in some cases even of external discipline , the church is limited , does it therefore follow that it is free in none ? or ty'd up onely to such rites and ceremonies , as hold no signal proportion with the reason of their institution ? this argument cuts their own throats , since by the significancy of the sitting posture at the communion , they ma●ntain the use of it ; for ( say their admonitioners ) it betokens rest , and full accomplishment of legal ceremonies in christ. they that scruple our mystical significant ceremonies , conceive that they are properly and meerly sacred , as having the honor of god for their direct and immediate end . these reasons are but snares for woodcocks . that the ultimate end of all our actions is , or at least ought to be ) the honor of god , admits no question ; but 't is not therefore the immediate end of every thing we do , nor in particular of ceremonies . the outward forms and rites of publick worship , direct partly to uniformity and order ; and partly to excite due reverence and affection in the discharge of holy duties , by sensible actions , and remarkable circumstances . but he persues his error ; and instances , that the surplice is not for gravity , nor meerly for decent distinction , but a religious mystical habit , the character or badge of a sacred office , or service conformable to the linnen ephod under the law. the grand exception against the surplice is matter of scandal , and that amounts to nothing , where people will be peevish , and carp at every thing . allow it what original he pleases : if it be neither unlawful in it self : nor wickedly applyed ; and by authority thought fit to be imposed ; why should it not be used ? what says the incomparable hooker , in this point ? [ to solemn actions of royalty , and state , their suitable ornaments are a beauty ; are they onely in religion a steyn ? ] and in another place . the names of our months , and of our days , we are not ignorant from whence they came , and with what dishonor unto god they are said to have been devised at the first . what could be spoken against any thing more effectual to stir hatred , then that which sometimes the antient fathers in this case spake ? yet those very names are at this day in use throughout christendom , without hurt or scandal to any . clear and manifest it is , that things devised by hereticks , yea , devised of a very herétical purpose , even against religion , and at their first devising worthy to have been withstood , may in time grow meet to be kept ; as that custome , the inventers whereof were the * eunomian hereticks . so that customs once established , and confirmed by use , being presently without harm , are not in regard of their corrupt original , to be held scandalous . but concerning those ceremonies , which they reckon for most popish , they are not able to avouch , that any of them was otherwise instituted , than unto good ; yea , so used at the first . ] the signing with the sign of the cross ( they conceive ) is more evidently sacred than the former . as baptism consecrates the child , so doth the cross. it is used as a sealing sign of our obligation to christ , as the words used in the application thereof do manifest , and the book of canons doth declare expresly , which saith , [ that it is an honorable badge , whereby the infant is dedicated to the service of him that died on the cross , as by the words used in the book of common-prayer it may appear . ] and therefore it is in that respect sacramental . observation 't is a well nurtur'd child that gives his mother the lye : and it is little better , to charge this sense upon the church of england , when by the very letter of the canon , an express care is taken to prevent all possibility of exception , by a clear explication of the churches judgment in that particular . the juggle is so gross , i need but cite the canon to confute it . first , the church of england , since the abolishing of popery , hath ever held and taught , and so doth hold and teach still , that the sign of the cross used in baptism , is no part of the substance of that sacrament ; for when the minister dipping the infant in water , or laying water upon the face of it ( as the manner also is ) hath pronounced these words , i baptize thee in the name of the father , and of the son , and of the holy ghost , the infant is fully and perfectly baptized . so as the sign of the cross being afterwards used , doth neither add any thing to the vertue or perfection of baptism ; nor being omitted doth detract any thing from the effect and substance of it . secondly , it is apparent in the communion book , that the infant baptized is by vertue of baptism , before it be signed with the sign of the cross , received into the congregation of christs flock , as a perfect member thereof , and not by any power ascribed unto the sign of the cross ; so that for the very remembrance of the cross , which is very precious to all them that rightly believe in jesus christ , and in the other respect mentioned : the church of england hath retained still the sign in baptism , following therein the primitive and apostolical churches , and accounting it a lawful outward ceremony , and honorable badge , whereby the infant is dedicated to the service of him that died upon the cross , as by the words used in the book of common-prayer it may appear . ] if this will not suffice to prove , that nothing sacramental is intended by it , let it be noted , that in private baptism the cross is totally omitted . his next exception is at holy-days : but i shall pass my bounds too far . i 'll borrow one maxim of the judicious hooker , ( upon th●t subject ) which shall serve for all . those things which the law of god leaveth arbitrary , and at liberty , are all subject unto positive laws of men : which laws , for the common benefit , abridge particular mens libertie in such things , as far as the rules of equity will suffer . after the quality of our ceremonies , the holy man will have one fling at the number of them . if the english ceremonies be warrantably used , what hinders the use of divers other ceremonies used in the roman church ? is it said , their multitude will become burthensome and inconvenient ? but who can determine the convenient number ? and however , an exchange of one ceremony for another were not unlawful . for what reason may not some other romish rites in baptism be used as well as the cross , seeing they are nothing less significant or inoffensive ; nay , peradventure much more inoffensive , because the papists by giving divine worship to the cross , have abused it to gross idolatry . observation beggars must be no choosers : must we use all , or none ? the english church hath made election of the english ceremonies ; what , and how many : being the proper judge both in the point of number and convenience . 't is not for us to question the authority , but to obey it . what if the cross hath been abused ? so hath the knee been bent ; the hands and eyes addressed to an idol . are we , because of this mis-application , prohibited to worship the true god , in the same manner , and posture ? now to the liturgy again . the presbyterians are not satisfied in the present liturgy , but desire it may be laid aside , or much reformed . and what solid reason withstands the equity of this desire ? this solid reason does withstand it . they beg like sturdy cripples , for christ's sake , with a cudgel . and 't is not safe for authority to give ground to a faction . whosoever observes impartially , shall find , that political prudence was joyn'd with christian piety , in composing the english service-book . ] and the same prudence is now joyn'd with the same piety , both in the right , and interest of preserving it . his next grief is a heavy one . canonical subscription lately impos'd , is a yoke of bondage , ( now mark him ) to be considered by all those that have a true regard to such liberty in religion , as equity and necessity pleads for . observation either this passage is seditious , and to enflame the people against authority , or i am no englishman . the canon ( says he ) requires a subscribing to the thirty nine articles ; to the common-prayer-book ; to the book of ordering bishops , priests , and deacons ; that all these contain in them nothing contrary to the word of god. this is unreasonable , unprofitable , and unnecessary . nay , let us take in the third article too , — to wit , [ that the nine and thirty articles are agreeable to the word of god. ] and now the form of subscription , viz. [ i do willingly , and ex animo , subscribe to these three articles above mentioned , and to all things that are contained in them . this is the yoke of bondage , which our reverend libertine complains of . first , to the unreasonableness of this subscription . touching the king's supremacy , asserted in the first article , he is silent ; and i suppose he would be thought consenting . as to the rest , what reason is there that any man should be admitted into the ministery , without subscribing to the constitution of that church , into which he seeks admitance ? if he cannot subscribe in conscience , he cannot be admitted in prudence : and if he refuses in point of stomach , that man is not of a gospel-temper . in fine , he that holds a fair opinion of the doctrine , and discipline of the church of england , may very reasonably set his hand to his opinion : and he that does not , may as reasonably be rejected because of such disagreement . so much for unreasonable ; neither is it unprofitable : for such as have any spark , either of honor , or shame , will in regard to such a testimony , be tender of giving themselves the lye , whatever they would do otherwise . his third cavil is , that it is unnecessary ; ( so are his exceptions . ) let any man consider ; when all these bars and limits are too little to restrain turbulent and sacrilegious spirits from dangerous and irreverent attempts : what seas of schism and heresie would break in upon us , were but these banks demolish'd . but he hath found out an expedient , how [ unity in doctrine , and uniformity in practise , may be as well attain'd , and far more kindly , without this enforced subscription : ( that is ) if no minister be suffered to preach , or write , any thing contrary to the establish'd doctrine , worship , or discipline , nor ordinarily for the main to neglect the establish'd rule . ] observation this last passage appears to me most spitefully pleasant . not ordinarily for the main , that is ; always sometimes he would neglect the establish'd rule . if the laws already in force against revolters , had been duly executed , 't is likely the interest of england , in the matter of religion , had not been now the question . but still this supposition does not imply an absolute sufficiency of that strictness to all intents and purposes of order and agreement . 't is what we think , not what we say ; the harmony of souls , more then of forms , which god regards : without that sacred , and entire consent of judgment , and affections , the rest is but a flat , and cold formality . not to act contrary to prescribed rules , ( where we are bound up by a penalty ) is but a negative and passive obedience ; a compliance rather with convenience , than duty , unless joyn'd with a prone , and full assent , both to the truth and equity of those determinations . for these and many reasons more , canonical subscription seems to me exceeding necessary . but for those people to decline it , ( upon pretence forsooth of conscience ) that upon pain of freedom , and estates , nay , and of hell it self , enforced the covenant , is most unequal . a presbyterian preacher , * refused to pray for sir william nesbett , late provost of edenburgh , when he was lying upon his death-bed , onely because he had not subscribed the covenant . let me be pardoned , if i understand not this incongruous holiness . as for the decrees and canons of the church , what rightful authority doth make them , as the law of the medes and persians that altereth not ? observation surely his reverence over-shoots himself . what rightful authority ? the kings : and by a less authority they cannot be discharged . by that authority , that licenses x] the excommunication of the impugners of the rites and ceremonies established in the church of england : — the opposers also of the y] government , by arch-bishops , bishops , &c. — by that authority , to which this gentleman hath forfeited the head he wears . well , but he tells us , the publick state of these differences is such , that the prelatists may , and ought to descend to the presbyterians , in the proposed moderate way ; but the presbyterians cannot come up to the prelatists in the height of their way . with the king's leave , had been good manners yet . by what authority , does presbytery pretend to unseat the hierarchy ? all the world knows , ( as much as they know any thing of that antiquity ) that bishops are of apostolical extraction : and we are not to imagine , that they died intestate , and their commission with them . but bishops have descended already , and what was the event of it ? truly it was as moderate an episcopacy as heart could wish : but , as i remember , their revenues were not employed to maintain a practical ministery . the rule is , — si vis scire an velim , effice ut possim nolle . but see the moderation of the man. some change ( he says ) in the outward form , and ceremonies , which are but a garb , or dress , is no real change of the worship . i thought we had differ'd upon point of conscience , about * [ ceremonies properly sacred , — and parts of worship . ] but now it seems 't is but the garb , or dress we stick at . the good-man has forgot himself ; and yet we had best be wary , for 't is but an untoward hint he gives us . oftentimes ( says he ) moderate reformations do prevent abolitions , and extirpations . ] observation they do so , often , and sometimes they cause them : that is , be the state never so distemper'd , where subjects turn reformers , the remedy is worse than the disease . in fine , when i look back , i find the very same desires of reformation originally pretended ; which ( after such descensions as never any prince before the blessed father of our gracious soveraign , made to his subjects ) proceeded yet to utter extirpation , root , and branch . the present face of things looks so like twenty years ago , i cannot choose but fear the same design from the same method ; the same effects from the same causes . is not that likely to be a blessed reformation , where faction dictates , and tumults execute ? but our pacifick moderator is of another temper sure ; he onely advises a yielding , for fear of worse : especially considering , that the party called presbyterian may be protected , and encouraged , and the episcopal not deserted nor disoblig'd . which is his resolution upon the second quaere presbyterian improvements are commonly a little sinister ; ( or , as a man may say , over the left shoulder ) they have something an odd way of making a glorious king , and a happy people . but we shall not dispute the possibility of doing many things which may be yet of dangerous experiment . i do believe it possible for a man to flie ; yet set him upon pauls , and lure him down , upon the trial , 't is at least six to four he breaks his neck . truly in my opinion , this proposal is all out as impracticable . but 't is all one to me. what if the two church-parties , can agree , or what if they cannot ? my business is to keep the presbyterian from laying violent hands upon the civil power , and to convince a party so denominated , of sedition , not of schism . his third enquiry follows . qu. iii. whether the upholding of both parties by a just and equal accommodation , be not in it self more desirable , and more agreeable to the state of england , than the absolute exalting of one party , and the total subversion of the other ? ( and thus he reasons . that state of prelacy which cannot stand without the subversion of the presbyterians , and that stands in opposition to regulated episcopacy , will become a mystery of a meer carnal and worldly state , under a sacred title , and venerable name of our mother the church . for in such opposition , of what will it be made up , but of lordly revenue , dignity , splendor , and jurisdiction , with outward ease and pleasure ! what will its design be from age to age , but to uphold and advance his own pomp and potency ? read the ecclesiastical histories , and you shall find the great business of the hierarchy hath been to contest with princes and nobles , and all ranks and degrees , about their immunities , privileges , preheminences , to multiply constitutions and ceremonies for props to their own greatness , but not to promote the spiritual kingdom of our lord jesus christ in the hearts of people , according to the life and power of christianity . observation let this serve for a taste of his pedantique boldness . whether the scandal , or the danger of these liberties is the greater , may be one question : and whether the usurper of this freedom is the better subject , or christian , may be another . if we respect the holy order of bishops , together with the sacred authority of law , by which they are here established , how scandalous and irreverend is this invective ! or if the unsetled humor of the people , how dangerous ! if we reflect either upon christian unity , or political obedience : how inconsistent is this manner of proceeding , with what we owe to god , and the king ! that state of prelacy , which cannot stand without the subversion of the presbyterians , &c. — 't is very well ; — and why the subversion of the presbyterians ? how those that never were vp , should be thrown down , i cannot imagine . by what law , or by what equity , do these people pretend to any interest of establishment in england ? those of the presbyterian judgment , that out of a real tenderness cannot comply in all particulars , will beyond doubt receive from his majesty such favour and indulgence , as may abundantly suffice to their relief . but that pretence doth not one jot entitle them to challenge a further influence upon the government . these wayward appetites and cravings , are but the sickly longings of a peevish woman : a kind of voluntary and privileged conscience they have , which if it happens to take a fancy even to the crown , monarchy it self must rather perish , than these poor wretches lose their longings . soberly i would advise them by any means , to waive these troublesome and groundless pretences . it starts a scurvy question , and makes men ask , how these people came by the right they challenge ? for the rest ; episcopacy is like to be well ordered , when the presbyterians have the regulation of it . there have been great contests ( no question ) mov'd by the hierarchy ; but i suppose this gentleman will not instance in many , ●ince the reformation , derogatory to the jurisdiction royal : whereas the whole course of the presbyterian discipline hath been tumultuous ; and their avowed principles are more destructive to royalty , than even the rankest of the jesuites themselves . having at length talk'd his fill against the pomp of prelacy ; and charg'd the arrogance of presbyters upon the bishops : thus he concludes , in very deed , the state here described , will never stand safely among a people that are free , serious , searching , and discerning in matters of religion . ] which to the many , sounds thus much . this is the pride and tyranny of bishops : and none but a slavish and besotted people will endure it . he that makes other of it , forces it . having by the spirit of natural divination foretold the effects which he himself intends to cause ; he gives this hint to the vulgar , that [ a hierarchy of this nature hath a strong bias toward popery . ] no doubt , and so had monarchy . was not this imputation , by the same party , cast upon the late king , and with the same measure of confidence and bitterness ? when yet we know , that those that charged him with it , did not believe themselves ; it was so rank , and evident a calumny . nor to insist upon the dying testimony of that incomparable prince ; ( which was but suitable to the pious practise and profession of his whole life ) that early protestation of his majesties , before his receiving of the holy eucharist at christ-church in oxon , 1643. will be more pertinent to my purpose . his majesty being to receive the sacrament from the hands of the lord arch-bishop of armagh , used these publick expressions immediately before his receiving the blessed elements , he rose up from his knees , and beckning to the arch-bishop for a short forbearance , made this protestation . my lord , i espy here many resolved protestants , who may declare to the world the resolution i now do make . i have to the utmost of my power prepared my soul to become a worthy receiver ; and may i so receive comfort by the blessed sacrament , as i do intend the establishment of the true reformed protestant religion , as it stood in its beauty in the happy days of queen elizabeth , without any connivence at popery . i bless god , that in the midst of these publick distractions , i have still liberty to communicate ; and may this sacrament be my damnation , if my heart do not joyn with my lips in this protestation . this was not yet enough to allay the clamour , till with his royal blood he had seal'd this protestation . if the objector can produce a fouler injury , either to religion , duty , truth , honor , or humanity , let it be done , to save the credit of the faction , unless they reckon the superlative perfection of their wickedness , a point of glory . his next remark is not amiss . [ let it be well observ'd , that the designs of suppressing puritans , and complying with papists , had their beginning both at once , and proceeded in equal paces . observation let it be here as well observ'd , that if by puritans be meant those of the separation , by papists is intended such as kept their stations : these squires of the revolt , esteeming as anti-christian , whatever stands in opposition to their heady purposes . we have this both from story and experience , that it hath been the constant practise of these unmannerly apostates , to speak evil of dignities ; & being fall'n off themselves , it is but carnal prudence , by damning of the authority to justifie the schism . no wonder then , if the designs of suppressing puritans , and complying with papists , had ( in his sense ) the same beginning , and proceeded in equal paces . to bring himself off , he shifts it thus . [ according to a vulgar sense , we take popery in the heighth thereof , for the heresies and idolatries ; and in the lower degree thereof , for the gross errors and superstitions of the church of rome . ] and 't is against english popery in the lower degree , that he plants his battery : arguing so formally against our going over to rome , that any stranger to the story would swear , — the prelates and the pope were more then half agreed already . having at length with great good-will advised the church of england as to the main , he concludes , that [ all approaches and motions towards rome are dangerous . ] but are not all recesses from truth , more dangerous : because in every thing we cannot agree with them , must we in nothing ? to me this appears rather petulancy , then pious reason . we are to hold fast the truth , where-ever it lyes : and to embrace what 's good , and laudable in any church , without adhering to the contrary . did not st. paul become all things to all men , that by all means he might gain some ? but if we walk upon the brink ( he tells us ) we may soon fall into the pit. ) these wary men forget , that there 's a gulf on the one hand , as well as a pit on the other : and that the narrow way is that which leads to eternal happiness . but as to reason of state ( he says that ) enmity with rome , hath been reputed the stability of england ; concerning which the duke of rhoan hath delivered this maxime ; [ that besides the interest which the king of england hath common with all princes , he hath yet one particular , which is , that he ought throughly to acquire the advancement of the protestant relig●●n , even with as much zeal as the king of spain appears protector of the catholick . allow this maxime good in state , he hath but found a rod to whip himself . the king of england ought to advance the protestant religion . ] content . what now if these disciplinarians prove no protestants ? but rather a schismatical , and dividing party , driving an interest of their own , under that specious name , and with great shew of holiness , opposing not only the practises and rules of the reformed churches , but even the fundamentals of christianity it self ? by whom will they be tryed , or on what judgement , and authority will they rest ? they quarrel with the order of bishops ; the common-prayer ; the rites and ceremonies of the church ; the law of the land , with customes , and antiquity : in short , with every thing but the geneva discipline . they do by that too , as our gallants do by french-fashions . the court of france being the standard of queint mode and dress , to the one , as is geneva of church order to the other : what is there used , though in it self extravagant enough , our humour is to over-do ; and if the french wear but wide breeches , we forsooth must wear petticoats . consult the learned and most eminent assertors of their discipline ; ask the grand architect himself , or indeed , any of his sectators , ( of fair and honourable credit ) concerning the subject of our present controversie . and 1. whether it be a protestant opinion , that the hierarchy is antich●istian ? ii. whether such laws of humane institution , as neither contradict the general laws of nature , nor any positive law in scripture , be binding or no ? iii. in case of male-administration , either in church , or state : whether the people may take upon them to reform ? but this they are not so stiff in , as to maintain it , but by blind inferences not worth regard . this is the state of our dispute ; and if in these particulars our anti-prelatists oppose the current of reformed divines : to advance their interest , is to undermine the common interest of the king , nation , and the protestant cause . needs must it move many revolts , and keep off many proselytes , to see such principles declared of the essence of christian religion , as a good honest pagan would be ashamed of . nor less repugnant are they to rules of society , than of conscience ; no tyranny so cruel and imperious ; no slavery so reprochful . set up their discipline , and we 're at school again . methinks i see a presbyter with his rod over every parish ; and the whole nation turning up their tails to a pack of pedants . yet hateful as it is , even that it self , establish'd by authority , might challenge our obedience . i have digress'd too far ; yet in convenient place , i must say something further upon this subject . if our new fangled polititian had consider'd , that the kings interest leads him to support , that which the presbyterians strive to overthrow , ( the protestant religion ) i am perswaded he would have spared the duke of rhoan in this particular . the maxime even as it lies before us , affording matter of dangerous deduction to his disadvantage : but taken in coherence , nothing can be more sharp and positive against him . that great and wise captain the duke of rhoan , discoursing upon what reasons of state , q. elizabeth acted toward spain , france , and the united provinces ; tells us particularly , how much she favoured the protestants in france , & germany . [ par toutes ces maximes , ( dit il ) cette sage princesse a bien fait comprendre , a ses successeurs , que outre l' interest que l' angleterre a commun avec tous les princes , &c. — by all these maximes ( says he ) this wise princess hath given her successors to understand , that besides the interest which england hath common with other princes , yet one particular it hath , which is to advance the protestant religion with the same zeal , the king of spain does the catholick . be it here noted , that when the queen was most concern'd , and busie to promote the protestant cause , even at that very time was she as much employ'd to crush the presbyterian faction , viz. cartwright , coppinger , arthington , hacket , and their confederates . the first of these was imprison'd , and fined for seditious and schismatical practises against the church and state. the second starved himself in a gaol ; the third repented , and publickly recanted : the fourth was put to death for horrid blasphemies . ( these people talk'd of a practical ministery too . — ( the men are gone , but their positions are still in being , and only attend a blessed opportunity to be put in execution . this may appear from divers late discourses , which are effectually no other then cartwrights principles , and model , couch'd in warier terms , and other authority than these , or such as these , i think the very authors of them will scarce pretend to . one observation more . our paraphrast renders the advancement of the protestant religion , — enmity with rome , to the great scandal of the reform'd profession . we have no enmity but with errour , which in a rigid puritan , to us , is the same thing as in a papist . but popery ( he tells us ) hath been ever infamous for excommunicating , murthering , and deposing princes . i am no advocate for the roman cause , but upon this account , i think betwixt the jesuite , and the puritan , it may be a drawn battel . and yet he follows , with an assurance that the protestant religion aims at nothing , but that the kings prerogative , and popular liberty , may be even ballanced . ( that is , the puritan , — the presbyterian religion , as he explains himself a little lower . i cannot call to mind one single passage in this whole discourse , concerning the kings power , or the peoples liberty ; which is not either worded doubtfully or with some popular limitation upon the royal authority . what does he mean by even ballancing ? cheek by joul ? or by what warrant from the word of god , does a presbyters religion intermeddle with popular liberty ? unless the holy man intends to bring homage to kings , within the compass of ceremonies of humane , and mystical institution . yet once again . the presbyterian principle ( he sayes ) is for subjection to princes , though they were hereticks , or infidels ; and if they differ herein from the prelatical protestant , ( i was afraid we had been all papists ) it is only that they plead for liberty , setled by known laws , and fundamental constitutiont . ] still ad populum ? these are the incantations which have bewitch'd this nation . this charm of qualify'd disloyalty , and conditional obedience . behold the very soul of the faction in these five lines ; a fair profession first to his majesty , and with the same breath a seditious hint to the people . what is that liberty he talks of , but a more colourable title to a tumult ? that legal freedome , to which both by the royal bounty , and our own birth-right we stand entituled , we ought not to contest for with our soveraign , and ( god be prays'd ) we need not , now for another fit of kindnesse . his majesty our native king , may govern as he pleases , without fear of hazards , by continuing to shew himself a common father . observation what 's this cause a kin to the third article of the covenant ? to preserve and defend the kings majesties person and authority , in the preservation and defence of the true religion , and liberties of the kingdoms , ] ( as who should say , if , he does otherwise , let him look to himself . the excessive dominion of the hierarchy , with the rigorous imposition of humane ceremonies was accounted much of the malady of former times , which ended in those deadly convulsions of church and state. observation since this pragmatical levite will provoke a controversie , i am content to entertain it . if the bishops excesses were the cause of war , how came the kings ruine to be the effect of it ? but 't is no new thing for a presbyterian to saddle the wrong horse . just in this manner did the covenanters treat his late majesty : and by those very troops that cryed down bishops was the king murther'd . ridiculous brutes , to boggle at a surplice , and yet run headlong into a rebellion . the grand source of our miseries was the covenant , by which , as by a spell ( in the name of the blessed trinity ) the people were insensibly bewitched into an aptnesse to work any wickednesse which the interpreters of that oracle should say was the intendment of it . the first notorious rupture was in scotland , in 1637. attended with a covenant , which without question was formerly agreed upon by the confederate faction of both kingdoms , as the most proper and least hazardous way of tasting the kings patience , and the peoples humours . that their design was laid and carried on by counsels , and intelligence as aforesaid , may be collected from the consequent , and brotherly agreements : and truly the retrospect of the act of indemnity seems to hint no lesse , for it commences from the first scottish broyls , tho' four or five years before the war brake out in england ; what was begun by covenant , was so prosecuted . by virtue of the covenant the kirk-party supply'd themselves with men and monies : armies were brought into the field ; and beyond doubt , many that truly loved the king , not knowing what they did , ingaged against him . to keep up this delusion , the press and pulpit did their parts , and to deal freely after this advance , i should as much have wondred if they had stop'd short of his death , as i find others wondering how they durst accomplish it . death with a bullet or an axe , is the same mischief to him that suffers it : and the same crime , wilfully done , in those that act it . no man can rationally allow one , and condemn the other : for if the violence be lawful ; why not as well in the field , as upon a scaffold ? in this particular , the doctor is beside his cushion . he makes me think of the marquiss of newcastle , upon a sawcy clergy-man . why should i remember that he 's a priest ( says my lord ) if he forgets it himself ? his next argument against prelacy is a modest , and ( as i take it , ) a queint one. can the self same state ( sayes he ) and frame of ecclesiasticks be now revived after so great and long continued alterations , by which the anti-prelatical party is exceedingly increased and strengthned ? surely this gentleman has a mind to give his brother crofton a visit . cannot prelacy be better restored after a discontinuance , then presbytery erected , where it never had a being ? the very laws are yet to make , for the one , and still in force for the other . but the great obstacle is , the anti-prelatical party is exceedingly increased , and strengthned . ] truly i think , if his majesty should lessen the number of them , by two or three of the promoters of that doctrine , the precedent might do some good upon the rest . can any thing be more feditious ? these hints upon fair grounds and given in private , might very well become the gravity of a churchman , or the profession of a loyal subject . but to the people , these calculations are dictates of sedition ; and only meant to engage the credulous and heady multitude in false opinions both of the tyranny of prelates , and their own power . thus far in observation upon the first part of the interest of england , in the matter of religion , &c. — the whole structure whereof ( in his own words ) rests upon these positions , as its adequate foundation . 1. that whilest the two forenamed parties remain divided , both the protestant religion , and the kingdome of england is divided against it self . 2. that the presbyterians cannot be rooted out , nor their interest swallowed up , whilest the state of england remaineth protestant . 3. that their subversion if it be possible to be accomplished , will be very pernicious to the protestant religion , and the kingdome of england . 4. that the coalition of both parties into one may be effected by an equal accommodation , without repugnancy to their conscientions principles on either side , in so much that nothing justifiable by religion or sound reason can put a bar to this desirable union . the whole matter ( in debate he tells us ) rests upon three main enquiries . i. qu. whether in justice or reason of state the presbyterian party should be rejected and depressed , or protected and incouraged . ii. qu. whether the presbyterian party may be protected and incouraged , and the episcopal not deserted nor dis-obliged . iii. qu. whether the upholding of both parties by a just and equal accommodation be not in it self more desireable and more agreeable to the state of england , than the absolute exalting of the one party and the total subversion of the other . observation i shall now offer some further reasonings of my own ; upon this subject ; therein proposing such brevity and clearnesse ; that both the lazy , and the busie may find time to read it , and the weakest not want capacity to understand it . his first position holds no further good , then as the presbyterians are first protestants in the matter of the difference , and then considerable in the ballance of the nation . religion led the quarrel , so let it the dispute . in using the word protestant , i follow custome , for i had rather call it catholick : but protestant let it be . i suppose by the protestant religion , we understand that of the reformed churches : to whose decision we shall willingly submit the sum of our disagreements : which may be stated under a reduction to these two questions . i. qu. whether or no the government of the church by archbishops & bishops — be antichristian , or unlawful ? ii. whether such laws of humane and significant institution , as are orderly made , and neither contradict the general laws of nature , nor any positive law in scripture , — be binding or not ? first , concerning the prelacy : luther himself distinguishes betwixt popish tyrants , and true bishops : professing his quarrel to them as popish not as bishops . the authors of the augustane confession , leave it upon record , that they would willingly preserve the ecclesiastical and canonical polity , if the bishops would cease to tyrannize over their churches . ] bucer advises by all means the restoring of such ecclesiastical governments as the canons prescribe , ( episcopis & metropolitanis ) to bishops and metropolitans . melancthon to luther , — you would not imagine ( says he ) how some people are netled to see church-policy restored : as if it were the romish soveraignty again . ] ita de regno suo , non de evangelio , dimicant socii nostri . calvin himself recommends the hierarchy to the king of poland : and treating concerning the primitive church , says , that the antient government by arch-bishops and bishops , and the nicene constitution of patriarchs , was for orders sake , and good government . [ ad disciplinae conservationem pertinebat . ] the same person being called to accompt by cardinal sadolet , concerning the geneva defection , and for subscribing the augustane confession , renders this answer . cursed be such as oppose that hierarchy , which submits it self to christ jesus . [ nullo non anathemate dignos censeo , quotquot illi hierarchiae , qui se domino jesu submittit , subjici nolunt . zanchi ( the compiler of the gallican confession ) observes a change of name , rather than of office , throughout most of the german churches . bishops and arch-bishops being onely disguised under the notion of super-intendents , and general-superintendents : acknowledging , that by the consent of histories , counsels , and the antient fathers , those orders have been generally allow'd by all christian societies . beza , ( the rigid successor of calvin ) being check'd by the arch-bishop of canterbury , for intermedling beyond his spheare , — we do not charge ( says he ) all archbishops and bishops with tyranny . — the church of england hath afforded many learned men , and many glorious martyrs of that function . if that authority be there still in beeing , may a perpetual blessing go along with it . [ fruatur sane istâ singulari dei beneficentiâ , quae utinam illi sit perpetua . ] this with all ceremony was addressed , — totius angliae primati : to the primate of all england , and in the name of the whole church of geneva . saravia makes him him speak yet plainer ; who arguing for the hierarchy out of the apostles canons , receives from beza this reply . this is no more then what we wish might be restored to all churches . [ quid aliud hic statuitur , quam quod in omnibus locis , ecclesiis restitutum cupimus ? ] zanchi comes up to the very case of england ; ( nay , and a little further too ) not onely affirming episcopacy to be agreeable to the word of god : but where it is in exercise , that it ought to continue , and where by violence it hath been abolish'd , that it ought to be restor'd . [ * vbi vigent ( isti ordines scil . ) non esse abolendos , & ubicunque iniquitas temporum eos abolevit restituendos . ] with what face now shall the enemies of bishops call themselves protestants , in this particular at least , wherein they evidently cross the whole stream of protestant divines ? now to the second quae●e . whether such laws of humane , and significant institution , as are orderly made , and neither contradict the general laws of nature , nor any positive law in scripture , be binding or not ? hear calvin first , [ quamvis quod oberuditur scandalum afferat , quia tamen verbo dei per se non repugnat concedi potest . ] scandals taken , without repugnancy to the word of god , are not sufficient to invalidate the obligation of a ceremony imposed by the church . beza himself , nay , mr. cartwright , the captain of our blessed legions , will allow , rather than quit a benefice , to wear a surplice . bucer thanks god with all his soul to see the english ceremonies so pure , and conform to the word of god , or at least , ( rightly understood ) not contrary to it . not to hunt further for particular authorities , i shall be bold with my own brother , and make use of some general collections which he hath gathered ready to my hand . nothing assuredly can be more demonstrative of the protestant tenets , than the confession of their several churches . that of helvetia first , [ churches have always used their liberty in rites , as being things indifferent , which we also do at this day . ] that of bohemia ; [ humane traditions and ceremonies brought in by a good custom , are with an uniform consent to be retained in the ecclesiastical assemblies of christian people , at the common service of god. ] the gallican ; [ every place may have their peculiar constitutions , as it shall seem convenient for them . ] the belgick ; [ we receive those laws as are fit , either to cherish or maintain concord , or to keep us in the obedience of god. ] that of ausburg ; [ ecclesiastical rites which are ordained by mans authority , and tend to quietness and good order in the church , are to be observed . ] that of saxony ; [ for order sake , there must be some decent and seemly ceremonies . ] that of swethland ; [ such traditions of men as agree with the scriptures , and were ordained for good manners , and the profit of men , are worthily to be accounted rather of god than of man. ] these were the tenents they publickly owned , nor did they act different from what they taught , ordaining churches , pulpits , prayers before and after sermon , administring the sacraments in churches , delivering the communion in the forenoon to women , baptizing infants , and several other things , not one whereof were directly commanded by either christ , or his apostles . from hence 't is manifest , we may divide from presbyterians , and yet the protestant religion not be divided against it self . a schism there is , but whether in the church , or in the faction , is onely a dispute for those that plead the authority of tumults . as their opinions are not one jot protestant , where they divide from bishops ; so neither are their morals any more warrantable , wherein they act as men. which shall we credit , words , or deeds ? will they not bite ; where they pretend to kiss ? a famous martyr of that party , ( hacket ) served a fellow so . some difference there had been , and they were to be made friends . hacket pretends a reconcilement ; takes the man in his arms , bites off his nose , and swallows it . this is that hacket that was joyn'd with coppinger , and archington , in a plot to murder the lords in the star-chamber , because they had committed cartwright , ( the great rabbi of the party ) whose crime was onely the erecting of the presbytery without , and against the queens authority . thus we see , that in queen elizabeth 's days too , the protestant religion was divided against it self . briefly , that it is not religion which moves these people , is most apparent , from their unquiet and distempered actings . proceed we now to enquire what it is , or in plain terms , to unmasque the holy cheat , and shew it bare-fac'd to the people . of all impressions , those of religion are the deepests ; and of all errors , the most to be lamented and indulged , are those of tender and mis-guided consciences . the clearness of this principle considered , it is no wonder that the foulest designs , put on the greatest shews of holiness , as the onely way to gain and rule affections , without which , no great matters can be accomplish'd . this is a truth well known to the presbyterians , and of experiment as antient as their discipline . we do not undertake to read their hearts , but their vvritings we may venture upon ; enquire a little into their practises , and by comparing both , give some tolerable guess at their intentions . the readiest way is to look back , and match them ; for the best prospect of the future is behind us . some grumblings toward the consistorian discipline , there were in the days of edw. 6. but the first notorious separation was that of frankford , ( in the reign of queen mary ) when gilby , goodman , and whitingham , with their companions , flew off , and went to geneva , from whence they returned into england , soon after queen elizabeth came to the crown . these led the dance in england ; knox in scotland : and at this day our presbyterians do but write after their copy : professing the same principles , pretending the same scruples , and beyond doubt proposing the same end ; which was to get the same dominion here , which calvin and beza exercised at geneva : to whom they still repair'd for counsel as they needed . cartwright and travers came in the breech of these , but not without consulting beza first , to learn the knack of the geneva model . these were the men that first brought into england that horrible position , that the geneva discipline was as essential a note of the church , as either the true preaching of the word , or the due administration of the sacraments . this is the principle which supports the presbyterian interest . for the first thirteen years of the queen's reign , they contented themselves to throw about their libels against ceremonies , and divide into conventicles . in the fourteenth of her majesty , they addressed two admonitions to the parliament ; the former in the quality of a remonstrance , with a platform ; the other , bolder , and more peremptory . this parliament was no sooner dissolved , but they fell presently to work upon their discipline ; the progress whereof is with great exactness set down in the third book of bancroft's dangerous positions . in 1572. a presbytery was erected at wandesworth in surrey , at which time they had also their conventicles in london , where little was debated , but against subscription , the attire , and book of common-prayer . in 82. a meeting was appointed of 60 ministers , out of essex , cambridge-shire , and norfolk , at cockfield ; to confer about the common-prayer , — what might be tolerated . ] in 83. the form of discipline was compiled , and decrees made touching the practise of it , which soon after were put in execution . ] in 87. the discipline was received , and put in practise in northampton-shire . ] in 88. a classical assembly at coventry . ] in 89. a general meeting in cambridge , and another at ipswitch . ] in 1590. vpon the detection of the premises , they refused to answer upon oath . being thus associated , they appropriate to their meetings the name of the church , and use the style . the offices of the lord arch-bishops , and bishops , &c. ( says martin junior ) are condemn'd by the doctrin of the church of england . ] by these degrees , the schismaticks advanced to a dangerous heighth , and boldness ; and of this temper and extraction are our presbyterians . after the aforemention'd discovery , a stricter eye and hand was kept upon them ; divers of the ring-leaders were imprison'd , and the covy broken . upon the coming in of king james , they began to stir again ; but he knew them too well , either to trust , or suffer them . how they behaved themselves towards the late king , is to the eternal infamy , not onely of the faction , but of the nation , too notorious : what they design toward the present government , that 's the question : and now i come to enquire . — whether in justice or reason of state the presbyterian party should be rejected and depressed , or protected and incouraged . before i fall upon the question , once again i explain my self . by presbyterian , i intend a faction , that under colour of setling a reform'd discipline , seeks to dissolve the frame of an establish'd government . and first , i am to prove that party so distinguish'd , such a faction , which both from their own practises , positions , and from common observation , and authority , i think i shall make good ; and that their last aim is to exercise that tyranny themselves , which they pretend to punish . we 'l first examine how they treat the civil power . if princes be tyrants against god and his truth , their subjects are freed from their oaths of obedience . kings , princes , and governors , have their authority of the people , and upon occasion , the people may take it away again . ministers ought not to obey the prince , when he prescribes ceremonies , and a fashion of apparel . evil princes ought by the law of god to be deposed . andrew melvil being cited to answer for treason delivered in a sermon , declined the judgment of the king , affirming , that what was spoken in pulpit , ought first to be tried and judged by the presbytery ; and that neither the king nor counsel might in primâ instantiâ , meddle therewith , although the speeches were treasonable . ] strike the basilique vein ; nothing but this will cure the plurisie of our state. let us never give over , till we have the king in our power , and then he shall see how good subjects we are . ( delivered in a sermon . ) it is lawful for subjects to make a covenant , and combination without the king. but to come nearer home , to shew that the whole gang is of the same leaven . worse than all this was daily printed against the late king , even by those persons that were in pay to the presbyterian faction : and yet at last , those outrages are justifi'd against the father , by such as would be thought loyal to the son. if parliaments think to scape better , they are deceived . if the brethren cannot obtain their will by suit , nor dispute , the multitude and people must do the feat . one preached , that though there were never so many acts of parliament against the covenant , yet it ought to be maintain'd against them all . the parliament can make no law at all concerning the church , but onely ratifie what the church decrees : and after it hath ratifi'd it , yet if the assembly of the church shall prohibite it , and repeal that decree of the church , all the subjects are discharged from yielding obedience to that act of parliament . an assembly may abrogate acts of parliament , if they any way reflect upon business of the church . reformation of religion belongs to the commonalty . of the parliament in the 24 year of the queen , ( says the supplication ) if the desired reformation be not granted . ] there shall not be a man of their seed that shall prosper , be a parliament man , or bear rule in england any more . concerning laws established ; they fall in consequence with the power that makes them . presbyterians opinion of bishops let us see now with what modesty they treat the church , and first the bishops . they are ordinances of the devil , — proud , popish , presumptuous , prophane , paltry , pestilent , pernicious prelates , and vsurpers , — robbers , wolves , simoniacks , persecutors , sowers of sedition , dragons , ( and so to the end of the chapter . ) their clergy , an antichristian , swinish rabble , — the ministers are neither proved , elected , called , nor ordained according to gods word . the ceremonies , — carnal , beggerly , antichristian pomps . presbyterian reformation . hitherto , the faults of governors , and government , now their proposals of amendment , and reformation ; by what rules , and by what means we may be governed better . thus then . let the whole government of the church be committed to ministers , elders , and deacons . very good , and to whom the government of the state ? why to them too . for the church wherein any magistrate , king , or emperor is a member , is divided into some that are to govern : viz. pastors , doctors , and elders : and into such as are to obey , viz. magistrates of all sorts , and the people . the question is next , about the extent of the ecclesiastical power , and in what manner that assumption hooks in all civil actions within their cognisance ? in ordine ad spiritualia , forsooth : by which rule nothing scapes them . 't is the desire of the admonitor ; that he and his companions may be deliver'd by act of parliament , from the authority of the civil magistrates : as justices , and others , and from their inditings , and finings . ] the eldership shall suffer no leud customs to remain in their parishes , either games , or otherwise . ] and further ; the office of the church-governors , is to decide controversies in doctrine and manners , so far as pertaineth to conscience and the church-censures . ] every fault ( says cartwright ) that tendeth either to the hurt of a man's neighbour , or to the hindrance of the glory of god , is to be examined and dealt in by the orders of the holy church . ] nay , knox goes further yet . the bare suspition of avarice , or of pride , superfluity , or riotousness in chear or rayment . ] — even this nicety falls within their censure . now would i know what need of a civil magistrate , when even our private thoughts are subjected to the scrutiny of a presbytery ? but will some say , what signifies the intemperance of particular tongues , as to the general of the party ? i am challenged by the author of the interest of england , to produce their actions : and that 's my next immediate business . the presbyter has now the chair , see how he manages his greatness . none of that tyranny ye found in bishops , i warrant ye : no groaning now under the yoke of antichrist ; the intolerable burthen of canonical subscription ; the imposition of ceremonies , properly sacred ; the injunction of the cross in baptism ; and that abominable idol , the common-prayer . some words perhaps may slip unwarily , that might have been as well let alone ; but alas good people , they mean no harm . suppose that some of this way were guilty of some provoking forwardness , should grave patriots , and wise counsellors thereupon destroy the weak party , or rather heal it ? 't is indeed possible , that in the heat of a reforming and spiritual zeal , they may have let fall speeches of holy indignation against the opposers of the * lord's ordinance . but have they shewed their disaffection either to * king or parliament , by any thing discernable in their outward behaviour : have they controlled the law of the land , or the just liberty of the people ? if they have not done all this , there 's a great failing both in our stories , and our memories . i know 't will be objected , they petition'd , and in a supplicant and humble way , suitable to the duty of good subjects . they did retition ; and in this manner — ( about the. 27. of the queen . ) may it please your majesty , &c. — that it may be enacted , &c. — that the book hereunto annexed , &c. intituled , a book of the form of common-prayers , administration of sacraments , &c — and every thing therein contain'd , may be from henceforth authorized , put in ure , and practised throughout all your majesty's dominions . herein they press upon the nation their own form , which would not yet allow of any other . what they could not get establish'd by law , they settle yet by practice , and privately agree upon a general endeavour to encrease the party . ] but say they should be opposed ? why then , have a fling at evil counsellors . [ if her majesty give ear to such counsellors , she may have cause one day to lament . ] then they remonstrate , how miserably poor men have been handled ; ] that godly ministers have been brought before the bars of justice ; ] and that if this persecution be not provided for , it is the case of many a thousand in england : great troubles will come of it . ] this numerous party will not vary from it self , &c. — the minds of men are fix'd in this opinion , and are not like to be reduced to the practise of former times . ] well said i. c. yet , thousands ( says another ) do sigh for this discipline ; and ten thousands have sought it . ] we do protest unto your majesty ( say the supplicators ) that we will be no longer subject unto the bishops unlawful , and usurped authority , &c. ] — and another . [ the truth will prevail ( speaking of the discipline ) in spight of your teeth , ( meaning the bishops ) and all other adversaries of it . ] in the late king's declaration concerning the tumults in scotland : this way of petitioning is very frequent : and this is that my friend hints , in saying , that the presbyterians have never ceased to sollicite , and supplicate , &c. ] but words draw no blood. 't is true , but such as these come very near it . we phancy first , defects in government ; then we discourse them ; after that , we propose a reformation , which , if rejected , we proceed to press it : the next step is a threat , and then a blow . where there are failings in authority , 't is not for private persons to take publick notice of them . who ever does that , would strike , if he durst . this is not meant of every slip , in common discourse , either of heat , or inadvertency ; yet that is very ill too ) but of deliberate affronts ; such as proceed from a form'd habit of irreverence : and in that case , i think 't were no hard measure , if he that sets his hand to the king's dishonor , should lose his head for 't . take it at worst . put case a prince misgoverns ; yet we are sure , that his superior does not ; and that respect we cannot pay to his failings , we must allow to his commission . from vvords proceed we now to actions . presbyterian practices toward their sovereign . the presbyterian is no sooner in the saddle , but ( in the name of reformation ) how the man gallops : kings , parliaments , laws and liberties , oathes and covenants , are but as feathers in his way . i shall not clog this section with many instances . the traiterous actings of the conventicle at glasgow , in 1638. the horrid outrages that usher'd it , and the most deplorable consequences that ensu'd upon it , contain enough to brand that faction to eternity . i shall the rather fix there , because it brings the case home ; and first , in regard that the schismaticks of both nations acted by the same tie of oath and interest . next , as it is the model , they have made the people swear they would be damn'd by . some of their many insolencies are these . i. the assembly is independent , either from king or parliament , in matters ecclesiastical . ii. it is lawful for subjects to covenant and combine without the king , and to enter into a bond of mutual defence against him . iii. an assembly may abrogate acts of parliament , and discharge their fellow-subjects from obedience to them , if they any way reflect upon the business of the church . iv. they deny the king 's right of calling or dissolving assemblies , and they continue to sit and act , notwithstanding his majesty's express order for their dissolution . ( see the king's declaration . ) these rebellious proceedings are yet darkned by the transcending usurpations that followed them . but here i am bounded ; this onely i may say ; who ever has a mind to run the extremities of another war , and to see another king murther'd , let him give his vote for presbytery . and here let every man look behind him , and lay his finger on his mouth . as the geneva discipline is injurious to kings , and stated laws , so it is most ridiculously tyrannous to the people . a great uproar arising in edinburgh , about the making of a robin-hood , they of the consistory did excommunicate the whole multitude . ] 't is a strange tenderness possesses these saints . one of them being to christen a child , brake off in the middle of the action , because he would not call it richard. ] i suppose no man knew this kind of cattel better than king james . i was persecuted ( says that learned prince ) by puritans , not from my birth onely , but even since four months before my birth . ] and to prince henry thus. take heed to such puritans , very pests in the church and common-weal , whom no deserts can oblige , neither oathes or promises bind ; breathing nothing but sedition , and calumnies , aspiring without measure , railing without reason , and making their own imaginations ( without any warrant of the word ) the square of their conscience . i protest before the great god , and since i am here as upon my testament , it is no place for me to lie in , that ye shall never find with any highlands or border-thieves , greater ingratitude , and more lies and vile perjuries , than with these phanatique spirits . and i think every man may say as much that hath but known them . we are at length by gods grert mercy , delivered from those evangelical impostors , and after all our wandrings brought once again , into the channel . we have our prince , our laws , our freedoms , our interest lies before us , and certainly we cannot be so mad , as now to dash a second time upon the same rock : yet they shall lose nothing for want of offering at it . the arguments of 1641. are set on foot again : the very same with cartwright's , ( that consistorian patriarch , as bancroft terms him ) nay , they are advanc'd already beyond pleading of their cause , to pressing of it , by sawcy importunities , and peremptory threatnings . from what i have deliver'd , it cannot be deny'd , but their positions are destructive to all civil government : and for their practices , the story is written in blood. this might suffice to end the controversie concerning reason of state , for certainly a faction so principled , cannot with safety to the publick be incorporated into any politick constitution . but i shall add some further reasons , why by no means they are to be admitted . 1. they 'r a party never to be gain'd by obligations ; and this is manifest from their proceedings toward the late king , whose most unhappy tenderness of nature rost him his life . and at this instant , that irreclaimable ingratitude is yet more clear toward his majesty in beeing : whose unexampled mercy , so much as lies in them , is converted to his dishonor , and destruction . 2. they ground their claim upon the equity of their cause , which if allow'd , by the same reason they may serve this king as they did his father . 3. their demands are endless , as well as groundless , and it is not prudential to grant any thing to a faction , that will be satisfi'd with nothing . it is but giving them a power to take the rest . 4. they expostulate , and what they get upon those terms , they look upon rather as a submission , than a concession . the very manner of their address has a spice of mutiny in it , and they will hardly make an honest use , of what they compass by dishonest means . 5. it is not advisable to encourage tumultuary combinations , by rewarding them . 6. the dispute is not so much what their consciences will bear , as what their importunities can obtain : and to feel the pulse of the supreme authority . in fine , it is a contest betwixt the law and a faction , and a fair step toward a new rebellion . so much for reason of state. now to the justice of their pretences . the quaere is . whether in justice or reason of state the presbyterian party should be rejected and depressed , or protected and incouaged . 't is one thing what the king may do in point of justice , and another thing what the presbyterians may demand upon that score . there is a justice of conscience , honor , and of prudence . by the first : his majesty is ty'd up in common with the meanest of his subjects . that is , if the king find himself in conscience bound to maintain episcopacy in the state he found it , ( legally settled ) he is not free to alter it . in point of honor : there 's more liberty , and whatever the king does in that particular , is well done . but his majesty not having as yet declar'd himself ; what do we know , how far even upon that point he may concern himself to reject the presbyterian's demands ? partly out of reverence to his royal father ; in part , out of a princely strictness to his own dignity : and partly out of a generous tenderness toward his ruin'd party . first , as to what may seem relating to his majesty's father . that which these people urge , is what the late king chose , rather to die , than grant : which in his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 is intimated in these words . in these two points , the preservation of establish'd religion and laws , i may ( without vanity ) turn the reproach of my sufferings , as to the worlds censure , into the honor of a kind of martyrdom , as to the testimony of my own conscience , the troublers of my kingdoms , having nothing to object against me but this , that i prefer religion and laws established , before these alterations they propounded . every word hath its weight , which fell from the pen of that pious and judicious prince . nor can i over-pass a caution of his learned father's ; when i consider the sum of their proposals , which in effect is but a condemnation of the late king , in the bold , needless justification of themselves . these are the words . as for offences against your own person and authority , since the fault concerneth your self , i remit to your own choice to punish or pardon therein as your heart serveth you , and according to the circumstances of the turn , and the quality of the committer . here would i also eike another crime to be unpardonable , if i should not be thought partial : but the fatherly love i bear you , will make me break the bounds of shame , in opening it unto you . it is then , the false and unreverent writing , or speaking of malicious men against your parents and predecessors . and a little further . it is a thing monstrous to see a man love the child , and hate the parents : as on the other part , the infaming and making ●dious of the parents , is the ready way to bring the son into contempt . and for conclusion of this point , i may also alledge my own experience : for besides the judgments of god , that with mine eyes i have seen fall upon all them that were chief traitors to my parents , i may justly affirm , i never found yet a constant biding by me in all my straits , by any that were of perfect ☞ age in my parents days , but onely , by such as constantly bode by them ; i mean , specially by them , that served the queen my mother ; for so that i discharge my conscience to you , my son , in revealing to you the truth , i care not what any traitor , or treason-allower , think of it . thus far his majesty may find himself concern'd in honour to his fathers ashes , now to his dying counsels . take heed of abetting any factions , or applying to any publick discriminations in matters of religion , contrary to what is in your judgement , and the church well setled . i cannot yet learn that lesson , nor i hope ever will you , that it is safe for a king to gratifie any faction with the perturbation of the laws , in which is wrapt up the publick interest , and the good of the community . what in effect do these people now desire , but that his majesty would rather take their counsel , than his fathers ? in the next page , the king expresses a more than ordinary earnestness , in these words . my counsel and charge to you is , that you seriously consider , the former real or objected miscarriages , which might occasion my troubles , that you may avoid them . herein , his majesty is tacitly conjured against them ; it being a most notorious certainty , that the late king lost both his crown and life by over-granting . the now-pretended cause of the quarrel , was not mentioned till after the war was begun . the colour of raising an army , being to fetch in delinquents . after which ( says his majesty ) among other lesser innovations , this chiefly was urged : the abolition of episcopal , and the establishment of presbyterian government . as to the point of imperial honour , wherein his majesty may possibly concern himself more immediately : it is a high excesse of goodnesse to make his favours common , where they are look'd upon so cheap , ( as here ; witness these daily new transgressions , since his most gracious pardon . ) [ some men ( sayes the late king ) have that height , as to interpret all fair condescendings , as arguments of feebleness , and glory most in an unflexible stiffness , when they see others most supple and inclinable to them . ] there remains yet a third question under this head of honour ; that is , how far his majesties generosity may extend it self , in favour , and protection of those persons that have serv'd him , through all extremities till they have nothing left them beyond the hopes of honourable epitaphs . these people have consciences too ; a sense of duty and religion . they reverence the episcopal order , and that , which through the sites of bishops , was equally wounded : the order of kings . at last , those that subverted the former , and usurped the latter , demand ( i think in reparation of their hazards ) a presbyterian government . in which particular , our duty teaches us not to direct our master : only we take a sober freedome to answer our accusers ; and to professe to all the world , that those who fought for king and bishops , were in our opinion as honest men at least as they that fought against them . to his majesties honourable consideration , i think in this point we may claim a right . we have suffer'd for , and with his royal father , and himself , and the main justice of the cause , betwixt the king and those that serv'd him , is the same thing : so that whoever strikes at vs , wounds our soverein . lastly , there is a justice of prudence , wherein a man may frame a thousand reasons against the encouraging of the presbyterians ▪ not speculative , and airy notions , but close , and pinching reasons , grounded upon weighty authority , and a never-failing course of long experience . ( yet not to dictate to his majesty , to whose will we submit our reasonings ) first , if their desires were modest , the manner yet of promoting them , is too rude and positive ; they preach and print their grievances , which is the way rather to stir a faction , than allay a scruple . lord , ( sayes mr. manton ) give us the liberty of the gospel , before we go hence and be no more seen . ] as if episcopacy , were paganisme . 't is dangerous to grant more , to those that take too much . how do i reverence the divine spirit of his late majesty . the great miscarriage i think is , that popular clamours and fury had been allowed the reputation of zeal , and the publick sence ; so that the study to please some parties , hath indeed injured all . and again ; take such a course as may either with calmness and charity quite remove the seeming differences and offences by impartiality , or so order affairs in point of power , that you shall not need to fear or flatter any faction ; for if ever you stand in need of them , or must stand to their courtesie , you are undone : the serpent will devour the dove : you may never expect lesse of loyalty , justice , or humanity , than from those who ingage into religious rebellion : their interest is always made gods , under the colours of piety , ambitious policies march , not only with greatest security , but applause , as to the populacy ; you may hear from them jacobs voice , but you shall feel they have esaus hands . to what i have said , i shall be bold to add a justice of proportion ; and thereupon two questions . 1. why should the presbyterians ; a small , irregular party , pretend to give the law to the supreme authority , the established constitution ; and incomparably the greater part of the nation ? 2. why should those people , that with a more then barbarous rigour press'd the covenant : ejecting , sequestring , imprisoning such as refused to take it , and without mercy or distinction : — those that in publick barr'd non-covenanters , the holy communion in express terms with adulterers , slanderers , and blasphemers , affirming in the pulpit , that all the non-subscribers to the covenant were atheists . — why should ( i say ) those people that with so unlimited a tyranny imposed upon the nation a rebellious league ; to the engagement of their souls in taking it ; their liberties and fortunes in refusing : — i say yet once again ; why should those people now at last demand an interest in that government , which root and branch they have laboured to extirpate ? or with what face can they pretend a right to an authority , where but by mercy they have none to life ? ( i speak of these late libellers and their abettors . ) let me be understood likewise by presbyterians , to intend those of the scottish race , to whom we are beholden for our discipline . that faction first advanced it self by popular tumult and rebellion . knox learned the trick on 't at geneva , and brought it into scotland ; we had our agents too , that did as much for us , these fellows conferr'd notes , set the wheel going , and we were never perfectly quiet since . vpon the whole matter aforegoing ( in the gentleman 's own words ) we firmly build this position , that the presbyterian party , ought not , either in justice or reason of state , in any wise to be encouraged , but rather rejected ; neither ought they to be protected in any inconformity to the law , but rather totally depressed . his second quaere is soon dispatch'd , viz. ii. qu. whether the presbyterian party may be protected and incouraged , and the episcopal not deserted nor dis-obliged . first , many things are possible , which are neither just nor rational ; and therefore it matters not much to allow it the one , if i prove it not to be the other ▪ imagine such a contemperation of episcopal , and presbyterian pretences , as might atone their present disagreements , yet where 's the king ? the interest that 's principal in the concern , is not so much as named in the question . the quarrel was about the militia , not lawn-sleeves , and the royal party is to be taken in , as well as the episcopal . the truth of it is ; this gentleman does not find it convenient at present to move an utter extirpation of bishops : but he proposes that , which granted , would most infallibly produce it . a consociation forsooth , that for the better credit of the project , shall be called a regulated episcopacy , which in good honest english is next door to a tyrannical presbytery . in fine , the episcopal authority is deserted and disobliged by the admittance of a presbyterian competition . yet pardon me , i have found a way to reconcile them , make but these squabling presbyterians , bishops , and the work 's done : as presbyters they are encouraged ; and ( i dare say ) not disobliged , as bishops . the plague of it is , there 's neither justice nor reason of state for 't , and so we are where we were again . we shall make short work too with his third question : for in effect it spells just nothing . iii. qu. whether the upholding of both parties by a just and equal accommodation be not in it self more desireable , and more agreeable to the state of england , than the absolute exalting of the one party , and the total subversion of the other . i must needs take notice here of two mistakes , the one in propriety of language , viz. the vpholding of both parties . one of those parties is not up , and cannot be upheld . the other , shifts the question , and states the difference betwixt the exaltation of the one , and the subversion of the other , when all that we desire is but to keep both where they were , without advancing or depressing either . if they have any title to the interest they challenge , the same had cromwel to the crown . this question must be better stated , before we think it worth an answer . one reflexion now upon the whole . here 's exaltation , — and subversion ; — but not a syllable of toleration : and what 's the reason of all this ? they are afraid that would be granted ; and how should they do then to pick a quarrel ? their way is never to be satisfi'd in conscience , with what the king can give in honor , and reason . ( his sacred majesty's observation ) a grand maxim with them was always to ask something , which in reason and honor must be deny'd , that they might have some colour to refuse all that was in other things granted ; setting peace at as high a rate as the worst effects of war. ] i have cited this already , but every line drawn by that hand deserves to be repeated . to this , there is another end that 's common to the gang , which is , to draw an odium upon one party , and a compassion toward the other . and other end than this do i see none at all , in his absoute exalting , — and total subversion . we covet no change , but desire the contrary . how little soever it may appear to our purpose , 't is very much to theirs , to have the people understand by absolute exalting , — the dangerous and intolerable pride of bishops ; and by their total subversion , on the other side , how sadly the word goes with the professors of the gospel . these trivial appearances have more weight , than commonly the world imagines : 't is not so much ( as hooker says ) how small the spark is that flyeth up , as how apt things about it are to take fire . their business is to stir the affections of the common people , which must be done by means and ways , to wise men , in themselves ridiculous , but in their applications of most desperate effect . i speak in earnest , that very tone they use in preaching ; that fellow-feeling-tone ( as they would have it understood ) is i believe of great use to their business . i have observed the groans that follow the ahi-mee's , and beyond doubt those snivelling affectations are not without their benefit . that 't is a forc'd and acted passion , is evident in this ; they almost all of them use the same emphasis . i would not for my hand let fall a syllable should cast a scandal upon that holy ordinance : and with my soul i reverence the grave and pious clergy . we cannot attribute enough to god ; assume too little to our selves . we cannot be too much afflicted for our sins , nor too sensible of our own unworthiness . yet i suppose a fit christian sorrow may be contain'd within such terms as to reach heaven , without disturbing the congregation . to come to a church-dore , and hear an out-cry , as if a man were cutting for the stone ; and what 's all this , but an afflicted pastor , mourning for those heavy judgments , that hang over the land because of common-prayer : and then the sisters groan so ruthfully , you 'd swear five hundred women were in labour . away with these ostentations of holiness , — but first away with the discourse of them . i must confess , the gentleman hath offered fair , and more i doubt then he can undertake for , were it accepted . what if six presbyterians of seven renounce his moderation , and say he treated without commission : where 's his pacifick coalition then ? 't is for a parity they struggle ; which when they have got , they shall as much contest among themselves to crush again , as ever they did to introduce it . just thus was the king treated ; he was to rule in consociation too , by the advise of his presbyters . and what came on 't ? the factions interfer'd ; the change went round the circle ; and at long-length ; in the place of a most gracious prince , up starts a most tyrannical protector . and yet i verily think , a way might be found out to work upon these people : let the king settle their strict form of discipline ; fill the presbyteries with episcopal divines , and elders of his own party ; i verily believe these very men would be as hot for bishops . i cannot comprehend the temper of that sacrilegious tenderness , that makes men digest bishops lands , and yet forsooth they cannot swallow the sleeves . onely this word . some of the authors i have quoted for episcopacy , ( to deal sincerely ) may be as well produc'd against it . for that , let them look to 't , i am innocent : and my cause clearer for it . they found it for their interest to engage their disciples in many opinions , which for their honor they would not undertake to defend against their equals . i should end here , were i not drawn out beyond my purpose , by a second part from the same hand ; which should not yet divert me from my first intention , could i but save my self , in letting it absolutely alone . by the formalities of title and connexion , it seems related to the former part , further then by some passages in the treatise it appears to be ; whereof some few i am concern'd to examine , and i shall shorten even that little i intend , as much as possible . he calls it — a deliberative discourse , proving , that it is not agreeable to sound reason to prefer the contracted and dividing interest of one party , before the general interest of protestantism , and of the whole kingdom of england , in which the episcopal and presbyterian parties may be happily vnited . we are agreed in all but in the main , and as to that , i have already shew'd , that in the subject of our difference , the presbyterian party ( that is , the kirk-party ) is divided from the protestant : so that unless it can be made out , by the judgment of the reformed churches , that prelacy is antichristian , and that instituted ceremonies are vnlawful ; the author of this deliberation overthrows himself by his own argument , of preferring the general interest of protestantism , before the contracted and dividing interest of one party . we should not take in discipline within the pale of religion , but against that party , which reckons it an essential mark of the church . and let them take their choice , whether it shall be accounted among things indifferent , or necessary . if the former , obey the imposition ; if the latter , let them produce their authority . the foundation being mis-lai'd , the building will hardly stand : or , which is worse , it falls upon the builder . he says , his aim is unity , and truly so is mine ; but vnity in such a composition will never set us right . two may agree in the same point of verity ; but then that truth must for it self be entertain'd , without considering one another . if about any thing material we differ , flie to the judge of truth : the scriptures , and the church : if about less , and common matters , go to the rule of duty , ( in such cases ) the setled law. but i forget my self . it must needs be ( says the deliberator ) the wisdom of this state to smother all dividing factions , and to abolish all partial interests , that the common interest of england may be alone exalted . observation i hope he does not mean , by state , the keepers of the liberties ; if the supreme authority of this nation as it is legally vested in the king , the man has kill'd himself . what are dividing factions , but such parties as start from that common rule the law , which every state is bound upon a principle of policy , and honor , to preserve sacred and inviolable ? the law is but the wisdom treasur'd up of many ages ; — onely an amass of all those lights , which long experience , strict search and industry ; and many consultations of great statesmen , have given to the discovery of our true interest . great reason is there to approve so great authority : and as great shame it were not to avow what we our selves have done ; ( the law being but an universal vote ) beside the penalty of disobedience . how mad then , how ignoble , and how desperate shall we esteem that faction , that breaks through all these bonds of reverence , honor , and prudential security , to force that sanctuary , wherein , as christians , and as men , we have reposed , first , the protection of our religion ; — and then the arbitration of our lives and fortunes . from such dividers , heaven deliver us , first , and then preserve us . all enterprises ( says our author very rationally ) that have their beginning in judgment , and not in passion , are directed to a certain end set up as a mark , and that end is not a business at rovers ; but some particular steady issue of things , certainly or probably apprehended and expected : wherefore let wise men consider the mark where at they level , and to what issue and state of things their actions tend . most certain 't is ; without that mark men go they know not whether . first the end ; then , the way ; is ( i suppose ) the common method of all wise men : and his advice to such , to look before them , might have been spared , they would have don 't without it . now to his business ; but first , i 'le clear the way to 't . the question is , whether the fomenting of these discords , ( viz. in matters of discipline ) do not proceed from a carual design ? and he debates the matter with the episcopalians . here is a numerous party not of the dregs and refuse of the nation , but of the judicious and serious part thereof : what will they do with them ? and how will they order the matter concerning them ? would they destroy them ? i solemnly profess , that i abhor to think so by the generality of the episcopal perswasion : i would disdain to mention such an unreasonable impiety , were it not to shew the inconsiderate and absurd proceedings of an unalterable opposition , as that it cannot drive to any formed end and issue . that protestants should destroy protestants , for dissenting in the point of ceremonies , and sole jurisdiction of bishops , is so dreadful a violation of charity and common honesty , that it is a most uncharitable and dishonest thing to suppose it of them . what then ? would they bear them down , or keep them under hard conditions ? shall all persons that cannot yield exact obedience to ecclesiastical injunctions concerning all the parts of the liturgy , and ceremonies , be suspended and deprived as formerly ? shall ministers of this judgment be cast and kept out of ecclesiastical preferment and employment ? shall all private conferences of godly peaceable christians , for mutual edification , be held unlawful conventicles ? it hath been thought by wise men to be against the rules of government , to hold under a rigid yoke a free people , of such a number and quality , and intermingled in all estates and ranks , and intimately conjoyned with all parts of the body politick , that it is almost impossible to exclude their interest from a considerable share in publick actions . observation we are so often told of this judicious serious party , pray let 's allow them to be a company of very fine gentlemen , and mind our business . i think he says they are numerous too . so were the frogs that came into the king's chamber : and what of that ? in good truth , altogether , it is a very pretty anagram of sedition . if it wants any single circumstance that 's needful to procure a tumult , i am exceedingly mistaken . mark it , here 's number ; conduct , and pretence of right , to embolden , and to fix the multitude . then , to provoke , and heighten them : old sores are rub'd ; they are minded how they were used so long ago ; and hinted yet of worse behind , if they have not a care betimes . what is all this to say ? but gentlemen , you remember how it was with you formerly ; if you have a mind to any more of that , so . but things are well enough yet ; there are those will stand by you that know what they have to do , and enow to make their hearts ake . — vvhy it is against all rule of government , to put this yoke upon a free people . — if the author be within hearing ; he should do well to be his own expositor . in the mean while , compare we the gloss with the text. he speaks now in his own words , which the reader may find by conferring them with the entire matter of the last quotation , to be extracted with the strictest justice to his meaning . here is ( says he ) a numerous party , of the judicious and serious part of the nation : what will they ( the episcopalians ) do with them ? &c. would they destroy them ? &c. i solemnly profess , that i abhor to think so of the generality of the episcopal perswasion , &c. shall they be suspended , and deprived as formerly ? shall all private conferences of godly , peaceable christians , for mutual edification , be held unlawful conventicles ? it hath been thought by wise men to be against the rules of government to hold under a rigid yoke a free people of such a number , and quality . — this is cutting of a man's throat with a whetstone . truly horace his saying would sound very well from this gentleman . — fungor vice cotis , acutum reddere quae ferrum valet , exors ipse secundi . my office is to whet , not cut. to tie him up now to his own philosophy , which is , ( according to his fore-alledg'd position ) that all rational enterprises propose some certain end , unto which end , all wise men conform their mediate actions . if it be so , ( as we are agreed upon it ) then by that very reason which directs him to chuse the means , are we enabled likewise to guess the end . his end , he says , is peace ; and in this treatise he hath chalk'd his way to 't . he 's a wise man , and certainly proceeds in order to the mark he levels at . let him be judge by his own rule . to mind the peevish of old grievances , and in so doing to transport the honest with a just sense of new indignities ; is this the way of peace ? to break a solemn law ; that law that saved the breakers of it ; to abuse the mercy of the prince that made it ; and to traduce the government of his father , whom they themselves destroyed ; and which is worse , to justifie all this : is this the way of peace ? to startle the mad brutish rabble with dangerous apprehensions ; to lay the justice of their cause before them , and when they are ripe for mischief , to shew them men and arms , — is this the way of peace ? — then let me learn which is the way of tumult . shall protestants destroy protestants , ( says he ) for dissenting in the point of ceremonies ? no , but the law shall destroy subjects , for attempting to rule their governors . touching their conventicles , since they fal● in my way , i think of them , as of the painter'● bad god that made a good devil : i take them to be none of the best churches , but for ought i know , they may make excellent — i beg ye onely to observe now , the equity o● these good folks . is it for the service of christ , and the encreas● of his kingdom the church , that so many abl● divines should be debarr'd the use of the lord talents , that so many laborious minister should sit still in silence ; that when christ teacheth us to pray that the lord would thrust forth labourers into his harvest , those labourers should be thrust out of his harvest ? surely this would make a cry in the ears of the lord of the harvest . observation do none of the woes in the gospel belong to this talker of it ? the service of god went merrily on , in the thorough reformation ; did it not ? when not a minister kept his living , but to the hazard of his soul ; and in several places ( where the allowance was small ) neither sacrament nor sermon , for divers years together . but in those days , the covenant kept all in good order . with what a monstrous confidence does this man press a text , which the whole nation knows is clear against him ! and all in scripture-phrase forsooth : ne sine formâ tantum scelus fiat , for the honour of the exploit . these people use religion , as your london-cooks do their pickled barbaries : they garnish with it . it serves for every thing : i know not how it is , but they do 't , because they find the women like it . when the episcopal , and loyal clergy , their wives , children , and families , were swept entirely away by th●t scotch plagve the covenant ; that made no cry sure in the ears of the lord of the harvest . let the great great judge of all the world determine it . if the neglect of brotherly pacification hold on , and the hierarchie resolve upon their own advancement to the highest pitch , one may well conclude , that they make a full reckoning to wear out the presbyterians , and to swallow up their interest , conceiving they are able to effect it by degrees ; and that greater changes than these have been wrought without much ado . let but the meanest soul alive now judge of these mens consciences . ( i speak of those that tumult since the act of pardon ) as deep a forfeiture as ever was made by mortals , the king hath remitted to them . they have cost the nation more then they have left it worth , beside the blood , the grief , and desolation they have brought upon it . this notwithstanding , they have at this instant the self same interest they ever had , as to freedome and safety , and otherwise more : they keep what they got ; beg , and get more ; and are not yet content unlesse they govern too . but this is but another alarm , as who should say ; look to your selves my masters ; lose not an inch , for if you do , they 'l do your business by degrees , by and by , among other concurring advantages , to the great changes queen elizabeth wrought in religion ; he reckons this for one . popery ( sayes he ) being in substance a religion con●rary to what was publickly professed , had no advantage for encrease by publick preaching , or books publickly allowed . observation nothing more certain then that the freedome of the press and pulpit , is sufficient to embroyl the best ordered government in the world. all governments have their disorders and their malecontents : the one makes use of the other , and here 's the ground of all rebellions . some real faults are first found and laid open to the people , which , if in matter of popular freedome , or religion ; so much the stronger is the impression ; the vulgar being natural●y stubborn ; and superstitious . bring it to this , a very little industry carries it on at pleasure . they shall believe impossibilities , act eagerly , they know not what , nor why ; ●nd while they reach at liberty , grasp their own fetters . their unhappiness is , they can ●etter phansy a government without any ●aults , then brook one that hath some . add ●ut to this distemper , licentious pamphlets , ●nd seditious sermons , the world shall never ●eep that people quiet . wherefore since on all hands it is agreed , that printing , and preaching in opposition to a ●ublick establishment , are of so dangerous con●equence , by the force of the gentlemans ●wn rule we ought to hear no more of their discipline from the press or pulpit . observe ●is next coherence . there are now in england thousands of ministers dissatisfied in the hierarchy and ceremonies , who are all competently and many of them eminently learned . they are not generally of light spirits , but steddy and well resolved , and tenderly affected touching their spiritual liberties . observation take notice first , how many , and how resolute they are . that is , take notice again for we have had it exceeding often . his resolute thousands make me think of the tribe● repairing to david . but they are dissatisfied he sayes : it may be 't is because they are no● bishops : yet truly if they be so well resolved methinks they should not be dissatisfi'd with tha● they cannot help . i 'll ask but two questions and i have done . 1. are any of those tender-conscienc'● thousandsthat are so tenderly affected toward spiritual liberties , those presbyterians that denye● the king the freedome of his own chaplains ? 2. had any of these eminently learned thousands a hand in the assemblies letter to th● reformed churches of france , the low-countries , &c. — ( as great a schism in learnin● as the other was in religion ) he comes now t● the point indeed . commonly ( sayes he ) those people who try all doctrines by scripture , and are swaye more by its authority than by the ordinanc● and customes of men , do much hesitate and stagger concerning the sole jurisdiction of bishops , the pomp of the hierarchy , and sacred mystical ceremonies of humane institution . and therefore let the episcopal party never look to be rid of these difficulties , till they remove the matters in question , whereat a knowing people are always ready to stumble . go to then , since the gentleman will have it so , grant for dispatch the thing he presses , to wit , — that they do hesitate , and stagger . 't is hard , that when upon a private search , the question hangs in ballance , the casting in the authority of the church , and the great weight of christian charity , should not be yet enough to turn the scale . he that doubts , sins , will not excuse that man , who because he thinks he stands , refuses to take heed of falling . but let him doubt , nay more , let him resolve ; all is but for himself still , not for me . when he comes once to muster up his thousands , and talk of parties , his plea of conscience is gone : and doublesse these violent and publick sticklers for the scrupulous , ( that is in such and such particulars ) are the greatest enemies they have . it casts a scandal upon the very cause of conscience , when those who evidently want it in themselves , plead for it in others . upon this subject , exceedingly well says mr. lloyd in a late treatise of primitive episcopacy , pag. 80. it becomes not good men to c●nsure us for using th●s● rights and ceremonies , which we are perswaded not to be prohibited by gods law , and both they and we do surely know to be commanded to be used by mans law duly made , which is gods ordinance , to which we must be subject for conscience sake . and a little after — if any will attempt to be authors of combinations , to extort by shew of multitudes and by tumults , the alteration or abrogation of any part of the established laws , civil or ecclesiastical , they will thereby evidently manifest themselves to be but meer pretenders to a tender conscience , and power of godlinesse ; for they that labour to extort a part , if they prevail , must have the whole in their power . and can they that attempt so great robbery , love god , and the power of godlinesse ? by this cursed fruit , we know these to be most vile-hypocrites . now to our adversary . the gentleman desires to clear the presbyterians of being no phanaticks : and we 'll give him the hearing . it is said that the presbyterians promoted the kings return , not out of good will to his majesty , or a love of order , and vnity , but out of fear of being destroy'd by the phanaticks . ] to this i shall say little but that i believe there was more in 't than so . let him argue upon it . the pretended reason of their insincerity seems to me to add much to their reputation in that behalf . for if the phanaticks would destroy them , it is manifest that they are none of them . phanaticks would not destroy themselves willingly . the several various sects will wrangle with each other in verbal contests ; but they never knowingly plotted or banded against each other upon the account of their different opinions , but did all unite in one common principle of pretended liberty of conscience , and in one common cause of vniversal toleration . a pleasant reasoning . a man would think christianity as strong a tye as phanaticisme , and yet we see christians destroy one another . but come to the point . what 's more familiar then for a couple of curs to hunt the same hare , and when they have catch'd her , worry one another for the quarry ? i 'll tell this gentleman a thing now , shall make him take me for a conjurer . i 'll tell him the true reason why those presbyterians help'd his majesty in , that are not quiet now they have him . not for feare of the phanatiques : he made that objection himself for ought i know ; but here ' t is . ( still saving to my self the freedome of interpreting my own words . ) i speak only of those presbyterians that since his maiesties happy return , are yet fomenting of new troubles . the presbyterian faction have been ever constant to the rule and method of doing their own businesse in the kings name ; and this went far with the simple , and well meaning people ; but let not any man believe this interest did their work . the ruin of his blessed majesty , was that unhappy agreement with the covenanters in 1639. after so horrid an expence of time and mony , as gave the greatest benefit imaginable to their interest , and an equal disadvantage to his own . the king by his expence being grown poor and they strong by the delay , was more and more oppressed , till at the last the field was clear'd : he and his party in appearance lost . what did these great pretenders then for the good of king and church , but share the booty , and exercise a power themselves ten thousand times more turkish then ever they called that they had abolished ? what hindered then the settlement of this nation upon its legal basis , ( as they phrase it ) if the good people had but had a mind to it ? who kept the king from his parliament ? — or was he ever nam'd but with relation to the losse of right as well of power . well , but at last , these people take their turns too , and then the king 's a gracious prince again . these factions are of kin to montaignes family , where the son beats the father from generation to generation . now we come near our purpose . look back into the scotch defeat in 1648. not any thing more clear sure , then that the presbyterian party , would they but frankly have closed with the kings tryed friends in that engagement ; without a miracle , they must have carried it . those few they had , did well nigh all that was considerable in the action . see afterward , in 50 , and 51. how dirtily upon this very accompt , the presbyterian crew treated his majesty : and look quite through their interregnum ; they have observ'd the same indisposition of uniting with the kings party , but still shaking the head , with an alass poor gentleman , at the mention of our persecuted soveraign . not to insist upon english particulars ; they never would joyn with vs to help his majesty , we never refused with them . now comes the mysterie of the reserve . say they , if we can order matters so as to get the king's person in the head of us , and keep out his party , their hands are ty'd by a principle of duty ; our power is enlarged upon an interest of favour , and we can play our game at pleasure . that is ; wee 'l not forget to mind him of his restorers , and now and then a whisper , how debauchd the gentry's grown ; how unfit this man is for trust , that for temper , and a third for conduct . we may then propose the naming of officers , and wee 'r to blame if we forget our selves . by these degrees , and wayes , time , and a little patience will wear them out ; or if it were nothing else , the very poverty we have reduced them to , would make them ●oon contemptible . whereas should we but offer once a general agreement with that party , our design 's spoyl'd , for they 'll be more than we shall well know how to master . that must not be . our interest lyes to take in just so many , as when they have done our work , we may be able to turn out again . so much for that . this is the very soul of the rigid presbyterians . poor worms , where is our charity and regard ( they crye ) to publick tranquillitie , if we reject the sure and only means of concord ? ] observation he should have rather said , where is our providence , if we admit so sure an introduction to confusion ? to comply with one importunity of this nature , is to authorize , and encourage more ; and to please all , is totally impossible . the canons stick in his stomach notably , they force too much , and bring in poperie [ shall not the laity be allow'd to search the scriptures , nor try the doctrines delivered , but acquiesce in what their teachers say without the exercise of their own reasoning , or judgment of discretion ? ] observation yes , let them search the scriptures , as their teachers may the lawes , yet by their leave , the church and bench must interpret them . what difference is there betwixt king james his phanatiques , and king charles his ; save that they ascribe one and the same effect to several causes . both claiming equal certainty , the one , from his judgement of discretion : the other , from divine impulse ? what work shall we have when every taylour shall with his judgement of discretion cut out his own discipline , and set it up for a fashion : when these men and their bibles are alone together ( as hooker sayes ) what phrensies do they not call directions of the spirit ? he comes now to the politicks . it is a chief point of knowledge in those whose work it is to mould and manage a nation according to any order of things , to understand what is the temper of the people , what principles possess and govern them , or considerable parties of them , and to what passe things are already brought among them . observation the more a prince considers this , the lesse will he afford a scotized english presbyterian . by temper he 's ambitious ; and vnthankful ; ever craving ; and never full : govern'd by principles insociable , and cruel . he rates his party , his piety , and his kindnesse , twenty times greater then they are , and rather than confesse that he is out in his reckoning , he shall face any other man down that one on the wrong side of a cipher is 1000 lastly , in considering to what passe things are brought among them , he will bethink himself likewise how they came to be so . a state may probably root out such opinions as it conceives to be heterodox and inconvenient , by using great severity in the beginning , when the opinions are but newly sowed in mens minds , and the people are of such a nature , as to abhor dangers , and aim to live securely , and when the nation in generall is devoted to the antient custom of their fore-fathers . but the same course may not be taken when the opinions have been deeply rooted and far spread by long continuance , in a nation of a free spirit , and zealous , and the generality of those , that in a law-sense are called cives , do not detest them . truly in this case , if heterodox opinions cannot be rooted out , the men that publiquely maintain them , must : and the rather , if they be free , and zealous : for there 's the more danger in their further progresse . especially if such opinions prescribe from the successe of treason . for there , even in matters of themselves very allowable , i would not leave the least marque of an approbation . it gives too great an honour to rebellion . provided alwayes that i act at liberty , and free from pre-ingagements . where there is such a real cause of fear , as is here shadow'd to us ; that prince that loves his empires or his honour , must struggle with it betimes : safety , or pleasure , such a people perhaps will be content to allow in exchange for soveraignty : but for the rest , that prince is lost that puts himself on the asking side . it never fayles , this rule : when subjects earnestly presse for more than they ought , they ayme at more yet than they aske . they are already past their duty , and short of their ambition . in such a case as this , rigour is the onely remedy : great aptnesse to forgive is entertain'd with greater pronesse to offend . let it be thought upon ; if any danger , where it lyes : not in the bare conceit of phancy , or dislike , for , or against the matter in dispute , but in the means that give form , growth , and strength to those unquiet motions ; and that assemble those loose scatter'd sparkes into one flame . these instruments are mercenary pulpit-men , and scriblers ; 't is but removing them , and the danger 's over . least he should seem to want a colour for these freedomes , he tells us , that [ the present age being more discerning , all sorts affect a greater liberty of judgement and discourse , than hath been used in former times . ] this we observ'd , but did not till now impute it to discretion . suppose they should grow more and more discerning , and their desires of liberty grow too ; would not these people soon grow wise enough to govern , that are already grown too good to obey ? 't is dangerous trusting of them ; yet he assures us otherwise . this kingdom , after the removing of foundations , is by a marvellous turn re-establish'd upon its antient basis . and verily that which hath wrought the change will settle it ; that which hath brought such things to pass , will keep them where they are , if we do not overlook and sleight it : and what was it , but the consent of the universality , the vote of all england ? observation if all that acted toward this late and blessed change meant to fix here : this needless , ill-timed , and dividing controversie , concerning ceremonies , would have been spared : and those which move the question with such earnestness ; at their prayers , rather than these expostulations . 't is an ill age when theeves arraign the law. that sort of men which ruin'd us , proposes now that very method , by which we were destroyed , to settle us , inviting the distemper'd people by this overture , to take their poysoners for their physicians . 't is very true , that ( under providence ) it was the common vote , and stirring of the nation , restored the king , and the law : and shall we now restrain that universal comfort to the particular advantage of that single party , that first invaded them ? how great a blemish were it to the honor , and wisdom of the nation , after so long , and hard a tugg , to throw away the sum of the contest : as if we had wrangled all this while for shadows ! but to explain my self . they that think matter of ceremony to be the true reason of the difference on either side , mistake themselves . it is the law it self , which is assaulted by the one party , and defended by the other , in the particular of ceremony : and it is the king himself that is affronted in the indignities they cast upon bishops . to leave the matter clear : there is a faction which would over-throw the law , and set up themselves above it ; and these contrivers put the people upon cavilling for ceremonies . they innocently , under a mistake of conscience , advance an interest of usurpation , taking that to be onely a dispute about the lawfulness of the practise , which rationally pinches upon the validity of the power . it ends in this . grant once , that a popular vote may over-rule a stated law , ( though but to the value of a hair ) the vertue of that reason extends to our freedoms , lives , and fortunes , which by the same rule they may take away as well as ceremonies . and ( as the case stands ) kings as well as bishops . but [ seeing this great revolution hath not happened by the prevailing force of one party , but by the unstrained motion of all england : what reason is there , that one party should thrust the other out of its due place of rest ; upon the common foundation ? no reason in the world . the law is our common resting place : the main foundation upon which we are all to bottom . the law is an impartial judge , let that determine which place belongs to bishops , which to presbyters ; what ceremonies are lawful , and which not . this is a short and a sure way , worth forty of his coalition . having pressed union hitherto , he proceeds now to remove certain impediments ; one whereof is an erroneous judgment touching the times foregoing the late wars . observation in truth 't is pity the people are no better instructed . then let them know from me , those very principles these folks contend for , were brought by knox about 1558. from geneva into scotland , from thence they were transmitted into england , since which time , the abettors of them in both nations , have never ceased by leagues , tumults , rebellions , and vsurpations , to embroile the publick peace , and affront the supreme authority . they have formally proceeded to the deposing of princes , the exercise of an absolute authority over the subject : the abrogation of laws , the imposition of taxes ; and , in fine , to all extremities of rigour , as well in matters of civil liberty , as of conscience . he that desires a presbytery , let him but read presbyter , for king , in the first book of samuel , and the eighth chapter , and he shall there find what he is reasonably to expect . these were the pranks foregoing the late wars : and such as these will be again , if people be not the wiser . but our camerade will be none of the party sure : for , i abhor ( says he ) to take upon me the defence of our late distracted times : the distempers thereof i would not in any wise palliate . ] is the wind in that dore ? now do i feel by his pulse , that crofton's laid by the heels . he hath forgot , that the war was between the king , and both houses of parliament . and that the presbyterian party in england never engaged under a less authority than that of both houses of parliament . ] and that presbyterians have never disclaimed , or abandon'd their lawful prince . ] it may be he means , that he will not justifie the distempers of the other side . but why do we contest ? since he tells us , that — it is the part of weak and selfish minds to contract religion to certain modes and forms which stand not by divine right , but by the wills of men , and which are of little efficacy , and very disputable , and if supposed lawful , ought to be governed by the rule of charity . observation i would fain know which is more tolerable ; for the church to impose upon the people , or the people upon the church ? for the people on the one side to exempt all , or for the church on the other side to bind all . order it self is of divine appointment ; but the manner of ordering ( save where god himself hath preimposed ) is left to humane liking and discretion . to think ( says he ) that none is a good christian , a sound protestant , a fit minister , that cannot subscribe to such modes , and forms , proceeds from a narrow , and ignoble judgment . he may be a fit teacher for geneva , that cannot subscribe to the form of england , and a fit minister for england , that cannot conform to the practise of geneva ; they may be both good christians too , and sound protestants ; yet neither of them fit in transposition . 't is one thing to be qualifi'd for the ministerial function , and another thing to be fit for such or such a constitution . 't is true , he officiates as a minister : but thus , — or so — as a subject , and that 's the real ground of their exception . they do not willingly admit the king's authority in matters of the church : and that , which effectually is but their own ambition , they obtrude upon the world , as a high point of tenderness to the people . there are beyond all doubt , weak consciences , fit objects for indulgence : but the less pardonable are their mis-leaders , whose business 't is for their own ends to engage the simple multitude in painful , and inextricable scruples . let them preach down-right treason , stir up the rabble to tumult , and sedition : if they chance to be caught and question'd for it : see with what softness they treat their fellows , and with what supercilious gravity their superiors . when some degree of forwardness breaks forth , it is encountred with that severity which hazards the undoing of the weak part , that should and might be healed . ] and again , to the same effect , ( concerning crofton's commitment , i imagine ) [ but suppose that some of this way were guilty of some provoking forwardness , should grave patriots and wise counsellors thereupon destroy the weak part , or rather heal it ? a prudent father is not so provoked by the stubbornness of a child , as to cast him out , and make him desperate while there is yet hope concerning him . it is meet indeed for princes to express their just indignation , when subjects presuming on their clemency do not contain themselves within their duty ; and the seasonable expression of such disdain , wisely managed , is of great force in government : nevertheless if it get the mastery , it is exceeding perilous . it was the counsel of indignation that proceeded from rehoboam 's young counsellors . ] what this language deserves both from the king and his counsel , let those that have authority to punish , judge . when governors resent the non-compliances of a party , their best remedy is to remove the occasions , when it may be done without crossing the interests of state , or maxims of government . observation that is , if the people will not yield to the prince , the prince should do well to yield to the people . a most excellent way for a king that hath to do with presbyterians : where he shall be sure never to want subject for his humility , nor ever to get thanks for his labour . where there are many sufferers upon a religious account , whether in truth or pretence , there will be a kind of glory in suffering , and sooner or later it may turn to the rulers detriment . observation there will not be many sufferers , where there are not many offenders ; and there will not be many offenders , where an early severity is used . but however , if any hazzard be , he that prints it , dictates , encourages , and promotes it , and deserves to suffer with the foremost . but the gentleman begins now to talk like a christian. i detest ( says he ) and abhor the tumults , and insurrections of the people , and the resisting of the soveraign power . ] observation this is honestly said yet : but hold a little . what is that soveraign power , which he abhorrs should be resisted by the tumults of the people ? even the two houses in co-ordination with the king. a little further , [ i am perswaded ( says he ) that the generality of the presbyterian denomination would endure extremities , before they would revenge or defend themselves by unlawful means , as rebelling against their lawful soveraign . observation this we shall understand too by confronting it , and find it onely the old fallacy , a little better colour'd . this part ( says he ) of the supreme power ( meaning the two houses ) is indeed capable of doing wrong , yet how it might be guilty of rebellion , is more difficult to conceive . ] now if the two houses cannot rebel , as being part of the supreme power ; ( by his argument ) neither can the presbyterians , in compliance with that party : so that by this mis-placing of the supreme authority , whatever hath been acted by vertue of any commission from the two houses , may be done over again , and no rebellion . by this device , he onely disavows rebellion so far as this , or that , is not rebellion according to his proposition , although the law determine otherwise . this is no more then what was ever maintained , even by those that stood themselves upon the highest terms of disobedience . did ever any man say , this is rebellion , and i 'll justifie it ? nay , i should be glad to hear any of them say , this was rebellion , and i 'm sorry for it . [ but it is evident , that the presbyterians love the king , and kingly government , and account themselves happy in his majesty's clemency , allowing them a just and inoffensive liberty in certain matters of conscience . ] observation the presbyterians may find many things to thank his majesty for : but i would they could hit upon a handsomer manner of doing it ; and not perpetually to be craving more , when they should be doing him service for what they have receiv'd already . they love the king , they say , but then their love is conditional , they must have something for it . would they expose themselves for twenty years together , to gaols and gibbets , all sorts of hazzards and misfortunes for their prince , and at the last sit down and sterve contentedly , out of a sense of honorable loyalty ? that subject is not right , who hath not brought his mind up to this frame ; however unhappy he may think himself in such encounters as put him to the trial of his utmost virtue . wise men inform us , that a prince by adhereing to one faction , may in time lift it up above his own imperial interest , which will be forced to give way to it as the lesser to the greater . and the prime leaders of the potent faction will sway more than the prince himself . they will become arrogant , unthankful , and boundless in their ambitious designs . this is a good rule , but ill apply'd ; unless return'd upon himself . i hope he will not call that party a faction , which submits all its actions to the clear letter of the law ; and he will hardly prove that to be none , which crosses this. if so , let common reason judge betwixt us . there is a saying , which by many hath been taken up for a proverb , no bishop , no king. i do not well understand the rise of this saying , and therefore dare not speak in derogation of their judgements who were the authors of it . but upon the matter it self , i crave to make this modest animadversion . and first it is some degrading to the transcendent interest of soveraignty , to affix unto it a necessity of any one partial interest for its support : for independency and self-subsistence , without leaning upon any party , is a prince his strength and glory . also it makes that party over-confident , and its opposite too despondent . such sayings as import a princes necessary dependence on any particular party , may in the mouthes of subjects be too presumptuous , and in the mouth of a prince too unwary . if we are not yet instructed in the weight and reason of that saying , — no bishop , no king ; sure we are past learning any thing . we found the sad truth of this judgment , in the event of the late war ; but that 's no rule . by no bishop no king , is not intended that bishops are the props of royalty , nor do the episcopalians understand it so : but that both one and the other are objects of the same fury , onely the church goes first : so that without presumption , a subject may affirm it ; and without loss of honor , a prince may grant it . i might draw arguments from the agreement of their original , the likeness of their constitution , the principles by which they are supported , and that they lye exposed to the same enemies , and the same method of destruction . but this would seem to imply a more inseverable interest then i aim at ; and raise the clergy above the proper state and orb of subjects . my meaning is more clear and open . all popular factions take the church in their way to the state ; and i am to seek where ever any prince quitted episcopacy , and saved himself . that is , his royal dignity ; for the empty name of king , is but the carkass of majesty . it is with the unruly populacy , as it is with raging tides , they press where the bank is weakest , and in an instant over-run all . if they had either modesty , or conscience , they would not force so far : if they have neither , will they stop there ? what did the late king grant ; or rather , what deny ? till by their mean abuse of his unlimited concessions , he lost his crown , and life ? yet what assurance words could give him , he wanted not : words wrapt up in the most tender and religious forms imaginable . but what are words where a crown lyes at stake ? in fine , treason 's a canker ; and where it seizes , that prince must early cut off the infected part , if he would save the sound . the true church lies in the middle between two extremes , formalists , and fanaticks . they are of circumspect and regular walking , no way forward in attempting or desiring alterations in a civil state. a prince doth hold them in obedience under a double bond . for they know they must needs be subject not only for wrath , but for conscience sake . indeed we will not conceal , that in lawfull wayes they assert that liberty which is setled by the known laws and fundamental constitutions , the maintaining whereof is the prince's as much as the peoples safety . if to be no way forward in promoting changes in the civil state , be a marque of the church : the presbyterians are out of the pale . it 's truth , they are , it seems , assertors of lawfull liberty , in lawfull waies ; but how is that i pray'e ? did they not tell us this when their swords were at our throats , when it was death to assist the king , when they were forc'd to flye to the equitable sense of the law , and quit the literal , and fetch their arguments , from inspiration , because they had none in reason . i shall here put an end to this discourse , which is become much longer already than i meant it , by reason of his addition . crofton's ill fortune i find hath made him wary , but not humble ; for he presses the same things in substance still , though in somewhat a differing manner of respect , and seeming candour . the good words he gives , belong to those persons which he shall vouchsafe to call serious , and to think worthy of them ; and the government is to be moulded , and disposed of as he pleases . finally , he pretends to ayme at a fair , and christian accord , and yet proceeds in a direct method of dividing : by sharp , and scandalous reflections upon the kings party . to say no more , his reasonings are dishonourable to the memory of the late king ; seditious , and provoking to the people ; bold , and imposing in themselves ; repugnant to the established law , and to the main scope of the general pardon . how out of all these ill ingredients should be composed a national , and healing balsome , i shall now give the reader leisure to consider . male imperatur , ubi regit vulgus duces . finis . a catalogue of some books printed for henry brome , at the gun in ivy-lane . the alliance of divine offices , exhibiting all the lyturgies of the church of england since the reformation , by hamon l'estrange esq in fol. the souls conflict , being eight sermons preach'd at oxford , and so much recommended by dr. hewit , in 8. dr. browns sepulchrall urns and garden of cyrus . in 8. two essayes of love and marriage in 12. the royal exchange , a comedy in 4. by r. brome . five new playes ▪ by r. brome , never before printed , in 8. poems by the vvits of both universities , in 8. a treatise of moderation , by mr. gaule , in 8. st. bonaventures soliloquies , in 24. mr baxter's treatise of conversion , in 4. the common law epitomiz'd , with directions how to prosecute and defend personal actions , very usefull for all gentlemen , to which is annexed the nature of a vvrit of errour , and the general proceedings thereupon , in 8. golden remains by that most learn'd r. stuart d. d. dean of westminster and clerk of the closet to king charles the first , being the last and best monuments that are likely to be made publick , in 12. mr. sprat's plague of athens , in 4. jews in america by mr. thorowgood , in 4. the royal buckler , or a lecture for traytors , in 8. a view of some late remarkable transactions , leading to the happy government under our gracious soveraign king charles the second , by r. l'estrange esq in 4. all the songs on the rump in 8. the pourtraicture of his sacred majesty king charles the second , from his birth 1630. till this present year 1661. being the whole story of his escape at worcester , his travailes and troubles . the covenant discarged by john russel , in 4. the compleat art of vvater-drawing in 4. mr. boys his translation of the 6th . book of virgil in 4. mr. walwin's sermon on the happy return of king charles the second . a perfect discovery of vvitchcraft , very profitable to be read by all sorts of people , especially judges of assize before they passe sentence on condemned persons for witches , in 4. a short view of the lives of the illustrious princes , henry duke of gloucester , and mary princess of orange deceased , by t. m. esq in 8. aeneas his voyage from troy to italy ; an essay upon the third book of virgil , by i. boys , esq in 8. trapp on the major prophets , in fol. songs and other poems , by a. brome , gent. mr. grenfeilds loyal sermon before the parliament . a caveat for the cavaliers . a modest plea both for the caveat and author , by r. l'estrange esq the history of portugall in 8. cases of conscience , in the late rebellion resolved by w. lyford b. d. minister of sherburn in dorsetshire . notes, typically marginal, from the original text notes for div a47873-e110 dowglas his coronation sermon , page 10. notes for div a47873-e2530 j. c. page 10. douglas . * epistle to the reader . marshall . * epistle to the reader . presbyterian regulation . exact collections , pag. 310. page 10. observation . page 12. observation . his majesty's speech for hastning the act of indempnity . his majesty's speech at the passing the act of indempnity . page 14. observation . page 19. page 20. page 23. * english and scotch presbytery , pag. 316. * hist. of the ch. of scotl. p. 479. the presbyterians practical ministery . pag. 25. observation . presbyterian liberty . page 27. page 28. the consequents of presbyterian liberty . page 29. observation . page 29. page 40. * note . crofton . page 41. page 42. presbytery antimonarchical . the two houses have no coercive power over the king. the covenant an oath of confederacy . * note . the covenant neither lawful nor binding . pag. 44. observation . some honest presbyterians . page 45. page 46. ibid. page 46. page 47. page 48. presbyterians seditious and impenitent . page 49. the two houses , not the parliament . the legislative power in the king. the two houses no court of judicature . presbyters serve king and bishops alike . exact col. 316. page 49. page 50. presbyterian loyalty . bodin . de rep. lib. 2. cap. 5. de rep. lib. 1. cap. 8. lib. 3. cap. 1. ibid. pag. 51. page 51. presbyterian positions . page 52. prelacy a more orderly constitution than presbytery . rom. 9.21 . page 53. page 53. ibid. observation . rellquiae sacrae corolinae . page 158. page 55. page 59. * note . * note . page 58. note . page 60. exact collections . pag. 531. history of independency . page 1. page 2. page 63. observation . page 65. page 66. page 70. page 70. observation . page 73. page 47. ibid. toleration . page 76. page 84. observation . page 86. observ. significant ceremonies not sacred . ibid. observation . ecclesiast . polit . lib. 5. sect. 29. ecclesiast . polity lib. 4. sect. 12. * the eunomian hereticks in dishonor of the blessed trinity , brought in the laying on of water but once , to cross the custom of the chur. which in baptism did it thrice . page 87. can. 30. eccles. polit . lib. 5. sect. 71. page 88. page 90. observation . page 91. observation . page 94. page 95. can. 36. observ. canonical subscription defended . page 97. * the late kings declaration concerning scotland , page 403. page 101. x] can. 6. y] can. 7. page 97. observation . page 103. observation . * pa. 84. page 103. page 111. observation . page 111. a voluntary conscience . pa. 114. observ. ibid. observ. bibliotheca regia , p. 58. his majestys protestation . page 115. page 116. pag. 120. observation . pag. 120. ibid. observation . english & scotch presbyterians no protestants . l' interest des princes discours . 7. puritan-protestants . page 121. observation . page 121. observation . pag. 122. observation . page 403. ibid. page 124. observation . page 17. part . 1. apol. confess : per pap. pag. 137. de reform . adver . eccles . pag. 95. bez. cont . sarav . p. 116. * note . calvin epist. pag. 341. scripta anglicana , p. 455. h. l. s. his affinity of sacred liturgies . pag. 27. cap. 27. cap. 15. act. 32. act. 32. act. 15. act. 20. cap. 14. the rise of presbytery . the process of presbytery . dangerous positions , pag. 43. dangerous pos. pag. 44. dangerous pos. pag. 45. dangerous pos. pag. 75. pag. 86. pag. 89. pag. 91. dangerous pos. pag. 120. pag. 125. presbyters doctr. concerning kings . knox to engl. and scotl. fol. 78. gilby obedience , p. 25. register , p. 48. goodman , p. 144. spotswoods history of the chur. of scotl. p. 330. scots plea p. 262. kings declaration concerning scotland , p. 404. ibid. p. 409. bancroft , p. 169. king's declaration , 404. ibid. 408. ibid. 411 knox. bancroft pag. 56. ibid. p. 58. admon . 1. cartwright . holy discipline , pag. 260. ibid. 284. ibid. ib. 285. inter. of engl. part. 2. p. 81. * by which term they difference their classical approbation , from episcopal ordination . * inter. of engl. par. 2. p. 5● . the reformers way of petitioning . holy discipline , p. 100. bancroft's dangerous posit . p. 53. ibid. p. 56. ibid. p. 57. inter. of engl. p. 29. ibid. bancroft pag. 138. ibid. 11. p● . 14● . inter. of engl. p. 53. positions of the conventicle at glasgow , an. 1638. presbytery tyrannous to the people . bancroft p. 20. ibid. p. 105. presbyters persecutors of k. james . k. james his works : pag. 305. ibib. p. 160. the antiquity of phanaticks . reasons against coalition . justice of conscience . justice of honor. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . pag. 239. k. james his works , p. 157. the late kings counsels . 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . page 236. ib. p. 239. ib. p. 240. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . pag. 62. ibid. pag. 169. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . page 182. ib. p. 236. the late kings declaration concerning scotland . pag. 404. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 . pag. 170. observation . page 14. the best rule of interest is the law. page 36. observation . page 33. page 36. the presbyterian method of making peace . page 38. page 39. observation . page 42. page 42. 1 chr. 12. page 43. observation . page 54. ibid. observation . the presbyterians do their own business in the kings name . page 60. page 61. page 62. page 63. observ. page 65 observation . page 66. page 67. observation . page 73. page 74. interest of england . part 1. page 13. part 1. page 49. ibid. 53. page 75. pag. 75. observation . page 78. page 81. page 83. page 84. page 98. interest of england . page 49 , ibid. 98. page 49. interest of england . page 101. pag. 104. observation . pag. 106. observation . page 116. observation .