the case of the lady wandesford wandesford, mary, lady. this text is an enriched version of the tcp digital transcription a78254 of text r223852 in the english short title catalog (wing c1102a). textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. the text has been tokenized and linguistically annotated with morphadorner. the annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). textual changes aim at restoring the text the author or stationer meant to publish. this text has not been fully proofread approx. 2 kb of xml-encoded text transcribed from 1 1-bit group-iv tiff page image. earlyprint project evanston,il, notre dame, in, st. louis, mo 2017 a78254 wing c1102a estc r223852 99897184 99897184 135633 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. a78254) transcribed from: (early english books online ; image set 135633) images scanned from microfilm: (early english books, 1641-1700 ; 2474:11) the case of the lady wandesford wandesford, mary, lady. 1 sheet ([1] p.) s.n., [london? : 1660] imprint from wing (cd-rom edition). reproduction of original in the folger shakespeare library. eng england and wales. -parliament. -house of commons -private bills -early works to 1800. real property -england -hampshire -early works to 1800. reclamation of land -england -hampshire -early works to 1800. a78254 r223852 (wing c1102a). civilwar no the case of the lady wandesford. wandesford, mary, lady 1660 277 0 0 0 0 0 0 0 a this text has no known defects that were recorded as gap elements at the time of transcription. 2008-03 tcp assigned for keying and markup 2008-06 spi global keyed and coded from proquest page images 2008-07 john pas sampled and proofread 2008-07 john pas text and markup reviewed and edited 2008-09 pfs batch review (qc) and xml conversion the case of the lady wandesford . that king charles the first by his letters pattents 4. car. i. did for a great and valuable consideration grant unto dame mary vvandesford , and vvilliam vvandesford , and their heirs , all the land in hampshire between high and low-water-marke , reserving 4.d . per acre fee farme rent . that the inning of the said lands , and securing them from the sea , will be a very great and chargeable undertaking , but being imbanked from the sea , will be of great profit and advantage to the kingdome , whereas now they yield no benefit to any ; not one blade of grass growing upon them . that for the encouragement of those who are to adventure their money upon so hazardous a work ; the lady vvandesford hath been advised to present a bill to this honourable house , which hath been read and committed . that at the reading of it many clauses in it did appear to be unreasonable , all which the committee have expunged . that there is a proviso for the saving all rights , so that nothing is passed to the lady vvandesford by this intended act , if it was not legally granted by the said pattent . and she doth humbly pray , that in regard this bill , if it be passed , cannot be a prejudice to any person ; and if it doth not passe , will be her utter undoing , ( having spent her whole estate upon it ) that by the justice of this honourable house it may passe . the propositions of sir anthony thomas, knight, and iohn worsop, esquire for making of the bargaine with the country, and henry briggs, professor of the mathematicks in the vniuersitie of oxford, heldebrand pruson, citizen and salter of london, and cornelius drible, engeneere, with the rest of the undertakers for the drayning of the levell within the sixe counties of norfolke, suffolke, cambridge, isle of elie, huntington, north-hampton and lincolne-shire, on the southside of gleane. thomas, anthony, sir. 1629 approx. 7 kb of xml-encoded text transcribed from 1 1-bit group-iv tiff page image. text creation partnership, ann arbor, mi ; oxford (uk) : 2007-10 (eebo-tcp phase 1). a13708 stc 24000.5 estc s2931 29511356 ocm 29511356 27989 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. a13708) transcribed from: (early english books online ; image set 27989) images scanned from microfilm: (early english books, 1475-1640 ; 1859:18) the propositions of sir anthony thomas, knight, and iohn worsop, esquire for making of the bargaine with the country, and henry briggs, professor of the mathematicks in the vniuersitie of oxford, heldebrand pruson, citizen and salter of london, and cornelius drible, engeneere, with the rest of the undertakers for the drayning of the levell within the sixe counties of norfolke, suffolke, cambridge, isle of elie, huntington, north-hampton and lincolne-shire, on the southside of gleane. thomas, anthony, sir. worsop, john. briggs, henry, 1561-1630. pruson, heldebrand. drebbel, cornelis, 1572?-1633. 1 sheet ([1] p.) s.n.], [london? : dated the 11. of ianuary, 1629. reproduction of original in: university of cambridge. archives. 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 reclamation of land -england -early works to 1800. fens -england -early works to 1800. 2006-05 tcp assigned for keying and markup 2006-09 spi global keyed and coded from proquest page images 2006-10 jason colman sampled and proofread 2006-10 jason colman text and markup reviewed and edited 2007-02 pfs batch review (qc) and xml conversion the propositions of sir anthony thomas knight , and iohn worsop esquire , for making of the bargaine with the country , and henry briggs professor of the mathematicks in the vniuersitie of oxford , heldebrand pruson , citizen and salter of london , and cornelius drible engeneere , with the rest of the vndertakers for the drayning of the levell within the sixe counties of norfolke , suffolke , cambridge , isle of elie , huntington , north-hampton and lincolne-shire , on the south side of gleane . whereas the countrie have offered to master burrell and his associates , for the drayning of the great levell in the sixe counties aforesayd , and for the maintenance of the worke , beeing done , the quantitie of 80000 acres , of which he offereth to ingage vnto the countrie but 10000 acres for the maintenance of the worke . wee offer , that if the countrie will or can allott the sayd proportion of 80000 acres to us , we will undertake to drayne the sayd levell , and will ingage 15000 acres , and a rent of 4 d. the acre out of the whole 80000 acres amounting to 1333 l. per annum , for the maintenance of our worke , and will give to every cottager , whose house shall happen to stand upon any part of the land allotted to us , the summe of foure pounds towards the erecting of a new house , in some other part of the common . but because we conceiue it very difficult ( if not impossible ) to apportion , and set out a certaine number of acres , out of so many and various particulars , as must necessarily be conteined in so great a quantitie of ground , unlesse the same should be taken only out of the commons , and the seueralls spared , which we cannot conceiue reasonable , we therefore propound as followeth . 1. first , whereas by the lawe , the commissioners of sewers have no power to make a bargaine for any composition of land , till a taxe be set , and not paid , at the day appointed : we desire that a taxe of tenne shilling be laid upon every acre of land , that lyeth under the high-water-marke , or is annoyed with fresh or salt water , or shall receive benefit , or ease by drayning within the levell ; to which lowe demand we are descended , for the ease of the countrie , which taxe must be paid at a day certaine , and to remaine in the hands of such as the commissioners shall thinke fit to keepe it , the vndertakers to have proportionably thereof , according to such parts and proportions of the said surrounded grounds , as they shall from time to time drayne ; provided that the sayd part be first adiudged drayned , and exceed the quantitie of 100000 acres . 2. secondly , for so much of this taxe , as shall not be paid at the day appointed ; we desire of the worst land , one halfe ; of the second sort , one third part ; of the third sort , one fourth part . 3. thirdly , whosoever shall thinke fit , to redeeme such part or proportion of his owne lands , being severall , as by the commissioners shall be allotted to the vndertakers , shall ( if he desire it ) adventure seven shilling for every acre of his land , cha●ged with the sayd taxe of tenne shilling ( the estimate being set downe under his hand , of the whole number of acres of his sayd land ) so , as it be within 5 of 100 , and 50 of 1000 ; and so shall not part with any land of his at all . 4. fovrthly , whosoever shall be unable or unwilling to pay the taxe of tenne shilling the acre , or to venture seven shilling the acre , and yet willing to redeeme his severalls , given by the commissioners . we therefore make this offer , that he shall , if he please , have a defeazance , or such other securitie , as by councell shall be advised from us : that if he pay thirteen shilling foure pence for e-every acre of his said severalls , charged with the said taxe of tenne shilling , after they are adiudged drayned by the commissioners , then he shall retaine all his severalls to himselfe . provided , that he demand the sayd defeazance , or other securitie , within one moneth after the act or decree of sewers , whereby his land shall be decreed to us . 5. fiftly , and because we desire to give all possible ease , and content to the country , wee are content that one shilling of the taxe of tenne shillings for euery acre be left in the hands of the owner , and one shilling of the seuen adventured , and one shilling foure pence of the mony due by the defeazance , shall remaine in the hands of the owners , 〈◊〉 urgent occasion and necessitie force vs to call , for some part , or the whole , which yet we hope we shall not need . but for the further ease of the country , we are content that they shall pay the said seven shillings adventure , for euery acre of their severalls , in manner and forme following . vz. two shillings within one moneth after the taxe is set , and two shilling two moneths after , and the other two shilling two moneths after that : one shilling being still left in their hands as aforesaid . and for the twelve shilling of the thirteene shilling foure pence , to be paid after the worke shall be adiudged drayned , we demand to have it paid as followeth ; vz. foure shillings within one moneth , and foure shillings three moneths after that , and the other foure shilling three moneths after that . ● . sixthly , if the house of any cottager shall happen to stand in any part of any common allotted to us , wee will build him an other in some convenient place in or upon the same common . if any of these three particular offers be accepted , we will undertake a generall drayning of the fennes , and other grounds annoyed with fresh or salt waters , within this levell , and will expect no recompence , but out of such lands , as shal be adiudged drayned , or such money as the countries shall agree to giue before hand by way of adventure . wee will undertake to make good and maintaine for ever , at our owne charge , all such draynes and workes , as wee shall make , and will ingage for the performance thereof , a reasonable proportion of land , as shall be agreed upon betweene us and the commissioners . that all the maine workes shall be made nauigable , and be built for the most part , with bricke and stone . that all owners of land and parties interessed shall haue libertie to adventure , after the rate of other adventurers . that wee will vndertake to performe all this within foure yeeres to bee accompted from the time , the bargaine shall be fully perfected , with the commissioners and the country . so vve receive no impediment from the commissioners , nor the country . dated the 11. of ianuary , 1629. an explanation of the drayning workes which have beene lately made for the kings maiestie in cambridge shire by the direction of sir cornelius virmuden wherein is discovered how the said sir cornelius hath abused the kings maiestie and many of his loving subjects / written by andrewes burrell. burrell, andrewes. this text is an enriched version of the tcp digital transcription a30503 of text r27138 in the english short title catalog (wing b5972). textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. the text has been tokenized and linguistically annotated with morphadorner. the annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). textual changes aim at restoring the text the author or stationer meant to publish. this text has not been fully proofread approx. 15 kb of xml-encoded text transcribed from 8 1-bit group-iv tiff page images. earlyprint project evanston,il, notre dame, in, st. louis, mo 2017 a30503 wing b5972 estc r27138 09674102 ocm 09674102 43950 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. a30503) transcribed from: (early english books online ; image set 43950) images scanned from microfilm: (early english books, 1641-1700 ; 1326:17) an explanation of the drayning workes which have beene lately made for the kings maiestie in cambridge shire by the direction of sir cornelius virmuden wherein is discovered how the said sir cornelius hath abused the kings maiestie and many of his loving subjects / written by andrewes burrell. burrell, andrewes. 12 p. s.n.], [london : 1641. reproduction of original in the bodleian library. eng vermuyden, cornelius, -sir, 1590-1677. drainage -england -cambridgeshire. reclamation of land -england -cambridgeshire. a30503 r27138 (wing b5972). civilwar no an explanation of the drayning vvorkes vvhich have beene lately made for the kings maiestie in cambridge shire, by the direction of sir corn burrell, andrewes 1641 2773 1 0 0 0 0 0 4 b the rate of 4 defects per 10,000 words puts this text in the b category of texts with fewer than 10 defects per 10,000 words. 2006-04 tcp assigned for keying and markup 2006-05 aptara keyed and coded from proquest page images 2006-09 judith siefring sampled and proofread 2006-09 judith siefring text and markup reviewed and edited 2007-02 pfs batch review (qc) and xml conversion an explanation of the drayning vvorkes vvhich have beene lately made for the kings maiestie in cambridge shire , by the direction of sir cornelius virmuden . written by andrewes burrell , gent. vvherein is discovered how the said sir cornelius hath abused the kings maiestie , and many of his loving subjects . printed in the yeare 1641. an explanation of the drayning workes which have been lately made for the kings majesty in cambridge shire , by the direction of sir cornelius virmuden . written by andrewes burrell , gent. wherein is discovered how the said sir cornelius hath abused the kings majesty , and many of his loving subjects . first , he hath disgraced the kings workes , by making weake bankes , when hee might have made them strong . secondly , by making hollow and counterfeit bankes of light moore hassocks , and sedge , skimming and destroying three times so much ground as would have performed the service , if he had taken the best of the soyle . thirdly , he hath disgraced the kings works in causing divers sluces and sasses to bee made of rotten timber , which ought to have beene made of the best brickes or stone , in regard they are to be placed for perpetuity . fourthly , he hath abused the king in misspending his treasure . fifthly , hee hath abused the late earle of bedford , and divers noblemen and gentlemen that adventured with him in his undertaking , by undervaluing the works which they made , and by hindering their proceedings , to their extream losse and disadvantage , and to the great hindrance of all those gentlemen that are interessed in that great levell , consisting of three hundred and seven thousand acres . sixthly , he hath abused divers of his majesties subjects , in taking their lands from them illegally , without any composition or satisfaction . seventhly , he hath exposed to wilfull and unnecessary hazard the lands , cattell , corne , and other goods of many of his majesties subjects , so that they are in great danger of being drowned this present winter , as doth appeare by this insuing discourse . the first worke hee caused to be made , was a sea bank in wysbeach saltmarsh , which is so slender , that three roods of the new sea banke hath not so much earth in it as one rood of the old sea banke . hee ought also to have armed the new sea banke with sods on that side which is next the sea : for being thus sleightly made , and not armed , the sea hath lately broke the new sea banke in divers places , and weakned it for a great space ; but in regard it was an easie flood , the damage is little in comparison of what it might have beene , that land being alwayes well stored with sheepe , that may soone be lost . the second worke which hee caused to bee made , was a sluce at the outfall of a draine , called the sheir draine , which worke he commanded to bee made in unseasonable weather , not knowing ( i am sure not attending or not heeding ) the danger , when it was plainly to bee perceived at the laying downe of the foundation : for at that time the losse might have beene prevented : it is said that that sluce , with the spadework and mischances which happened whilest the pit was making , by the seas breaking in twice upon them , did cost the king at the least three thousand pounds , which money is every penny lost . the third worke was the inlarging of a part of wysbeach river for the space of a mile , wherein he was as much wanting of the depth of the earle of bedfords worke , as he exceeded in unnecessary bredth , ( leaving the river as narrow as the earle left it , two miles above the new worke , and two miles below it , ) a worke that is broad and shallow may be made without skill or care . and if the truth may bee spoken without offence , such is that worke . the depth of that new worke cannot be perceived above one month in the yeare , and that is when the winter floods have recovered the outfall to the sea ; for so soone as the waters doe rise in the river , it seemeth to them that know not the difference , to be a very great inlargement , being very faire to the eie , but wanting depth can performe no better then eye-service . whereas the river of wysbeach runneth from the towne bridge to guyherne fix measured miles of the way towards peterborough in a neare and safe tract , in regard the soyle where the river now runneth , is clay , earth , or silt ; that substance would have inlarged the bankes on either side of the river , to so great a proportion , that the countries lying on either side would have been much better secured then ever they were in the times which are past : yet sir cornelius virmuden either through wilfulnesse or weaknesse , left the safe and nearest way where hee might have enlarged the river to what proportion hee pleased , and secured the lands on either side from danger , as is said before , and made a new banke of hassockes , light spungy moore , and sedge , in a fenne called walterley , where there is neither clay , earth , nor silt , unlesse it be at the first entrance , for the space of a furlong . the new banke so made , is more then two miles and three quarters in length ; in which worke he misspent at the least two thousand and three hundred pounds ( or thereabouts . ) besides which great losse to the king , and damage to the owners of the lands , his intent is to lay foure hundred seventy foure acres of the said land , waste to the said river , upon which land there is three tenements newly erected , and two other that are ancient : and this he will doe , as he falsly pretendeth , to make that land a receptacle for the common waters : whereas in truth he doth it of purpose to doe me a mischiefe , in regard i did contravert some of his opinions before the late lord treasurer , when my selfe was a commissioner for his majesty in october 1638. when god knoweth that which i spake was in the sincerity of my heart , for the advancement of his majesties service , without any by respects . one of the workes which i then propounded , was the making of a bricke sluce below spaulding , to keep out the sea floods : and sir cornelius disliked it , affirming that there was no way to draine the fennes , but by making of large bankes : yet now that he doth what he pleaseth , he himselfe hath very lately not onely approved in speech , ( for therein he is very giddy ) but he hath covenanted with a workman to make a timber sluce with a sasse beside it , to bee placed in the same place , for which the king is to pay three thousand and five hundred pounds , wherein appeareth his deceitfull dealing with the lord treasurer , lord cottington , and my lord banckes , at that time the kings atturney . and if the old firme banke were cut , so that the common waters might come to the new hollow bank which he hath caused to be made , it is undoubtedly certaine , that they will drown all the rest of the said lands , being at the least foure thousand acres ; and if that were effected , it would bee no way beneficiall to the generall drayning , as doth appear by a certificate made by the principall gentlemen , and land holders in that country . these lands were banked and drained by an act of parliament made the fourth of king iames , and have ever since that time beene maintained and upheld , and were not questioned in the earle of bedfords undertaking . besides there is no mention of making this receptacle for the common waters in those propositions which sir cornelius did deliver to the kings majesty in ianuary 1638. yet contrary to all justice , hee hath taken these lands from the owners , without any composition or satisfaction , and intends to drowne all the rest . fifthly , he hath caused a banke of h●ssockes and light spungy moore ( which in three or four yeares will shrinke to lesse then halfe the proportion which it now hath , and after that to be so much lesse , as it will bee little better then nothing , for it will bee hollow and spungy still . ) such a banke he hath caused to bee made from guy herne to the east end of wittelsey . he hath also continued the same banke ( but in a better soyle ) from the west end of wittelsey to stanground , intending thereby to keepe the river neene from drowning those fennes which lye betwixt these new bankes and the north bank of bedford river : and certainly they will secure them this present winter from neene . but if the north banke of bedford river bee setled so low that the river of owse overtop it , and make breaches in it ( as i beleeve it will ) those false fires will soone bee discerned . i have often heard sir cornelius fleight all the workes which were made by the late earle , as if they were rather hurtfull then beneficiall to the country . but hee did the earle great wrong , for if those workes faile , all his hassock banks will not be worth three pence . nor could hee have made them , if the earle had not opened wysbeach river to the sea , and kept the sea from choaking it againe ; which was a worke farre exceeding all that sir cornelius hath done . his plot is by subtilty to rob the late earle and those adventurers of the credit of their works , and after that to make all such as know not the truth , beleeve that himselfe with ten thousand pounds , will presently make one hundred thousand acres fit for the plow , which is a meere delusion . and as it is wicked in it selfe , so is it attended with a danger much worse then all that hath beene yet discovered . and it is a question whether it be not past recovery . this mischiefe hee hath cast upon many of his majesties subjects , inhabiting the low lands , called holland in lincolne shire , and the north side of wysbeach , both which countries are full of people , and well stored with cattell : they lye betweene the fennes and the sea , and are much lower then the common fennes : they are preserved from inundation by bankes consisting of a sandy substance , and are so low , that they cannot defend the said countries from inundation . now sir cornelius hath turned the southerne waters upon them ; for there will come three times so much water upon them now as did before . the new bankes were made in regard neene cannot passe in its owne chanell to the sea , nor dilate it selfe over the face of those fennes which lye on the south side of wittelsey , as formerly they did . sixtly , he hath caused a timber sasse to bee placed neare stanground , which hath cost the king eight hundred pounds at the least . the use of the sasse i beleeve will be good ( in convenient time ) but i like not his direction , who dares to spend the kings money in timber workes , when indeed they ought to be made of the best brickes or stone , i thinke rather stone then brickes , in regard that country affordeth great plenty of good stone at very cheape rates . this sasse is not onely made of timber , but of firre timber , and that so rotten that it was not fit to be used in the making of a good stable ; and in stead of oken plankes three inches thicke , it is planked with deale boards but one inch thicke , which will be rotten before the other works are finished . seventhly , he hath caused divers petty sluces to be made of the like timber and deal boards , which ought to have beene made of brickes or stone , in regard they are intended for perpetuity . eightly , he hath misspent the kings treasure , in giving over large wages unto many workmen ; for since michaelmasse last , money being wanting to forward this goodly designe , sir cornelius procured some assistance from those gentlemen whose lands lye on the south side of wittelsey , ( in regard these new bankes will be some advantage unto them ) paying the workmen part of their wages , in bullockes , sheepe , beere , cloth , and other commodities ; amongst them there were some payd part of their wages in wheat at fifteene shillings the combe , which did the next day sell the same wheat for nine shillings the comb. and if their wages were not extraordinary large , the condition of those workmen is such , that they will not worke two weekes to an end , unlesse they doe receive the due of what they earne , much lesse continue working two months without pay , and then accept of nine shillings for fifteene . and here i beseech you give me leave to give my deceased master , and those noblemen and gentlemen that adventured with him , their due praise ; from the first to the last of their undertaking , their workmen never wanted their wages , but were duly paid every weeke , untill the untimely difference in the yeare 1637. the reason why i mention this , is , that you may the better discerne how grosly the kings majesty hath beene abused , not onely in the losse of his treasure , but in paying the workmen with commodities , and in commodities much inferiour to them which i have named , and indeed not fit to name , which for their basenesse i omit . and all this to support an unadvised action , which i am confident will occasion a thousand times more losse , then all the good which can be expected , if duly considered . lastly , if it be objected , that i have informed against sir cornelius in discontent , or because he by his subtilty did defeat me of my imployment in those workes , after i had undergone the greatest difficulties , and meanest servitude , from the first day to the last of the late earles undertaking , or that i have wronged him in this my information , and cannot justifie every particular which is here expressed ; instead of relieving me , let mee undergoe the displeasure of all them whose helpe i doe implore . but if that which i have discovered be true , i doe most humbly pray that the remainder of my meane estate may by your justice be kept from utter ruine ; and that a commission of inquiry may be directed to examine and certifie my present losse , and future danger ; and that they may also consider whether the drowning of the foure hundred seventy foure acres before mentioned , will bee beneficiall to the generall drayning or not . and that in the meane time it may be ordered , that the old banke may not bee cut . finis . the picklock of the old fenne project: or, heads of sir john maynard his severall speeches, taken in short-hand, at the committee for lincolneshire fens, in the exchequer chamber. consisting of matter of fact. matter of law. presidents quæres and answers. maynard, john, sir, 1602-1690. this text is an enriched version of the tcp digital transcription a88998 of text r206914 in the english short title catalog (thomason e594_4). textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. the text has been tokenized and linguistically annotated with morphadorner. the annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). textual changes aim at restoring the text the author or stationer meant to publish. this text has not been fully proofread approx. 34 kb of xml-encoded text transcribed from 10 1-bit group-iv tiff page images. earlyprint project evanston,il, notre dame, in, st. louis, mo 2017 a88998 wing m1457 thomason e594_4 estc r206914 99866004 99866004 118263 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. a88998) transcribed from: (early english books online ; image set 118263) images scanned from microfilm: (thomason tracts ; 91:e594[4]) the picklock of the old fenne project: or, heads of sir john maynard his severall speeches, taken in short-hand, at the committee for lincolneshire fens, in the exchequer chamber. consisting of matter of fact. matter of law. presidents quæres and answers. maynard, john, sir, 1602-1690. [2], 16, [2] p. printed by j.b., london : 1650. the words "maater of fact .. answers" are bracketed together on the title page. the final leaf is blank. annotation on thomason copy: "feb 22 1649". reproduction of the original in the british library. eng reclamation of land -law and legislation -england. drainage -england -history -sources. fens, the (england) a88998 r206914 (thomason e594_4). civilwar no the picklock of the old fenne project: or, heads of sir john maynard his severall speeches,: taken in short-hand, at the committee for linc maynard, john, sir 1650 5928 5 0 0 0 0 0 8 b the rate of 8 defects per 10,000 words puts this text in the b category of texts with fewer than 10 defects per 10,000 words. 2007-04 tcp assigned for keying and markup 2007-04 aptara keyed and coded from proquest page images 2007-06 angela berkley sampled and proofread 2007-06 angela berkley text and markup reviewed and edited 2008-02 pfs batch review (qc) and xml conversion the picklock of the old fenne project : or , heads of sir john maynard his severall speeches , taken in short-hand , at the committee for lincolneshire fens , in the exchequer chamber . consisting of matter of fact . matter of law . presidents quaeres and answers . london , printed by j. b. 1650. the picklock of the old-fenne-project . mr. goodwin , i shall observe this method in answering the councell on the other side : first , i shall speake to the matter of fact . secondly , to the matter of law . and thirdly , i shall cite some presidents in the point . sir william killagrew hath mis-stated the matter of fact in his printed case , for therein he alleadges that the commissioners first invited the king to recommend to them an undertaker ; whereas it appears otherwise in the kings letters , and in three of his letters the king varies . the undertakers , which no question was by sir robert killagrew , sir william killagrew , and master robert longs procurement . the kings first letter is most observable , therein are couched all the fallacies of the undertakers , and the foundation of the project : they informed and perswaded the king , that he might appoint and command a tax to be laid of a marke the acre , without any respect to the interest of particular persons , or consult the owners : and further , that the tax should be made by the commissioners on you , without verdict ; and that their judgement must be the rule of proceedings in this case , and not the consent of the owners , whose aversenesse must not prejudice the publique good . in the kings second letter , the earl of lindsey , sir rob. killagrew , sir william killagrew , are recommended by way of mandamus to be undertakers , as we expect , and we do command all manner of persons to forbeare to make any particular bargains or works , &c. in the third letter it is still by way of mandamus , we have made choice of him ( meaning the earle of lindsey ) to be the vndertaker . and in the kings last letter , the king offers to give his royall assent . the commissioners began legally , for they impannel'd a jury of the neighbourhood , of twenty five , who found that the levell was not hurtfully surrounded . when mr. robert long saw how the countrey was bent , he wisely sold his share for 1500l . to mr. herne , mr. nicholas love , and one mr. hoyden , and they were to be at the charge of draining . likewise mr. long perswaded mr. thomas killagrew , and mr. henry , to sell their shares , but sir william killagrew would not be advised , but built a faire house on another folks lands , and fortified it , and furnished it with men , ammunition , and artillery . muskets , horsemen , and pistols , in a warlike manner , and entertained french and dutch . yet the countrey would never yeeld possession , but alwaies opposed sir william , and the rest of the undertakers , the countrymen were pursuivanted , imprisoned by councell-table-warrants ; some we heare were wounded and affrighted with mastiffe-dogs . many men were utterly undone and wearied out , and forced to subscribe and enter into bonds . assoone as the courtiers saw the commissioners joyned with the countrey , they procured worthy patriots to be put out of commission , and courtiers , servants to the undertakers , and many of themselves were jndges and parties ; after the jury found the levell not hurtfully surrounded , they were laid aside . and the commissioners , many being undertakers ( and consequently judges and parties ) got upon boston steeple , and adjudged all they saw was hurtfully surrounded . they might , as well have got upon pauls steeple , and adjudged all the rich meadows and marshes on both sides the thames to be hurtfully surrounded , when they are overflowne by land-floods . if you will see to the end , you must observe the meanes , the undertakers gave the king 3000. acres by way of bribe ; and the king gave them 14000. acres , for being judges and parties ; they might be their own carvers . likewise the undertakers gave some thousands of acres to divers lords of the councell , and both the secretaries . i pray observe some materiall circumstances : first the time when this project was set on foot . it was in the intervals of parliaments , the onely harvest for projectors , then parliaments were damn'd at court . and observe the persons that were the patrons of those projectors ; they were inveterate enemies to parliaments . the lord treasurer weston , who was accused by sir john elliot in 3 car. and most instrumentall to imprison those worthy members , and sir john elliot died a martyr for the parliament in the tower : the earle of lindsey , father and son , and all the undertakers , have been against the parliament . alas there is a bed-roule of other grievances , and 200. witnesses were examined when mr. ellis had the chaire . so much in brief to the matter of fact . for the matter of law , we conceive these undertakers are higher offenders then the earle of strafford , for they have not onely indeavoured , but traiterously , maliciously , and premeditately , against the light of their own consciences and knowledges , have actually subverted the fundamentall lawes of the land , and introduced an arbitrary and tirannicall government : for contrary to the 29. chap. of magna charta ( which is confirmed by thirty two sessions of parliament , whereof the petition of right , and the act for the abolishing the star-chamber are two ; they have imprisoned our persons , and destroyed juries , and put out the two eyes of the law , liberty , and property . likewise contrary to the 15 and 16 chap. of the great charter , wherein it is expressed , that no man shall be compelled and distrained to make new ban●● or bridges , but as formerly ; the same is confirmed in the 25. ed. the 3. ch. 2. the 1. of h. 4. chap. 12. the 6. of h. 6. chap. 5. the 8. of h. 6. chap. 2. the 12. ed. 4. ch. 7. the 6. of h. 8. chap. 10. all which are knit up in the 23. of h. 8. chap. the 5. yet the undertakers , many being commissioners , have acted point blank against these known laws . for the commissioners could do nothing without the jury , which are judges of the matter of fact , and they are to finde the defaulters according to the 12. of edw. 4. and the 23. of h. 8. and to amerce individuals , and not a generall levell ; and the commissioners are to approve of such amerciaments . object . but say they the undertakers , by the 23. of hen. 8. the commissioners may proceed without juries by view , according to their discretion . answ. sir edward cook explains discretion , which is secundum consuetudines & leges angliae , otherwise their proceedings are irrationall and illegall ; besides the commissioners could not lay a tax , because they were new moulded of courtiers which were judges and parties , and the countrey gentlemen contrary to usance , custom , and law , were put out and strangers put in , some not worth fourty marks per annum , which by the law they ought to have been ; so they were not legall commissioners , because they were undertakers , and consequently judges and parties , and could not contract with themselves : had they been legall commissioners they could not do it without juries , and they laid it likewise upon no body , for generals signifies nothing , but as i said formerly , it must be done by the jury upon individuals . all the kings letters , which are supposed to be indited by master role ● long , were diametrially contrary to law ; the king could lay no tax , nor give the commissioners leave to proceed without juries , nor to appoint undertakers , which is contrary to the 43. of eliz and the 4. and 7. of king iames : in the 43. of elizabeth there is the first mention of an undertaker , and therein he is limited and directed , what , how , ●●d with whom he must contract : a commissioner likewise hath no authority to contract , but the contract must be by the direction and approbation of the lords , owners , and commoners , under their hands and seals in writing indented : here was no such matter , they followed their own lights , which were ignes fatui , and so fell into those pits they digged for others . they made a contract with the king , which was an evil bargain , and they had the kings royall assent , which signifies nothing out of parliament , who ought by law to speak onely by his writs ; for det lex regi quod rex legi , quae rex jure potest , rex ea sola potest ; but my fellow courtiers , thought they were above and beyond the arm of the law , though they were both reached and over-reached at the last . the judges for ship money were accused for treason , by reason it was destructive to propriety , yet that was not three in the pound ; but the fenne-project cuts our estates asunder at a blow . in ship-money the king had a judgement by the sworn , or rather forsworn judges , but the undertakers were the old levelling courtiers , destroyers of propriety , and got the kings hand to letters of their own inditing ; and just as the earl of strafford produced blanks for all his horrid illegall acts , as disarming the protestants and arming the papists , so did the undertakers produce the kings letters upon all occasions , especially to destroy jucies , and to take away our reall estates , without consulting the owners . it is the same with the forrest business , for the judges some of them would have made all england a forrest ; so this generation of undertakers would have incorporated , and got a standing commission in all counties , and so made england the levell , and england to be surrounded , and in short time would have taken all we had ; this was as bad as their levying war against the parliament : and we conceive sir william killagrew did actually levy war against the nation , and had his project succeeded we had been no more a people : alas the law of the land was used by the undertakers as a murderer in frame , whose joynts are broken on the wheel , whilest he is yet alive , and in good health . i should answer the counsellors prolix argument , but i know not how to finde the beginning , nor end of his ravelled discourse ; he hath played the part of a flourishing writer , who usually buries the capitall letter in a curious knot , and instead of enucleating the business , i can see no kernell but husks and shels . in my apprehension the gentleman that spake last hath gleaned his argument from my lord finch , and some of the ship-money judges ; all he hath spoken , is for the kings prerogative against the law , that is not now ala mode . but master goodwin , i beseech you observe , this honourable committee hath spent one quarter of a year on the point of possession , and i hope we have beaten the undertakers from that post . then they pressed to state their case in law , and shew their title , so that we hope now we have gained that post likewise , and not only got possession , which is eleven points in law , but the twelfth likewise . now the undertakers are building castles in the ayre , or rather upon a quicksandy foundation of the old arbitrary government of conveniency and inconveniency , if that poynt crack , then they will flie to necessity , the old court retreat : let , them traverse their ground and sence as well as they can , we shall hit them still , and beat them at their own weapon . the presidents . in queen elizabeths days this project was set on foot by the then earl of lincoln , who procured a patent from the queen to drain some of these fens : when he was making his works and new drains , contrary to law , the country rose , and the lord willoughby of erby , then governour of berwick , raised the trained bands and assisted the countrey in beating the workmen off : the earl of lincoln , complained to the queen of the riot committed by the lord willoughby , who was sent for to the councell table : the lord willoughby proved the earl of lincoln had not the countreys consent , but some few tenants and others of his own faction , that it was for private ends and lucre , not onely to drayne himself and drown his neighbours , but to take great propoitions of land , which were never drowned for melioration ; and the means my lord of lincoln used was bribes to courtiers to procure such an illegall commission that himself and his friends might be judges and parties ; and that it was against the 23. of h. 8. the queen upon full hearing of the business in great passion resumed her commission , and was wroth with the earl of lincoln , who had been committed to prison , but that his lordship made great friends at court , and the queen thanked the lord willoughby of erby for assisting her good people in so honest and just a cause . in the first of king james the same project was set on foot and a petition was delivered unto his majestie as though it had proceeded from the country , just such a petition as sir william killagrew procured by two ale-house keepers : for it was onely a few of the undertakers faction , like to the agreement of the people : sir , miles sandes had made many friends at court , and the king was prepossessed it was a glorious work , and for the publique good , and the king was made believe the isle of ely , and the southside the river grant was hurtfully surrounded ; but when the king was hunting , the lord garret of chippenbam , sir john cotton of chenely , sir john paytan of iselham , and sir thomas gee acquainted the king with all the cheats of the undertakers , that they being judges and parties had made many thousand acres , that were never drowned , and the most part of the land which was the better by overflowing in the nature of river meadows , to be land hurtfully surrounded . that they dreyned and meliorated a little hurtfully surrounded lands of their own , and pejorated ten times as much lands ; which were never hurtfully drowned before , and that which was most gross and palpable , they must not onely have a third part of that land so pejorated , but a third of such lands as were never drowned , for melioration : when the king was fully instructed , he injoyned secrecy , and went up to the parliament and discovered all the undertakers fallacies , and concluded wittily . it is just the same case , my lords , at though a pack of thieves should give me 20000 l to give them a pat●● under my broad seal to rob my loyall subjects of 200000 l. by the which i should perjure my self , and become a theif and tyrant : thereupon the parliament ●ung it out for a base cheating monopoly ; some of sir miles sands friends moved he might have satisfaction for the vast sums he had expended ; sir edward cook answered , let those pay him that set him a work , and further added , that it was fit sir miles should give compensation to the oppressed country ; for trying experiments against the owners consents . the maxime is , plura potest interrogare asmus , quam respondere aristotele . but let the undertakers ask as many and what questions they please , we hope to give full satisfaction to this honourable committee ; but i wil state the most difficult quaeres , i ever heard of from the undertakers , and give them satisfactory answers . the quaeries . 1. quaere . why did not the countrey pay the tax of a mark the acre ? answ. because it was illegall in many respects . first the commissioners were illegall that laid it on the countrey , for the nobility and gentry were put out of commission , and there was a new commission where the earl of lindsey , sir robert killagrew , sir william killagrew , master robert long , and divers privie counsellors who were bribed , and courtiers were put in their rooms contrary to usance , prescription and custom , which is the law of the land ; and many of them had not a foot of land in the country , whereas by law they ought to have fourty marks per annum . had the commissioners been legall they could not lay a tax without a jury , and had the commissions and juries been legall they could neither lay a tax to make new works , which is cleared by the 15. and 16. chap. of the great charter : likewise neither the kings commissioners nor jurors have any thing to do with the matter of undertaking , that belongs onely to the major part of lords , owners and commoners ; for they may contract under hand and seal with whom they please , so that commissioners cannot be undertakers , for then they should be judges and parties : likewise it is against sence and reason that commissioners and undertakers ( as they were ) should contract with themselves , and give the countreys lands one to another , as my lord of lindsey gave a warrant to the commissioners to judge 14000. acres dreyned , his lordship being the chief undertaker himself : besides the tax was laid on no body , because it was laid on the levell in generall , whereas by law it ought to be laid on particular towns and individuals , so it could not be paid legally by any body . 2. quaere . whether is not dreyning good for the common wealth ? answ. there are two kindes of dreyning , the one is by the ancient commissions of sewers . the other by the more recent way of undertaking ; both these are legall and illegall . legall dreyning ( viz. ) by commissioners of sewers of the nobility , and wel-affected gentry of their own country , and honest goodmen of the neighbourhood , who are to be jurors , and consequently judges of the matter of fact , who return defaultors according to the 12. of edw. the 4. and thereupon , the commissioners confirm their amerciaments : were the old dreyns thus legally scowred twice or thrice the year , there would little land lye hurtfully surrounded , this is good for the common-wealth . but illegall dreyning , that is , to put in courtiers , sharers , sharks and strangers to be commissioners , and by the kings prerogative to make them judges and parties , and to impower them to take away the free peoples estates against their consents by view onely , without juries , and to make new works for private ends , contrary to the great charter , which is confirmed by 32 sessions of parliament : this is destructive to propriety , and the bane of the common-wealth : undertaking is a distinct thing from the commissions of sewers , neither has the kings commissioners of sewers nor jurors any thing to do with the matter or manner of undertaking : this is likewise two fold , legall or illegall ; legall undertaking , according to 43 eliz. is when the major part of the lords , owners , and commoners , do agree with any person or persons , or corporations , for a certain sum of money under their hands and seales , for the draining such lands as they finde hurtfully surrounded . this is good for the common-wealth , because it is with their free consents , so volenti non sit injuria . illegall undertaking is when the kings commissioners of sewers , or others by vertue of the kings authority , by violence , oppression , or councell-table-warrants , will act as undertakers against the owners consents ; this is the heighth of arbitrary government , and tiranny it self , which is a speedy destruction to a nation , and the pest of the common-wealth . 3 quaere . whether drayning land hurtfully surrounded , is good for the common-wealth ? answ. if the drayners be legall , and do more good then hurt , it may be good for the common-wealth ; but if they do more hurt then good , it must of necessity be bad for the common-wealth . the undertaker is like the tinker , he stops one hole , and makes two ; he draynes one acre for himself , and drownes two of his neighbours ; nay sometimes twenty : certainly this is bad for the common-wealth . yet he hath drained lands hurtfully surrounded , and drowned lands not hurtfully surrounded , and must have a third part of those lands that were never hurtfully drowned for melioration , so the same former distinction still holds good , legall is good , illegall is bad for the common-wealth . 4 quaere . whether is this levell of the earle of lindsey hurtfully surrounded ? answ. there are two verdicts , and fourty witnesses , that have proved it is not hurtfully surrounded ; but if draining lands hurtfully surrounded were good , then draining lands not hurtfully surrounded certainly is bad for the commonwealth . for to draine dry land , it is to take away the humidum radicale , and so consequently to spoile it : besides to drain the lands floods from our fodder-fens , and to divert the rivers from overflowing , we should not have half so much fodder for our cattell in winter . this levell is of this condition in both respects , and the earles new draines do much more hurt then good , by draining dry grounds , which the undertakers keep for themselves , and leaves the worst to the country , and so contrives their new draines , that they hurtfully surround those lands which were not hurtfully surrounded before ; so they drown us to drain us , but the remedy is worse then the disease . there are severall witnesses that have proved this , and we can demonstrate it mathematically . that by opening the old draines , it would be far more beneficiall to the commonwealth , and it would not stand the country in the tenth part of the charge : all which can and will be done by a legall commission of sewers , of the well-affected gentry of the countrey , and honest jurors of the neighbourhood . 5. quaere . why hath not the countrey drained themselves all this while , will they be like the dog in the manger , neither do their selves good , nor suffer others to help them ? ans. the country are , and have been ever willing , but they have been obstructed these sixty yeares by powerfull courtiers , as lord keepers , attorneys-generall , and the dissolution and intervals of parliaments have impeded us ; but when we are rid of the undertakers , the worke will quickly be done , both for the honour and profit of the nation , without fraud or coven . 6 quaere , but had not the earle of lindsey the major part of the lords , owners , and commoners consents , his lordship had a petition signed with many hands . answ. ten for one of the lords , owners , and commoners , are against the earls undertaking ; those hands for the earle were procured by two alehouse-keepers , and most of them were cottagers , no lords , and but very few owners and commoners . 7 quaere . would it not be a brave improvement to have rape and cole-seed , hemp , flax , and likewise corne ? answ. they calculate and reckon without their host , that the customes will amount to 10000 l. 1 s. 8 d. ob . per annum . this is ala mountebanco , or sharlaton like : our fens as they are , produce great store of wooll and lambe , and large fat mutton , besides infinite quantities of butter and cheese , and do breed great store of cattell , and are stockt with horses , mares , and colts , and we send fat beefe to the markets , which affords hides and tallow , and for corne , the fodder we mow off the fens in summer , feeds our cattell in the winter : by which meanes wee gather such quantities of dung , that it inriches our upland , and corne-ground , ( which are contiguous halfe in halfe . besides , our fennes relieves our neighbours , the uplanders , in a dry summer , and many adjacent counties : so thousands of cattell besides our owne are preserved , which otherwise would perish . so take away a third of our fens , you extinguish our rents in our commoning houses , and our pastures , and corne-ground , proportionably ; besides thousands of cottagers which have no right of commoning , must go a begging , which the owners connive at , because they cannot prevent it , being so numerous . so that rape , cole-seed , and hemp , is a dutch commodity , and but trash and trumpery , and pils land in respect of the afore recited commodities , which are the oare of the common-wealth . 8 quaere . is it not pitty , when sir william killagrew having done so much good by his drayning , and hath spent 30000 l. but that the countrey should re-imburse his moneys , there is all the conscience and reason in the world for this ? answ. first , it hath been proved , he hath done a great deale more hurt then good by his new dreyners , and when the countrey shall make use of the undertakers dreynes , we will give satisfaction for them , but they are uselesse , nay pernicious and broken cisternes to the commoners in summer , both by dreyning our dry grounds , so we are constreyned to buy water , and to drive our cattell very far in summer to water them ; whereas our old dreynes have ever furnished us with water enough . then on the other extreame , their new works have so hurtfully surrounded us , that our upland and corne-grounds have been spoyled by them ; this is fully proved by many uninteressed witnesses , the countrey is daminified at the least 60000 l. by these undertakers . 9 quaere . whether are the old draynes or the new , most usefull for dreyning ? answ. the old dreynes are as the naturall sinks , or rather vent of the body of the fens ; suppose a mans fundament were stopped , and that a hundred issues were made in the body , the whole masse of blood would quickly be corrupted , and the body would breake out in botches and biles . so stop the old sewers , you will quickly perceive the sores or quagmires will increase ; and whereas there is but one acre now hurtfully surrounded were the old draines duly scowred , if they be stopped there will be tenne . this is proved by master thorpe mathematician , and he gives his reason , which is mathematicall and necessary . because the old dreynes have farre greater descents then the new , so that the old dreynes were never without water in summer , which now they want exceedingly , by reason of these undertakers dreynes ; which was proved before master ellis , when he had the chaire , by twenty witnesses . likewise the new dreynes , wanting that descent the old had , the least floods in summer or winter overflow those lands sooner and longer , which is the cause that these fennes are ten times more hurtfully surrounded then before . this is not my bare information , but mathematicall , or necessary , and proved by many witnesses : for i say what master walpoole hath alleadged is not mathematicall at all , but pragmaticall and fantasticall . it is a strange chymaera and phrenzie in the undertakers to expect satisfaction of the parliament for the money they have expended ; it were just the same , as though the old ship-money judges should be preferred to be judges , and that their fines should be restored , and they rewarded over and above , and the present reverend judges who have adhered to the parliament should be displaced and fined . o monstrum horrendum in forme ingens . quodcunque ostendas , mihi , sie incredulus odi . we hope the parliament will either fine them , as they did the ship-money judges , or the old farmers of the custom-house ; and that this fine shall be imployed by lawfull commissioners of sewers , towards the doing of the work , or relieving the poor ; or that we shall be left to the common-law , as the parliament left sir robert barkham , captain hall , and master waldrum . if sir william killagrew finde himself agrieved , he may then appeal to the parliament . the rule in divinity is , deus non vult contradictoria , sic parliamentum non vult contradictoria ; in the first grand remonstrance , this individuall business is declared to be an injustice , oppression , violence , project and grievance , and they particularize it , for this horrid project furnished the parliament with those choice materials , which builded their grand remonstrance . these are their express words : large quantities of commons and severalls have been taken away by the colour of the statute of improvement , that is , by falsifying and adulterating it , which is meant by the 43. of eliz. and by abuse of the commission of sewers ( which dissolves that excellent law of the 23. of h. the 8. without their consent , and against it ) which is the destruction of the great charter , petition of right , the act for abolishing the star-chamber , and all the fundamentall laws of the land . and against twenty of the parliaments declarations , which are in print to the view of all the world ; yet the undertakers are so impudent that they are confident to pass a law , and to inslave us , who have conquered them ; but we so confide in our trustees , that we know it is impossible , being contrary to the principles of a republique , who acknowledge the supream power resides in the people , and the supream authority is derived from them , and the soul and heart of the common-wealth is liberty and property . these undertakers were formidable monsters to the countrey , and had they continued a little longer , probably they would not only have torn in pieces , but devoured and swallowed up the whole nation ; for they were legislators out of parliament , and anti-legislators , parliamentarians , and anti-parliamentarians , bribers , judges , juries and parties . they were legislators , for they have made severall laws , and they bribed the king with 3000. acres to purchase his royall assent , though i believe they might have had it for nothing . this was the root of all our miseries ; for could the parliament by their humble petitions have obtained the kings royall assent , as these courtiers could do with ease by their importunity , opportunity and flattery , this war had probably been prevented : certainly the undertakers were the onely impeders and partition walls betwixt king and people ; and they had closed and been reconciled , had it not been for such imposters as they , who cared not for god , king , nor countrey , but sought themselves and preferred their owne gaine before the publique . that prince is unhappy that prefers persons or individuals , before the representative of so numerous a people and great nation . they were anti-legislators , for all their laws were point blank against the great charter , petition of right , and all the fundamentall laws of the land ; they were parliamentarians to call a parliament , to sell ship-money for twelve subsidies , and to raise money to make wars against the scots , who wrestled for their liberties , and were not such tame slaves , as they expected : when the parliament would give no subsidies to inslave themselves , then the courtiers dissolved that parliament . that the undertakers were bribers is upon record , and likewise that they were judges , juries , and parties : sir edward cook was wont to say , that it never failed , that those which brake parliaments were alwayes broken by them ; yet these undertakers hope to be repayred for their project , which was onely to keep off parliaments ; and this one project ( had it succeeded ) would have commanded all the land in england to have been at the kings disposing ; then all had been their own ; for the king was little the better by such projects , the courtiers gained all . finis . a briefe relation discovering plainely the true causes why the great levell of fenns in the severall counties of norfolk, suffolk, cambridge, huntington, northampton, and lincolne shires, being three hundred and seven thousand acres of low-lands, have been drowned and made unfruitfull for many yeares past and as briefly how they may be drained, and preserved from inundation in the times to come : humbly presented to the honourable house of commons assembled in parliament / by andrewes burrell, gent. burrell, andrewes. this text is an enriched version of the tcp digital transcription a30500 of text r2671 in the english short title catalog (wing b5969). textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. the text has been tokenized and linguistically annotated with morphadorner. the annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). textual changes aim at restoring the text the author or stationer meant to publish. this text has not been fully proofread approx. 40 kb of xml-encoded text transcribed from 15 1-bit group-iv tiff page images. earlyprint project evanston,il, notre dame, in, st. louis, mo 2017 a30500 wing b5969 estc r2671 12630204 ocm 12630204 64729 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. a30500) transcribed from: (early english books online ; image set 64729) images scanned from microfilm: (early english books, 1641-1700 ; 252:e148, no 18) a briefe relation discovering plainely the true causes why the great levell of fenns in the severall counties of norfolk, suffolk, cambridge, huntington, northampton, and lincolne shires, being three hundred and seven thousand acres of low-lands, have been drowned and made unfruitfull for many yeares past and as briefly how they may be drained, and preserved from inundation in the times to come : humbly presented to the honourable house of commons assembled in parliament / by andrewes burrell, gent. burrell, andrewes. [6], 22 p. printed for francis constable, london : 1642. reproduction of original in thomason collection, british library. eng drainage -england. reclamation of land -england. fens, the (england) a30500 r2671 (wing b5969). civilwar no a briefe relation discovering plainely the true causes why the great levell of fenns in the severall counties of norfolk, suffolk, cambridge burrell, andrewes 1642 7274 0 0 0 0 0 0 0 a this text has no known defects that were recorded as gap elements at the time of transcription. 2006-04 tcp assigned for keying and markup 2006-07 spi global keyed and coded from proquest page images 2006-08 judith siefring sampled and proofread 2006-08 judith siefring text and markup reviewed and edited 2006-09 pfs batch review (qc) and xml conversion a briefe relation discovering plainely the true causes why the great levell of fenns in the severall counties of norfolk , suffolk , cambridge , huntington , north-hampton , and lincolne shires ; being three hundred and seven thousand acres of low-lands , have been drowned , and made unfruitfull for many yeares past . and as briefly how they may be drained , and preserved from inundation in the times to come . humbly presented to the honourable house of commons assembled in parliament . by andrewes burrell , gent. london , printed for francis constable . 1642. to the honovrable house of commons , assembled in parliament . great and honourable workes ought to bee directed by great and honourable councells ; and therefore to the intent this noble enterprise may not be undervalued ( as it is by some ) i humbly informe this honourable court , that besides sundry attempts made by divers noble men , who desired to improve the great levell of fenns ; the undertaking was so well esteemed by king james , that hee really intended to take it into his owne care ; the diversion of his royall intention is unknowne . after him the late earle of bedford and his friends adventured great summes of money to recover them ; but before their workes were finished , they were circumvented and outed of all their intendments . the last undertaking was attempted by the kings majesty that now is ; but the greatest part of his money being mis-spent , and all his intended workes misled by sir cornelius vermuden's mysticall designe , his now majesty hath declined his undertaking also , so that it is like to returne to the now earle of bedford and his friends . this noble enterprise being thus misguided , lyeth now before your grave wisdomes , expecting direction from this honourable assembly , and wanting a better friend to petition for them , ( there being an order made by the honourable committee for the fens , the twenty five of february last , that all men whom it may concern may offer any other designe ; in regard a perfect designe concerneth the preservation of many mens estates , which also may be ruined , impaired , or cast into eminent danger . ) i am humbly bold to informe you , that unlesse this honourable court command the now intended works to be published to the severall counties ( as was once intended by the honourable committee ) so that the countries approbation , or exceptions may bee valued ( or at the least heard . ) and that before the works beginne , equall compositions may bee made with all those whose lands shall bee impaired , endangered , or taken from them : many men may bee ruined in their just estates . there are two reasons that make me earnest in this cause : the one is the former ill designing , and ill mannaging of the workes , wherein wilfulnesse and ignorance ( in the kings name ) over-ruled the countries . the other concernes my selfe , first , in taking a great part of my owne land ( and some of that which i farme ) from me , without satisfaction , composition , or leave to cut it ; and which is much worse , by bringing all the rest of my inheritance , and leas't lands ( which together are not lesse than three thousand acres ) into eminent danger of drowning , by cutting my old firme banck , and exposing my lands to bee defended from the common waters by a hollow counterfeit banck , made of so light a composition , that it will both burne and swim . and here i beseech you give mee leave to tell you , that for want of iustice in england , and peace in ireland , my aged mother ; my selfe and foure brethren , have within a few yeares lost nine hundred and sixty pounds per annum : which when time will give me leave , i hope to prove before this honourable parliament ; which makes me the more earnestly implore your aide in this my great necessity . to conclude , if this noble enterprise by your honourable paines , be well designed , and so prosecuted ; the improvement will not only returne a sufficient satisfaction to the adventurers , but the common-wealth will sweetly rellish the great improvement which will follow . but because it is not safe to be over large in great promises , i will say no more ; but god grant the fenns may in due time be made vvinter grounds , not impairing any private mans estate . so prayeth your honours humble supplyant , andrewes burrell . a briefe relation of the true causes why the fenns in norfolk , suffolk , cambridge , huntington , northampton , and lincolne shires , have beene drowned . and as briefly how they may be drained , and preserved from inundation . before i declare the reasons why those low lands are subject to drowning ; i conceive it is fit to discover to them that doe not know those countries , in what condition the fens were before they were drowned : how they are seated , and how they are drowned . mr. cambden in his brittania , folio 449. referres his readers to william of malmesbury , who reporteth the lordship of thorney in his time to be so fruitfull and fragrant , that for delight it resembled heaven it selfe . that lordship is indeed a large and rich piece of land , consisting of eighteen thousand acres , or thereabouts , and pertaineth to the earles of bedford . but having lost the beauty lately mentioned ( nay to be plaine ) being quite lost , and perpetually drowned , save onely one hillocke where the abbey standeth , was the cause that induced the late earle to undertake the drayning of the great levell . in which service , by reason of my imployment under his lordship in the yeare 1635. in deepning wisbeach river , i discovered a stony bottome , upon which there was found lying at severall distances seven boates , which for many yeares had laine buried eight foot under the bottome of the river , as it was before the late earles undertaking . and it is very likely , that when thorney flourished , neene did run as deepe as that bottome . after this discovery , it was intended by the late earle that the river neene should have been enlarged and deepned from wisbeach to stanground ( by the tract of mourton leame ) as now it is from wisbeach to guyherne . and i am very confident that if neene were made a hundred foot broad , and so deepe as it is in wisbeach towne , from wisbeach to stanground , thorney fens in a few yeares would be as fruitfull and rich as ever they were in malmesburies time , whose story is , that they represented a very paradise , for that in pleasure and delight , it resembled heaven it selfe , in the very marishes bearing trees , that for their straight tallnesse , and the same without knots , strive to touch the stars : a plaine is there as even as the sea , which with green grasse allureth the eye ; so smooth and levell , that if any walk along the fields they shall finde nothing to stumble at ; there is not the least parcell of ground that lieth waste and void there . here shall you finde the earth rising some where for apple trees : there shall you have a field set with vines , which either creep upon the ground , or mount on high upon poles to support them : a mutuall strife there is betweene nature and husbandry , that what the one forgetteth , the other might supply and produce : what will be said of the faire and beautifull buildings , &c. this great levell of low-lands , whereof thorney is a part , is almost compassed about with high lands , and lyeth betwixt the high lands and the sea . the superficies thereof being generally as high as the superficies of the sea in ordinary tides , commonly called neape tides ; but foure or five foot lower than the superficies of the sea , when the sea is at the highest , which is in the spring tides , whereof some doe very much exceed others , being ruled by the windes : such tides doe happen twenty or thirty dayes in the course of a yeare ; some yeares more than the most , and some yeares lesse than the least , as the stormy windes doe force the spring tides into the bay , which is betwixt burnham in norfolk , and winthorp in lincolnshire ; whereby it is apparant that the rivers which are in the fens cannot empty themselves into the sea , but at such times as the sea floods are returned out of the rivers to the place from whence they came ; by reason whereof the fens are often drowned , two , three , or foure foot deepe , according as the floods are greater or lesse . betwixt the fens and the sea there is much good land that is improved and defended by substantiall bankes made of clay and silt , which doe preserve them from being drowned by the sea on the one side , and the high land waters on the other : the common fens being at the least five foot higher than some of those lands ; so that the sea commeth not neare the fens by six miles , or thereabouts . the fresh water rivers which doe passe through this levell , are principally owse and neene : the rest are but branches that doe fall into owse at their severall distances . the neerest way that any part of the river owse doth run from the high land to the sea , is thirty six miles , but the greatest part of it runneth fifty six miles , or thereabouts . the river neene runneth through this levell before it falleth into the sea , twenty miles , or thereabouts . so much for the scituation and condition of the fens . the reasons why the fens are drowned , are principally six . first , because the superficies of the fens lyeth lower than the superficies of the sea , when the spring tides are at the highest . secondly , because the high land floods must of necessity passe through that great levell of low lands , having very little descent to enforce a streame from the high lands to the sea , but at such times as the sea floods by retiring themselves doe leave the rivers empty , which many times is not above eight houres in twenty foure . a third reason is , the rivers through which the high land waters should passe , are not large enough to convey them to the sea , nor are they armed with sufficient banks to keepe the sea and land floods from dilating themselves over the face of the whole levell ; and it is a hard question , whether the sea or the land floods are the most potent enemies to the fenns ; but this is most certaine , that when the sea floods and the land floods meet , as they often times doe , halfe way betwixt the high lands and the sea , in that very place like two powerfull enimies joyning in one , they doe over-run the levell , and drowne it from one end unto the other . a fourth reason why the fenns are drowned , is occasioned by the sea floods , the violence whereof maketh so loud a noise at the first comming into the river owse , that it is oft times heard by those that are two miles from it ; and after the eager is past , for the space of foure houres there followeth a mighty flood streame that runneth into the country neere forty miles ; which waters returning more slowly , must of necessity have more time to empty themselves then was spent in receiving them ; for those waters which the sea forces into the rivers , must all returne before the high country waters can possibly be admitted to passe . the disadvantage is very plaine , the high land waters comming from betwixt the hills are continually running into the fens , and the sea floods are continually interrupting and repelling them where they should passe out of the fens into the sea , and will not suffer them to run above foure houres in twelve : which is one chiefe cause why the fens neare ely are so often drowned . a fifth reason is the ill disposition of the sea in those parts , which being troubled by stormy windes , doe carry such abundance of silt or sand into the rivers in the sommer season , that for want of a fresh water streame to wash them back into the sea , the rivers are choked and lost ; which silt or sands soon after the spring tides are past doe lie dry , and presently gaine a firmenesse , so that men and horses travell upon them ; and in the beginning of winter they doe much hinder the streame of the high land waters as they passe to the sea , untill by many land floods they are removed and washed into the sea from whence they came ; but it is so long before that can be effected , in regard the high land floods compared with the sea floods , are very weake , that when it is done it is too late for the country , being seldome wrought before the end of winter : the dryer the sommer is , the more the rivers are filled and choked with silt and sand against winter ; and it is commonly seen , that after much drought there falleth much raine , which oftentimes occasioneth the greatest inundations . the sixt and last reason why the fens are often drowned , is because there is no land eayes to receive the surplussage of the waters which proceed from raine and snow falling upon the high lands adjacent to the fens , and to carry them into those rivers or draines which are next unto them . now i have briefly showne the true causes why and how the great levell of fens are drowned ; i will particularly declare what works must be made to draine and preserve those low lands from inundation , so that the greatest part of them may be made culturable grounds . to remove the first and second causes of inundation , there must be a descent gained from the high lands to the sea , which is a work of a double consequence , and indeed it is one of the greatest works which is to be effected . the waters in the fens may be fitly compared to the beame of a paire of skales when it hangeth levell , which being raised at one end doth at the same instant settle as much at the other ; such a contrivement must be made of the fal that is to be gained betwixt the high lands and the sea ; the one halfe must be gained by raising the waters next the high lands by banks of a convenient heigth , and by setling of the waters in that part of the rivers that is next unto the sea , which latter work must be wrougt by mending and enlarging of the old rivers and draines where they are crooked , and where they are too narrow , or too shallow , and by placing of sluces to repell the sea floods . to remove the third impediment , it is necessary that every river and rivolet should be enlarged to such a breadth and depth as may convey the greatest winter floods the nearest way from the high land to the sea , and on either side of them to have a continued bank able to keepe the high land waters from spreading over the superficies of the fens ; the rivers being so perfected , there must bee many draines opened which are now lost , and some new made for the leading of the waters to the next adjacent river . there must be also many division dikes which will lead the raine waters into the neighbouring draines . the particulars will in this place take up too much time , i will therefore leave them to the designe it selfe . there must be a large sluce placed upon the outfall of owse that may be able to repell the sea-floods , and keep up the high land waters in dry sommers ; of which kinde there is already one upon the river neene , built by the late earle of bedford : at which time had neene beene enlarged to a sufficient bredth and depth , from the sluce to peterborough , and the banks continued and maintained on both sides at the same heigth that the southside banks were once made , having a sasse placed at stanground , as was intended , to keep all neene to wisbeach , the petty draines and division-dikes being also made , that side of the fenns will be perfectly drained ; but as it is , there is but a part of that work perfected . the making of sluces is very chargeable , and so difficult , that every bank-maker doth not understand how to place them nor make them ; but the advantage which they bring , being well built , cureth the fourth and fifth inconvenience , and indeed is very materiall to the perfect draining of the fenns . the last work is a great work , and will cost much money : it is the making of so many land eayes as may receive the surplussage of the waters which doe fall upon the high lands that are next the fenns , and convey them to the next river , rivolet , or draine , so that they may not offend the neighbouring fenns . having acquainted you with the scituation and condition of the great levell , and briefely declared how they may be preserved from inundation , i am humbly bold to present my designe unto this honourable court , therein expressing every particular work , together with the totall charge and time when the works may be perfected . to enlarge wisbeach river from the sluce to guihern , so that it may be twenty foot broader than now it is from the top to the bottome , and to take up the two ten foot banks which do lie hid under water , on each side of the river one ; and to leave a foreland of thirty foot broad on the south side from the brink upwards , being in all six measured miles , whereof there is one mile halfe wrought by sir cornelius , at the rate of forty shillings the rod , is , three thousand five hundred and twenty pounds . to purchase divers lands and tenements which doe stand upon the brink of wisbeach river , and must be removed before the river can be enlarged , with the extraordinary charge of carting the earth out of the town , may cost twelve hundred pounds . to make a wharfe of brick fourteen foot high , foure foot thick in the bottome , and two foot thick on the top , from elme sluce to the town bridge , being an hundred and twenty rods ; the stuffe , workmanship and earth work at the rate of seven pounds the rod , will cost eight hundred and forty pounds . to make a cart bridge in wisbeach town in the same place where the old bridge did stand , may cost two hundred and fifty pounds . to remove the bank which is now on the south side of mourton leame , so farre back , that there may bee thirty foot foreland betwixt the new bank and the brink of the leame , being ten miles in length , at three shillings foure pence the rod , it will cost six hundred and forty pounds . to make mourton leame an hundred foot broad from guihern to stanground , it must be enlarged fifty six foot on the north side to the same depth which the south side now hath , which was six foot when it was wrought , being twelve miles in length at twenty foure shillings the rod , will cost foure thousand six hundred and eight pounds . to make the old and new works as deep as the bottome of wisbeach river , being three foot and a halfe , and with that manure to heighten the banks on either side of the leame leaving thirty foot foreland to each bank at forty shillings the rod , it will cost seven thousand six hundred and eighty pounds . to pile the dike ends , swamps and low lands which break off the banks in many places , and convey by boat so much earth thither as will make the banks as high there as they will be elsewhere , which may bee eight foot , may cost three hundred pounds . to make an indike on the southside of the south bank twenty five foot broad at guihern , and fifteene foot broad at witelsey high lands , six foot deep at guiherne , and five foot deep at witelsey , at twelve shillings the rod , will cost one thousand nine hundred and twenty pounds . to make an indike on the north side of the north bank twenty foot broad at guihern , and fifteene foot broad at stanground , six foot deep at guihern and five foot deep at stanground , at ten shillings the rod , it will cost one thousand nine hundred and twenty pounds . to make the twenty five foot draine which is on the north side of the leame , two foot deeper than now it is , will cost three shillings the rod , which is five hundred seventy six pounds . to make two cart bridges over mourton leame neere witelsey town , each of them to have two peeres and no more , may cost three hundred and sixty pounds . to make new doores for the sasse at stanground , with spring doores in them that may open on a sudden ; and that for the safety of the country in times of danger , some part of the extreame floods may be turned into witelsey meare , and the other adjacent meares , which being empty , will receive a great water without prejudice to any , may cost fourscore pounds . to place a brick sasse on south eay draine neare guyherne crosse twenty foot broad , the bottome to lie even with the bottome of wisbeach river , with spring doores , that may open on a sudden to receive some part of a great flood in times of danger , the draines being empty ; this sasse may cost one thousand foure hundred pounds . the like sasse to be placed on bevill leame , that in times of danger some part of the great floods may be turned into march river : it may cost one thousand foure hundred pounds . to make south eay twenty five foot broad , and three foot deeper than now it is , being twelve miles in length , at eight shillings the rod , it will cost one thousand five hundred thirty six pounds . to make cats water twenty foot broad , and six foot deep , being nine miles in length , at eight shillings the rod , it will cost one thousand one hundred fifty two pounds . to open the shire draine , and to continue it from hills sluce to the south east corner of sutton marsh , being a mile and a quarter , at twenty shillings the rod , is six hundred pounds to make a brick sluce twenty foot broad , with two paire of doores to keepe out the sea , and one paire to keepe up the fresh waters , to be placed at the south east corner of satton marsh , in regard it must stand very deep on a sandy foundation : it may cost two thousand foure hundred pounds . to bring the many crooked channels which are in the washes into one straight channell , is a work that must be first wrought with the spade , and after that is accomplished , there must bee many jetties made with piles , stones , and brushwood , to keepe the channell straight from the lower end of wisbeach river to the sea deepe , being a work of great consequence , it may cost foure thousand pound . bedford river . to make bedford river five foot broader on either side , and three foot deeper than now it is , and to cast all the manure which now lyeth upon the forelands , with that which will be taken out of the bottome of the river upon the banks , being twenty one miles and a halfe in length , at thirty five shillings the rod , it will cost twelve thousand and forty pounds . to pile the dike ends and swamps , which else will not be able to support the banks when more waight shall be laid upon them , and to convey by boat so much earth thither as will make the defective places as high as the banks are generally else where , may cost foure hundred pound . to make the two indikes ten foot broader on the fen side , and foure foot deeper then now they are , and to cast all the manure that commeth out of them upon the bank , at ten shillings the rod , for each indike , it will cost six thousand eight hundred and fourescore pound . to make two brick sluces at the outfall of the two indikes , that each of them may have sixteene foot waterway , with a paire of doores to keepe out the sea floods , and a paire of doores to keep up the fresh waters , may cost two thousand foure hundred pounds . to make two bridges of foure foot broad over bedford river , one at welney , and the other at maney , and to make a cart bridge at mepell , may cost two hundred and forty pounds . to make the west water twenty five foot broad and six foot deep from erith to plantwater , being nineteene miles in length , at twelve shillings the rod , it will cost three thousand six hundred forty eight pounds . to make a sasse in the northbank of bedford river twenty foot broad , to be placed in the roome of a little sluce at the entrance of the west water , being within halfe a mile of erith : it must have two paire of doores against the water in bedford river , that boats may passe at all times , and may cost one thousand foure hundred pounds . to make elme leame forty foot broad and six foot deeper than now it is from wisbeach river to march streame , will mend the outfall of vvisbeach river , and maintain the navigation from vvisbeach to norfolk , suffolk , cambridge , and huntington shires . the work is six miles in length , and will bee very chargeable for the space of a mile , and may therefore cost five and forty shillings the rod , one with another , which is foure thousand three hundred and twenty pounds . to make a brick sasse twenty foot broad , where elme leame falls into wisbeach river , with two paire of doores to keep out neene , and one paire of doors to keep up the back water , may cost one thousand eight hundred pounds . to make two cart bridges and one foot bridge over elme leame , being made of oken timber with brick pieres , may cost three hundred and forty pounds . to make witelsey meare draine two foot deeper than now it is from guyherne to the meare , being thirteen miles in length at foure shillings the rod , it will cost eight hundred thirty two pounds . to make two cart bridges over witelsey meare draine right against witelsey high lands , may cost eighty pounds . these generall works , together with a land eaye from peterborough to the crosse neere crowland and the division-dikes , will be sufficient for that part of the levell which lieth on the north side of bedford river , being much about one halfe of the levell ; provided alwayes that the river welland be kept to its proper outfall , which may be effected by mending the new bank that the late earle of bedford caused to be made from waldram hall to crowland , and by maintaining the queenes bank at a sufficient heigth from crowland to spalding , which at this time is much setled and in great decay . the river of owse . to make a bank of six foot high on either side of the river owse , from erith to southery ferry , on the south and east side , and to salters load on the north and west side , leaving twenty foot foreland between the banks and the river . these banks are to be made of the manure which riseth out of the indikes , being twenty foot broad , and six foot deep : either of these banks will be twenty eight miles in length , and being for the most part silt , will cost ten shillings the rod , which is eight thousand nine hundred and sixty pounds . to make a bank on either side of the river grant from harimer to clay hive , six foot high , leaving twenty foot foreland between the banks and the river . these banks are to be made of the manure which riseth out of the twenty foot indike , six foot deep , being ten miles in length , at ten shillings the rod , will cost three thousand two hundred pounds . to take up the hards or shoulds which are in the river grant , betwixt harimer and cambridge , being gravell , sand , or chalk , and nine in number , whereof some are long and some are short , is a work that must be performed by a water engine , which may cost two thousand foure hundred pounds . to maintaine the navigation from lyn to cambridge , there must be a brick sasse made at harimer two and twenty foot broad , with four paire of doores , so that the boats may passe at all times , which may cost sixteen hundred pounds . to make another brick sasse at harimer on the west side of the great sasse , sixteen foot broad for the waters of the two indikes of owse and grant , with two paire of doores to keepe out owse , and one paire of doores to keepe up the water in sommer , may cost twelve hundred pounds . to make a brick sasse neere breame , sixteen foot broad , with two paire of doores to keepe out owse , and one other paire to keepe up the water in the sommer , to be placed at the outfall of the indike , which will be betweene erith and breame , on the north side of owse , may cost twelve hundred pound . to make grunty fen draine twenty foot broad at the outfall , and ten foot broad at the head , and six foot deepe , being two miles in length , and a great part of that very deepe worke , it may cost ten shillings the rod , which is three hundred and twenty pounds . to make the new draine which is between little-port chaire and turbesey , ten foot broader on either side , and foure foot deeper than now it is , leaving twenty foot foreland between the river and the banks ; and to cast the manure which commeth out of the river upon the banks on either side , being three miles and a halfe in length , at forty five shillings the rod , will cost two thousand five hundred and twenty pounds . to make a sasse twenty foure foot broad , at little-port chaire , at the lower end of the last work , for the preservation of the navigation from lyn to cambridge , may cost two thousand and two hundred pounds . to make two indikes of fifteen foot broad and six foot deepe , the manure to be cast upon the maine banks , may cost six shillings the rod , is six hundred seventy two pounds . to make two brick sluces of ten foot broad at the ends of the two last indikes , may cost six hundred pounds . to make a bank on either side of milnall river from prickwillow to milnall , six foot high , leaving twenty foot foreland betweene the river and the banks , being eleven miles in length , at ten shillings the rod , will cost three thousand five hundred and twenty pounds . to make a brick sasse twenty foot broad , with foure paire of doores , so that boats may passe at all times , and to place it at the lower end of milnall river , may cost eighteen hundred pounds . to make a brick sasse for the north west indike of milnall river , and the south indike of grant , sixteen foot broad , with two paire of doores to keepe out owse , and two other paire of doores to keepe up the water in the sommer , may cost twelve hundred pounds . to make a dam crosse the river of owse at turbesey to be piled and wrought to the same heigth that the banks are else where , may cost three hundred pounds . to make a bank on either side of brandon river , from priests houses to brandon , six foot high , leaving twenty foot foreland betweene the bank and the river , being twenty miles in length , at ten shillings the rod , may cost six thousand foure hundred pounds . to make a brick sasse at the outfall of brandon river , twenty foure foot broad , with foure paire of doores , so that the boats may passe at all times , may cost two thousand two hundred pounds . to make a brick sasse for the west indike of brandon river , and the south indike of owse , from milnall sasse to brandon sasse , sixteen foot broad , having two paire of doores to keepe out owse , and two other paire to keep up the water in the sommer time , may cost fifteen hundred pounds . to make a brick sasse at southery ferry for the indike which will be on the east side of brandon river , and also for the indike which will be on the east side of owse , from brandon sasse to southery ferry , sixteene foot broad , with two paire of doores to keep out owse , and two other paire of doores to keepe up the water in the sommer time , it may cost fifteen hundred pounds . to remove the banks of feltwell cut , so that there may be twenty foot foreland on either side , and to make the draine two foot deeper than now it is , being five miles in length , at eight shillings the rod , it will cost six hundred and forty pound . to make an indike of ten foot broad , and five foot deep on either side of feltwell cut , and to cast all the manure to the two banks , at three shillings the rod , it will cost foure hundred and fourscore pounds . to make two brick sluces at the outfall of the two indikes , six foot broad , with one paire of doores to keepe out owse , and one other paire to keepe up the water in the sommer time , may cost foure hundred pounds . to make a bank of six foot high on either side of stoke river , from the river owse to stoke bridge , leaving twenty foot foreland between the river and the banks , being ten miles in length , at ten shillings the rod , it will cost three thousand two hundred pounds . to make a brick sasse at the outfall of stoke river , twenty foot broad , having foure paire of doores , so that the boats may passe at all times , may cost eighteen hundred pounds . to make a brick sluce and a brick sasse upon the river owse neere mandlin falls , that may have one hundred sixty foot water-way , with double doors in every arch to keepe out the sea floods , and land doores to keepe up the fresh waters ; and those land doores must have spring doores in them to discharge the fresh waters on a sudden , for the better maintaining and preserving of the channell from the sluce to the sea . the sluce , the sluce-pit , and the casting of water , together with the cutting of a new river to and from the sluce , and making of a dam in the old river , may cost one and twenty thousand pounds . to make so many land eayes as may convey the downfall of all the high land waters into their proper streames , so that they may not drown those fens which are next them , may be a work of one hundred and five miles in length , considering one place with another , they may cost ten shillings the rod , which is sixteen thousand and eight hundred pounds . the purchasing of several , through which many of the draines are to be made , may cost six thousand pounds . to make horse-mills , tun-mills , wheele-barrowes , store-houses , and work houses , and to buy spars , deals , nailes , ginropes , and such like materials which will be used in this work , may cost foure thousand five hundred pounds . the making of division draines may cost five thousand pounds . the sallary of officers imployed in this work may in foure years amount to foure thousand pounds . it is knowne to builders that after great care and examination of their intended charge , there will be some nailes omitted . for which reason , if you please , you may cast the odde money into this estimate , and reckon the totall charge to be one hundred and fourescore thousand pounds : and that with this caution , that the springs of the yeares must not be lost for want of money . the works above mentioned cannot be performed in lesse time than foure compleat sommers . the placing of a great sluce upon the river owse neare lyn , together with those other works which are here designed under the title of that river , will draine all the fenns that are on the southside of bedford river , so that the greatest part of them will be culturable grounds ; and peradventure it will spare the charge of those banks which are intended to bee made on either side of the river owse , from salters load to little-port . but the making of that sluce is a work of so great a consequence , that of my selfe i dare not absolutely resolve it . it is true that the fens are drowned by the high land waters onely ; yet an i have said before , the sea floods are as potent an enemy to the fenns as the land floods are . in confideration wherof , my conclusion is , that the making of a sluce upon the river owse , neare lyn , to keepe out the sea floods , will undoubtedly prevent and remove one halfe of that cause which occasioneth the drowning of that great and rich levell . the objections that will be made against the making of that sluce will be three : and under favour of this honourable court , i conceive they will bee weak in comparison of the great benefit which that work will produce by keeping out the sea floods . the first objection is , the greatnesse of the charge . the second is , the hazzard in placing of it . the third is , the oppositions that cambridge and lyn will make against it , in regard of their navigation , which consisteth principally of three parts . the first and greatest is , whether the repulsing of the sea floods will impaire lyn haven or not . the second is , that for want of a flood stream , the keeles must of necessity make lesse speed in their passage from lyn to cambridge . the third and last objection will be , some losse of time by staying the keeles at the sluce , in regard they must take their turnes in passing through it ; which i humbly leave to the grave consideration of this honourable court . being serious for the fens , these objections were once strooke out ; for it is not a question whether this be the best way to drain the fens or not . these doubts therefore were only inserted in regard of lyn haven , and the navigation from lyn to cambridge ( as is said before . ) but being awfull of what i present to this great councell , i durst not omit them : and now having with all care and diligence finished my designe , i earnestly implore your noble acceptance , humbly entreating you to heare all , chuse the best , and god grant the kingdom may flourish in your honourable resolves . finis . an answer (to a printed paper dispersed by sir john maynard entituled, the humble petition of the owners and commoners of the towne of isleham in the county of cambridge, and to the exceptions thereto annexed against the act for the dreyning of the great level of the fennes) whereby the honour and justice of the late parliament is vindicated, the scandals and untruths in the said printed paper discovered, some vaine objections answered, and the truth of the proceedings in the work of dreyning (so much conducing to the honour and profit of the common-wealth) held forth to all sober and uninteressed [sic] persons. this text is an enriched version of the tcp digital transcription a25545 of text r18361 in the english short title catalog (wing a3338). textual changes and metadata enrichments aim at making the text more computationally tractable, easier to read, and suitable for network-based collaborative curation by amateur and professional end users from many walks of life. the text has been tokenized and linguistically annotated with morphadorner. the annotation includes standard spellings that support the display of a text in a standardized format that preserves archaic forms ('loveth', 'seekest'). textual changes aim at restoring the text the author or stationer meant to publish. this text has not been fully proofread approx. 41 kb of xml-encoded text transcribed from 14 1-bit group-iv tiff page images. earlyprint project evanston,il, notre dame, in, st. louis, mo 2017 a25545 wing a3338 estc r18361 11938447 ocm 11938447 51226 this 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(eebo-tcp ; phase 1, no. a25545) transcribed from: (early english books online ; image set 51226) images scanned from microfilm: (early english books, 1641-1700 ; 48:21) an answer (to a printed paper dispersed by sir john maynard entituled, the humble petition of the owners and commoners of the towne of isleham in the county of cambridge, and to the exceptions thereto annexed against the act for the dreyning of the great level of the fennes) whereby the honour and justice of the late parliament is vindicated, the scandals and untruths in the said printed paper discovered, some vaine objections answered, and the truth of the proceedings in the work of dreyning (so much conducing to the honour and profit of the common-wealth) held forth to all sober and uninteressed [sic] persons. maynard, john, sir. humble petition of the owners and commoners of the towne of isleham in the county of cambridge. 14 p. printed for richard baddeley ..., london : 1653. caption title. imprint from colophon. eng reclamation of land -law and legislation -england. drainage -england -history -sources. fens, the (england) a25545 r18361 (wing a3338). civilwar no an answer (to a printed paper dispersed by sir john maynard entituled the humble petition of the owners and commoners of the towne of isleha [no entry] 1653 7501 11 0 0 0 0 0 15 c the rate of 15 defects per 10,000 words puts this text in the c category of texts with between 10 and 35 defects per 10,000 words. 2003-12 tcp assigned for keying and markup 2004-01 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 an answer ( to a printed paper dispersed by sir john maynard entituled the humble petition of the owners and commoners of the towne of isleham in the county of cambridge , and to the exceptions thereto annexed against the act for the dreyning of the great level of the fennes ; ) whereby the honour and iustice of the late parliament is vindicated , the scandals and untruths in the said printed paper discovered , some vaine objections answered , and the truth of the proceedings in that work of dreyning ( so much conducing to the honour and profit of this common-wealth ) held forth to all sober and uninteressed persons . the substance of the said petition falling under these four generals , viz. first , that parties interessed are by the said act made judges . secondly , that the said act destroyes propriety . thirdly , that the said act doth enact impossibilities and falsities . and lastly , that dreyning is declared a monopoly by the remonstrance of the late parliament in the year 1641 and the said act obtained , because there were so many parliament men parties interessed when the said act was passing , the petitioners being unheard . it is answered to the first , that this charge is uncertaine and scandalous ; there being no particular person named , nor in truth could they justly name any ; for amongst the judges named by the said act ( which are above sixty in number ) there is never a party interessed named a judge ( but iohn trenchard esquire , who was an adventurer for one thousand acres , and thereupon declared he was a party interessed , and refused to act as a judge . ) it is true , that all the iudges of the courts of westminster for the present , and in succession , being appointed judges by the said act in general words and not by name , it fell out that the lord chief justice saint iohn , who was an adventurer for one thousand acres onely , was then chief justice of the common pleas , and thereupon never appeared or acted in the businesse , or was present at any session of the commissioners appointed judges . to the second charge , that the said act destroyes propriety : it is answered , that this is a mistake ; for it is , and ought to be the care of the supreme power to provide for the good of the whole , and to compel every man so to use his owne , as it may be serviceable to the common good ( yet with as little prejudice to each particular as may be ) and this hath been observed in all times upon various occasions ; whereof instances are obvious : and in particular , of recovering surrounded grounds , viz. the stat. of 23. eliz. cap. 13. for dreyning the marshes of erith , and plumpsted , and a moiety given for dreyning : the stat. 4to iaco. cap. 8o for dreyning the marshes of lesnes , and font in kent : and a moiety given for dreyning ; in both which cases they were freed from tithes for seven years as a priviledge and incouragement of their industry . and when they could not dreyn it within the time limited , the time was lengthened and more lands given , and yet these undertakers were to maintaine the work but one year , and the undertakers by this act are to maintaine this level for ever ; by the statute of 4o iaco. cap. 13. a place called waldersey in the isle elie , is appointed to be dreyned by undertakers , and two third parts given for dreyning . and the benefit redownding to the common-wealth by such dreyning appears in a great part by the very statute of 43o eliz. cap. 11o ( mentioned by the petitioners ) viz. not onely great and inestimable benefit to the supreme magistrate , but to the people , and increase of able people : and this very level of the fens hath been several times heretofore endeavoured to be dreyned by others , though in vaine ; and was a work worthy of the care of a parliament , and it is so expressed in the said act , thereby to recover above 300000. acres of surrounded grounds for arrable meadow , and pasture : and not onely fit for cole-seed ( though oile be no contemptible commodity to this nation ) but for wheat , and all other graine , and for hemp , and flax , which may be of great concernment to this common-wealth . and if any desire to be further satisfied of the excellency of this work , let him consult mercators geography of the world , printed at amsterdam in 1636. fo. 67. wherein the fame of the undertaking is taken notice of , and published to the world , though undervalued by some of this nation who are ignorant of the concerment of this common-wealth therein . and men which broach such principles , as that acts of parliament ( wherein all mens consents are included ) destroy propriety ; would be carefully heeded in time ; lest the consequence may tend to bring in question , not only many things well setled by acts of parliament for publick good in most ( if not all ) former parliaments , but interrupt the great affaires of this common-wealth , if such an unsound , destructive principle ( that a commoners right cannot be bound by an act of parliament , ) should be taken up by tumultuous giddy people . to the third charge of impossibility and falsities in the act ; it is answered by denial , that there is any impossibility or falsity in the act ; for it appears to any man that will have patience , carefully to peruse the said act , that only the surrounded grounds within the said level are to be dreyned , and no other : and if any person be compelled to contribute to the dreyning , who is not bettered thereby , the commissioners appointed judges by the said act , have power to give relief ; and the right honourable the councel of state have likewise for ease of the countrey , authorized other commissioners , living in the said level , and near thereunto to heare and determine the same upon the place in a short and easie way . and it is an unheard of boldnesse to charge the parliament with falsity in matters of fact , declared by them in the act it self , and the consequence no other , then to make acts of parliament lesse certain then a chancery-decree , and subject to re-examination , as oft as it shall please any troublesome discontented person . to the last charge , that this dreyning was declared a monopoly , by the declaration of the late parliament in 1641. and the said act unduly obtained , by reason so many parliament men became interessed therein , at the passing of the said act ; it is answered , that the first part of the charge is grounded upon a mistake , the said declaration being against improvements , taken out of commons , by the late king , queen , and other lords of mannors to the prejudice of the commoners without law , whereas the work of dreyning this level , was then under the care of a committee of parliament , to provide for dreyning thereof , and declared to be a great work and no colour of a monopoly if the act be perused ; and the very original undertaking proceeds from the sollicitation of the countrey . and to the second part of this charge , of the undue gaining of the said act , through the interest of parliament men : it is answered that this general charge , without naming any particular person , is in it self a great scandal to all the members of the late parliament ; and it is affirmed , and a certain truth , that there were but foure members of the late parliament , who claimed to be adventurers , ( and foure are no great number amongst some hundreds of parliament men , ) and yet those foure were excluded by order of parliament , to have any vote at the debate of the businesse , and all their adventure-lands together , but 3050. acres , which was of so little value and concernment to some of them , as they lost their land for not paying taxes . and of those foure also , when the said act passed , there was but one single person of them , ( namely the said mr. trenchard ) who sate in the house at passing of the said act ; and surely the said sir iohn maynard , ( who was a member of the late parliament , and present at most of the debates touching the said dreyning ) cannot but feare some condigne punishment to overtake him , thus to traduce and scandalize the supream powers and government . and to the last part of the charge , that the petitioners were not heard ; it is answered , and ready to be made good to every mans satisfaction , that the committee of the late parli . in consideration of the said act , before they proceeded therein , sent letters to the several sheriffes of the counties of norfolk , suffolk , lincolne , northampton , huntington and cambridge , and also to the town of lynne , and to the committee of the respective counties , and of the isle of elie , to give notice to the inhabitants ; and that such as desired to be heard should attend the committee ; and notice was accordingly given , and many of the countrey came in , and were heard what they could say , and particularly the said sir iohn maynard , and these three things were chiefly in debate before the said committee ; 1. whether the said level were hurtfully surrounded . 2. whether the work was feasible . and 3. whether it were beneficial to the common-wealth : and after witnesses examined at the said committee , and above fourty hearings before them , ( in the space of almost three years ) and satisfaction given therein , and many amendments made , and provisions inserted to the advantage of the countrey ( brought in by the councel for the countrey , ) the said act passed . and thus farre in answer to the said paper called the petition . here followeth an answer to the exceptions against the act , printed with the said paper . first , some matters of fact suggested in those exceptions to be contained in the said act of parliament , are either maliciously , or through wilful ignorance mistaken ; for whereas it is suggested , that by the said act thorney-abbey is excepted from the dreyning , and yet it is part of the said level , and hurtfully surrounded ; it is answered , that thorney-abbey is not excepted by the said act , but contrariwise in recompence of the dra●●ing of the surrounded ground of thorney , there are 4000 acres taken out , and adjudged to the undertakers as part of the 95000 acres appointed by the act of parliament for the recompence of dreyning . secondly , that whereas there are several exceptions grounded upon the title of the act , & upon pretence of fallacies and equivocations in the word level , and great level : it is answered , that there is no force in those exceptions , for the said act of parliament doth appoint no grounds to be dreyned , but the moores , marishes , fenny and low-surrounded grounds , within the bounds of the said level , and though there may be a little reed grounds part of the said surrounded level , ( not considerable , in reference to the making so many thousand acres improveable for the common-wealth ) the same ought not to hinder so publick a work : and for such part of the said level where sedge is only to be had , it is apparent , and every mans reason will conclude , that it cannot but be of greater concernment to the common-wealth to improve it for meddow-pasture or arrable ; and for osyers and other plants of that nature they will be very much increased . to the exceptions of the preamble of the said act , which recites , that the said surrounded grounds have been of small and uncertain profit , but if dreyned , may be improved , and to the suggestion in the exceptions , of the profit made before the dreyning ; it s evident , that the stock of cattel of all sorts kept by the commoners generally in the fens now , are more then doubled to what they were before the first undertaking of dreyning by the late earle of bedford ; and many thousand acres of the said fennes sowne already with wheat , rie , barley , beanes , oates , cole-seed , rape-feed , hemp and flax ; the latter whereof , though by the printed paper stiled trash and trumpery , yet to such as know the concernments of this common-wealth , are , if not of absolute necessity , yet certainly of great and high advantage to this nation . and the customes at the port of lynne , for such of the said commodities , as were thence transported for the yeare , ending in june , 1653. came to about 1300 li. besides what was used at home , and the advantage to the common-wealth by setting many thousands of poor people on work . to the exception mentioned to be the third , touching the particular bounds of the level , wherein the petitioners referre to their first exception ; it is answered in the former answer to that particular , wherby it will appear the grosse mistake of the petitioners , as conceiving that the bounds of the said level to be dreyned by the said act , did comprehend all the grounds within those bounds , whereas it is only the moores , marishes , fenny and low grounds within those bounds , and no other , which appeares by the plain words of the said act . to the objection , that the consideration moving the passing the said act was that the earle of bedford had 95000 acres decreed to him in the thirteenth year of king charles , which decree was procured by bribing the king with 12000. acres and that the consent of the lords and commons was not had thereunto according to the statute of the fourty third year of queen elizabeth , it is answered , first , that the petitioners wilfully omit the first and maine consideration in reference to the now e. of bedford , which was , that francis late earle of bedford ( a man known to be of a publick spirit ) did undertake the said dreining , which undertaking was in the year 1630. ( seven yeares before the said decree ) and not a businesse sought by him , but a work whereinto he was drawn after two years consideration , and solicitation of many worthy persons lords and owners of the said fennes , and after many attempts and former undertakings by others , which proved fruitlesse . and there were no lesse then fourty seven commissioners ( all land-owners within the said level ) who made it their suite in behalf of themselves and the country , to undertake the same , and offered him 95000 acres for recompence of the dreyning : which was as little , if not a lesse proportion of ground then any other would accept for to do the said work ; and the whole businesse was settled and agreed by a law of sewers at lyn in norfolk in the said year 1630. by fourty seven comissioners upon their oaths and was a chief and prime motive for the said act of parliament . in the second place it is denied that any bribe of 12000. acres was given to the late king for the said decree of the thirteenth year of the said late king , nor can it be apprehended that any such thing shold be , in regard the said decree of the thirteenth yeare of the said king did onely set out the 95000. acres , after the work adjudged done , which by the law of sewers made at lin , in the said year 1630. was decreed to be set out . it is true , that by the said law of sewers made at lynne , ( which was near seven years before the said dreyning , ) that the late king was to have 12000. acres , parcell of the said 95000. acres , but for what consideration , or upon what agreement , the present undertakers are ignorant of , nor is it materiall to them , they engaging their estates in the said work of dreyning upon the strength and security of the said act of parliament which gave them as well the said 12000. acres , as the residue of the 95000 , acres , and without which they had never engaged in the said work , or adventured any further summe of money therein . and to the last part of this exception , it is answered , that it carries no weight in it , for that if the said work of dreyning had been pursuant to the statute of the 43. year of queene elizabeth , it would not have needed any new act of parliament . and it is very clear , that as the parliament in the 43. year of the late queene , had power to make one law for dreyning , so the late parliament might , and all succeeding parliaments may make other lawes likewise for dreyning and improving lands for publike advantage . and in truth in a work of so great concernment , and vaste circuit of grounds , and wherein so many persons were concerned , as lords and commoners . it was almost , if not altogether impossible to know who were the major part , or to have the consent of the major part . ( sir iohn maynard acknowledging many thousand persons to be therein concerned . ) and upon this ground it was necessary to obtaine the said act of parliament before they should further engage in the said work : and if this be a materiall exception , then the before mentioned statutes for dreyning made in the time of queene elizabeth and king iames are liable to the like exception , and by consequence this and all succeeding parliaments disabled to make any law for improving any waste or surrounded grounds to the benefit of the common-wealth . to the exception , that the earle of bedford and his participants made no progresse in the work , but only to divide the 95000 acres by shares and lots , and that it was found by a jury at huntington 14 car. that the said earle and his participants had not meliorated the fennes ; it is answered : first , that there was above 100000. livre. disbursed by the said late earle of bedford , and participants by advice of the best artists that were to be gotten after his undertaking of the said work in the yeare 1630. and before the decree , or setting out , or dividing the same , in the thirteenth yeare of the late king . and secondly , that the proceedings at huntington , in the fourteenth of the late king , urged by the petitioners , ( wherein sir iohn maynard an old courtier , was not a little active and busie to advance the late kings interest ) and the decree thereupon , was undue and illegal , and in order to a project then in hand , to deprive the late earle of bedford , and all his then participants of the said whole 95000 acres , after all the expence of money , and to give the said whole 95000 acres , and 57000 acres more from the countrey to the late king to become the undertaker ; which proceedings were condemned by the parliament . and the petitioners themselves in the latter part of their exceptions confesse that the decree of sewers at huntington was illegal , and therefote null . and these very commissioners of sewers at huntington , ( though of the late kings choice , and most of his servants ) were so much convinced of the right of the said late earle of bedford and his participants , that in their decree they did acknowledg that divers great sluces , rivers , dreins , cuts , and other works , had been made and erected by the said earle and his participants , at his and their great charges within the said level , which did much conduce to the dreyning of some part of the said level , and which would be of good use , to the further dreyning , imbanking and recovering of the said fennes , and that the said late earle and his then participants , were worthy of 40000. acres for their recompence , in regard of their charge then expended : and if it be considered , now that those unrighteous commissioners adjudged 40000 acres ; was but a moderate recompence for above 100000 li. then expended ; and that all the addition of recompence by the late act , is but 55000 acres more , for which the present undertakers have expended above 200000 livre. since the said act ; it will appear that the now undertakers are great sufferers and losers by the said undertaking , and those who maligne the undertaking , would be loth to reimburse the money expended with damages , and take the land dreyned now all the hazard is past , subject to the charge of future maintaining the works . to the pretence , that there was no interruption to the work but feares that the undertaking was declared against in the beginning of the late parliament in december 1641 the same is formerly answered , that declaration being against improvements by the late king , queen , and lords of wastes without law , and not concerning this dreyning , which was then under consideration of a committee of parliament ; but their feares were , that some tumultuous and busie narrow-hearted men ( who savour nothing of publick concernment , which is crosse to their private humour , ) might give interruption to the work , if not setled by act of parliament , and thereupon did resolve not to engage their estates further in it , but by the authority and countenance of parliament . to the exception , which saves to the undertakers breaches by inevitable accidents , which are in convenient time to be repaired and made good ; it is answered ; that in reason no further provision can be made for the countrey in that particular , then is by the said act , in regard provision is made for the dreining and imbanking , and making the same winter-ground in such manner as the rivers which did overflow the same or any of them should not overflow the grounds within the said level : which thing is already done , and works made which have not onely been adjudged to be sufficient ; but have by experience proved so , and their own concernment , as to their 95000. acres is a sufficient obligation upon them to preserve the same : but if by some inevitable passage of providence , any extraordinary flood or storme should come , or any water coming through any quick-sand under a bank ) not by humane reason , charge , or industry , to be foreseen , or prevented ) any work should faile , and that they repaire it in convenient time , the late parliament did , and all reasonable men will conceive that they have performed their undertaking , and without that provision , no rational man would have ingaged in the said work . to the exception , that there is a liberty of leaving 15000 acres for beds & receptacles for waters , whereby the drowned land of thorney and whittlesey might be dreyned , and dry land drowned . it is answered : first , that there was a necessity for such a provision , and 15000. acres was but a small proportion to be alloted in so great a level as above 300000 acres . but secondly , that this exception appears to be vaine and malicious , the petitioners not so much as affirming ( now the work is done ) that there hath been any such fraudulent and indirect use made of that provision ; and as it is a vaine pretence that beds and receptacles for waters should be made upon dry lands ( which is the higher ground ) so it would have been very imprudent in the undertakers to drowne dry ground , in regard the said act gives relief to any that by dreyning in one part , should be drowned in another . to that exception in the act , that the ordinary course of commissioners as to this level is altered ; it is answered : first , that there are above 50 commissioners of sewers appointed by name in the said act for the said levell , besides the judges of the courts at westminster for the time being , all named by the late parliament , and such as by the view of their names will appear to be persons of great worth and understanding . and secondly , by the said act the commissioners for the great seale ( who appointed commisssioners of sewers upon all commissions ) have power to nominate others in their roomes . and lastly , there was great necessity to take care in this particular , for whereas upon other commissions of sewers all the lands within the danger of surrounding , are liable to contribute to the charge of maintaining the works by this act the 95000. acres designed to the undertakers , are onely made liable to the charge and the maintaining the work , and the residue of the level being above 200000. acres freed from it , so that the land-owners within the said levell , who were , not to be contributary to the charge , were justly excluded from being commissioners of sewers . to that exception which suggests that upon the petitioners complaint to the committee named in the said act , iuly 6. 1653. they found no redress ; and to that other exception which suggests that in the adjudication no care was taken to provide that lands which should receive no benefit by the dreyning , might not be made contributary : and to another exception , that the said commissioners adjudged the grounds dreyned without hearing the petitioners ; it is answered ; first , that the commissioners appointed by the said act sitting in the temple hall the said sixth of iuly 1653. upon complaint made by sir iohn maynard in the name of himself and other inhabitants of isleham , did give him a full hearing , and did offer him , that if he would make it appear that there were any ground unequally and unduly taken out of isleham , they would give relief ; or if he could not prove it there , and could prove it in the countrey , they would award a commission into the countrey to indifferent commissioners there to examine the same , but the said sir iohn maynard then and there declared that he would petition the parliament ; so that this part of the suggestion is altogether untrue and scandalous : and for the care taken in the adjudication ; it is answered and ready to be proved , that the commissioners appointed by the said act , for adjudging the same , after they had received sufficient information , that one part of the said level was dreyned according to the said act , would not proceed to adjudge the same , until they had sent out summons to all the parishes in that part of the level , concerned , to give notice of their intended sessions , and then after made a personal view , and after that had oath made of due notice of their summons , and then heard all complaints , and did receive all their witnesses on all parts , and did upon all complaints which they found just , give relief according to the said act , and did observe the same course upon their latter adjudication of the residue of the said level , and notice of the said commissioners session was timely given , and the commissioners did at their several sessions make several orders , for relief in all cases , where they found the complaints just ; and that this suggestion may appear to bear no colour of truth ; it will appear by the order made upon the last adjudication at elie , upon a petition then exhibited in the name of the inhabitants of isleham , who suggested , that too great a proportion was taken out of their commons , that the commissioners did then , by the consents of the then petitioners , and of the undertakers , referre the examination of the truth of the fact , to commissioners named by the then petitioners and undertakers , and a day was appointed for hearing witnesses on both sides ; but the then petitioners , finding that they were not able to make good the truth of their petition , did wave any further proceedings upon their petition . to the exception , which gives power to the commissioners to make lands improved , though not within the said level , to be contributory to the undertakers ; it is answered , that the reading of that clause in the said act will satisfie any uninteressed person : for whereas it was pretended that in the setting out of the 95000 acres , some were drawn to contribute to the same and receive no benefit by the dreyning , and others would receive benefit by the said dreyning , who did not contribute thereunto ; the act doth provide to relieve the former , and also that such lands as shall be better in quality or condition , by reason of the said dreyning , or be thereby secured from overflowing , and inundations shall contribute proportionable to the benefit which the owners , and occupiers of such lands , shall receive thereby as may appear by the words of the said act which no reasonable man can opposse ; and yet the undertakers hitherto have made no benefit of that clause in the said act : whereby the troublesome disposition of such as prosecute the said petition and complaint , may appear by this causelesse exception . the exception to the said act for repealing the two laws of sewers , viz. 19. iac. et . 14. car. because they were illegal , and therefore in themselves null , is vain and frivolous ; for if it be admitted that they were illegal and null ( whereof many learned men did doubt ) it is far from a fault to declare them so by an act of parliament . for the exception to the comissioners named in the said act in regard , as is suggested , that some of them cannot act , many have not acted , and some who have acted , have put the petitioners out of possession of 930. acres of their fennes ( unheard ) whose names they know not : charged those commissioners to have adjudged lands dreyned , which were never drowned , and those hurtfully surrounded which were bettered by overflowing , and therefore conceive they have just cause to except against the said commissioners ; there is no force in the first part of the objection , and if it were material , yet unlesse it were specified which of the said commissioners cannot act , or which have not acted ; it is not possible to answer to it . but to the other scandalous part of that exception it is answered . first , that the names of the commissioners who made the several adjudications appear upon record , and their names with the judgements are enrolled in chancery , and if the petitioners have cause of complaint against them , it were but just they should be heard to make their defence . secondly , that the suggestion that the judgement was without hearing , hath no truth in it , as may appear by what is formerly said . thirdly , that the said commissioners have given no such judgement , as is untruly suggested but they have proceeded justly according to the said act , and the level being dreyned , have so adjudged it , and set out the 95000. acres as the said act requires , whereof 930. acres parcel of 3125. acres of isleham fennes are part , but they did withal at the same adjudication , according to the said act , upon complaint of the inhabitants of isleham , referre to commissioners by consent , to examine whether a greater proportion were taken , then by the said act was intended , and surely such as are in authority will be sensible of the honour of the commissioners appointed by the said act , who were all named by the parliament , and have no benefit , but much trouble by that service . and for the petitioners surmise , that some should be disabled to act , ( not naming any , ) if that should be true , yet there being above fifty in all , and of great honour and integrity , there would be no cause of any more commissioners : howbeit , to prevent all colour of complaint therein . it hath pleased his excellency the lord general and councel of state to name twenty four other commissioners dwelling in and neere the said level to heare and determine any complaint according to the said act so as it may appeare that such as prosecute this petition are of a restlesse spirit . for that exception of depriving the petitioners of the benefit of commissions of sewers according to the statute of the twenty third yeare of henry the eighth , and that the scouring of the old dreynes would leave very little land in the said level , hurtfully surrounded : and that there is a sufficient provision for dreyning made by the stat. of the fourty third yeare of q. elizabeth , most part of this is formerly answered , yet finding these exceptions made double in their petition and exceptions as if some great weight lay in them . it is further answer'd . first , that the evidence of the thing is undeniable proof , that the scouring the old dreynes would not recover the said level from surrounding which had lien hundreds of years , hurtfully surrounded ; and the maine question in the late parliament was , whether the work were any way feazible . secondly , that the said act of parliament exempts the country from charge of maintaining the work which lay upon them by the ordinary commission of sewers upon the statute of the twentythird year of h. 8. and lastly , it was almost , if not altogether impossible to know the certain number of all persons concerned in the said level , whereby to have gotten the major part of their hands and seals to our indenture according to the statute of the 43. eliz. and yet admitting it had been possible , it is no argument for the petitioners to complain of a parliament , for making a subsequent act of parliament for publike good . for the general charge in the exception , mentioning , first , that the said act is without the petitioners consent . secondly , against it . 3. unreasonable . and fourthly unnecessary ; the two first of these suggestions are not , nor ought to be of weight against an act of parliament , wherein the consent of the whole nation is involved , and such pretences tend to the subversion of the government of the common-wealth , for if lawes may not be made without particular consents of private persons , there is no hope that ever any law shall be made for publike good , ( the generality of men being for the most part covetous , and self-seekers ; minding their own private before the publick concernments , ) and if it rested in their will , would never part with any of their private estates for publike uses , nor suffer any thing they enjoy to be employed for publike services , which all parliaments prefer before any private concernment whatsoever . and to the pretence of the unreasonablenesse of the said act being a general exception ; abundantly answered by denying it , and by referring to the act it selfe , and to the clear answers formerly given to every particular exception , wherein any pretence of unreasonablenesse is surmized , and whether the work was unnecessary or not , ( besides the authority and judgement of the late parliament , which doth and ought to answer and silence that pretence , ) let all reasonable and uninteressed persons judge , whether it were not a work necessary for the parliament to redeem and recover above 300000 acres of surrounded grounds within this island , and make them good arrable land , meddow and pasture , by improvement whereof this common-wealth may not only be supplied with cordage , linnen and other necessaries , but many hundred thousand pounds raised yearly within this common-wealth , by corne , oyle , hemp , flax , and other commodities , thousands of poor set on work , and the rage and violence of the waters , which threatned ruine and destruction to many adjacent parts , be stopped and prevented . the length of this answer , is necessarily occasioned , by the many untrue and groundless surmises in the petition and exceptions , and to manifest the integrity of the vndertakers , and justice of proceedings , through all this chargable and hazardous work ; originally undertaken by francis late earle of bedford , at the countries sollicitation for publick good : that the profit was not considerable to the charge and hazard , nor will it yet answer the vast summs of money expended by the said vndertakers , and some of them being ruined in their estates by reason thereof . most of the present vndertakers became engaged in the perfecting the said work , upon the authority and credit of the said act of parliament , and have expended near 300000 li. upon that security ; and the charges for repairs yearly are estimated to be 10000 li . the works for the dreyning , are such as are not elsewhere to be seen in england , scarce in the christian world , worthy the care and countenance of a parliament , the act it self just , honourable and necessary , and sufficient provision thereby for just complaints , and only the vndertakers therein , the great sufferers and losers , and will appear guilty of ●●other fa●l● , sav● indiscretion to hazard their estates for the good of the publick . and whereas sir iohn maynard hath been pleased to commend reede and sedge to the common-wealth , as rich commodities to be taken care of , and hath stiled those , produced by the labour and cost of the undertakers , upon the improvement to be trash and trumpery ; yet such as they are , and the advantages this yeare arising by them , out of a small part of the fennes coming lately to hand , is hereby offered to the consideration of prudent persons . there was 28000 acres of the aforesaid fenn-ground , sowen with cole-seed , wheat , barley ; oates and flax.   li . sh . d. 1. every acre for hassocking , burning the hassocks , plowing , burning the sword , and sowing with cole-seed , cost one pound , which came into the hands of such as would work , whether poor or rich . 28000. 00. 00 2. every acre of seed , wheat , barley or oates that were sowen , being near 10000 acres cost in seed , 8s . per acre , which came to the hands of the countrey . 4000. 00. 00 3. the small division dykes , since the adjudication , came clear to the poor labourers . 3000. 00. 00 4. expended for timber , carpenters , bricklayers , and other labourers , in building houses above . 10000. 00. 00 5. the reaping , threshing and carriage of cole-seed , to be fit for the boats , to poor labourers , at 3 li. per last . 25000. 00. 00 6. the reaping , threshing and carriage of wheat , rie , oates , barley and flax to labourers . 5000. 00. 00 7. the carriage of farre above 5000 of cole-seed , and above 1000 of wheat and other commodities , to the watermen of lyn and wisbeach . 2700. 00. 00 8. the transportation by water , of materials for houses , to watermen and other works . 300. 00. 00 9. the chambering of 3000. last at the least in lyn , and thereabouts at 4d . the last per week for 13. weeks . 650. 00. 00 10. at lyn to meeters and porters at 12d . per last . 150. 00. 00 11. 100 last of seed , wheat and other graine to london , and other parts by shipping . 10000. 00. 00 12. there is this present year , in order for the next yeare , expended to workmen and labourers in hassocking , plaining , burning , sowing , and of cropps . 30000. 00. 00 13. the state in custome , excise 〈…〉 impost , for cole-seed , oyle and otherwise . 5000. 00. 00 by which , besides the great charge of dreyning , this yeare it appears there is expended to the labourers , workmen and others . 95000 li. 00 00 in lyn , chambers , porters and watermen . 3600 00 00 the shipping . 10000 00 00 the state . 5000 00 00 these are the advantages which have accrued to the state , the countrey , and th● 〈◊〉 this yeare by a small quantitie , of about 28000 acres , beside the intrinsecal value of the commodities themselves produced by this charge to the common-wealth not here set down . 113600 li. 00 s. 00 d. and if above 100000 livre. advantage ariseth by so small a quantity , under so many discouragements , a good common-wealths-man will easily judge , what annual profit and benefit will redound to this nation , by the improvement of the whole . london , printed for richard baddeley within the middle-temple-gate . 1653. notes, typically marginal, from the original text notes for div a25545e-30 see the 〈…〉 der par●●●ment . ●●feb. 16●● see the 〈…〉 der . of 1646. of the mensuration of running waters an excellent piece written in italian by don benedetto castelli ... ; englished from the third and best edition ; with the addition of a second book not before extant / by thomas salusbury. della misura dell'acque correnti. english castelli, benedetto, 1577 or 8-1643. 1661 approx. 330 kb of xml-encoded text transcribed from 68 1-bit group-iv tiff page images. text creation partnership, ann arbor, mi ; oxford (uk) : 2008-09 (eebo-tcp phase 1). a31214 wing c1222 estc r19153 12363252 ocm 12363252 60312 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. a31214) transcribed from: (early english books online ; image set 60312) images scanned from microfilm: (early english books, 1641-1700 ; 651:11) of the mensuration of running waters an excellent piece written in italian by don benedetto castelli ... ; englished from the third and best edition ; with the addition of a second book not before extant / by thomas salusbury. della misura dell'acque correnti. english castelli, benedetto, 1577 or 8-1643. salusbury, thomas. mathematical collections. [12], 118, [5] p. : ill. printed by william leybourn, london : 1661. errata: prelim. p. [12]. "a table ..." [i.e. index]: p. [1]-[5] at end. added t.p. on p. [35]: geometrical demonstrations of the measure of running waters. also appears in the 2d tome, 2d pt. of salusbury's mathematical collections, ... 1661. reproduction of original in 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. 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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 mensuration -early works to 1800. stream measurements -early works to 1800. reclamation of land -early works to 1800. 2006-06 tcp assigned for keying and markup 2006-06 aptara keyed and coded from proquest page images 2007-06 ali jakobson sampled and proofread 2007-06 ali jakobson text and markup reviewed and edited 2008-02 pfs batch review (qc) and xml conversion of the mensuration of running waters . an excellent piece written in italian by don benedetto castelli , abbot of st. benedetto aloysio , and professour of the mathematicks to pope urban viii . in rome . englished from the third and best edition , with the addition of a second book not before extant : by thomas salusbury . london , printed by william leybourn , 1661. the authours epistle to pope vrban viii . i lay at the feet of your holinesse these my considerations concerning the mensuration of running waters : wherein if i shall have succeeded , being a matter so difficult and unhandled by writers both ancient modern , the discovery of any thing of truth hath been the effect of your holinesses command ; and if through inability i have missed the mark , the same command will serve me for an excuse with men of better judgment , and more especially with your holinesse , to whom i humbly prostrate my self , and kisse your sacred feet . from rome . your holinesses most humble servant benedetto . a monk of cassino . an account of the authour and work. don benedetto castelli , the famous authour of these ensuing discourses of the mensuration of running waters , is descended from the worshipful family of the castellii , and took his first breath near to the lake thrasimenvs , ( where hanibal gave a fatal overthrow to the roman legions ) in that sweet and fertile part of happy italy , called the territory of perugia , a branch of the dukedome of tuscany , which at present submitteth to the jurisdiction of the church , as being a part of st. peter's patrimony . his parents , who were more zealous of the good of his soul than observant of the propension of his genius , dedicated him ( according to the devotion of that country ) to the service of the church ; and entered him into the flourishing order of black-friers , called from the place moncks of monte casino , and from the founder benedictines . nature , that she might consummate the profusion of her favours upon him , sent him into the world in an age that was so ennobled and illuminated with eminent scholars in all kinds of literature , that hardly any century since the creation can boast the like . § . in particular , the sciences mathematical had then got that fame and esteem in the learned world , that all men of spirit or quality became either students in , or patrons of those sublime knowledges . on this occasion the curiosity of our authour being awakened , his active wit could not endure to be any longer confined to the slavish tuition of hermetical pedagogues ; but in concurrence with the genius of the age , he also betook himself to those most generous and liberal studies . his helps in this his design were so many , and so extraordinary , that had his inclination been weaker , or his apprehension lesser , he could hardly have failed attaining more than a common eminency in these sciences . for besides the deluge of learned and vseful books , which the presse at that time sent forth from all parts of europe , he had the good fortune to fall into the acquaintance , and under the instruction of the most demonstrative and most familiar man in the world , the famous galileo : whose successe being no lesse upon this his pupil than upon the rest of those illustrious and ingenious persons that resorted from all parts to sit under his admirable lectures , he in a short time attained to that name in the mathematicks , that he was invited to rome , complemented , and preferred by his then holinesse the eighth urban , upon his very first accession to the papacy , which was in the year 1623. § . this pope being moved with a paternal providence for the concerns of his subjects in that part of italy about bologna , ferrara , and commachio , lying between the rivers of po and reno , which is part of lo stato della chiesa , or the church patrimony , appoints this our castelli in the year 1625 , to accompany the right honourable monsignore corsini ( a most observant and intelligent person in these affaires , and at that time superintendent of the general draines , and president of romagna ) in the grand visitation which he was then ordered to make concerning the disorders occasioned by the waters of those parts . § . castelli , having now an opportunity to employ , yea more , to improve such notions as he had imbued from the lectures of his excellent master , falls to his work with all industry : and in the time that his occasions detained him in romagna he perfected the first book of this his discourse concerning the mensuration of running waters . he confesseth that he had some years before applyed himself to this part of practical geometry , and from several observations collected part of that doctrine which at this time he put into method , and which had procured him the repute of so much skill that he began to be courted by sundry princes , and great prelates . in particular about the beginning of the year 1623. and before his invitation to rome he was employed by prince ferdinando i , grand duke of tuscany , to remedy the disorders which at that time happened in the valley of pisa in the meadows that lye upon the banks of serchio and fiume morto : and in the presence of the grand duke , grand dutchesse mother , the commissioners of sewers , and sundry other persons in a few hours he made so great a progresse in that affair , as gave his most serene highnesse high satisfaction , and gained himself much honour . § . no sooner had he in his fore-mentioned voiage to romagna ( which was but few moneths after , in the same year ) committed his conceptions to paper , but he communicated them to certain of his friends . in which number we finde signore ciampoli secretary of the popes private affaires ; whom in the beginning of the first book he gratefully acknowledgeth to have been contributary , in his purse , towards defraying the charge of experiments , and in his person , towards the debating and ●●●pleating of arguments upon this subject . some few years after the importunity of friends , and the zeal he had for the publique good prevailed with him to present the world with his first discourse , accompanied with a treatise of the geometrical demonstrations of his whole doctrine . what reception it found with the judicious must needs be imagined by any one that hath observed how novelty and facility in conjunction with verity make a charm of irresistable operation . § . new it was , for that no man before him had ever attempted to demonstrate all the three dimensions , to wit , the length , breadth and profundity , of this fluid and current element . and he detecteth such grosse errours in those few that had untertook to write upon the subject ( of which he instanceth in frontinus and fontana , as those that include the rest ) and delivereth such singular and unheard-of paradoxes ( for so they sound in vulgar eares ) as cannot but procure unspeakable delight to his reader . § . easie it is likewise and true ; and that upon so familiar experiments and manifest demonstrations , that i have oft questioned with my self which merited the greater wonder , he , for discovering , or all men that handled the argument before him for not discovering a doctrine of such strange facility and infallibility . but yet as if our authour designed to oblige the whole world to him by so excellent a present , he selects a subject that he knew would be carressed by all persons of nobler souls , upon the accounts afore-named , and by all mankind in general , as gratifying them in their much adored idol utility . and to render his art the more profitable , he reduceth the lofty , and easie-to-be-mistaken speculations of the theory , into certain and facile directions for practice ; teaching us how to prevent and repaire the breaches of seas , and inundations of rivers ; to draine and recover fenns and marches ; to divert , conveigh and distribute waters for the flowing and stercoration of grounds , strengthening of fortifications , serving of aquaducts , preserving of health ( by cleansing streets , and scowring sewers ) and maintaining of commerse ( by defending bridges , cleering rivers , and opening ports and channels ) with innumerable other benefits of the like nature . and , that i may omit no circumstance that may recommend my authour , the fortune of this his treatise hath been such , that as if he intended a plus ultra by it , or as if all men despaired to out-do it , or lastly , as if castelli hath been so great a master that none have presumed to take pencil in hand for the finishing of what he pourfoild , this small tract like the arabian phoenix ( of which it is said unica semper avis ) did for several years together continue single in the world , till that to verifie it to be truly phoenician , it renewed its age by undergoing a second impression . and as if this did not make out the immortal vertue of it , it hath had anno 1660 a third circulation , and risen in this last edition as it were from the vrne of its authour ; and that so improved by the addition of a second part , that it promiseth to perpetuate his merits to all posterity . to be brief , the meer fame of this work resounded the honourable name of castelli into all the corners of italy , i may say of europe ; insomuch , that , in hopes to reap great benefit by his art , the respective grandees of the adjacent countries courted his judgment and advice about their draining of fenns , diversion of rivers , evacuation of ports , preventing of inundations , &c. so that every summer he made one or more of these journies or visitations . particularly , the senate of venice consulted him about their lake ; to whom he delivered his opinion in may 1641. and upon farther thoughts he presented them with another paper of considerations the 20 december following . prince leopoldo of tuscany likewise requested his advice in the beginning of the ensuing year 1642 , which occasioned his letter to father francesco di san giuseppe , bearing date february 1 , to which signore bartolotti opposing , he writes a second letter , directed to one of the commissioners of sewers , vindicating his former , and refuting bartolotti , both which i here give you . § . the preferments which his merits recommended him unto , were first to be abbot of cassino , from which he was removed anno 1640 , or thereabouts , unto the abbey of santo benedetto aloysio ; and much about the same time preferred to the dignity of chief mathematician to his grand patron pope urban viii . and publique professour of mathematicks in the vniversity of rome . § . here a stop was put to the carier of his fortunes , and being fuller of honour than of years , was by death , the importunate intrerupter of generous designs , prevented in doing that farther good which the world had good reason to promise it self from so profound and industrious a personage , leaving many friends and disciples of all degrees and qualities to lament his losse , and honour his memory . § . his singular virtues and abilities had gained him the friendship of very many ; as to instance in some , he had contracted strict amity with monsignore maffei barberino a florentine , praefect of the publique wayes , and afterwards pope with the name of urban viii . as was said before ; with the above-named monsignore corsini superintendant of the general draines : with monsignore piccolomini arch-bishop of siena : with cardinal serra : with cardinal caponi , who hath studied much and writ well upon this subject ; and with cardinal gaetano who frequently consulted with him in his design of draining the fenns of romagna . moreover prince leopoldo , and his brother the grand duke had very great kindnesse for him ; which speaks no small attractions in him , considering him as a favourite of the family of barberini , between whom and the house of medeci there is an inveterate fewd . amongst persons of a lower quality he acknowledgeth signore ciampoli the popes secretary , sig. ferrante cesarini , sig. giovanni basadonna senator of venice ; and i find mentioned sig. lana , sig. albano , padre serafino , pad . francesco de san. giuseppe , and many others . § . the works in which he will survive to all succeeding ages are first his solid and sober confutation of the arguments of signore lodovico dell columbo , and signore vincentio di gratia against the tract of galileo delle cose che stanno sopra aqua , wherein he vindicates bis said master with a gratitude that tutors very rarely reap from the pains they take in cultivating their pupils . this apology was first printed anno 1615. and was a second time published , as also those of his antagonists , amongst the works of galileo , set forth by the learned viviani 1656. he hath likewise writ several other curious pieces , as i am informed by the most courteous carolo manolessi of bologna ; amongst others an excellent treatise concerning colours , which he putteth me in hopes to see printed very speedily . and last of all these discourses and reflections upon the mensuration of running waters , with the addition of a second book , three epistles , and four considerations upon the same argument , which conduce much to illustrate his doctrine and facilitate the practice of it ; and which with a relation of monsignore corsini , make the second part of my first tome . § . i might here sally forth into the citation of sundry authours of good account , that have transmitted his character to posterity , but shall confine my self to onely two ; the one is of his master , the other of his scholar ; than whom there cannot be two more competent judges of his accomplishments . to begin with his master , the quick-sighted , and truly lyncean galileo , who speaking of his abilities in astronomy saith a che la felicità del suo ingegno non la fà bisognosa dell ' opera suo . and again , submitting a certain demonstration , which he intended to divulge , to the judgment of this our abbot , he writes to him in this manner : b questo lo comunico a v. s. per lettera prima che ad alcun altro , con attenderne principalmente il parer suo , e doppo quello de' nostri amici discosti , conpensiero d' inviarne poi altre copie ad altri amici d' italia , e di francia , quando io ne venga da lei configliato : e qui pregandola a farci parte d' alcuna delle sue peregrine speculationi ; con sincerissimo affetto , &c. and the most acute mathematician signore evangelista terricelli , late professour to the grand duke in immediate succession after galileo , maketh this honourable and grateful mention of him , and his book : c omitto magnum illum nutantis maris motum ; praetereo etiam omnem fluminum , aquarumque currentium tum mensurum , tum usum , quarum omnis doctrina reperta primum fuit ab abbate benedicto castellio preceptore meo . scripsit ille scientiam suam , & illam non solum demonstratione , verum etiam opere confirmavit , maxima cum principum & populorum utilitate , majore cum admiratione phylosophorum . extat illius liber , vere aureus . § . i have onely two particulars more to offer the english reader : the one concerns the book , and it is this , that after the general aprobation it hath had in italy , i cannot but think it deserveth the same civil entertainment with us , in regard that it cometh with no lesse novelty , facility , verity , and utility to us than to those whom the authour favoured with the original . our rivers and sewers through publique distractions and private incroachments are in great disorder , as those channels for instance which formerly were navigable unto the very walls of york and salisbury , &c : our ports are choaked and obstructed by shelfes and setlements : our fenns do in a great part lie waste and unimproved : now all these may be ( and , as i find by the confession of some whose practises upon the copy of the first book onely of our authour hath got them both money and reputation , in part have been ) remedied by the ways and means he here sets down . the truth is the argument hath been past over with an vniversal silence ; so that to this day i have not seen any thing that hath been written demonstratively and with mathematical certainty concerning the same , save onely what this learned prelate hath delivered of his own invention in these treatises : who yet hath so fully and plainly handled the whole doctrine , that i may affirm his work to be every way absolute . it must be confest the demonstration of the second proposition of the second book did not well please the authour , and had he lived he would have supplyed that defect , but being prevented by death , the reader must content himself with the mechanical proof that he giveth you of the truth of so excellent a conclusion . § . the other particular that i am to offer is , that out of my desire to contribute what lyeth in me to the compleating of this piece for english practice , i have exeeded my promise not onely in giving you the second and following books which were not extant at the time of tendering my overtures , but also in that i have added a map or plat of all the rivers , lakes , fenns , &c. mentioned thorowout the work. and if i have not kept touch in point of time , let it be considered that i am the translator and not the printer . to conclude , according to your acceptance of these my endeavours , you may expect some other tracts of no lesse profit and delight . farewell . t. s. errata of the second part of the first tome . in preface , read ferdinando ii. ibid. l'aqua . page 2. line 26 , for must read much . p. 3. l. 22 , r. and let . l. 25. r. water , 〈…〉 . 41. r. tappe , ( as every where else ) . page 4. l. 18. r. cords . page 6. l. 9. r. acquire , or ▪ page 9. l. 1. r. irreperable . p. 10. l. 13. r. dissimboguement . for page 17. r. p. 15. p. 15. l. 27 , r. in . l. 36 , r. is as . l. 38 , r. 〈◊〉 . p. 17. l. 12 , giuli● . l. ●7 . r. measurers . l. 25 , r. measured it , r. necessarily . p. 23. l. 19. r. for help . for page 31. r. p. 32. p. 24 ▪ l. 14 , r. to . l. 17 , r. namly , of the. l. 23 , r. easie . p. 25. l. 38. r. cock. p. 29. l. 7. r. lasted , p. 31. l. 32. r. soe . p. 41. l. 20. r. to the line . p. 48. l. 19. r. us the * . id . figure false p. 52. l. 30 , and 31. for theorem r. proposition . p. 53. l. 29. r. again . p. 57. l. 19 , r. same if ▪ l. 44. r. bodily . p. 58. l. 9. r. gathering . l. 40. omit ; . p. 60. l. 2. omit , if . p. 65. l. 1. r. tid● dele ; . p. 66. l. 35. r. stoppage of . p. 68. l. 12 , for lords the r. lords . l. ult . for they r. it . p. 69. l. 14. r. to one . id . carried dele to . p. 71. l. 20 , r. and that . l. 25 , r. braces ; it . l. 29. r. braces . l. 44 , r. the brent . p. 72. l. 23. r. serene highnesse . p. 73. l. 24 , r. deliberation : l. 26 , for summe r. moddel . l. 40. r. months . p. 79. l. 18. r. that into . p. 82. l. 22. dele ; . p ▪ 85. l. 9 , 10. dele a free drame . p. 88. l. 5. r. palmes . p. 89. l. 8. r. princes . p. 92. l. 3. r. discourses . p. 93. l. 31. r. tautologie . p. 94. l. 9. r. miracle ; . p. 97. l. 13. r. weighty . p. 101. l. 21. r. marrara . p. 107. l. 28 , r. patrimony . l. 40. r. above . p. 111. l. 16. r. said . for p. 432. r. p. 114. p. 114. l. 35. r. of 200. l. 41. r. closed . p. 115. l. 29. r. constant ; . of the mensuration of running waters . lib . i. what , and of how great moment the consideration of motion is in natural things , is so manifest , that the prince of peripateticks pronounced that in his schools now much used sentence : ignorato motu , ignoratur natura . thence it is that true philosophers have so travailed in the contemplation of the celestial motions , and in the speculation of the motions of animals , that they have arrived to a wonderful height and sublimity of understanding . under the same science of motion is comprehended all that which is written by mechanitians concerning engines moving of themselves , machins moving by the force of air , and those which serve to move weights and immense magnitudes with small force . there appertaineth to the science of motion all that which hath been written of the alteration not onely of bodies , but of our minds also ; and in sum , this ample matter of motion is so extended and dilated , that there are few things which fall under mans notice , which are not conjoyned with motion , or at least depending thereupon , or to the knowledge thereof directed ; and of almost every of them , there hath been written and composed by sublime wits , learned treatises and instructions . and because that in the years past i had occasion by order of our lord pope vrban 8. to apply my thoughts to the motion of the waters of rivers , ( a matter difficult , most important , and little handled by others ) having concerning the same observed some particulars not well observed , or considered till now , but of great moment both in publick and private affairs ; i have thought good to publish them , to the end that ingenious spirits might have occasion to discusse more exactly then hitherto hath been done , so necessary and profitable a matter , and to supply also my defects in this short and difficult tractate . difficult i say , for the truth is , these knowledges , though of things next our senses , are sometimes more abstruce and hidden , then the knowledge of things more remote ; and much better , and with greater exquisitness are known the motions of the planets , and periods of the stars , than those of rivers and seas : as that singular light of philosophie of our times , and my master signore galileo galilei wisely observeth in his book concerning the solar spots . and to proceed with a due order in sciences , i will take some suppositions and cognitions sufficiently clear ; from which i will afterwards proceed to the deducing of the principal conclusions . but to the end that what i have written at the end of this discourse in a demonstrative and geometrical method , may also be understood of those which never have applyed their thoughts to the study of geometry ; i have endeavoured to explain my conceit by an example , and with the consideration of the natural things themselves , must after the same order in which i began to doubt in this matter ; and have placed this particular treatise here in the beginning , adverting nevertheless , that he who desires more full and absolute solidity of reasons , may overpass this prefatory discourse , and onely consider what is treated of in the demonstrations placed towards the end , and return afterwards to the consideration of the things collected in the corollaries and appendices ; which demonstrations notwithstanding , may be pretermitted by him that hath not seen at least the first six books of the elements of euclid ; so that he diligently observeth that which followeth . i say therefore , that having in times past , on divers occasions heard speak of the measures of the waters of rivers , and fountains , saying , such a river is two or three thousand feet of water ; such a spring-water is twenty , thirty , or forty inches , &c. although in such manner i have found all to treat thereof in word and writing , without variety , and as we are wont to say , constanti sermone , yea even artists and ingeneers , as if it were a thing that admitted not of any doubt , yet howsoever i remained still infolded in such an obscurity , that i well knew i understood nothing at all , of that which others pretended full and clearly to understand . and my doubt arose from my frequent observation of many trenches and channels , which carry water to turn mills , in which trenches , and channels , the water being measured , was found pretty deep ; but if afterwards the same water was measured in the fall it made to turn the wheel of the mill , it was much lesse , not amounting often to the tenth part , nor sometimes to the twentieth , insomuch , that the same running water came to be one while more , another while less in measure , in divers parts of its channel ; and for that reason this vulgar manner of measuring running waters , as indeterminate and uncertain , was by me justly suspected , the measure being to be determinate , and the same . and here i freely confesse that i had singular help to resolve this difficulty from the excellent & accurate way of discoursing , as in allother matters , so also in this , of the right honourable and truly noble signior ciampoli , secretary of the popes secret affairs . who moreover , not sparing for the costs of the same , generously gave me occasion a few years past to try by exact experiments that which past concerning this particular . and to explain all more clearly with an example ; we suppose a vessel filled with water , as for instance a butt , which is kept full , though still water runneth out , and the water run out by two taps equal of bignesse , one put in the bottom of the vessel , and the other in the upper part ; it is manifest that in the time wherein from the upper part shall issue a determinate measure of water from the inferiour part there shall issue four , five , and many more of the same measures , according to the difference of the height of the taps , and the distance of the upper tap from the superficies and level of the water of the vessel : and all this will alwayes follow , though , as hath been said , the taps be equal , and the water in discharging keep the said taps alwayes full . where first we note , that , although the measure of the taps be equal , neverthelesse there issueth from them in equal times unequal quantities of water , and if we should more attentively consider this businesse , we should find , that the water by the lower tap , runneth and passeth with much greater velocity , then it doth by the upper , whatever is the reason . if therefore we would have such a quantity of water discharge from the upper tap , as would discharge from the neather in the same time , it is plain , that either the upper tap● must be multiplyed in such sort , that so many more taps in number be placed above than below , as the neather tap shall be more swift than the upper , or the upper tap made so much bigger than the nether , by how much that beneath shall be more swift than that above ; and so then in equal times , the same quantity of water shall discharge from the upper , as doth from the neather part . i will declare my self by another example . if we should imagine , that two cords or lines of equal thickness , be drawn through two holes of equal bore ; but so that the first pass with quadruple velocity to the second : it is manifest , that if in a determinate time , we shall by the first bore have drawn four ells of the line , in the same time , by the second hole we shall have drawn but one ell of cord onely ; and if by the first there passe twelve ells , then through the second there shall passe onely three ells ; and in short the quantity of cord shall have the same proportion to the cord , that the volocity hath to the velocity . and therefore we desiring to compensate the tardity of the second cord , and maintaining the same tardity to draw through the second hole as much cord as through the first , it will be necessary to draw through the second bore four ends of cord ; so that the thickness of all the cords by the second hole , have the same proportion to the thickness of the cord which passeth onely by the first , as the velocity of the cord by the first hole hath reciprocally to the velocity of the cod's by the second hole . and thus its clear , that when there is drawn through two holes equal quantity of cords in equal time , but with unequal velocity , it will be necessary , that the thickness of all the four cords shall have the same reciprocal proportion to the thickness of the swifter cord , that the velocity of the swifter cord hath to the velocity of the slower . the which is verified likewise in the fluid element of water . and to the end that this principal fundamental be well understood , i will also note a certain observation made my me in the art of wyer-drawing , or spinning gold , silver , brass , and iron , and it is this ; that such artificers desiring more and more to disgrosse and subtillize the said metals , having wound about a rocket or barrel , the thread of the metal , they place the rocket in a frame upon a stedfast axis , in such sort that the rocket may turn about in it self ; then making one end of the thread to passe by force through a plate of steel pierced with divers holes , greater and lesser , as need requireth , fastning the same end of the thread to another rocket , they wind up the thread , which passing through a bore less than the thicknesse of the thread , is of force constrained to disgrosse and subtillize . now that which is intensly to be observed in this business , is this , that the parts of the thread before the hole , are of such a thicknesse , but the parts of the same thread after it is passed the hole , are of a lesser thicknesse : and yet neverthelesse the masse and weight of the thread which is drawn forth , is ever equal to the masse and weight of the thread which is winded up . but if we should well consider the matter , we should finde , that the thicker the thread before the hole is , than the thread passed the hole , the greater reciprocally is the velocity of the parts of the thread passed the hole , than the volocity of the parts before the hole : insomuch that if v●rbi gratia the thicknesse of the thread before the hole , were double to the thicknesse after the hole , in such case the velocity of the parts of the thread passed the hole , should be double to the velocity of the parts of the thread before the hole ; and thus the thicknesse compensates the velocity , and the velocity compensates the thicknesse . so that the same occurreth in the solid metals of gold , silver , brass , iron , &c. that eveneth also in the fluid element of water , and other liquids , namely , that the velocity beareth the same proportion to the velocity , that the thicknesse of the metal , or water , hath to the thicknesse . and therefore granting this discourse , we may say , that as often as two taps with different velocity discharge equal quantities of water in equal times , it will be necessary that the tap lesse swift be so much greater , and larger , than the tap more swift , by how much the swifter superates in velocity the slower ; and to pronounce the proposition in more proper terms , we say ; that if two taps of unequal velocity , discharge in equal times equal quantities of water , the greatnesse of the first shall be to the greatnesse of the second , in reciprocal proportion , as the velocity of the second to the velocity of the first . as for example , if the first tap shall be ten times swifter than the second tap , it will be necessary , that the second be ten times bigger and larger than the first ; and in such case the taps shall discharge equall quantities of water in equal times ; and this is the principal and most important point , which ought to be kept alwayes in minde , for that on it well understood depend many things profitable , and worthy of our knowledge . now applying all that hath been said neerer to our purpose , i consider , that it being most true , that in divers parts of the same river or current of running water , there doth always passe equal quantity of water in equal time ( which thing is also demonstrated in our first proposition ) and it being also true , that in divers parts the same river may have various and different velocity ; it follows of necessary consequence , that where the river hath lesse velocity , it shall be of greater measure , and in those parts , in which it hath greater velocity , it shall be of lesse measure ; and in sum , the velocity of several parts of the said river , shall have eternally reciprocall and like proportion with their measures . this principle and fundamental well established , that the same current of water changeth measure , according to its varying of velocity ; that is , lessening the measure , when the velocity encreaseth , and encreasing the measure , when the velocity decreaseth ; i passe to the consideration of many particular accidents in this admirable matter , and all depending on this sole proposition , the sense of which i have oft repeated , that it might be well understood . corollarie i. and first , we hence conclude , that the same streams of a torrent , namely , those streams which carry equal quantity of water in equal times , make not the same depths or measures in the river , in which they enter , unlesse when in the entrance into the river they acquired ; or to say better , keep the same velocity ; because if the velocicities acquired in the river shall be different , also the measures shall be diverse ; and consequently the depths , as is demonstrated . corollarie ii. and because successively , as the river is more and more full , it is constituted ordinarily in greater & greater velocity : hence it is that the same streams of the torrent , that enter into the river , make lesse and lesse depths , as the river grows more and more full ; since that also the waters of the torrent being entered into the river , go acquiring greater and greater velocities , and therefore diminish in measure and height . corollarie iii. we observe also , that while the main river is shallow , if there fall but a gentle rain , it suddenly much increaseth and riseth ; but when the river is already swelled , though there fall again another new violent shower , yet it increaseth not at the same rate as before , proportionably to the rain which fell : which thing we may affirm particularly to depend on this , that in the first case , while the river is low , it is found also very slow , and therefore the little water which entereth into it , passeth and runs with little velocity , and consequently occupieth a great measure : but when the river is once augmented , by new water being also made more swift , it causeth the great flood of water which falleth , to bear a lesse measure , and not to make such a depth . corollarie iv. from the things demonstrated is manifest also , that whilst a torrent entereth into a river , at the time of ebbe , then the torrent moveth with such a certain velocity , what ever it be , passing by its extreamest parts , wherewith it communicateth with the river ; in which parts , the torrent being measured , shall have such a certain measure : but the river swelling and rising , also those parts of the torrent augment in greatnesse and measure , though the torrent , in that instant , dis-imbogue no more water than it did before : so that the river being swelled , we are to consider two mouths of the same torrent , one lesse before the rising , the other greater after the rising , which mouths discharge equal quantities of water in equal times ; therefore the velocity by the lesser mouth shall be greater than the velocity by the greater mouth ; and thus the torrent shall be retarded from its ordinary course . corollarie v. from which operation of nature proceedeth another effect worthy of consideration ; and it is , that the course of the water retarding , as hath been said in those ultimate parts of the torrent , if it shall happen that the torrent grow torbid and muddy , and its streame be retarded in such a degree , that it is not able to carry away those minute grains of earth , which compose the muddinesse ; in this case the torrent shall clear away the mud , and carry away the sand at the bottome of its own chanel , in the extream parts of its mouth , which raised and voided sand , shall again afterwards be carried away , when the river abating , the torrent shall return to move with its primitive velocity . corollarie vi. whilst it is demonstrated , that the same water hath different measures in its chanel or course , according as it varieth in velocity ; so that the measure of the water is alwayes greater , where the velocity is lesser ; and on the contrary , the measure lesser , where the velocity is greater : from hence we may most elegantly render the reason of the usual proverb , take heed of the still waters : for that if we consider the self same water of a river in those parts , wherein it is less swift , and thence called still or smooth water , it shall be , of necessity , of greater measure than in those parts , in which it is more swift , and therefore ordinarily shall be also more deep and dangerous for passengers ; whence it is well said , take heed of the still waters ; and this saying hath been since applied to things moral . corollarie vii . likewise , from the things demonstrated may be concluded , that the windes , which stop a river , and blowing against the current , retard its course and ordinary velocity shall necessarily amplifie the measure of the same river , and consequently shall be , in great part , causes ; or we may say , potent con-causes of making the extraordinary inundations which rivers use to make . and it s most certain , that as often as a strong and continual wind shall blow against the current of a river , and shall reduce the water of the river to such tardity of motion , that in the time wherein before it run five miles , it now moveth but one , such a river will increase to five times the measure , though there should not be added any other quantity of water ; which thing indeed hath in it something of strange , but it is most certain , for that look what proportion the waters velocity before the winde , hath to the velocity after the winde , and such reciprocally is the measure of the same water after the winde , to the measure before the winde ; and because it hath been supposed in our case that the velocity is diminished to a fifth part , therefore the measure shall be increased five times more than that , which it was before . corollarie viii . we have also probable the cause of the inundations of tyber , which befel at rome , in the time of alexander the sixth , & of clement the seventh ; which innundations came in a serene time , and without great thaws of the snows ; which therefore much puzzled the wits of those times . but we may with much probability affirm , that the river rose to such a height and excresence , by the retardation of the waters dependant on the boistrous and constant winds , that blew in those times , as is noted in the memorials . corollarie . ix . it being most manifest , that by the great abundance of water the torrents may increase , and of themselves alone exorbitantly swell the river ; and having demonstrated that also without new water , but onely by the notable retardment the river riseth and increaseth in measure , in proportion as the velocity decreaseth : hence it is apparent , that each of these causes being able of it self , and separate from the other to swell the river ; when it shall happen that both these two causes conspire the augmentation of the river , in such a case there must follow very great and irrepable innundations . corollarie x. from what hath been demonstrated , we may with facility resolve the doubt which hath troubled , and still poseth the most diligent , but incautelous observers of rivers , who measuring the streams and torrents which fall into another river ; as those for instance , which enter into the po , or those which fall into tiber ; and having summed the total of these measures , and conferring the measures of the rivers and brooks , which fall into tiber , with the measure of tiber , and the measures of those which disimbogue into po , with the measure of po , they find them not equal , as , it seems to them , they ought to be , and this is because they have not well noted the most important point of the variation of velocity , and how that it is the most potent cause of wonderfully altering the measures of running waters ; but we most facilly resolving the doubt , may say that these waters diminish the measure , being once entered the principal channel , because they increase in velocity . corollarie xi . through the ignorance of the force of the velocity of the water , in altering its measure , & augmenting it when the velocity diminisheth ; and diminishing it when the velocity augmenteth : the architect giovanni fontana , endeavoured to measure , and and to cause to be measured by his nephew , all the brooks and rivers which discharged their waters into tiber , at the time of the innundation ; which happened at rome in the year 1598 , and published a small treatise thereof , wherein he summeth up the measures of the extraordinary water which fell into tiber , and made account that it was about five hundred ells more than ordinary ; and in the end of that treatise concludeth , that to remove the innundation wholly from rome , it would be necessary to make two other channels , equal to that at present , and that lesse would not suffice ; and finding afterwards that the whole stream passed under the bridge quattro-capi , ( the arch whereof is of a far less measure then five hundred ells ) concludeth , that under the said bridge past a hundred fifty one ells of water compressed , ( i have set down the precise term of comprest water , written by fontana ) wherein i finde many errors . the first of which is to think that the measures of these waters compressed in the channels of those brooks and rivers , should maintain themselves the same in tiber , which by his leave , is most false , when ever those waters reduced into tiber , retain not the same velocity which they had in the place in which fontana and his nephew measured them : and all this is manifest from the things which we have above explained ; for , if the waters reduced into tiber increase in velocity , they decrease in measure ; and if they decrease in velocity , they increase in measure . secondly , i consider that the measures of those brooks and rivers , which enter into tiber at the time of innundation , are not between themselves really the same , when their velocities are not equal , though they have the same names of ells and feet ; for that its possible that a disinboguement of ten ells requadrated ( to speak in the phrase of fontana ) of one of those brooks , might discharge into tiber at the time of innundation , four , ten , and twenty times less water , than another mouth equal to the first in greatness , as would occur when the first mouth were four , ten , or twenty times less swift than the second . whereupon , whilst fontana summes up the ells and feet of the measures of those brooks and rivers into a total aggregate , he commits the same error with him , which would add into one summe diverse moneys of diverse values , and diverse places , but that had the same name ; as if one should say ten crowns of roman money , four crowns of gold , thirteen crowns of florence , five crowns of venice , and eight crowns of mantua , should make the same summe with forty crowns of gold , or forty crowns of mantua . thirdly , it might happen that some river or current in the parts nearer rome , in the time of its flowing , did not send forth more water than ordinary ; and however , it s a thing very clear , that whilst the stream came from the superior parts , that same brook or river would be augmented in measure , as hath been noted in the fourth corollary ; in such sort , that fontana might have inculcated , and noted that same river or current as concurring to the innundation , although it were therein altogether unconcerned . moreover , in the fourth place we must note , that it might so fall out , that such a river not onely was uninteressed in the innundation , though augmented in measure , but it might i say happen , that it was instrumental to the asswaging the innundation , by augmenting in the measure of its own channel ; which matter is sufficiently evident ; for if it be supposed that the river in the time of flood , had not had of it self , and from its proper springs more water than ordinary , it s a thing certain , that the water of tiber rising and increasing ; also that river , to level it self with the water of tiber , would have retained some of its waters in its own chanel , without discharging them into tyber , or else would have ingorged and swallowed ( if i may so say ) some of the water of tyber ; and in this case , at the time of inundation , lesse abundance of water would have come to rome , and yet neverthelesse the measure of that river would have been increased . fifthly , fontana deceiveth himself , when he concludeth , that to remove the inundation from rome , it would be necessary to make two other chanels of rivers , that were as large as that , which is the present one , and that less would not suffice , which , i say , is a fallacy : and to convince him easily of his errour , it sufficeth to say , that all the streams being passed under the bridge quattro-capi , as he himself attests , a channel would suffice only of the capacity of the said bridge , provided that the water there might run with the same velocity , as it did under the bridge at the time of inundation ; and on the contrary , twenty currents of capacity equal to the present one , would not suffice , if the water should run with twenty times less velocity , than it made at the time of the inundation . sixthly , to me it seemeth a great weaknesse to say , that there should passe under the bridge quattro-capi , an hundred fifty one ells of water compressed ; for that i do not understand that water is like cotton or wool , which matters may be prest and trod , as it happeneth also to the air , which receiveth compression in such sort , that after that in some certain place a quantity of air shall be reduced to its natural constitution ; and having taken up all the said place , yet neverthelesse compressing the first air with force and violence , it is reduced into far less room , and will admit four or six times as much air , as before , as is experimentally * seen in the wind-gun , invented in our dayes by m. vincenzo vincenti of vrbin , which property of the air of admitting condensation , is also seen in the portable fountains of the same m. vincenzo : which fountains spirt the water on high , by force of the air compressed , which whilst it seeks to reduce its self to its natural constitution , in the dilation causeth that violence . but the water can never , for any thing i know , crowd , or press so , as that if before the compression it held or possest a place , being in its natural constitution , i believe not , i say , that it is possible , by pressing and crowding to make it possess less room , for if it were possible to compress the water , and make it to occupy a less place , it would thence follow , that two vessels of equal measure , but of unequal height , should be of unequal capacity , and that should hold more water which was higher ; also a cylinder , or other vessel more high than broad , would containe more water erected , than being laid along ; for that being erected , the water put therein would be more pressed and crowded . and therefore , in our case , according to our principles we will say , that the water of that stream passeth all under the said bridge quattro-capi , for that being there most swift , it ought of consequence to be less in measure . and here one may see , into how many errours a man may run through ignorance of a true and real principle , which once known and well understood , takes away all mists of doubting , and easily resolveth all difficulties . corollarie . xii . through the same inadvertency of not regarding the variation of velocity in the same current , there are committed by ingineers and learned men , errours of very great moment ( and i could thereof produce examples , but for good reasons i pass them over in silence ) when they think , and propose , by deriving new channels from great rivers , to diminish the measure of the water in the river , and to diminish it proportionally , according to the measure of the water which they make to pass through the channel , as making v.g. a channel fifty foot broad , in which the derived water is to run waste , ten foot deep , they think they have diminished the measure of the water in the river five hundred feet , which thing doth not indeed so fall out ; and the reason is plain ; for that the chanel being derived , the rest of the main river , diminisheth in velocity , and therefore retains a greater measure than it had at first before the derivation of the chanel ; and moreover , if the chanel being derived , it shall not conserve the same velocity which it had at first in the main river , but shall diminish it , it will be necessary , that it hath a greater measure than it had before in the river ; and therefore to accompt aright , there shall not be so much water derived into the channel , as shall diminish the river , according to the quantity of the water in the channel , as is pretended . corollarie . xiii . this same consideration giveth me occasion to discover a most ordinary errour , observed by me in the businesse of the water of ferara , when i was in those parts , in service of the most reverend and illustrious monsignor corsini ; the sublime wit of whom hath been a very great help to me in these contemplations ; it s very true , i have been much perplexed , whether i should commit this particular to paper , or passe it over in silence , for that i have ever doubted , that the opinion so common and moreover confirmed with a most manifest experiment , may not onely make this my conjecture to be esteemed far from true , but also to discredit with the world the rest of this my treatise : neverthelesse i have at last resolved not to be wanting to my self , and to truth in a matter of it self , and for other consequences most important ; nor doth it seem to me requisite in difficult matters , such as these we have in hand , to resigne our selves to the common opinion , since it would be very strange if the multitude in such matters should hit on the truth , nor ought that to be held difficult , in which even the vulgar do know the truth and right ; besides that i hope moreover to prove all in such sort , that persons of solid judgment , shall rest fully perswaded , so that they but keep in mind the principal ground and foundation of all this treatise ; and though that which i will propose , be a particular , as i have said , pertaining onely to the interests of ferara ; yet neverthelesse from this particular doctrine well understood , good judgement may be made of other the like cases in general . i say then , for greater perspecuity , and better understanding of the whole , that about thirteen miles above ferara , near to stellata , the main of po , branching it self into two parts , with one of its arms it cometh close to ferara , retaining the name of the po of ferara ; and here again it divideth it self into two other branches , and that which continueth on the right hand , is called the po of argenta , and of primaro ; and that on the left the po of volana . but for that the bed of the po of ferara being heretofore augmented and raised , it followeth that it resteth wholly deprived of the water of the great po , except in the time of its greater swelling ; for in that case , this po of ferara being restrained with a bank near to bondeno , would come also in the overflowings of the main po , to be free from its waters : but the lords of ferara are wont at such time as the po threateneth to break out , to cut the bank ; by which cutting , there disgorgeth such a torrent of water , that it is observed , that the main po in the space of some few hours abateth near a foot , and all persons that i have spoken with hitherto , moved by this experiment , think that it is of great profit and benefit to keep ready this vent , and to make use of it in the time of its fullnesse . and indeed , the thing considered simply , and at the first appearance , it seemeth that none can think otherwise ; the rather , for that many examining the matter narrowly , measure that body of water which runneth by the channel , or bed of the po of ferara , and make account , that the body of the water of the great po , is diminished the quantity of the body of the water which runneth by the po of ferara . but if we well remember what hath been said in the beginning of the treatise , and how much the variety of the velocities of the said water importeth , and the knowledge of them is necessary to conclude the true quantity of the running water , we shall finde it manifest , that the benefit of this vent is far lesse than it is generally thought : and mereover , we shall finde , if i deceive not my self , that there follow from thence so many mischiefs , that i could greatly incline to believe , that it were more to the purpose wholly to stop it up , than to maintain it open : yet i am not so wedded to my opinion , but that i am ready to change my judgement upon strength of better reasons ; especially of one that shall have first well understood the beginning of this my discourse , which i frequently inculcate , because it s absolutely impossible without this advertisement to treat of these matters , and not commit very great errours . i propose therefore to consideration , that although it be true , that whilst the water of the main po is at its greatest height , the bank and dam then cut of the po of ferara , and the superior waters having a very great fall into the channel of ferara , they precipitate into the same with great violence and velocity , and with the same in the beginning , or little lesse , they run towards the po of volana , and of argenta on the sea coasts ; yet after the space of some few hours , the po of ferara being full , and the superior waters not finding so great a diclivity there , as they had at the beginning of the cutting , they fall not into the same with the former velocity , but with far lesse , and thereby a great deal lesse water begins to issue from the great po ; and if we diligently compare the velocity at the first cutting , with the velocity of the water after the cutting made , and when the po of ferara shall be full of water , we shall finde perhaps that to be fifteen or twenty times greater than this , and consequently the water which issues from the great po , that first impetuosity being past , shall be onely the fifteenth or twentieth part of that which issued at the beginning ; and therefore the waters of the main po will return in a small time almost to the first height . and here i will pray those who rest not wholly satisfied with what hath been said , that for the love of truth , and the common good , they would please to make diligent observation whether in the time of great floods , the said bank or dam at bondeno is cut , and that in few hours the main po diminisheth , as hath been said about a foot in its height ; that they would observe i say , whether , a day or two being past , the waters of the main po return almost to their first height ; for if this should follow , it would be very clear , that the benefit which resulteth from this diversion or vent , is not so great as is universally presumed ; i say , it is not so great as is presumed ; because , though it be granted for true , that the waters of the main po , abate at the beginning of the vent , yet this benefit happens to be but temporary and for a few hours : if the rising of po , and the dangers of breaking forth were of short duration , as it ordinarily befalleth in the overflowings of torrents , in such a case the profit of the vent would be of some esteem : but because the swellings of po continue for thirty , or sometimes for forty dayes , therefore the gain which results from the vent proveth to be inconsiderable . it remaineth now to consider the notable harms which follow the said sluice or vent , that so reflection being made , and the profit and the detriment compared , one may rightly judge , and choose that which shall be most convenient . the first prejudice therefore which ariseth from this vent or sluice , is ; that the channels of ferara , primaro , and volana filling with water , all those parts from bondeno to the sea side are allarmed and endangered thereby . secondly , the waters of the po of primaro having free ingresse into the upper valleys , they fill them to the great damage of the fields adjacent , and obstruct the course of the ordinary trenches in the same valleys ; insomuch that all the care , cost , and labour about the draining , and freeing the upper valleys from water , would also become vain and ineffectual . thirdly , i consider that these waters of the po of ferara being passed downwards towards the sea , at the time that the main po was in its greater excrescences and heights , it is manifest by experience , that when the great po diminisheth , then these waters passed by the po of ferara begin to retard in their course , and finally come to turn the current upwards towards stellata , resting first in the intermediate time , almost fixed and standing , and therefore deposing the muddinesse , they fill up the channel of the river or current of ferara . fourthly and lastly , there followeth from this same diversion another notable damage , and it is like to that which followeth the breaches made by rivers ; near to which breaches in the lower parts , namely below the breach , there is begot in the channel of the river , a certain ridge or shelf , that is , the bottom of the river is raised , as is sufficiently manifest by experience ; and thus just in the same manner cutting the bank at bondeno , there is at it were a breach made , from which followeth the rising in the lower parts of the main po , being past the mouth of pamaro ; which thing , how pernitious it is , let any one judge that understandeth these matters . and therefore both for the small benefit , and so many harms that ensue from maintaining this diversion , i should think it were more sound advice to keep that bank alwaies whole at bondeno , or in any other convenient place , and not to permit that the water of the grand po should ever come near to ferara . corollarie xiv . in the grand rivers , which fall into the sea , as here in italy po , adige , * and arno , which are armed with banks against their excrescencies , it s observed that far from the sea , they need banks of a notable height ; which height goeth afterwards by degrees diminishing , the more it approacheth to the sea-coasts : in such sort , that the po , distant from the sea about fifty or sixty miles at ferara , shall have banks that be above twenty feet higher than the ordinary water-marks ; but ten or twelve miles from the sea , the banks are not twelve feet higher than the said ordinary water-marks , though the breadth of the river be the same , so that the excrescence of the same innundation happens to be far greater in measure remote from the sea , then near ; and yet it should seem , that the same quantity of water passing by every place , the river should need to have the same altitude of banks in all places : but we by our principles and fundamentals may be able to render the reason of that effect , and say ; that that excesse of quantity of water , above the ordinary water , goeth alwaies acquiring greater velocity ; the nearer it approacheth the sea , and therefore decreaseth in measure , and consequenly in height . and this perhaps might have been the cause in great part , why the tyber in the innundation anno 1578. issued not forth of its channel below rome towards the sea. corollarie xv. from the same doctrine may be rendred a most manifest reason why the falling waters go lessening in their descent , so that the same falling water , measured at the beginning of its fall , is greater , and bigger , and afterwards by degrees lesseneth in measure the more it is remote from the beginning of the fall . which dependeth on no other , than on the acquisition , which it successively makes of greater velocity ; it being a most familiar conclusion among philosophers , that grave bodies falling , the more they remove from the beginning of their motion , the more they acquire of swiftnesse ; and therefore the water , as a grave body , falling , gradually velocitates , and therefore decreaseth in measure , and lesseneth . corollarie xvi . and on the contrary , the spirtings of a fountain of water , which spring on high , work a contrary effect ; namely in the beginning they are small , and afterwards become greater and bigge ; and the reason is most manifest , because in the beginning they are very swift , and afterwards gradually relent their impetuosity , and motion , so that in the beginning of the excursion that they make , they ought to be small , and afterwards to grow bigger , as in the effect is seen . appendix i. into the errour of not considering how much the different velocities of the same running water in several places of its current , are able to change the measure of the same water , and to make it greater ; or lesse , i think , if i be not deceived , that giulio frontino a noble antient writer , may have faln in the second book which he writ , of the aqueducts of the city of rome : whilst finding the measure of the water * commentariis lesse than it was in erogatione 1263. quinaries , he thought that so much difference might proceed from the negligence of the measures , and when afterwards with his own industry he measured the same water at the beginnings of the aqueducts , finding it neer 10000. quinaries bigger than it was in commentariis he judged , that the overplus was imbeziled by ministers and partakers ; which in part might be so , for it is but too true , that the publique is almost alwayes defrauded ; yet neverthelesse , i verily believe withal , that besides the frauds of these officers , the velocities of the water in the place wherein frontino measured , it might be different from those velocities , which are found in other places before measured by others ; and therefore the measures of the waters might , yea ought necessarily to be different , it having been by us demonstrated , that the measures of the same running water have reciprocal proportion to their velocities . which frontino not well considering , and finding the water in commentariis 12755. quinaries in erogatione 14018 , and in his own measure ad capita ductuum , at the head of the fountain 22755. quinaries , or thereabouts , he thought , that in all these places there past different quantities of water ; namely , greater at the fountain head then that which was in erogatione , and this he judged greater than that which was in commentariis . appendix ii. a like mistake chanced lately in the aqueduct of acqua-paola , which water should be 2000 inches , and so many effectively ought to be allowed ; and it hath been given in so to be by the signors of bracciano to the apostolick-chamber ; and there was a measure thereof made at the beginning of the aqueduct ; which measure proved afterwards much lesse and short , considered and taken in rome , and thence followed discontents and great disorders , and all because this property of running-waters , of increasing in measure , where the velocity decreased ; and of diminishing in measure , where the velocity augmented , was not lookt into . appendix iii. a like errour , in my judgement , hath been committed by all those learned men , which to prevent the diversion of the reno of bologna into po by the channels , through which it at present runneth , judged , that the reno being in its greater excrescence about 2000 ▪ feet , and the po being near 1000. feet broad , they judged , i say , that letting the reno into po , it would have raised the water of po two feet ; from which rise , they concluded afterwards most exorbitant disorders , either of extraordinary inundations , or else of immense and intolerable expences to the people in raising the banks of po and reno , and with such like weaknesses , often vainly disturbed the minds of the persons concerned : but now from the things demonstrated , it is manifest , that the measure of the reno in reno , would be different from the measure of reno in po ; in case that the velocity of the reno in po , should differ from the velocity of reno in reno , as is more exactly determined in the fourth proposition . appendix iv. no less likewise are those ingeneers and artists deceived , that have affirmed , that letting the reno into po , there would be no rise at all in the water of po : for the truth is , that letting reno into po , there would alwaies be a rising ; but sometimes greater , sometimes lesse , as the po shall have a swifter or slower current ; so that if the po shall be constituted in a great velocity , the rise will be very small ; and if the said po shall be slow in its course , then the rise will be notable . appendix v. and here it will not be besides the purpose to advertise , that the measures , partments , and distributions of the waters of fountains , cannot be made exactly , unless there be considered , besides the measure , the velocity also of the water ; which particular not being thorowly observed , is the cause of continual miscariages in such like affairs . appendix vi. like consideration ought to be had with the greater diligence , for that an errour therein is more prejudicial ; i say , ought to be had by those which part and divide vvaters ; for the watering of fields , as is done in the territories of brescia , bergama , crema , pavia , lodigiano , cremona , and other places : for if they have not regard to the most important point of the variation of the velocity of the vvater , but onely to the bare vulgar measure , there will alwaies very great disorders and prejudices ensue to the persons concerned . appendix vii . it seemeth that one may observe , that whilst the water runneth along a channel , current , or conduit , its velocity is retarded , withheld , and impeded by its touching the bank of side of the said channel or current ; which , as immoveable , not following the motion of the vvater , interrupteth its velocity : from which particular , being true , as i believe it to be most true , and from our considerations , we have an occasion of discovering a very nice mistake , into which those commonly fall who divide the vvaters of fountains . vvhich division is wont to be , by what i have seen here in rome , performed two wayes ; the first of which is with the measures of like figures , as circles , or squares , having cut through a plate of metal several circles or squares , one of half 〈◊〉 inch , another of one inch , another of two , of three , of four , &c. with which they afterwards adjust the cocks to dispence the vvaters . the other manner of dividing the vvaters of fountains , is with rectangle paralellograms , of the same height , but of different bases , in such sort likewise , that one paralellogram be of half an inch , another of one , two , three , &c. in which manner of measuring and dividing the water it should seem that the cocks being placed in one and the same plain , equidistant from the level , or superior superficies of the water of the well ; and the said measures being most exactly made , the vvater ought consequently also to be equally divided , and parted according to the proportion of the measures . but if we well consider every particular , we shall finde , that the cocks , as they successively are greater , discharge alwaies more vvater than the just quantity , in comparison of the lesser ; that is , to speak more properly , the vvater which passeth through the greater cock , hath alwaies a greater proportion to that which passeth through the lesser , than the greater cock hath to the lesser . all which i will declare by an example . the like errour occurreth also in the other manner of measuring the vvater of a fountain , as may easily be collected from what hath been said and observed above . appendix viii . the same contemplation discovereth the errour of those architects , who being to erect a bridge of sundry arches over a river , consider the ordinary breadth of the river ; which being v. g. fourty fathom , and the bridge being to consist of four arches , it sufficeth them , that the breadth of all the four arches taken together , be fourty fathom ; not considering that in the ordinary channel of the river , the water hath onely two impediments which retard its velocity ; namely , the touching and gliding along the two sides or shores of the river : but the same water in passing under the bridge , in our case meeteth with eight of the same impediments , bearing , and thrusting upon two sides of each arch ( to omit the impediment of the bottom , for that it is the same in the river , and under the bridge ) from which inadvertency sometimes follow very great disorders , as quotidian practice shews us . appendix ix . it is also worthy to consider the great and admirable benefit that those fields receive , which are wont to drink up the rain-water with difficulty , through the height of the water in the principal ditches ; in which case the careful husbandman cutteth away the reeds and rushes in the ditches , through which the waters pass ; whereupon may be presently seen , so soon as the reeds and rushes are cut , a notable ebb in the level of the water in the ditches ; insomuch that sometimes it is observed , that the water is abated after the said cutting a third and more , of what it was before the cutting . the which effect seemingly might depend on this , that , before those weeds took up room in the ditch , and for that cause the water kept a higher level , and the said plants being afterwards cut and removed , the water came to abate , possessing the place that before was occupied by the weeds : which opinion , though probable , and at first sight satisfactory , is nevertheless insufficient to give the total reason of that notable abatement which hath been spoken of : but it is necessary to have recourse to our consideration of the velocity in the course of the water , the chiefest and true cause of the variation of the measure of the same running-water ; for , that multitudes of reeds , weeds , and plants dispersed through the current of the ditch , do chance notably to retard the course of the water , and therefore the measure of the water increaseth ; and those impediments removed , the same water gaineth velocity , and therefore decreaseth in measure , and consequently in height . and perhaps this point well understood , may be of great profit to the fields adjacent to the pontine fens , and i doubt not but if the river ninfa , and the other principal brooks of those territories were kept well cleansed from weeds , their waters would be at a lower level , and consequently the drains of the fields would run into them more readily ; it being alwayes to be held for undoubted , that the measure of the water before the cleansing , hath the same proportion to the measure after cleansing , that the velocity after the cleansing hath to the velocity before the cleansing : and because those weeds being cleansed away , the course of the water notably increaseth , it is therefore necessary that the said water abate in measure , and become lower . appendix . x. we having above observed some errors that are committed in distributing the waters of fountains , and those that serve to water fields ; it seemeth now fit , by way of a close to this discourse , to advertise by what means these divisions may be made justly and without error . i therefore think that one might two several wayes exquisitly divide the water of fountains ; the first would be by diligently examining , first , how much water the whole fountain dischargeth in a determinate time , as for instance : how many barrels , or tuns it carrieth in a set time ; and in case you are afterwards to distribute the water , distribute it at the rate of somany barrels or tuns , in that same time ; and in this case the participants would have their punctual shares : nor could it ever happen to send out more water , than is reckoned to be in the principal fountain ; as befel giulio frontino , and as also it frequently happeneth in the modern aqueducts , to the publick and private detriment . the other way of dividing the same waters of a fountain , is also sufficiently exact and easie ; and may be , by having one onely size for the cock or pipe , as suppose of an inch , or of half an inch ; and when the case requireth to dispence two , three , and more inches , take so many cocks of the said measure as do evacuate the water , which is to be emitted ; and if we are to make use onely of one greater cock , we being to place one to discharge for example four inches ; and having the former sole measure of an inch , we must make a cock that is bigger , its true , than the cock of one inch ; but not simply in a quadruple proportion , for that it would discharge more than just so much water , as hath been said above ; but we ought to examine diligently how much water the little cock emitteth in an hour ; and then enlarge , and contract the greater cock , so , that it may discharge four times as much water as the lesser in the same time ; and by this means we shall avoid the disorder hinted in the seventh appendix . it would be necessary nevertheless , to accommodate the cocks of the cistern so , that the level of the water in the cistern may alwayes rest at one determinate mark above the cock , otherwise the cocks will emit sometimes greater , and sometimes lesse abundance of water ▪ and because it may be that the same water of the fountain may be some times more abundant , sometimes less ; in such case it will be necessary to adjust the cistern so , that the excess above the ordinary water , discharge into the publick fountains , that so the particular participants may have alwayes the same abundance of water . appendix xi . much more difficult is the division of the waters which serve to water the fields , it not being possible to observe so commodiously , what quantity of water the whole ditch sends forth in one determinate time , as may be done in fountains : yet nevertheless , if the second proposition by us a little below demonstrated , be well understood , there may be thence taken a very safe and just way to distribute such waters . the proposition therefore by us demonstrated is this : if there be two sections , ( namely two mouths of rivers ) the quantity of the water which passeth by the first , hath a proportion to that which passeth by the second , compounded of the proportions of the first section to the second , and of the velocity through the first , to the velocity through the second : as i will declare for example by help of practice , that i may be understood by all , in a matter so important . let the two mouths of the rivers be a , and b , and let the mouth a be in measure and content thirty two feet , and the mouth b , eight feet . here you must take notice , that it is not alwayes true , that the water which passeth by a , hath the same proportion to that which passeth by b , that the mouth a hath to the mouth b ; but onely when the velocityes by each of those passages are equal : but if the velocityes shall be unequal , it may be that the said mouths may emit equal quantity of water in equal times , though their measure be unequal ; and it may be also , that the bigger doth discharge a greater quantity of water : and lastly , it may be , that the less mouth dischargeth more water than the greater ; and all this is manifest by the things noted in the beginning of this discourse , and by the said second proposition . now to examine the proportion of the water that passeth by one ditch , to that which passeth by another , that this being known , the same waters and mouths of ditches may be then adjusted ; we are to keep account not onely of the greatness of the mouths or passages of the water , but of the velocity also ; which we will do , by first finding two numbers that have the same proportion between themselves , as have the mouths , which are the numbers 32 and 8 in our example : then this being done , let the velocity of the water by the passages a and b , be examined ( which may be done keeping account what space a piece of wood , or other body that swimmeth , is carried by the stream in one determinate time ; as for instance in 50 pulses ) and then work by the golden rule , as the velocity by a , is to the velocity by b , so is the number 8 , to another number , which is 4. it is clear by what is demonstrated in the said second proposition , that the quantity of water , which passeth by the mouth a , shall have the same proportion of that which passeth by the mouth b , that 8 hath to 1. such proportion being composed of the proportions of 32 to 8 , and of 8 to 4 ; namely , to the greatness of the mouth a , to the greatness of the mouth b , and of the velocity in a , to the velocity in b. this being done , we must then contract the mouth which dischargeth more then its just quantity of water , or enlarge the other which dischargeth less , as shal be most commodious in practice , which to him that hath understood this little that hath been delivered , will be very easie . appendix xii . these opperations about water , as i have hitherto on sundry occasions observed , are involved in so many difficulties , and such a multiplicity of most extravagant accidents , that it is no marvel if continually many , and very important errours be therein committed by many , and even by ingeneers themselves , and learned-men ; and because many times they concern not onely the publique , but private interests : hence it is , that it not onely belongeth to artists to treat thereof , but very oft even the vulgar themselves pretend to give their judgement therein : and i have been troubled many times with a necessity of treating , not onely with those , which either by practice , or particular study , understood somewhat in these matters ; but also with people wholly void of those notions , which are necessary for one that would on good grounds discourse about this particular ; and thus many times have met with more difficulty in the thick skulls of men , than in precipitous torrents , and vast fennes . and in particular , i had occasion some years past to go see the cave or emissary of the lake of perugia , made many years agon by braccio fortobraccio , but for that it was with great ruines by time decayed , and rendred unuseful , it was repaired with industry truly heroicall and admirable , by monsignor maffei barberino , then prefect for the wayes , and now pope . and being necessitated , that i might be able to walk in the cave , and for other causes , i let down the sluices of the said cave , at the mouth of the lake : no sooner were they stopt , but a great many of the people of the towns and villages coasting upon the lake flocking thither , began to make grievous complaints , that if those sluices were kept shut , not onely the lake would want its due vent , but also the parts adjacent to the lake would be over flown to their very great detriment . and because at first appearance their motion seemed very reasonable , i found my self hard put to it , seeing no way to perswade such a multitude , that the prejudice which they pretended i should do them by keeping the sluices shut for two dayes , was absolutely insensible ; and that by keeping them open , the lake did not ebb in the same time so much as the thickness of a sheet of paper : and therefore i was necessitated to make use of the authority i had , and so followed my business as cause required , without any regard to that rabble tumultuously assembled . now when i am not working with mattock or spade , but with the pen and discourse , i intend to demonstrate clearly to those that are capable of reason , and that have well understood the ground of this my treatise , that the fear was altogether vain which those people conceited . and therefore i say , that the emissary or sluice of the lake of perugia , standing in the same manner as at present , and the water passing thorow it with the same velocity as now ; to examine how much the lake may abate in two days space , we ought to consider , what proportion the superficies of the whole lake hath to the measure of the section of the emissary , and afterwards to infer , that the velocity of the water by the emissary or sluice , shall have the same proportion to the abatement of the lake , and to prove thorowly and clearly this discourse , i intend to demonstrate the following proposition . that which hath been demonstrated in the vessel , falls out exactly also in our lake of perugia , and its emissary ; and because the immensity of the superficies of the lake is in proportion to the superficies of the emissary or sluice , as many millions to one , as may be easily calculated ; it is manifest , that such abatement shall be imperceptible , and almost nothing , in two dayes space , nay in four or six : and all this will be true , when we suppose that for that time there entreth no other water into the lake from ditches or rivolets , which falling into the lake would render such abatement yet less . now we see , that it 's necessary to examine such abatements and risings , with excellent reasons , or at least , with accurate experiments , before we resolve and conclude any thing ; and how farre the vulgar are distant from a right judgement in such matters . appendix xiii . for greater confirmation of all this which i have said , i will instance in another like case , which also i met with heretofore , wherein , for that the business was not rightly understood , many disorders , vast expences , and considerable mischiefs have followed . there was heretofore an emissary or sluice made to drain the waters , which from rains , springs , and rivolets fall into a lake ; to the end , the shores adjoyning on the lake , should be free from the overflowing of the waters ; but because perhaps the enterprize was not well managed and carried on , it fell out , that the fields adjacent to the said chanel could not drain , but continued under water ; to which disorders a present remedy hath been used , namely , in a time convenient to stop up the sluice , by meanes of certain floodgates kept on purpose for that end ; and thus abating the level of the water in the emissary , in the space of three or four dayes , the fields have been haply drained . but on the other part , the proprietors bordering on the lake opposed this , grievously complaining , that whilst the floodgates are shut , and the course of the water of the sluice hindered , the lake overflowes the lands adjacent , by meanes of the rivers that fell into it , to their very great damage ; and so continuing their suits , they got more of vexation than satisfaction . now , being asked my opinion herein , i judged it requisite ( since the point in controversie was about the rising and falling of the lake ) that the said abatement , when the floodgates are open , and increase when they are shut should be exactly measured , and told them , that it might be easily done at a time when no extraordinary waters fell into the lake , neither of rain , or otherwise ; and the lake was undisturbed by winds that might drive the water to any side , by planting neer to an islet , which is about the middle of the lake , a thick post , on which should be made the marks of the lakes rising and falling for two or three dayes . i would not , at that time , pawn , or resolutely declare , my judgment , in regard i might be , by divers accidents missed . but this i told them , that ( by what i have demonstrated , and particularly that which i have said above touching the lake of perugia ) i inclined greatly to think , that these risings and fallings would prove imperceptible , and inconsiderable ; and therefore , that in case experience should make good my reason , it would be to no purpose for them to continue disputing and wrangling , which causeth , ( according to the proverb ) a great deal of cry , but produceth not much wool. lastly , it importing very much to know what a rain continued for many dayes can do in raising these lakes , i will here insert the copy of a letter , which i writ formerly to signior galilaeo galilaei , chief philosopher to the grand duke of tuscany , wherein i have delivered one of my conceits in this businesse , and it may be , by this letter , i may , more strongly , confirm what i have said above . the copy of a letter to signore galilaeo galilaei , chief philosopher to the most serene great duke of tvscany . worthy and most excellent sir , in satisfaction of my promise , in my former letters of representing unto you some of my considerations made upon the lake thrasimeno , i say , that in times past , being in perugia , where we held our general convention , having understood that the lake thrasimeno , by the great drought of many moneths was much abated , it came into my head , to go privately and see this novelty , both for my particular satisfaction , as also that i might be able to relate the whole to my patrons , upon the certitude of my own sight of the place . and so being come to the emissary of the lake , i found that the level of the lakes surface was ebbed about five roman palmes of its wonted watermark , insomuch that it was lower than the transome of the mouth of the emissary , by the length of — this described line , and therefore no water issued out of the lake , to the great prejudice of all the places and villages circumjacent , in regard that the water which used to run from the said lake turned 22 mills , which not going , necessitated the inhabitants of those parts to go a dayes journey and more , to grinde upon the tiber. being returned to perugia , there followed a rain , not very great , but constant , and even , which lasted for the space of eight hours , or thereabouts ; and it came into my thoughts to examine , being in perugia , how much the lake was increased and raised by this rain , supposing ( as it was probable enough ) that the rain had been universal over all the lake ; and like to that which fell in perugia , and to this purpose i took a glasse formed like a cylinder , about a palme high , and half a palme broad ; and having put in water sufficient to cover the bottome of the glasse , i noted diligently the mark of the height of the water in the glasse , and afterwards exposed it to the open weather , to receive the raine-water , which fell into it ; and i let it stand for the space of an hour ; and having observed that in that time the water was risen in the vessel the height of the following line — , i considered that if i had exposed to the same rain such other vessels equal to that , the water would have risen in them all according to that measure : and thereupon concluded , that also in all the whole extent of the lake , it was necessary the water should be raised in the space of an hour the same measure . yet here i considered two difficulties that might disturb and altar such an effect , or at least render it inobserveable , which afterwards well weighed , and resolved , left me ( as i will tell you anon ) in the conclusion the more confirmed ; that the lake ought to be increased in the space of eight hours , that the rain lasted eight times that measure . and whilst i again exposed the glass to repeat the experiment , there came unto me an ingeneer to talk with me touching certain affairs of our monastary of perugia , and discoursing with him , i shewed him the glass out at my chamber window , exposed in a court-yard ; and communicated to him my fancy , relating unto him all that i had done . but i soon perceived that this brave fellow conceited me to be but of a dull brain , for he smiling said unto me ; sir , you deceive your self : i am of opinion that the lake will not be increased by this rain , so much as the thicknesse of a * julio . hearing him pronounce this his opinion with freeness and confidence , i urged him to give me some reason for what he said , assuring him , that i would change my judgement , when i saw the strength of his arguments : to which he answered , that he had been very conversant about the lake , and was every day upon it , and was well assured that it was not at all increased . and importuning him further , that he would give me some reason for his so thinking , he proposed to my consideration the great drought passed , and that that same rain was nothing for the great parching : to which i answered , i believe sir that the surface of the lake , on which the rain had fallen was moistned ▪ and therefore saw not how its drought , which was nothing at all , could have drunk up any part of the rain . for all this he persisting in his conceit , without yielding in the least to my allegation ; he granted in the end ( i believe in civility to me ) that my reason was plausible and good , but that in practise it could not hold . at last to clear up all , i made one be called , and sent him to the mouth of the emissary of the lake , with order to bring me an exact account , how he found the water of the lake , in respect of the transome of the sluice . now here , signore galilaeo , i would not have you think that i had brought the matter in hand to concern me in my honour ; but believe me ( and there are witnesses of the same still living ) that my messenger returning in the evening to perugia , he brought me word , that the water of the lake began to run through the cave ; and that it was risen almost a fingers breadth above the transome : insomuch , that adding this measure , to that of the lowness of the surface of the lake , beneath the transome before the rain , it was manifest that the rising of the lake caused by the rain , was to a hair those four fingers breadth that i had judged it to be . two dayes after i had another bout with the ingeneer , and related to him the whole business , to which he knew not what to answer . now the two difficulties which i thought of , able to impede my conclusion , were these following : first , i considered that it might be , that the wind blowing from the side where the sluice stood , to the lake-ward ; the mole and mass of the water of the lake might be driven to the contrary shore ; on which the water rising , it might be fallen at the mouth of the emissary , and so the observation might be much obscured . but this difficulty wholly vanished by reason of the aires great tranquility ; which it kept at that time , for no wind was stirring on any side , neither whilst it rained , nor afterwards . the second difficulty which put the rising in doubt , was , that having observed in florence , and elsewhere , those ponds into which the rain-water , falling from the house , is conveyed through the common-shores : and that they are not thereby ever filled , but that they swallow all that abundance of water , that runs into them by those conveyances which serve them with water ; insomuch that those conveyances which in time of drought maintain the pond , when there comes new abundance of water into the pond , they drink it up , and swallow it : a like effect might also fall out in the lake , in which there being many veins ( as it is very likely ) that maintain and feed the lake ; these veins might imbibe the new addition of the rain-water , and so by that means annull the rising ; or else diminish it in such sort , as to render it inobservable . but this difficulty was easily resolved by considering my treatise of the measure of running-waters ; forasmuch as having demonstrated , that the abatement of a lake beareth the reciprocal proportion to the velocity of the emissary , which the measure of the section of the emissary of the lake , hath to the measure of the surface of the lake : making the calculation and account , though in gross ; by supposing that its veins were sufficiently large , and that the velocity in them were notable in drinking up the water of the lake ; yet i found nevertheless , that many weeks and moneths would be spent in drinking up the new-come abundance of water by the rain , so that i rested sure , that the rising would ensue , as in effect it did . and because many of accurate judgement , have again caused me to question this rising , setting before me , that the earth being parched by the great drought , that had so long continued , it might be , that that bank of earth which environed the brink of the lake , being dry , and imbibing great abundance of water from the increasing lake , would not suffer it to increase in height : i say therefore , that if we would rightly consider this doubt here proposed , we should , in the very consideration of it , see it resolved ; for , it being supposed that that list or border of banks which was to be occupied by the increase of the lake , be a brace in breadth quite round the lake , and that by reason of its dryness it sucks in water , and that by that means this proportion of water co-operates not in raising of the lake : it is absolutely necessary on the other hand , that we consider , that the circuit of the water of the lake being thirty miles , as it s commonly held , that is to say , ninety thousand braces of florence in compass ; and therefore admitting for true , that each brace of this bank drink two quarts of water , and that for the spreading it require three quarts more , we shall finde , that the whole agregate of this portion of water , which is not imployed in the raising of the lake , will be four hundred and fifty thousand quarts of water ; and supposing that the lake be sixty square miles , three thousand braces long , we shall finde , that to dispence the water possest by the bank about the lake , above the total surface of the lake , it ought to be spread so thin , that one sole quart of water may over-spread ten thousand square braces of surface : such a thinness , as must much exceed that of a leaf of beaten gold , and also less than that skin of water which covers the bubbles of it : and such would that be , which those men would have substracted from the rising of the lake : but again , in the space of a quarter of an hour at the beginning of the rain , all that bank is soaked by the said rain , so that we need not for the moistning of it , imploy a drop of that water which falleth into the lake . besides we have not brought to account that abundance of water which runs in time of rain into the lake , from the steepness of the adjacent hills and mountains ; which would be enough to supply all our occasions : so that , neither ought we for this reason to question our pretended rising . and this is what hath fallen in my way touching the consideration of the thrasimcnian lake . after which , perhaps somewhat rashly , wandring beyond my bounds , i proceeded to another contemplation , which i will relate to you , hoping that you will receive it , as collected with these cautions requisite in such like affairs ; wherein we ought not too positively to affirm any thing of our own heads for certain , but ought to submit all to the sound and secure deliberation of the holy mother-church , as i do this of mine , and all others ; most ready to change my judgement , and conform my self alwaies to the deliberations of my superiors . continuing therefore my above-said conceit about the rising of the water in the glass tried before , it came into my minde , that the forementioned rain having been very gentle , it might well be , that if there should have faln a rain fifty , an hundred , or a thousand times greater than this , and much more intense ( which would insue as oft as those falling drops were four , five or ten times bigger than those of the above-mentioned rain , keeping the same number ) in such a case its manifest , that in the space of an hour the water would rise in our glass , two , three , and perhaps more yards or braces ; and consequently , if such a raine should fall upon a lake , that the said lake would rise , according to the same rate : and likewise , if such a rain were universall , over the whole terrestriall globe , it would necessarily , in the space of an hour , make a rising of two , or three braces round about the said globe . and because we have from sacred records , that in the time of the deluge , it rained fourty dayes and fourty nights ; namely , for the space of 960 houres ; its clear , that if the said rain had been ten times bigger than ours at perugia , the rising of the waters above the terrestrial globe would reach and pass a mile higher than the tops of the hills and mountains that are upon the superficies of the earth ; and they also would concur to increase the rise . and therefore i conclude , that the rise of the waters of the deluge have a rational congruity with natural discourses , of which i know very well that the eternal truths of the divine leaves have no need ; but however i think so clear an agreement is worthy of our consideration , which gives us occasion to adore and admire the greatnesse of god in his mighty works , in that we are sometimes able , in some sort , to measure them by the short standard of our reason . many lessons also may be deduced from the same doctrine , which i passe by , for that every man of himself may easily know them , having once stablished this maxime ; that it is not possible to pronounce any thing , of a certainty , touching the quantity of running waters , by considering only the single vulgar measure of the water without the velocity ; and so on the contrary , he that computes only the velocity , without the measure , shall commit very great errours ; for treating of the measure of running waters , it is necessary , the water being a body , in handling its quantity , to consider in it all the three dimensions of breadth , depth , and length : the two first dimensions are observed by all in the common manner , and ordinary way of measuring running waters ; but the third dimension of length is omitted ; and haply such an oversight is committed , by reason the length of running water is reputed in some sense infinite , in that it never ceaseth to move away , and as infinite is judged incomprehensible ; and such as that there is no exact knowledge to be had thereof ; & so there comes to be no account made thereof ; but if we should make strict reflection upon our consideration of the velocity of water , we should find , that keeping account of the same , there is a reckoning also made of the length ; forasmuch as whilst we say , the water of such a spring runs with the velocity of passing a thousand or two thousand paces an hour : this in substance is no other than if we had said , such a fountain dischargeth in an hour a water of a thousand or two thousand paces long . so that , albeit the total length of running water be incomprehensible , as being infinite , yet neverthelesse it s rendered intelligible by parts in its velocity . and so much sufficeth to have hinted about this matter , hoping to impart on some other occasion other more accurate observations in this affair . lavs deo . geometrical demonstrations of the measure of running waters . by d. benedetto castelli , abbot of cassina , and mathematician to p. vrban . viii . dedicated to the most illustrious , and most excellent prince don thaddeo barberini , prince of palestrina , and general of the holy church . london , printed anno domini , mdclxi . of the mensuration of running waters . supposition i. let it be supposed , that the banks of the rivers of which we speak be erected perpendicular to the plane of the upper superficies of the river . supposition ii. we suppose that the plane of the bottome of the river , of which we speak is at right angles with the banks . supposition iii. it is to be supposed , that we speak of rivers , when they are at ebbe , in that state of shallownesse , or at flowing in that state of deepnesse , and not in their transition from the ebbe to the flowing , or from the flowing to the ebbe . declaration of termes . first . if a river shall be cut by a plane at right angles to the surface of the water of the river , and to the banks of the river , that same dividing plane we call the section of the river ; and this section , by the suppositions above , shall be a right angled parallelogram . second . we call those sections equally swift , by which the water runs with equal velocity ; and more swift and less swift that section of another , by which the water runs with greater or lesse velocity . axiome i. sections equal , and equally swift , discharge equal quantities of water in equal times . axiome ii. sections equally swift , and that discharge equal quantity of water , in equal time , shall be equal . axiome iii. sections equal , and that discharge equal quantities of water in equal times , shall be equally swift . axiome iv. when sections are unequal , but equally swift , the quantity of the water that passeth through the first section , shall have the same proportion to the quantity that passeth through the second , that the first section hath to the second section . which is manifest , because the velocity being the same , the difference of the water that passeth shall be according to the difference of the sections . axiome v. if the sections shall be equal , and of unequal velocity , the quantity of the water that passeth through the first , shall have the same proportion to that which passeth through the second , that the velocity of the first section , shall have to the velocity of the second section . which also is manifest , because the sections being equal , the difference of the water which passeth , dependeth on the velocity . petition . a section of a river being given , we may suppose another equal to the given , of different breadth , heigth , and velocity . proposition i. the sections of the same river discharge equal quantities of water in equal times , although the sections themselves he unequal . let the two sections be a and b , in the river c , running from a , towards b ; i say , that they discharge equal quantity of water in equal times ; for if greater quantity of water should pass through a , than passeth through b , it would follow that the water in the intermediate space of the river c , would increase continually , which is manifestly false , but if more water should issue through the section b , than entreth at the section a , the water in the intermediate space c , would grow continually less , and alwaies ebb , which is likewise false ; therefore the quantity of water that passeth through the section b , is equal to the quantity of water which passeth through the section a , and therefore the sections of the same river discharge , &c. which was to be demonstrated . proposition ii. in two sections of rivers , the quantity of the water which passeth by one section , is to that which passeth by the second , in a proportion compounded of the proportions of the first section to the second , and of the velocitie through the first , to the velocitie of the second . let a , and b be two sections of a river ; i say , that the quantity of water which passeth through a , is to that which passeth through b , in a proportion compounded of the proportions of the first section a , to the section b ; and of the velocity through a , to the velocity through b : let a section be supposed equal to the section a , in magnitude ; but of velocity equal to the section b , and let it be g ; and as the section a is to the section b , so let the line f be to the line d ; and as the velocity a , is to the velocity by b , so let the line d be to the line r : therefore the water which passeth thorow a , shall be to that which passeth through g ( in regard the sections a and g are of equal bigness , but of 〈◊〉 equal velocity ) as the velocity through a , to the velocity through g ; but as the velocity through a , is to the velocity through g , so is the velocity through a , to the velocity through b ; namely , as the line d to the line r : therefore the quantity of the water which passe the through a , shall be to the quantity which passeth through g , as the line d is to the line r ; but the quantity which passeth through g , is to that which passeth through b , ( in regard the sections g , and b , are equally swift ) as the section g to the section b , that is , as the section a , to the section b ; that is , as the line f to the line d : therefore by the equal and perturbed proportionality , the quantity of the water which passeth through a , hath the same proportion to that which passeth through b , that the line f hath to the line r ; but f to r , hath a proportion compounded of the proportions of f to d , and of d to r ; that is , of the section a to the section b ; and of the velocity through a , to the velocity through b ▪ therefore also the quantity of water which passeth through the section a , shall have a proportion to that which passeth through the section b , compounded of the proportions of the section a , to the section b , and of the velocity through a , to the velocity through b : and therefore in two sections of rivers , the quantity of water which passeth by the first , &c. which was to be demonstrated . corollarie . the same followeth , though the quantity of the water which passeth through the section a , be equal to the quantity of water which passeth through the section b , as is manifest by the same demonstration . proposition iii. in two sections unequal , through which pass equal quantities of water in equal times , the sections have to one another , reciprocal proportion to their velocitie . let the two unequal sections , by which pass equal quantities of water in equal times be a , the greater ; and b , the lesser : i say , that the section a , shall have the same proportion to the section b , that reciprocally the velocity through b , hath to the velocity through a ; for supposing that as the water that passeth through a , is to that which passeth through b , so is the line e to the line f : therefore the quantity of water which passeth through a , being equal to that which passeth through b , the line e shall also be equal to the line f : supposing moreover , that as the section a , is to the section b , so is the line f , to the line g ; and because the quantity of water which passeth through the section a , is to that which passeth through the section b , in a proportion composed of the proportions of the section a , to the section b , and of the velocity through a , to the velocity through b ; therefore the line e , shall be the line to f , in a proportion compounded of the same proportions ; namely , of the proportion of the section a , to the section b , and of the velocity through a , to the velocity through b ; but the line e , hath to the line g , the proportion of the section a , to the section b , therefore the proportion remaining of the line g , to the line f , shall be the proportion of the velocity through a , to the velocity through b ; therefore also the line g , shall be to the line e , as the velocity by a , to the velocity by b : and conversly , the velocity through b , shall be to the velocity through a , as the line e , to the line g ; that is to say , as the section a , to the section b , and therefore in two sections , &c. which was to be demonstrated . corollarie . hence it is manifest , that sections of the same river ( which are no other than the vulgar measures of the river ) have betwixt themselves reciprocal proportions to their velocities ; for in the first proposition we have demonstrated that the sections of the same river , discharge equal quantities of water in equal times ; therefore , by what hath now been demonstrated the sections of the same river shall have reciprocal proportion to their velocities ; and therefore the same running water changeth measure , when it changeth velocity ; namely , increaseth the measure , when it decreaseth the velocity , and decreaseth the measure , when it increaseth the velocity . on which principally depends all that which hath been said above in the discourse , and observed in the corollaries and appendixes ; and therefore is worthy to be well understood and heeded . proposition iv. if a river fall into another river , the height of the first in its own chanel shall be to the height that it shall make in the second chanel , in a proportion compounded of the proportions of the breadth of the chanel of the second , to the breadth of the chanel of the first , and of the velocitie acquired in the chanel of the second , to that which it had in its proper and first chanel . let the river ab , whose height is ac , and breadth cb , that is , whose section is acb ; let it enter , i say , into another river as broad as the line ef , and let it therein make the rise or height de , that is to say , let it have its section in the river whereinto it falls def ; i say , that the height ac hath to the height de the proportion compounded of the proportions of the breadth ef , to the breadth cb , and of the velocity through df , to the velocity through ab . let us suppose the section g , equal in velocity to the section ab , and in breadth equal to ef , which carrieth a quantity of water equal to that which the section ab carrieth , in equal times , and consequently , equal to that which df carrieth . moreover , as the breadth ef is to the breadth cb , so let the line h be to the line i ; and as the velocity of df is to the velocity of ab , so let the line i be to the line l ; because therefore the two sections ab and g are equally swift , and discharge equal quantity of water in equal times , they shall be equal sections ; and therefore the height of ab to the height of g , shall be as the breadth of g , to the breadth of ab , that is , as ef to cb , that is , as the line h to the line i : but because the water which passeth through g , is equal to that which passeth through def , therefore the section g , to the section def , shall have the reciprocal proportion of the velocity through def , to the velocity through g ; but also the height of g , is to the height de , as the section g , to the section def : therefore the height of g , is to the height de , as the velocity through def , is to the velocity through g ; that is , as the velocity through def , is to the velocity through ab ; that is , finally , as the line i , to the line l ; therefore , by equal proportion , the height of ab , that is , ac , shall be to the height de ; as h to l , that is , compounded of the proportions of the breadth ef , to the breadth cb , and of the velocity through df , to the velocity through a b : so that if a river fall into another river , &c. which was to be demonstrated . proposition v. if a river discharge a certain quantitie of water in a certain time ; and after that there come into it a flood , the quantity of water which is discharged in as much time at the flood , is to that which was discharged before , whilst the river was low , in a proportion compounded of the proportions of the velocity of the flood , to the velocity of the first water , and of the height of the flood , to the height of the first water . suppose a river , which whilst it is low , runs by the section af ; and after a flood cometh into the same , and runneth through the section df , i say , that the quantity of the water which is discharged through df , is to that which is discharged through af , in a proportion compounded of the proportions of the velocity through df , to the velocity through af , and of the height db , to the height ab ; as the velocity through df is to the velocity through af ; so let the line r , to the line s ; and as the height db is to the height ab , so let the line s , to the line t ; and let us suppose a section lmn , equal to df in height and breadth ; that is lm equal to db , and mn equal to bf ; but let it be in velocity equal to the section af , therefore the quantity of water which runneth through df , shall be to that which runneth through ln , as the velocity through df , is to the velocity through ln , that is , to the velocity through af ; and the line r being to the line s , as the velocity through df , to the velocity through af ; therefore the quantity which runneth through df , to that which runneth through ln , shall have the proportion of r to s ; but the quantity which runneth through ln , to that which runneth through af , ( the sections being equally swift ) shall be in proportion as the section ln , to the section af ; that is , as db , to ab ; that is as the line s , to the line t : therefore by equal proportion , the quantity of the water which runneth through df , shall be in proportion to that which runneth through af , as r is to t ; that is , compounded of the proportions of the height db , to the height ab , and of the velocity through df , to the velocity through af ; and therefore if a river discharge a certain quantity , &c. which was to be demonstrated . annotation . the same might have been demonstrated by the second proposition above demonstrated , as is manifest . proposition vi. if two equal streams of the same torrent , fall into a river at divers times , the heights made in the river by the torrent , shall have between themselves the reciprocal proportion of the velocities acquired in the river . let a and b , be two equal streams of the same torrent , which falling into a river at divers times , make the heights cd , and fg ; that is the stream a , maketh the height cd , and the stream b , maketh the height fg ; that is , let their sections in the river , into which they are fallen , be ce , and fh ; i say , that the height cd , shall be to the height fg , in reciprocal proportion , as the velocity through fh , to the velocity through ce ; for the quantity of water which passeth through a , being equal to the quantity which passeth through b , in equal times ; also the quantity which passeth through ce , shall be equal to that which passeth through f h : and therefore the proportion that the section ce , hath to the section fh ; shall be the same that the velocity through fh , hath to the velocity through ce ; but the section ce , is to the section fh , as cd , to fg , by reason they are of the same breadth : therefore cd , shall be to fg , in reciprocal proportion , as the velocity through fh , is to the velocity through ce , and therefore if two equal streams of the same torrent , &c. which was to be demonstrated . of the mensuration of running waters . lib. ii. having , in the close of my treatise of the mensuration of running waters promised to declare upon another occasion other particulars more obscure , and of very great concern upon the same argumement : i now do perform my promise on the occasion that i had the past year 1641. to propound my thoughts touching the state of the lake of venice , a business certainly most important , as being the concernment of that most noble and most admirable city ; and indeed of all italy , yea of all europe , asia , & africa ; & one may truly say of all the whole world. and being to proceed according to the method necessary in sciences , i wil propose , in the first place certain definitions of those terms whereof we are to make use in our discourse : and then , laying down certain principles we will demonstrate some problemes and theoremes necessary for the understanding of those things which we are to deliver ; and moreover , recounting sundry cases that have happened , we will prove by practice , of what utility this contemplation of the measure of running waters is in the more important affairs both publique and private . definition i. two rivers are said to move with equal velocity , when in equal times they passe spaces of equal length . definition ii. rivers are said to move with like velocity , when their proportional parts do move alike , that is , the upper parts alike to the upper , and the lower to the lower ; so that if the upper part of one river shall be more swift than the upper part of another ; then also the lower part of the former shall be more swift than the part correspondent to it in the second , proportionally . definition iii. to measure a river , or running water , is in our sense to finde out how many determinate measures , or weights of water in a given time passeth through the river , or channel of the water that is to be measured . definition iv. if a machine be made either of brick , or of stone , or of wood , so composed that two sides of the said machine be placed at right angels upon the ends of a third side , that is supposed to be placed in the bottom of a river , parallel to the horizon , in such a manner , that all the water which runneth through the said river , passeth thorow the said machine : and if all the water coming to be diverted that runneth through the said river , the upper superficies of that third side placed in the bottom do remain uncovered and dry , and that the dead water be not above it ; this same machine shall be called by us * regulator : and that third side of the machine which standeth horizontally is called the bottom of the regulator ; and the other two sides , are called the banks of the regulator ; as is seen in this first figure : abcd , shall be the regulator ; bc the bottom ; and the other two sides ab , and cd are its banks . definition v. by the quick height , we mean the perpendicular from the upper superficies of the river , unto the upper superficies of the bottom of the regulator ; as in the foregoing figure the line . gh . definition vi. if the water of a river be supposed to be marked by three sides of a regulator , that rightangled parallelogram comprehended between the banks of the regulator , and the bottom , and the superficies of the water is called a section of the river . annotation . here it is to be noted , that the river it self may have sundry and divers heights , in several parts of its chanel , by reason of the various velocities of the water , and its measures ; as hath been demonstrated in the first book . supposition i. it is supposed , that the rivers equal in breadth , and quick height , that have the same inclination of bed or bottom , ought also to have equal velocities , the accidental impediments being removed that are dispersed throughout the course of the water , and abstracting also from the external windes , which may velocitate , and retard the course of the water of the river . supposition ii. let us suppose also , that if there be two rivers that are in their beds of equal length , and of the same inclination , but of quick heights unequal , they ought to move with like velocity , according to the sense explained in the second definition . supposition iii. because it will often be requisite to measure the time exactly in the following problems , we take that to be an excellent way to measure the time , which was shewed me many years since by signore galilaeo galilaei , which is as followeth . a string is to be taken three roman feet long , to the end of which a bullet of lead is to be hanged , of about two or three ounces ; and holding it by the other end , the plummet is to be removed from its perpendicularity a palm , more or less , and then let go , which will make many swings to and again , passing and repassing the perpendicular , before that it stay in the same : now it being required to measure the time that is spent in any whatsoever operation , those vibrations are to be numbred , that are made whilst the work lasteth ; and they shall be so many second minutes of an hour , if so be , that the string be three roman feet long , but in shorter strings , the vibrations are more frequent , and in longer , less frequent ; and all this still followeth , whether the plummet be little or much removed from its perpendicularity , or whether the weight of the lead be greater or lesser . these things being pre-supposed , we will lay down some familiar problems , from which we shall pass to the notions and questions more subtil and curious ; which will also prove profitable , and not to be sleighted in this business of waters . proposition i. probleme i. a chanel of running-water being given , the breadth of which passing through a regulator , is three palms ; and the height one palm , little more or less , to measure what water passeth through the regulator in a time given . first , we are to dam up the chanel ; so that there pass not any water below the dam ; then we must place in the side of the chanel , in the parts above the regulator three , or four , or five bent-pipes , or syphons , according to the quantity of the water that runneth along the chanel ; in such sort , as that they may drink up , or draw out of the chanel all the water that the chanel beareth ( and then shall we know that the syphons drink up all the water , when we see that the water at the dam doth neither rise higher , nor abate , but alwaies keepeth in the same level . ) these things being prepared , taking the instrument to measure the time , we will examine the quantity of the water that issueth by one of those syphons in the space of twenty vibrations , and the like will we do one by one with the other syphons ; and then collecting the whole summe , we will say , that so much is the water that passeth and runneth thorow the regulator or chanel ( the dam being taken away ) in the space of twenty second minutes of an hour ; and calculating , we may easily reduce it to hours , dayes , months , and years : and it hath fallen to my turn to measure this way the waters of mills and fountains , and i have been well assured of its exactness , by often repeating the same work . consideration . and this method must be made use of in measuring the waters , that we are to bring into conducts , and carry into cities and castles , for fountains ; and that we may be able afterwards to divide and share them to particular persons justly ; which will prevent infinite suits and controversies that every day happen in these matters . proposition ii. theorem i. if a river moving with such a certain velocitie through its regulator , shall have a given quick height , and afterwards by new water shall increase to be double , it shall also increase double in velocitie . let the quick height of a river in the regulator abcd , be the perpendicular fb , and afterwards , by new water that is added to the river , let the water be supposed to be raised to g , so that gb may be double to eb . i say , that all the water gc shall be double in velocity to that of ec : for the water gf , having for its bed the bottom ef , equally inclined as the bed bc , and its quick height ge being equal to the quick height ec , and having the same breadth bc , it shall have of it self a velocity equal to the velocity of the first water fc : but because , besides its own motion , which is imparted to it by the motion of the water ec , it hath also over and above its own motion , the motion of ec . and because the two waters gc , and ec , are alike in velocity , by the third supposition ; therefore the whole water gc shall be double in velocity to the water ec ; which was that which we were to demonstrate . this demonstration is not here inserted , as perfect , the authour having by several letters to his friends confessed himself unsatisfied therewith ; and that he intended not to publish the theorem without a more solid demonstration , which he was in hope to light upon . but being overtaken by death , he could not give the finishing touch either to this , or to the rest of the second book . in consideration of which , it seemed good to the publisher of the same , rather to omit it , than to do any thing contrary to the mind of the authour . and this he hints , by way of advertisement , to those that have manuscript copies of this book , with the said demonstration . for this time let the reader content himself with the knowledge of so ingenious and profitable a conclusion ; of the truth of which he may , with small expence and much pleasure , be assured by means of the experiment to be made in the same manner , with that which is laid down in the second corollary of the fourth theorem of this , with its table , and the use thereof annexed . corollarie hence it followeth , that when a river increaseth in quick height by the addition of new water , it also increaseth in velocity ; so that the velocity hath the same proportion to the velocity that the quick height hath to the quick height ; as may be demonstrated in the same manner . propos . iii. probleme ii. a chanel of water being given whose breadth exceeds not twenty palms , or thereabouts , and whose quick height is less than five palms , to measure the quantity of the water that runneth thorow the chanel in a time given . place in the chanel a regulator , and observe the quick height in the said regulator ; then let the water be turned away from the chanel by a chanellet of three or four palms in breadth , or thereabouts : and that being done , measure the quantity of the water which passeth thorow the said chanellet , as hath been taught in the second proposition ; and at the same time observe exactly how much the quick height shall be abated in the greater chanel , by means of the diversion of the chanellet ; and all these particulars being performed , multiply the quick height of the greater chanel into it self , and likewise multiply into it self the lesser height of the said bigger chanel , and the lesser square being taken , from the greater , the remainder shall have the same proportion to the whole greater square , as the water of the chanellet diverted , hath to the water of the bigger chanel : and because the water of the chanellet is known by the method laid down in the first theorem , and the terms of the theorem being also known , the quantity of the water which runneth thorow the bigger chanel , shall be also known by the golden rule , which was that that was desired to be known . we will explain the whole business by an example . let a chanel be , for example , 15 palms broad , its quick height before its diversion by the chanellet shall be supposed to be 24 inches ; but after the diversion , let the quick height of the chanel be onely 22 inches . therefore the greater height to the lesser , is as the number 11. to 12. but the square of 11. is 121 , and the square of 12. is 144 , the difference between the said lesser square and the greater is 23. therefore the diverted water , is to the whole water , as 23. to 144 : which is well near as 1 to 6 6 / 23 : and that is the proportion that the quantity of the water which runneth through the chanellet shall have , to all the water that runneth thorow the great chanel . now if we should finde by the rule mentioned above in the first proposition , that the quantity of the water that runneth through the chanellet , is v. g. an hundred barrels , in the space of 15 second minutes of an hour , it is manifest , that the water which runneth through the great chanel in the said time of 35 min. sec . shall be about 600 barrels . the same operation performed another way . and because very often in applying the theory to practice it happeneth , that all the necessary particulars in the theory cannot so easily be put in execution ; therefore we will here add another way of performing the same problem , if it should chance to happen that the chanellet could not commodiously be diverted from the great chanel , but that it were easier for the water of another smaller chanel to be brought into the greater chanel ; which water of the smaller chanel might be easily measured , as hath been shewen in the first probleme ; or in case that there did fall into a greater chanel , a lesser chanel that might be diverted and measured . therefore i say in the first case , if we would measure the quantity of the water that runneth in a certain time thorow the greater chanel , into which another lesser chanel that is measurable may be brought , we must first exactly measure the chanellet , and then observe the quick height of the greater chanel , before the introduction of the lesser ; and having brought in the said chanellet , we must agnin find the proportion that the water of the chanellet hath to all the water of the great chanel ; for these terms of the proportion being known , as also the quantity of the water of the chanellet , we shall also come to know the quantity of the water that runneth thorow the great chanel . it is likewise manifest , that we shall obtain our intent , if the case were that there entered into the great chanel , another lesser chanel that was measurable , and that might be diverted . consideration . it would be necessary to make use of this doctrine in the distribution of the waters that are imploy'd to overflow the fields , as is used in the brescian , cremonese , bergamase , lodigian , milanese territories , and many other places , where very great suits and differences arise , which not being to be determined with intelligible reasons , come oftentimes to be decided , by force of armes ; and instead of flowing their grounds with waters , they cruelly flow them with the shedding of humane blood , impiously inverting the course of peace and justice , sowing such disorders and feuds , as that they are sometimes accompanied with the ruine of whole cities , or else unprofitably charge them with vain , and sometimes prejudicial expences . propos . iv. theor. ii. if a river increase in quick height , the quantitie of water which the river dischargeth after the increase , hath the proportion compounded of the proportions of the quick height to the quick height , and of the velocity to the velocity . let there be a river , which whilst it is low , runneth thorow the regulator df , with the quick height ab , and afterwards let a flood come ; and then let it run with the height db , i say , that the quantity of the water that is discharged through df , to that which dischargeth through af , hath the proportion compounded of the proportions of the velocity through df to the velocity through af , and of the height db to the height ab . as the velocity through df is to the velocity through af , so let the line r be to the line s ; and as the height db is to the height ab ; so let the line s be to the line t. and let a section be supposed lmn equal to the section df in height and length , but let it be in velocity equal to the section af. therefore the quantity of the water that runneth through df to that which runneth through ln , shall be as the velocity through df , to the velocity of ln , that is , to the velocity through ln , that is , to the velocity through af. therefore the quantity of water which runneth through df , to that which passeth through ln , shall have the proportion that r hath to s ; but the quantity of the water that runneth through ln , to that which runneth through af ; ( the sections being equally swift ) shall have the proportion that the section ln hath to the section af , that is , that the height bd hath to the height ba , that is , that s hath to t. therefore , by equal proportion , the quantity of the water which runneth by df , to that which runneth by af , shall have the proportion of r to t , that is , shall be compounded of the proportions of the height db , to the height ab ; and of the velocity through df , to the velocity through af. and therefore if a river increase in quick height , the quantity of the water that runneth after the increase , to that which runneth before the increase , hath the proportion compounded , &c. which was to be demonstrated . corollarie i. hence it followeth , that we having shewn , that the quantity of the water which runneth , whilst the river is high , to that which ran , whilst it was low , hath the proportion compounded of the velocity to the velocity , and of the height to the height . and it having been demonstrated , that the velocity to the velocity is as the height to the height ; it followeth , i say , that the quantity of the water that runneth , whilst the river is high , to that which runneth , whilst it is low , hath duplicate proportion of the height to the height , that is , the proportion that the squares of the heights have . corollarie ii. vpon which things dependeth the reason of that which i have said , in my second consideration , that if by the diversion of 5 / 9 of the water that entereth by the rivers into the moor or fen , the water be abated such a measure , that same shall be only one third of its whole height ; but moreover diverting the 4 / 9 , it shall abate two other thirds , a most principal point ; and such , that it s not having been well understood , hath caused very great disorders , and there would now , more than ever , follow extream dammage , if one should put in execution the diversion of the sile and other rivers ; and it is manifest , that in the same manner , wherewith it hath been demonstrated , that the quantity of the water increasing quadruple , the height would increase onely double , and the quantity increasing nonuple , the height increaseth triple ; so that , by adding to units all the odde numbers , according to their series , the heights increase according to the natural progression of all the numbers , from units . as for example , there passing thorow a regulator such a certain quantity of water in one time ; adding three of those measures , the quick height is two of those parts , which at first was one ; and continuing to adde five of those said measures , the height is three of those parts which at first were one ; and thus adding seven , and then nine , and then 11. and then 13 , &c. the heights shall be 4. then 5 , then 6. then 7 , &c. and for the greater facility of the work , we have described the following table , of which we will declare the use : the table is divided into three series or progressions of numbers : the first series containeth all the numbers in the natural progression , beginning at a unit , and is called the series of the heights ; the second containeth all the odde numbers , beginning at an unit , and is called the series of the additions : the third containeth all the square numbers , beginning at an unit , and is called the series of quantity . heights . 1 2 3 4 5 6 7 8 9 10 11 additions . 1 3 5 7 9 11 13 15 17 19 21 quantities . 1 4 9 16 25 36 49 64 81 100 121 the use of the afore-mentioned table . first , if we suppose the whole quick height of a river of running water to be divided into any number of equal parts , at pleasure , and would abate the same one fift , by means of a division ; let there be found in the table in the series of heights the number 5. the denominator of the part which the river is to abate , and take the number that is immediately under it in the row of additions , which is 9. which let be substracted from the number 25. placed underneath the same in the row of quantities , the remainder 16. signifieth that of the 25. parts of water that ran in the river , whilst it was 5 measures high , there do onely run 16. parts ; so that to make it abate 1 / 5 it is necessary to take 9 / 25 from the water that the whole river did carry ; so that with substracting somewhat more than one third of the water of the river , it is abated but only one fift . 2. and thus , in the second place , if one the contrary , one would know how much water is to be added to the said river to make it increase one fift more in height , so as that it may run in the regulator 6. of those parts high ; of which it ran before but 5. let 6 be found in the row of heights , and let the number 11. standing under the same be taken and added to the number 25. that is placed under the number 9. in the additions , and 5. in the heights , and you shall have 36 ; which is the quantity of the water that runneth with the height of the river , when it is high 6 of those parts , whereof it was before but 5. 3. but if it should be desired , to know how much water it is requisite to add to make the river rise so , as that it may run in height 8. of those parts of which before it ran but 5 ; one ought to take the sum of the number of the series of additions standing under 8. 7. and 6 , which are 15. 13. and 11. that is , 39. and this shall be the summe that must be added to 25 : so that to make the river to run 8. of those parts in height , of which it before did run 5 , it will be necessary to add 39. of those parts , of which the river before was 25. 4. likewise the same table giveth the quantity of water that runneth from time to time through a river , that increaseth by the addition of new water to the same in one of its heights , the quantity of its water be known . as for example : if we knew that the river in one minute of an hour dischargeth 2500. of those measures of water , and runneth in height 5. parts in the regulator , and afterwards should see that it runneth 8 palms high , finding in the row of quantity the number placed under 8. which is 64. we would say that the river heightned , carrieth of water 64. of those parts whereof it carried before but 25 ; and because before it carried 2500. measures , by the golden rule we will say , that the river carrieth 6400. of those measures , of which before it carried 2500. in this progress of nature , is one thing really curious , and that at first sight seemeth to be somewhat paradoxal , that we proceeding ordinately in the diversions and additions , with additions and diversions so unequal , the abatings do notwithstanding alwaies prove equal , and so do the risings : and who would ever think that a river in height , v. g. 10. palms , running and carrying an hundred measures in a minute of an hour , is to abate but one palm , onely by the diversion of 19. of those measures ; and then again , that the buisiness cometh to that pass , that it abateth likewise a palm by the diversion of three onely of those measures , nay , by the diversion of but one measure ? and yet it is most certain : and this truth meets with so manifest proofs in experience , that it is very admirable ! and for the full satisfaction of those , who not being able to comprehend subtil demonstrations , desire to be clearly inform'd by the matters of fact , and to see with their bodily eyes , and touch with their hands , what their understanding and reason cannot reach unto : i will hear add another very easie way to reduce all to an experiment , the which may be made in little , in great , or in very great ; of which i make use frequently , to the admiration of such as see it . i prepared an hundred siphons , or , if you will , bowed pipes , all equal ; and placed them at the brim of a vessel , wherein the water is kept at one and the same level ( whether all the syphons work , or but a certain number of them ) the mouths by which the water issueth being all placed in the same level , parallel to the horizon ; but lower in level than the water in the vessel ; and gathered all the water falling from the syphons into another vessel standing lower than the former , i made it to run away thorow a chanel , in such manner inclined , that wanting water from the syphons , the said chanel remained quite dry . and this done , i measured the quick height of the chanel with care , and afterwards divided it exactly into 10 equal parts , and causing 19. of those syphons to be taken away , so that the chanel did not run water , save onely with 81 of those syphons , i again observed the quick height of the water in the same site observed before , and found that its height was diminished precisely the tenth part of all its first height ; and thus continuing to take away 17. other syphons , the height was likewise diminished 1 / 10 of all its first quick height ; and trying to take away 15. syphons , then 13 , then 11 , then 9 , then 7 , then 5 , and then 3. alwaies in these diversions , made in order as hath been said , there ensued still an abatement of 1 / 10 of the whole height . and here was one thing worthy of observation , that the water encreasing in [ or through ] the chanel , its quick height was different in different sites of the chanel , that is still lesser , the more one approached to the out-let ; notwithstanding which the abatement followed in all places proportionably , that is in all its sites the first part of the height of that site diminished : and moreover the water issued from the chanel , and dilated into a broader course , from which likewise having divers out-lets and mouths ; yet nevertheless in that breadth also the quick heights successively varied and altered in the same proportions . nor did i here desist my observation , but the water being diminished , that issued from the syphons , and there being but one of them left that discharged water ; i observed the quick height that it made in the above-said sites , ( the which was likewise 1 / 10 of all the first height ) there being added to the water of that syphon , the water of three other syphons ; so that all the water was of 4 syphons , and consequently quadruple to the first syphon ; but the quick height was onely double , and adding five siphons , the quick height became triple , and with adding seven syphons , the height increased quadruple ; and so by adding of 9. it increased quintuple , and by adding of 11. it increased sextuple , and by adding of 13. it increased septuple , and by adding of 15. octuple , and by adding of 17. nonuple , and lastly by adding 19. syphons ; so that all the water was centuple to the water of one syphon , yet nevertheless the quick height of all this water was onely decuple to the first height conjoyned by the water that issued from one onely syphon . for the more clear understanding of all which , i have made the following figure ; in which we have the mouth a , that maintaineth the water of the vessel bc in the same level ; though it continually run ; to the brim of the vessel are put 25. syphons ( and there may be many more ) divided into 5 classes , defgh , and the first d , are of one onely syphon ; the second e , of three syphons ; the third f , of five ; the fourth g , of 7 ; the fifth h , of 9 ; and one may suppose the sixth of 11 , the seventh of 13 syphons , and so of the other classes , all containing in consequent odd numbers successively ( we are content to represent in the figure no more but the five forenamed classes to avoid confusion ) the gathered water defgh , which runneth thorow the chanel ikl , and falleth into the out-let mnop ; and so much sufficeth for the explanation of this experiment . propos . v. prob. iii. any river of any bigness , if being given to examine the quantity of the water that runneth thorow the river in a time assigned . by what we have said already in the two preceding problems , we may also resolve this that we have now before us ; and it is done , by diverting in the first place from the great river a good big measurable chanel , as is taught in the second probleme , and observing the abatement of the river , caused by the diversion of the chanel ; and finding the proportion that the water of the chanel hath to that of the river , then let the water of the chanel be measured by the second probleme , and work as above , and you shall have your desire . consideration . i. and although it seemeth as if it might prove difficult , and almost impossible to make use of the regulator number , if one be about to measure the water of some great river , and consequently would be impossible , or at least very difficult to reduce the theory of the first probleme into practice : yet nevertheless , i could say that such great conceits of measuring the water of a great river , are not to come into the minds of any but great personages , and potent princes ; of whom it is expected for their extraordinary concerns , that they will make these kinde of enquiries ; as if here in italy it should be of the rivers tyber , velino , chiana , arno , serchio , adice , in which it seemeth really difficult to apply the regulator , to finde exactly the quick height of the river : but because in such like cases sometimes it would turn to account to be at some charge , to come to the exact and true knowledge of the quantity of water which that river carrieth , by knowledge whereof , other greater disbursments might afterwards be avoided , that would oft times be made in vain ; and prevent the disgusts , which sometimes happen amongst princes : upon this ground i think it will be well to shew also the way how to make use of the regulator in these great rivers ; in which if we will but open our eyes , we shall meet with good ones , and those made without great cost or labour , which will serve our turn . for upon such like rivers there are wears , or lockes made , to cause the waters to rise , and to turn them for the service of mills , or the like . now in these cases it is sufficient , that one erect upon the two extreames of the weare two pilasters either of wood or brick , which with the bottome of the weare do compose our regulator , wherewith we may make our desired operation , yea the chanel it self diverted shall serve , without making any other diversion or union . and in brief , if the businesses be but managed by a judicious person , there may wayes and helps be made use of , according to occasion , of which it would be too tedious to speak , and therefore this little that hath been hinted shall suffice . consideration ii. from what hath been declared , if it shall be well understood , may be deduced many benefits and conveniences , not onely in dividing of running waters for infinite uses that they are put to in turning of corne-mills , paper-mills , gins , powder-mills , rice-mills , iron-mills , oil-mills , sawing-mills , mirtle-mills , felling-mills , fulling-mills , silk-mills , and such other machines ; but also in ordering navigable chanels , diverting rivers and chanels of waters , or terminating and limiting the sizes of pipes for fountains : in all which affairs there are great errours com●●●ed , to the losse of much expence , the chanels and pipes that are made , sometimes not being sufficient to carry the designed waters , and sometimes they are made bigger than is necessary ; which disorders shall be avoided , if the engineer be advised of the things abovesaid : and in case that to these notions there be added the knowledge of philosophy and mathematicks , agreeable to the sublime discoveries of signore galilaeo , and the further improvement thereof by signore evangelista torricelli , mathematician to the grand duke of tuscany , who hath subtilly and admirably handled this whole businesse of motion , one shall then come to the knowledge of particular notions of great curiosity in the theoricks , and of extraordinary benefit in the practicks that daily occur in these businesses . and to shew , in effect , of what utility these notions are , i have thought fit to insert , in this place , the considerations by me made upon the lake of venice , and to represent , at large , by the experience of the last year 1641. the most serene erizzo , then duke of the said republique . being therefore at venice , in the year aforesaid , i was requested by the most illustrious and most excellent signore giovanni basadonna , a senatour of great worth and merit , that i would ingenously deliver my opinion touching the state of the lake of venice ; and after i had discoursed with his honour several times , in the end i had order to set down the whole businesse in writing , who having afterwards read it privately , the said signore imparted the same , with like privacy , to the most serene prince , and i received order to represent the same to the full colledge , as accordingly i did in the moneth of may , the same year , and it was as followeth . considerations concerning the lake of venice . by d. benedetto castelli , abbot of s. benedetto aloysio , mathematician to pope vrban viii . and professor in rome . consideration i. though the principal cause be but one onely , that in my judgment threatneth irreparable ruine to the lake of venice , in the present state in which it now stands ; yet neverthelesse , i think that two heads may be considered . and this consideration may peradventure serve us for to facilitate and explain the opportune remedies , though not to render the state of things absolutely unchangeable and eternal : an enterprize impossible , and especially in that which having had some beginning , ought likewise necessarily to have its end ; or at least to prevent the danger for many hundreds of years ; and possibly it may , in the mean time , by the mutation it self be brought into a better condition . i say therefore , that the present disorder may be considered under two heads ; one is the very notable discovery of land that is observed at the time of low water , the which , besides the obstructing of navigation in the lake and also in the chanels , doth likewise threaten another mischief and disorder worthy of very particular consideration , which is , that the sun drying up that mudde , especially in the times of hot summers , doth raise thence the putrified and pernicious vapours , fogs , and exhalations that infect the air , and may render the city unhabitable . the second head is the great stoppage that daily is growing in the ports , especially of venice , at malamoco ; concerning which matters i will hint certain general points , and then will proceed to the more particular and important affairs . and first , i say , that i hold it altogether impossible to effect any thing , though never so profitable , which doth not bring with it some mischief ; and therefore the good and the hurt ought to be very well weighed , and then the lesse harmful part to be imbraced . secondly , i propose to consideration , that the so notable discovery of earth & mud , hath not been long observed , as i understand , from old persons that can remember passages for fifty years past ; which thing being true , as to me it seemeth most true , it should appear that it could not but be good to reduce matters to that passe that they were at formerly , ( laying aside all affection or passion that self-flattering minds have entertained for their own conceits ) or at least it shall be necessary speedily to consult the whole . thirdly , i hold that it is necessary to weigh , whether from the foresaid discovery of land , it followeth , that onely the earth riseth , as it is commonly thought by all , without dispute ; or whether the waters are abated and faln away ; or else whether it proceedeth from both the one and other cause . and here it would be seasonable to enquire , what share the said causes may have , each considered apart in the foresaid effect . for , in the first case , if the earth have been raised , it would be necessary to consider of taking it down , and removing it : but if the waters have failed or abated , i believe that it would be extreamly necessary to restore and raise them : and if both these reasons have conspired in this effect , it will be necessary to remedy them each apart . and i do , for my part , think , that the so notable appearance of shelves at the time of low water , proceeds principally from the decrease and abatement of the waters , which may confidently be affirmed to need no other proof , in regard that the brent hath been actually diverted which did formerly discharge its water into the lake . as to the other point of the great stoppage of ports , i hold , that all proceedeth from the violence of the sea , which being sometimes disturbed by windes , especially at the time of the waters flowing , doth continually raise from its bottome immense heaps of sand , carrying them by the tide ; and force of the waves into the lake ; it not having on its part any sttength of current that may raise and carry them away , they sink to the bottom , and so they choke up the ports . and that this effect happeneth in this manner , we have most frequent experiences thereof along the sea-coasts : and i have observed in tuscany on the roman-shores , and in the kingdom of of naples , that when a river falleth into the sea , there is alwaies seen in the sea it self , at the place of the rivers out-let , the resemblance , as it were , of an half-moon , or a great shelf of settled sand under water , much higher then the rest of the shore , and it is called in tuscany , il cavallo ; and here in venice , lo s●anto : the which cometh to be cut by the current of the river , one while on the right side ; another while on the left , and sometimes in the midst , according as the wind sits . and a like effect i have observed in certain little rillets of water , along the lake of bolsena ; with no other difference , save that of small and great . now whoso well considereth this effect , plainly seeth that it proceeds from no other , than from the contrariety of the stream of the river , to the impetus of the sea-waves ; seeing that great abundance of sand which the sea continually throws upon the shore , cometh to be driven into the sea by the stream of the river ; and in that place where those two impediments meet with equal force , the sand setleth under water , and thereupon is made that same shelf for cavallo ; the which if the river carry water , and that any considerable store , it shall be thereby cut and broken ; one while in one place , and another while in another ; as hath been said , according as the wind blows : and through that chanel it is that vessels fall down into the sea , and again make to the river , as into a port. but if the water of the river shall not be continual or shall be weak , in that case the force of the sea-wind shall drive such a quantity of sand into the mouth of the port , and of the river , as shall wholly choak it up . and hereupon there are seen along the sea-side , very many lakes and meers , which at certain times of the year abound with waters , and the lakes bear down that enclosure , and run into the sea. now it is necessary to make the like reflections on our ports of venice , malamocco , bondolo , and chiozza ; which in a certain sense are no other than creeks , mouths , and openings of the shore that parts the lake from the main sea ; and therefore i hold that if the waters in the lake were plentiful , they would have strength to scowr the mouths of the ports thorowly , & with great force ; but the water in the lake failing , the sea will without any opposal , bring such a drift of sand into the ports ; that if it doth not wholly choke them up , it shall render them at least unprofitable , and impossible for barks and great vessels . many other considerations might be propounded concerning these two heads of the stoppage of the ports , and of the appearance of the ouze and mud in the lakes , but so much shall suffice us to have hinted , to make way for discoursing of the operations about the oportune remedies . yet before that i propound my opinion , i say , that i know very well that my proposal , at first sight , will seem absurd and inconvenient ; and therefore , as such , will perhaps be rejected by the most : and so much the rather , for that it will prove directly contrary to what hath hitherto been , and as i hear , is intended to be done : and i am not so wedded to my opinions , but that i do consider what others may judge thereof : but be it as it will , i am obliged to speak my thoughts freely , and that being done , i will leave it to wiser men than my self ; when they shall have well considered my reasons , to judge and deliberate of the quid agendum : and if the sentence shall go against me , i appeal to the most equitable and inexorable tribunal of nature , who not caring in the least to please either one party or another , will be alwaies a punctual and inviolable executrix of her eternal decrees , against which neither humane deliberations , nor our vain desires , shall ever have power to rebell . i added by word of mouth that which followeth . though your highness interest your self in this noble colledge , and cause it to be confirmed in the * senate by universal vote , that the winds do not blow , that the sea doth not fluctuate , that the rivers do not run ; yet shall the winds be alwaies deaf , the sea shall be constant in its inconstancy , and the rivers most obstinate : and these shall be my judges , and to their determination i refer my self . by what hath been said , in my opinion , that is made very clear and manifest , which in the beginning of this discourse i glanced at ; namely , that the whole disorder , although it be divided into two heads , into the discovery of the mud , and of the stoppage ports , yet nevertheless , by the application of one onely remedy , and that in my esteem very easie , the whole shall be removed : and this it is ; that there be restored into the lake as much water as can be possible , and in particular from the upper parts of venice , taking care that the water be as free from mud as is possible . and that this is the true and real remedy of the precedent disorders , is manifest : for in the passage that this water shall make thorow the lakes , it shall of it self by degrees clear the chanels in sundry parts of them , according to the currents that it shall successively acquire , and in this manner being dispersed thorow the lake , it shall maintain the waters in the same , and in the chanels much higher , as i shall prove hereafter ; a thing that will make navigation commodious ; and that , which moreover is of great moment in our businesse ; those shelves of mud which now discover themselves at the time of low-waters shall be alwayes covered , so that the putrefaction of the air shall also be remedied . and lastly , this abundance of water being alwayes of discharge it self into the sea by the ports , i do not doubt , but that their bottomes will be scoured . and that these effects must follow , nature her self seemeth to perswade , there remaining onely one great doubt , whether that abundance of water that shall be brought into the lake may be really sufficient to make the waters rise so much as to keep the shelves covered , and to facilitate navigation , which ought to be at least half a * brace , or thereabouts . and indeed it seemeth at first sight to be impossible , that the sole water of the * brent let into the lake , and dispersed over the same , can occasion so notable an height of water ; and the more to confirm the difficulties , one might say , reducing the reason to calculation , that in case the brent were 40. braces broad , and two and an half high , and the breadth of the lake were 20000. braces , it would seem necessary that the height of the water of the brent dilated and distended thorow the lake would be but onely 1 / 200 of a brace in height , which is imperceptible , and would be of no avail to our purpose ; nay more , it being very certain that the brent runneth very muddy and foul , this would occasion very great mischief , filling and contracting the lake , and for that reason this remedy ought , as pernicious , to be totally excluded and condemned . i here confesse that i am surprized at the forme of the argument , as if i were in a certain manner convinced , that i dare not adventure to say more , or open my mouth in this matter ; but the strength it self of the argument , as being founded upon the means of gemoetrical and arithmetical calculation , hath opened me the way to discover a very crafty fraud that is couched in the same argument , which fraud i will make out to any one that hath but any insight in geometry and arithmetick . and as it is impossible , that such an argument should be produced by any but such as have tasted of these , in such affairs , most profitable , and most necessary sciences ; so do not i pretend to make my self understood , save onely by such , to whom i will evince so clearly , as that more it cannot be desired , the errour and fraud wherein those ancients and moderns have been , and alwayes are intangled , that have in any way yet handled this matter of considering the measure and quantity of the waters that move . and so great is the esteem that i have for that which i am now about to say touching this particular , that i am content that all the rest of my discourse be rejected ; provided , that that be perfectly understood , which i am hereafter to propose , i holding and knowing it to be a main principle , upon which all that is founded that can be said either well or handsomely on this particular . the other discourses may have an appearance of being probable , but this hits the mark as full as can be desired , arriving at the highest degree of certainty . i have , seventeen years since , as i represented to the most serene prince , and to the right honourable the president of the lords the commissioners of the * sewers , written a treatise of the measure of the waters that move , in which i geometrically demonstrate and declare this businesse , and they who shall have well understood the ground of my discourse , will rest fully satisfied with that which i am now about to propose : but that all may become rhe more easie , i will more briefly explicate and declare so much thereof as i have demonstrated in the discourse , which will suffice for our purpose : and if that should not be enough , we have alwayes the experiment of a very easie and cheap way to clear up the whole businesse . and moreover i will take the boldnesse to affirm , that in case there should not for the present any deliberation be made concerning this affair , according to my opinion ; yet neverthelesse it will be , at some time or other ; or if it be not , things will grow worse and worse . for more clear understanding , therefore , it ought to be known , that it being required , as it is generally used , to measure the waters of a river , its breadth and its depth is taken , and these two dimensions being multiplied together , the product is affirmed to be the quantity of that river : as for example , if a river shall be 100. feet broad , and 20. feet high , it will be said , that that river is 2000 feet of water , and so if a ditch shall be 15. feet broad , and 5. feet high , this same ditch will be affirmed to be 75. feet of water : and this manner of measuring running water hath been used by the ancients , and by moderns , with no other difference , save onely that some have made use of the foot , others of the palme , others of the brace , and others of other measures . now because that in observing these waters that move , i frequently found , that the same water of the same river was in some sites of its chanel pretty big , and in others much lesse , not arriving in some places to the twentieth , nor to the hundreth part of that which it is seen to be in other places ; therefore this vulgar way of measuring the waters that move , for that they did not give me a certain and stable measure and quantity of water , began deservedly to be suspected by me , as difficult and defective , being alwayes various , and the measure , on the contrary , being to be alwayes determinate , and the same ; it is therefore written , that pondus & pondus , mensura & mensura , utrumque abominabile est apud deum , exod. i considered that in the territory of brescia , my native countrey , and in other places , where waters are divided to overflow the grounds , by the like way of measuring them , there were committed grievous and most important errours , to the great prejudice of the publique and of private persons , neither they that sell , nor they that buy understanding the true quantity of that which is sold and bought : in regard that the same square measure , as is accustomed in those parts , assigned one particular person , carried to sometimes above twice or thrice as much water , as did the same square measure assigned to another . which thing proveth to be the same inconvenience , as if the measure wherewith wine and oil is bought and sold , should hold twice or thrice as much wine or oil at one time as at another . now this consideration invited my minde and curiosity to the finding out of the true measure of running waters . and in the end , by occasion of a most important businesse that i was imployed in some years since , with great intensenesse of minde , and with the sure direction of geometry , i have discovered the mistake , which was , that we being upon the businesse of taking the measure of the waters that move , do make use of two dimensions onely , namely , breadth and depth , keeping no account of the length . and yet the water being , though running , a body , it is necessary in forming a conceit of its quantity , in relation to another , to keep account of all the three dimensions , that is of length , breadth , and depth . here an objection hath been put to me , in behalf of the ordinary way of measuring running waters , in opposition to what i have above considered and proposed : and i was told , it s true , that in measuring a body that stands still , one ought to take all the three dimensions ; but in measuring a body that continually moveth , as the water , the case is not the same : for the length is not to be had , the length of the water that moveth being infinite , as never finishing its running ; and consequently is incomprehensible by humane understanding , and therefore with reason , nay upon necessity it cometh to be omitted . in answer to this , i say , that in the abovesaid discourse , two things are to be considered distinctly ; first , whether it be possible to frame any conceit of the quantity of the body of the water with two dimensions onely . and secondly , whether this length be to be found . as to the first , i am very certain that no man , let him be never so great a wit , can never promise to frame a conceit of the quantity of the body of water , without the third dimension of length : and hereupon i return to affirm , that the vulgar rule of measuring running water is vain and erroneous . this point being agreed on , i come to the second , which is , whether the third dimension of length may be measured . and i say , that if one would know the whole length of the water of a fountain or river , thereby to come to know the quantity of all the water , it would prove an impossible enterprize , nay the knowing of it would not be useful . but if one would know how much water a fountain , or a river carrieth in a determinate time of an hour , of a day , or of a moneth , &c. i say , that it is a very possible and profitable enquiry , by reason of the innumerable benefits that may be derived thence , it much importing to know how much water a chanel carrieth in a time given ; and i have demonstrated the same above in the beginning of this book ; and of this we stand in need in the businesse of the lake , that so we may be able to determine how much shall be the height of the brent , when it is spread all over the lake : for the three dimensions of a body being given , the body is known ; and the quantity of a body being given , if you have but two dimensions , the third shall be known . and thus diving farther and farther into this consideration , i found that the velocity of the course of the water may be an hundred times greater or lesser in one part of its chanel than in another . and therefore although there should be two mouths of waters equal in bignesse ; yet nevertheless it might come to passe , that one might discharge an hundred or a thousand-times more water than another : and this would be , if the water in one of the mouths should run with an hundred or a thousand times greater velocity , than the other ; for that it would be the same as to say , that the swifter was an hundred or a thousand times longer , than the slower : and in this manner i discovered that to keep account of the velocity , was the keeping account of the length . and therefore it is manifest , that when two mouths discharge the same quantity of water in an equal velocity , it is necessary that the less swift mouth be so much bigger than the more swift ; as the more swift exceedeth in velocity the less swift ; as for example . in case two rivers should carry equal quantity of water in equal times , but that one of them should be four times more swift than the other , the more slow should of necessity be four times more large . and because the same river in any part thereof alwaies dischargeth the same quantity of water in equal times ( as is demonstrated in the first proposition of the first book * of the measure of running waters ; ) but yet doth not run thorowout with the same velocity : hence it is , that the vulgar measures of the said river , in divers parts of its chanel , are alwaies divers ; insomuch , that if a river passing through its chanel had such velocity , that it ran 100 braces in the 1 / 60 of an hour-and afterwards the said river should be reduced to so much tardi , ty of motion , as that in the same time it should not run more than one brace , it would be necessary that that same river should become 100. times bigger in that place where it was retarded ; i mean , 100. times bigger than it was in the place where it was swifter . and let it be kept well in mind , that this point rightly understood , will clear the understanding to discover very many accidents worthy to be known . but for this time let it suffice , that we have onely declared that which makes for our purpose , referring apprehensive and studious wits to the perusal of my aforenamed treatise ; for therein he shall finde profit and delight both together . now applying all to our principal intent , i say , that by what hath been declared it is manifest , that if the brent were 48. braces broad , and 2 ½ high , in some one part of its chanel , that afterwards the same water of the brent falling into the lake , and passing thorow the same to the sea , it should lose so much of its velocity , that it should run but one brace , in the time wherein whilst it was in its chanel at the place aforesaid , it ran 100. braces . it would be absolutely necessary , that increasing in measure , it should become an hundred times * thicker ; and therefore if we should suppose that the lake were 20000. braces , the brent that already hath been supposed in its chanel 100. braces , being brought into the lake , should be 100. times 100. brates ; that is , shall be 10000. braces in thickness , and consequently shall be in height half a brace ; that is , 100 / 200 of a brace , and not 1 / 200 of a brace , as was concluded in the argument . now one may see into what a gross errour of 99. in 100. one may fall through the not well understanding the true quantity of running water , which being well understood , doth open a direct way to our judging aright in this most considerable affair . and therefore admitting that wich hath been demonstrated , i say , that i would ( if it did concern me ) greatly encline to consult upon the returning of the brent again into the lake : for it being most evident , that the brent in the chanel of its mouth , is much swifter than the brent being brought into the lake , it will certainly follow thereupon , that the thickness of the water of brent in the lake , shall be so much greater than that of brent in brent , by how much the bront in brent is swifter than thh brent in the lake . 1. from which operation doth follow in the first place , that the lake being filled and increased by these waters , shall be more navigable , and passible , than at present we see it to be . 2. by the current of these waters , the chanels will be scoured , and will be kept clean from time to time . 3. there will not appear at the times of low-waters so many shelves , and such heaps of mud , as do now appear . 4. the ayr will become more wholesom , for that it shall not be so infected by putrid vapours exhaled by the sun , so long as the miery ouze shall be covered by the waters . 5. lastly , in the current of these advantagious waters , , which must issue out of the lake into the sea , besides those of the tyde , the ports will be kept scoured , and clear : and this is as much as i shall offer for the present , touching this weighty business ; alwaies submitting my self to sounder judgements . of the above-said writing i presented a copy at venice , at a full colledge , in which i read it all , and it was hearkned to with very great attention ; and at last i presented it to the duke , and left some copies thereof with sundry senators , and went my way , promising with all intenseness to apply my pains with reiterated studies in the publick service ; and if any other things should come into my minde , i promised to declare them sincerely , and so took leave of his serenity , and that noble council . when i was returned to rome , this business night and day continually running in my mind , i hapned to think of another admirable and most important conceit , which with effectual reasons , confirmed by exact operations , i with the divine assistance , made clear and manifest ; and though the thing at first sight seemed to me a most extravagant paradox , yet notwithstanding , having satisfied my self of the whole business , i sent it in writing to the most illustrious and most noble signore gio. basadonna ; who after he had well considered my paper , carried it to the council ; and after that those lords had for many months maturely considered thereon , they in the end resolved to suspend the execution of the diversion which they had before consulted to make of the river sile , and of four other rivers , which also fall into the lake ; a thing by me blamed in this second paper , as most prejudicial , and harmful . the writing spake as followeth . considerations concerning the lake of venice . part ii. if the discoursing well about the truth of things , most serene prince , were as the carrying of burdens , in which we see that an hundred horses carry a greater weight than one horse onely ; it would seem that one might make more account of the opinion of many men , than of one alone ; but because that discoursing more resembleth running , than carrying burdens , in which we see that one barb alone runneth faster than an hundred heavy-heel'd jades ; therefore i have ever more esteemed one conclusion well managed , and well considered by one understanding man , although alone , than the common and vulgar opinions ; especially , when they concern abstruce and arduous points : nay in such cases the opinions moulded and framed by the most ignorant and stupid vulgar , have been ever suspected by me as false , for that it would be a great wonder if in difficult matters a common capacity should hit upon that which is handsom , good , and true . hence i have , and do hold in very great veneration the summe of the government of the most serene , and eternal republick of venice ; which although , as being in nature a common-wealth , it ought to be governed by the greater part ; yet nevertheless , in arduous affairs , it is alwaies directed by the grave judgement of few , and not judged blindly by the plebeian rout. t is true , that he that propoundeth propositions far above the reach of common capacity , runneth a great hazard of being very often condemned without further process , or knowledge of the cause ; but yet for all that , the truth is not to be deserted in most weighty affairs , but ought rather to be explained in due place and time with all possible perspicuity ; that so being well understood , and considered , it may come afterwards for the common good to be embraced . this which i speak in general , hath often been my fortune in very many particulars , not onely when i have kept within the bounds of meer speculation , but also when i have chanced to descend to practice , and to operations : and your highness knoweth very well what befel me the last summer 1641. when in obedience to your soveraign command , i did in full colledge represent my thoughts touching the state of the lake of venice ; for there not being such wanting , who without so much as vouchsafing to understand me , but having onely had an inkling , and bad apprehension of my opinion , fell furiously upon me , and by violent means both with the pen and press , full of gall , did abuse me in reward of the readiness that i had exprest to obey and serve them : but i was above measure encouraged and pleased , to see that those few who vouchsafed to hear me , were all either thorowly perswaded that my opinion was well grounded , or at least suspended their prudent verdict to more mature deliberation . and though at the first bout i chanced to propose a thing that was totally contrary to the most received and antiquated opinion , and to the resolutions and consultations taken above an hundred years ago : moved by these things , and to satisfie also to the promise that i had made of tendering unto them what should farther offer it self unto me touching the same business ; i have resolved to present to the throne of your highness , another consideration of no less importance , which perhaps at first sight will appear a stranger paradox ; but yet brought to the test and touch-stone of experience , it shall prove most clear and evident . if it shall be accounted of , so that it succeedeth to the benefit of your highness , i shall have obtained my desire and intent : and if not , i shall have satisfied my self , and shall not have been wanting to the obligation of your most faithful servant , and native subject . that which i propounded in the mouths pass , touching the most important business of the lake , though it did onely expresly concern the point of the diversion of the mouth of the lake , already made and put in execution ; yet it may be understood and applyed also to the diversion under debate , to be made of the other five rivers , and of the sile in particular . now touching this , i had the fortune to offer an admirable accident that we meet with when we come to the effect , which i verily believe will be an utter ruine to the lake of venice . i say therefore , that by diverting these five rivers that remain , although their water that they discharge for the present into the lake is not all taken together 4 / 5 parts of what the brent alone did carry , yet neverthelesse the abatement of the water of the lake which shall ensue upon this last diversion of four parts , which was the whole water , shall prove double to that which hath happened by the diversion of brent onely , although that the brent alone carried five parts of that water , of which the rivers that are to be diverted carry four : a wonder really great , and altogether unlikely ; for the reducing all this proposition to be understood , is as if we should say , that there being given us three rivers , of which the first dischargeth five parts , the second three , and the third one , and that from the diversion of the first , there did follow such a certain abatement or fall ; from the taking away of the second there ought to follow also so much more abatement ; and lastly , from the withdrawing of the third the water ought to fall so much more , which is wholly impossible : and yet it is most certain , and besides the demonstration that perswades me to it , which i shall explain in due time , i can set before your eyes such an experiment as is not to be denied by any one , although obstinate : and i will make it plainly seen and felt , that by taking away only four parts of the five , which shall have been taken away , the abatement proveth double to the abatement ensuing upon the diverting first of the five onely ; which thing being true , as most certainly it is , it will give us to understand how pernicious this diversion of five rivers is like to prove , if it shall be put in execution . by this little that i have hinted , and the much that i could say , let your highnesse gather with what circumspection this businesse ought to be managed , and with how great skill he ought to be furnished who would behave himself well in these difficult affairs . i have not at this time explained the demonstration , nor have i so much as propounded the way to make the experiment , that i am able to make in confirmation of what i have said , that so by some one or others mis-apprehending the demonstration , and maiming the experiment , the truth may not happen to shine with lesse clarity than it doth , when all mists of difficulty are removed : and if so be , no account should be made of the reasons by me alledged , and that men should shut their eyes against the experiments that without cost or charge may be made , i do declare and protest that there shall follow very great dammages to the fields of the main land , and extraordinary summes shall be expended to no purpose . the lake undoubtedly will become almost dry , and will prove impassible for navigation , with a manifest danger of corrupting the air : and in the last place there will unavoidably ensue the choaking and stoppage of the ports of venice . upon the 20th . of december , 1641. i imparted this my second consideration to the most excellent signore basadonna , presenting him with a copy thereof amongst other writings , which i have thought good to insert , although they seem not to belong directly to our businesse of the lake . the way to examine the mud and sand that entereth and remaineth in the lake of venice . to the most excellent signore gio. basadonna . two very considerable objections have been made against my opinion concerning the lake of venice : one was that , of which i have spoken at large in my first consideration , namely , that the brents having been taken out of the lake , cannot have been the occasion of the notable fall of the waters in the lake , as i pretend , and consequently , that the turning brent into the lake would be no considerable remedy , in regard that the water of brent , and the great expansion of the lake over which the water of brent is to diffuse and spread being considered , it is found that the rise proveth insensible . the second objection was , that the brent is very muddy , and therefore if it should fall muddy into the lake , the sand would sink and fill up the same . touching the first query , enough hath been said in my first consideration , where i have plainly discovered the deceipt of the argument , and shewn its fallacy ; it remaineth now to examine the second : to which in the first place i say , that one of the first things that i proposed in this affair was , that i held it impossible to do any act , though never so beneficial , that was not also accompanied by some inconvenience and mischief ; and therefore we are to consider well the profit , and the losse and prejudice ; and they both being weighed , we shall be able to choose the lesser evil : secondly , i admit it to be most true , that brent is at some times muddy , but it is also true , that for the greater part of the year it is not muddy . thirdly , i do not see nor understand what strength this objection hath , being taken so at large , and in general ; and methinks that it is not enough to say , that the brent runneth muddy , and to assert that it deposeth its muddinesse in the lake , but we ought moreover to proceed to particulars , and shew how much this mud is , and in what time this choaking up of the ports may be effected . for the reasons are but too apparent and particular , that conclude the ruine of the lake , and that in a very short time , ( for mention is made of dayes ) the waters diversion being made , and moreover we have the circumstance of an experiment , the state of things being observed to have grown worse since the said diversion . and i have demonstrated , that in case the diversion of the sile and the other rivers should be put in execution , the lake would in a few dayes become almost dry ; and the ports would be lost , with other mischievous consequences . but on the other side , although that we did grant the choaking of them , we may very probably say , that it will not happen , save onely in the succession of many and many centuries of years . nor can i think it prudent counsel to take a resolution and imbrace a designe now , to obtain a benefit very uncertain , and more than that , which only shall concern those who are to come very many ages after us , and thereby bring a cetain inconvenience upon our selves , and upon our children that are now alive and present . let it be alledged therefore , ( although i hold it false ) that by the diversions of the rivers the lake may be kept in good condition for several years to come . but i say confidently , and hope to demonstrate it ; that the diversions will bring the lake , even in our dayes , to be almost dry , and at least will leave so little water in it , that it shall cease to be navigable , and the ports shall most infallibly be choaked up . i will therefore say upon experience , in answer to this objection , that it is very necessary first well to discourse , and rationally to particularize and ascertain the best that may be this point of the quantity of this sinking mud or sand. now i fear i shall make my self ridiculous to those , who measuring the things of nature with the shallownesse of their brains do think that it is absolutely impossible to make this enquiry , and will say unto me , quis mensus est pugillo aquas , & terram palmo ponderavit ? yet nevertheless i will propound a way whereby , at least in gross , one may find out the same . take a vessel of cylindrical figure , holding two barrels of water , or thereabouts ; and then fill it with the water of brent , at its mouth or fall into the lake ; but in the lake at the time that the brent runneth muddy , and after it hath begun to run muddy for eight or ten hours , to give the mud time to go as far as s. nicolo , to issue into the sea ; and at the same time take another vessel , like , and equal to the first , and fill it with the water of the lake towards s. nicolo , ( but take notice that this operation ought to be made at the time when the waters go out , and when the sea is calm ) and then , when the waters shall have setled in the aforesaid vessels , take out the clear water , and consider the quantity of sand that remains behind , and let it be set down , or kept in mind : and i am easily induced to think , that that shall be a greater quantity of sand which shall be left in the first vessel , than that left in the second vessel . afterwards when the brent shall come to be clear , let both the operations be repeated , and observe the quantity of sand in the aforesaid vessels ; for if the sand in the first vessel should be most , it would be a sign , that in the revolution of a year the brent would depose sand in the lake : and in this manner one may calculate to a small matter what proportion the sand that entreth into the lake , hath to that which remains : and by that proportion one may judge how expedient it shall be for publick benefit . and if at several times of the year you carefully repeat the same operations , or rather observations , you would come to a more exact knowledge in this business : and it would be good to make the said operations at those times , when the lake is disturbed by strong high winds , and made muddy by its own mud , raised by the commotion of the waters . this notion would give us great light , if the same observations should be made towards the mouth of lio , at such time as the waters flow and ebb , in calm seasons ; for so one should come to know whether the waters of the lake are more thick at the going out , than at the entrance . i have propounded the foregoing way of measuring sands and mud , to shew that we are not so generally , and inconsiderately to pronounce any sentence , but proceed to stricter inquiries , and then deliberate what shall be most expedient to be done . others may propose more equisite examinations , but this shall serve me for the present . i will add onely , that if any one had greater curiosity ( it would be profitable to have it ) in investigating more exactly the quantity of the water that entereth into the lake , by the means that i have shewen in the beginning of this book : when he shall have found the proportion of the quantity of water to the quantity of sand or mud , he shall come to know how much sand the brent shall leave in the lake in the space of a year . but to perform these things , there are required persons of discretion , and fidelity , and that are imployed by publick order ; for there would thence result eminent benefit and profit . here are wanting letters from several persons . to the reverend father , francesco di s. giuseppe . in execution of the command that you laid upon me in your former letters , by order from the most serene , my lord , prince leopold ; that i should speak my judgement concerning the disimboguement of the river called fiume morto , whether it ought to be let into the sea , or into serchio ; i say , that i chanced 18. years since to be present , when the said mouth was opened into the sea , and that of serchio stopt ; which work was done to remedy the great innundation that was made in all that country , and plain of pisa , that lyeth between the river arno , and the mountains of s. giuliano , and the river serchio ; which plain continued long under water , insomuch that not onely in the winter , but also for a great part of the summer , those fields were overflowed ; and when that the mouth of fiume morto was effectually opened into the sea , the place was presently freed from the waters . and drained , to the great satisfaction of the owners of those grounds . and here i judge it worth your notice , that for the generality of those that possess estates in those parts , they desired that the mouth of fiume morto might stand open to the sea , and those who would have it open into serchio , are persons that have no other concernment there , save the hopes of gaining by having the dispose of commissions , and the like , &c , but for the more plain understanding of that which is to be said , it must be known , that the resolution of opening the said mouth into serchio , was taken in the time of the great duke ferdinando the first , upon the same motives that are at this time again proposed , as your letters tell me , since that , it manifestly appearing , that fiume morto had , and hath its mouth open to the sea , the plain hath been kept dry ; and it being also true , that the fury of the south , and south-west-winds carryed such abundance of sand into the mouth , or out-let of fiume morto , that it wholly stopt it up : especially when the waters on pisa side were low and shallow , and they think , that turning the lake of fiume morto into serchio , and the serchio maintaining continually its own mouth with the force of its waters open to the sea , and consequently also fiume morto , they would have had the out-let clear and open ; and in this manner they think , that the plain of pisa would have been freed from the waters . the business passeth for current , at first sight ; but experience proveth the contrary , and reason confirmeth the same : for the height of the water of those plains , was regulated by the height of the waters in the mouth of fiume morto ; that is , the waters at the mouth being high , the waters also do rise in the fields ; and when the waters at the mouth are low , the waters of the fields do likewise abate : nor is it enough to say , that the out-let or vent of fiume morto is continual , but it must be very low : now if fiume morto did determine in serchio , it is manifest that it would determine high ; for serchio terminating in the sea , when ever it more and more aboundeth with water , and riseth , it is necessary that also fiume morto hath its level higher , and consequently shall keep the waters in the plains higher . nay , it hath happened sometimes ( and i speak it upon my own sight ) that fiume morto hath reversed its course upwards towards pisa ; which case will ever happen , whensoever the pisan waters chance to be lower than the level of those of serchio ; for in that case the waters of serchio return back upon the plains thorow fiume morto in such sort , that the muddinesses , and the serchio have been observed to be carried by this return as farr as the walls of pisa ; and then before such time as so great waters can be asswaged , which come in with great fury , and go out by little and little , there do pass very many days , and moneths , nay sometimes one being never able to find the waters of serchio , when at the shallowest , so low as the sea in level ; ( which is the lowest place of the waters ) it thence doth follow , that the waters of fiume morto should never at any time of the year , so long as they determine in serchio , be so low ; as they come to be when the same fiume morto determineth in the sea. t is true indeed , that the mouth of fiume morto , opened into the sea , is subject to the inconvenience of being stopt up by the force of winds : but in this case , it is necessary to take some pains in opening it ; which may easily be done , by cutting that sand a little which stayeth in the mouth , after that the wind is laid , and it is enough if you make a trench little more than two palms in breadth ; for the water once beginning to run into it , it will in a few hours carry that sand away with it , and there will ensue a deep and broad trench that will drain away all the water of the plains in very little time . and i have found by practice , that there having been a great quantity of sand driven back , by the fury of the south-west-wind , into the mouth of fiume morto , i having caused the little gutter to be made in the morning , somewhat before noon , a mouth hath been opened of 40. braces wide , and notably deep , insomuch that the water , which before had incommoded all the champian ran away in less than three dayes , and left the country free and dry , to the admiration of all men . there was present upon the place , at this business , on the same day that i opened the mouth , the most serene great duke , the most serene arch-dutchess mother , all the commissioners of sewers ; with many other persons and peasants of those parts ; and they all saw very well , that it was never possible that a little bark of eight oars , which was come from legorn to wait upon the great duke , should ever be able to master the current , and to make up into fiume morto ; and his highness , who came with an intent to cause the said mouth towards the sea to be stopt ; and that into serchio to be opened , changed his judgement , giving order that it should be left open towards the sea , as it was done . and if at this day it shall return into serchio , i am very certain that it will be necessary to open it again into the sea. and there was also charge and order given to a person appointed for the purpose , that he should take care to open the said mouth , as hath been said upon occasion . and thus things have succeeded very well unto this very time . but from the middle of october , until this first of february , there having continued high south , and south-west-winds , with frequent and abundant rains ; it is no wonder that some innundation hath happened ; but yet i will affirm , that greater mischiefs would have followed , if the mouth had been opened into serchio . this which i have hitherto said , is very clear and intelligible to all such as have but competent insight , and indifferent skill in these affairs . but that which i am now about to propose farther , will , i am very certain , be understood by your self , but it will seem strange and unlikely to many others . the point is , that i say , that by raising the level of fiume morto , one half brace , onely at its mouth , ( it will penipenitrate into serchio farther than it would into the sea ) it shall cause the waters to rise three , or perhaps more braces upon the fields towards pisa , and still more by degrees as they shall recede farther from the sea-side ; and thus there will follow very great innundations , and considerable mischiefs . and to know that this is true , you are to take notice of an accident , which i give warning of in my discourse of the measure of running waters : where also i give the reason thereof , * coroll . 14. the accident is this , that there coming a land-flood , for example , into arno , which maketh it to rise above its ordinary mouth wthin pisa , or a little above or below the city six or seven braces ; this same height becometh alwaies lesser and lesser , the more we approach towards the sea-side ; insomuch , that near to the sea the said river shall be raised hardly half a brace : whence it followeth of necessary consequence , that should i again be at the sea-side , and knowing nothing of what hapneth , should see the river arno raised by the accession of a land-flood , one third of a brace ; i could certainly infer , that the same river was raised in pisa those same six or seven braces . and that which i say of arno , is true of all rivers that fall into the sea. which thing being true , it is necessary to make great account of every small rising , that fiume morto maketh towards the sea-side by falling into serchio . for although the rising of fiume morto , by being to disgorge its waters into serchio , towards the sea , were onely a quarter of a brace ; we might very well be sure , that farr from the sea , about pisa , and upon those fields the rise shall be much greater , and shall become two or three braces : and because the countrey lyeth low , that same ●ise will cause a continual innundation ▪ of the plains , like as it did before ; i caused the mouth to be opened into the sea. and therefore i conclude that the mouth of fiume morto , ought by no means to be opened into serchio ; but ought to be continued into the sea , using all diligence to keep it open after the manner aforesaid , so soon as ever the wind shall be laid . and if they shall do otherwise , i confidently affirm , that there will daily follow greater damages ; not onely in the plains , but also in the wholesomness of the air ; as hath been seen in times past . and again , it oughs with all care to be procured , that no waters do by any means run or fall from the trench of libra , into the plain of pisa , for these waters being to discharge into fiume morto , they maintain it much higher than is imagined , according to that which i have demonstrated in my consideration upon the state of the lake of venice . i have said but little , but i speak to you , who understandeth much , and i submit all to the most refined judgment of our most serene prince leopold , whose hands i beseech you in all humility to kiss in my name , and implore the continuance of his princely favour to me ; and so desiring your prayers to god for me , i take my leave . rome 1. feb. 1642. your most affectionate servants , d. benedetto castelli . the answer to a letter written by bartolotti , touching the difficultyes observed . the former part of the letter is omitted , and the discourse beginneth at the first head. and first i say , whereas i suppose that the level of the serchio is higher than that of fiume morto ; this is most true , at such time as the waters of fiume morto are discharged into the sea ; but i did never say that things could never be brought to that pass , as that the level of fiume morto should be higher than serchio : and so i grant that it will follow , that the waters of fiume morto shall go into serchio , and it s very possible , that the drain of fiume morto into serchio may be continuate ; and i farther grant , that its possible , that the serchio doth never disgorge thorow fiume morto towards pisa ; nay , i will yet farther grant that it might have happened , that fiume morto might have had such a fall into serchio , as would have sufficed to have turned mills : but then i add withall , that the plains of pisa , and the city it self must be a meer lake . 2. signore bartolotti saith confidently , that when the sea swelleth by the south-west , or other winds , the level of serchio in the place marked a in the platt , distant about 200. braces , riseth very little : but that fiume morto in d , and in e , many miles more up into land riseth very much , and that certain fishermen confirm this , and shew him the signes of the rising of the water . i grant it to be very true , and i have seen it with my own eyes : but this cometh to pass , when the mouth of fiume morto is stopt up by the sea ; as i shall shew by and by . and this rising near the sea-side , is of no considerable prejudice to the fields . and this is as much as i find to be true in the assertion of signore bartolotti , ( without his confirming it by any other proof ; as indeed it needs none ) that the level of fiume morto riseth in e , and many miles farther upwards it riseth much ; nor did i ever affirm the contrary . 3. concerning the difficulty of opening the mouth of fiume morto into the sea , that which il castellano saith is most certain ; namely , that at the entrance upon the opening of the mouth , it is necessary to make a deep trench : but i say , that at that time it is difficult to open it , unless upon great occasions ; for that the difficulty proceedeth from the waters of fiume morto being low , and the fields drained . 4. as to the particular of the causes that you tell me men press so much unto the most serene grand duke , and to the prince , i have not much to say , because it is not my profession ; nor have i considered of the same : yet i believe , that when the prince and his highnesse see the benefit of his people and subjects in one scale of the ballance , and the accomodation of huntsmen in the other , his highnesse will incline to the profit of his subjects ; such have i alwayes found his clemency and noblenesse of minde . but if i were to put in my vote upon this businesse , i would say , that the points of spears , and the mouths of guns , the yelping of dogs , the wilynesse of huntsmen , who run thorow and narrowly search all those woods , thickets and heathes , are the true destroyers of bucks and boares , and not a little salt-water , which setleth at last in some low places , and spreadeth not very far . yet neverthelesse , i will not enter upon any such point , but confine my self solely to the businesse before me . 5. that experiment of joyning together the water of fiume morto , and that of serchio by a little trench to see what advantage the level e hath upon the level i , doth not give me full satisfaction , taken so particularly , for it may come to passe , that sometimes e may be higher , and sometimes a lower , and i do not question but that when serchio is low , and fiume morto full of water , the level of fiume morto will be higher than that of serchio . but serchio being full , and fiume morto scant of water , the contrary will follow , if the mouth shall be opened to the sea. and here it should seem to me , that it ought to be considered , that there is as much advantage from e to the sea through the little trench opened anew into serchio , as from e to the sea by the mouth of fiume morto . but the difficulty ( which is that we are to regard in our case ) is , that the course of the waters thorow the trench is three times longer than the course of the mouth of fiume morto , as appeareth by the draught or plat which you sent me , which i know to be very exactly drawn , for that the situation of those places are fresh in my memory . here i must give notice , that the waters of fiume morto determining thorow the trench in serchio ( the waters of which fiume morto are , for certain , never so low as the sea ) their pendency or declivity shall , for two causes , be lesse than the pendency of those waters through the mouth towards the sea , that is , because of the length of the line through the trench , and because of the height of their entrance into serchio , a thing which is of very great import in discharging the waters which come suddenly , as he shall plainly see , who shall have understood my book of the measure of running waters . and this was the reason why all the countrey did grow dry upon the opening of the mouth into the sea. and here i propose to consideration that which the peasants about pisa relate , namely , that the water in the fields doth no considerable harm by continuing there five or six , yea , or eight dayes . and therefore the work of the countrey is to open the mouth of fiume morto , in such manner , that the water being come , they may have the trench free and ready , when that the water cometh it may have a free drain , and may not stay there above eight or nine dayes , for then the overflowings become hurtful . it is to be desired also , that if any proposition is produced touching these affairs , it might be propounded the most distinctly that may be possible , and not consist in generals , especially when the dispute is of the risings , of velocity , of tardity , of much and little water ; things that are all to be specified by measures . 6. your letter saith , in the next place , that signore bartolotti confesseth , that if the mouth of the fiume morto might alwayes be kept open , it would be better to let it continue as it is : the which , that i may not yield to him in courtesie , i confesse , for the keeping it stopt on all sides would be a thing most pernicious . but admitting of his confession i again reply , that fiume morto ought not to be let into serchio , but immediately into the sea ; because although sometimes the mouth to sea-wards be stopt up , yet for all that , the raising of the bank above the plains ( which is all the businesse of importance ) shall be ever lesser , if we make use of the mouth leading to the sea , than using that of serchio . 7. i will not omit to mention a kinde of scruple that i have concerning the position of sign . bartolotti , that is , where he saith that the two mouths a and d are equal to the like mouths into the sea ; now it seems to me , that the mouth a of fiume morto into serchio is absolutely within serchio , nor can it be made lower , and is regulated by the height of serchio : but the mouth of fiume morto terminates , and ought to be understood to terminate in the sea it self , the lowest place . and this i believe was very well perceived by sig. bartolotti , but i cannot tell why he past it over without declaring it : and we see not that the mouth d falleth far from the sea , which mouth ought to be let into the sea it self , and so the advantage of the mouth into the sea more clearly appeareth . 8. that which sig. bartolotti addeth , that when it is high waters , at such time as the waters are out , and when winds choak up fiume morto , they not only retard it , but return the course of the waters upwards very leasurely , perswadeth me more readily to believe that sig. bartolotti knoweth very well , that the mouth of fiume morto let into serchio is hurtful : for by this he acknowledgeth that the mouth towards the sea doth in such sort drain the countrey of the waters , as that they become very low ; and therefore upon every little impetus the waters turn their course : and from the motions , being exceeding slow , is inferred , that the abundance of sea-water that cometh into fiume morto , is so much as is believed , and as sig. bartolotti affirmeth . 9. after that sig. bartolotti hath said what he promiseth above , namely , that when the windes blowing strongly do stop up fiume morto , and not onely retard but turn the course upwards , the time being rainy , and the mouth of fiume morto shut up , the waves of the sea passe over the bank of fiume morto ; at that time , saith signore bartolotti , the champain shall know the benefit of fiume morto discharged into serchio , and the mouth a shall stand alwayes open ; and fiume morto may alwayes constantly run out , as also the rains and rain-waters , although the hurtful tempest should last many dayes , &c. and i reply , that all the art consists in this ; for the benefit of those fields doth not depend on , or consist in saying , that fiume morto is alwayes open , and fiume morto draineth continually ; but all the businesse of profit lyeth and consisteth in maintaining the waters low in those plaines , and those ditches , which shall never be effected whilst the world stands , if you let fiume morto into serchio ; but yet it may , by opening the mouth into the sea : and so much reason and nature proveth , and ( which importeth ) experience confirmeth . 10. in the tenth place i come to consider the answer that was made to another proposition in the letter which i writ to father francesco , which prudently of it self alone might serve to clear this whole businesse . i said in my letter , that great account is to be made of every small rising and ebbing of the waters neer to the sea in fiume morto , for that these risings and fallings , although that they be small neer to the sea-side , yet neverthelesse , they operate and are accompanied by notable risings and fallings within land , and far from the sea-side , and i have declared by an example of arno , in which a land-flood falling , that made it increase above its ordinary height within pisa six or seven braces , that this height of the same flood becometh still lesser , the neerer we approach to the sea-coasts . nor shall the said river be raised hardly half a brace ; whereupon it necessrily followeth , that if i should return to the sea-side , and not knowing any think of that which happeneth at pisa , and seeing the river arno raised by a land-flood half a brace , i might confidently affirm the said river to be raised in pisa those six or seven braces , &c. from such like accidents i conclude in the same letter , that it is necessary to make great account of every little rise that fiume morto shall make towards the sea. now cometh bartolotti ( and perhaps because i knew not how to express my self better , understandeth not my proposition ) and speaketh that which indeed is true , but yet besides our case : nor have i ever said the contrary ; and withall doth not apply it to his purpose . nay i say , that if he had well applyed it , this alone had been able to have made him change his opinion . and because he saith , that i said , that it is true , when the abatement proceedeth from some cause above , as namely by rain , or opening of lakes ; but when the cause is from below , that is , by some stop , as for instance some fishers wears or locks , or some impediment remote from the sea , although at the level it shall rise some braces where the impediment is , yet that rising shall go upwards ; and here he finisheth his discourse , and concludeth not any thing more . to which i say first , that i have also said the same in the proposition , namely , that a flood coming ( which maketh arno to rise in pisa six or seven braces ( which i take to be a superiour cause whether it be rain or the opening of lakes , as best pleaseth bartolotti ) in such a case i say , and in no other ( for towards the sea-coasts it shall not cause a rising of full half a brace ; and therefore seeing arno at the sea-side to be raised by a flood , whether of rain , or of opening of lakes half a brace ) it may be inferred , that at pisa it shall be raised those six or seven braces ; which variety , well considered , explaineth all this affair in favour of my opinion : for the rising that is made by the impediment placed below , of fishing weares and locks , operateth at the beginning , raising the waters that are neer to the impediment ; and afterwards less and less , as we retire upwards from the impediment : provided yet that we speak not of a flood that commeth by accession , but onely of the ordinary water impeded . but there being a new accession , as in our case , then the water of the flood , i say , shall make a greater rising in the parts superiour , far from the impediment ; and these impediments shall come to be those that shall overflow the plains , as happened eighteen or nineteen years ago , before the opening of fiume morto into the sea , the same will certainly follow , if fiume morto be let into serchio . here i could alledge a very pretty case that befell me in la * campagna di roma , neer to the sea-side . where i drained a bog or fen , of the nature of the waters of pisa , and i succeeded in the enterprize , the waters in their site towards the sea abating only three palmes , and yet in the fen they fell more than fifteen palmes . but the businesse would be long , and not so easily to be declared , and i am certain that sig. bartolotti having considered this , would alter his judgment , and withall would know that remitting that impediment anew , which i had left for lesse than three i almes towards the sea , the waters in the fen would return with the first floods and raines to the same height as before , as likewise fiume morto will do if it shall be let again into serchio . here i intreat your honour to do me the favour to importune p. francesco in my behalf , that he would be pleased to declare my meaning in the aforesaid letter to sig. bartolotti , for i hope that if he will understand this point , he will be no longer so tenacious in his opinion . next that these lords in the commission of sewers , with the right honourable the marquesse of s. angelo , and your honour do approve of my judgment , doth very much rejoyce me ; but because that i know that they do it not in design to complement me , but onely to serve his highness our grand duke , i freely profess that i will pretend no farther obligations from them therein , than i account my self to owe to those whose opinions are contrary to mine , for that i know that they have the same end . the definitive sentence of this whole business is , that they give these plains , these draines , and these waters farre fetcht appellations . 11. as to the quantity of the water that fiume morto dischargeth into the sea , there are very great disputes about it , and i have been present at some of them . but let your honour believe me , that as this is not continual , but only during a few dayes , so it will never be of any great prejudice to these fields ; and if your lordship would be ascertained thereof , you may please to go to fiume morto at about a mile's distance from the sea , in the time of these strong windes , and observe the current from thence upwards , for you shall finde it extream slow , and consequently will know that the quantity of the water that is repuls'd is very small . and this seems to be contradicted by the rule of risings proceeding from causes below , which occasion no considerable alteration far from the sea. i am necessitated to go to morrow out of rome with his eminence cardinal gaetano about certain affairs touching waters , therefore i shall not farther inlarge , but for a close to this tedious discourse , i conclude in few words , that fiume morto is by no means to be let into serchio , nor are there any means intermediate courses to be taken , for they will alwayes be prejudicial ; but fiume morto is to be discharged immediately into the sea. when it is stopt up by the fury of the sea-waves , i affirm that it is a sign that there is no need of opening it ; and if there be any occasion to open it , it is easily done . as for the rest your lordship may please to keep account of all the particulars that occur , for the memory of things past is our tutresse in those that are to come . if occasion shall offer , i intreat you to bow humbly in my name to his highness the grand duke , and the most serene prince leopold ; and to attend the service of their highnesses , for you serve princes of extraordinary merit ; and to whom i my self am also exceedingly obliged . in the controversies that arise respect the pious end of speaking the truth , for then every thing will succeed happily . i kiss the hands of padre francesco , of sig. bartolotti , and of your lordship . rome , 14. march 1642. your honours most obliged servant d. benedetto castelli . vpon this occasion i will here insert a discourse that i made upon the draining and improvement of the pontine fens , for that i think that whatsoever may be done well and to purpose in this matter hath absolute dependance on the perfect knowledge of that so important proposition , by me demonstrated and explained in my treatise of the mensuration of running waters , namely , that the same water of a river doth continually change measures , according as it altereth and changeth the velocity of its course ; so that the measure of the thicknesse of a river in one site , to the measure of the same river in another site , hath the same proportion reciprocally that the velocity in this site hath to the velocity in the first site . and this is a truth so constant and unchangeable , that it altereth not in the least point on any occurrences of the waters that change : and being well understood , it openeth the way to the knowledge of sundry advertisements in these matters , which are all resolved by this sole principle ; and from it are derived very considerable benefits ; and without these it is impossible to do any thing with absolute perfection . a consideration upon the draining of the pontine fenns . by d. benedetto castelli , abbot of s. benedetto aloisio , and professor of the methematicks to p. vrban viii . in the university of rome . consideration iii. amongst the enterprizes by me esteemed , if not absolutely impossible , , at least exceeding difficult , one was that famous one of draining the pontine fenns ; and therefore i was thorowly resolved never to apply my minde thereunto , although by my patrons i should be commanded to the same : accounting that it was an occasion rather of losing reputation by the miscarriage of the attempt , than of gaining fame by reducing things to a better pass then they now are at . yet nevertheless , having of late years observed the place , and sailed through those chanels , and those waters ; after i had made some reflection thereupon , i thought that the enterprize was not so difficult as i had at first conceited it to be ; and i am the more confirmed in this opinion , upon the inducement of that which i have written geometrically in my treatise of the mensuration of running waters ; so that talking with several persons , i adventured to affirm , in discoures , that this improvement might possibly be brought into a good estate . now i have resolved to set down my thoughts in writing , and to honour this my paper with the noble name of your lordship , to render it the more credible and conspicuous at the first view , if it should chance that the subject i treat of , were not of such moment , as that it did deserve to be valued for any other reason . pardon me , sir , if i have been too bold , and continue me in the number of your servants . the enterprize of draining a great part of the territories of the pontine fenns , hath been undertaken both in the time of the antient romans , and last of all , in our days ; yea in the late times by sixtus v. i do not doubt in the least , but that it will be possible yet to reduce things to a very good pass ; and if i be not mistaken , with a very small charge in comparison of the profit that would be received from those rich grounds . this improvement was of great expence in the time of sixtus quintus , but by reason the thing was not rightly understood , there were made many drains ; a great part of which were unprofitable and vain : and amongst so many operations , there hapned some to be made that succeeded , as was desired ; but not being understood , they were held in no account ; and thus the business being neglected , the waters are returned into the same state as they were at first , before the improvement . here i have by familiar discourses with my friends , explained this enterprize undertaken by sixtus v. and haply also by some more antient , with the example of the fable of orilo , in ariosto . this monster was made up with such enchantment , that men fought with him alwayes in vain ; for though in the combate he were cut in pieces , those divided members presently re-united , and returned to the fight more fierce then ever . but the paladine astolfo coming to undertake him , after a long dispute , at the end he cut his head sheer off from the shoulders at one blow ; and nimbly alighting from his horse , took the monstrous head , and mounting again , as he rid away he fell to shave the pole of that monster , and so he lost the lock of hair , in which alone the enchantment lay ; and then the horrible head in an instant manifested signs of death , and the trunk which ran , seeking to reunite to it anew , gave the last gasp , and in this manner the enchantment ended . the book of fate served admirably to the paladine , whereby he came to understand that charm ; for by shaving his whole head , the enchanted hairs came to be cut off amongst the rest : in the same manner , i say , that i● hath sometimes happened in draining those fields ; for that amongst so many tryals as have been made , that also was light upon , on which the improvement and remedy to the disorder did depend . and to us my fore-named treatise shall serve for a rule , which being well understood , shall make us to know wherein consisteth , and whereon dependeth this miscarriage , and consequently it will be easie to apply thereunto a seasonable remedy . another head to which these harms may be reduced , but proceeding from the same root , which hath a great part in this disorder , is the impediment of those wears in the river which are made by heightning the bed of the same , for placing of fishing-nets ; of which piscaries i reckoned above ten , when i made a voyage thorow those waters to sandolo . and these fishing-wears are such impediments , that some one of them makes the water of the river in the upper part to rise half a palm , and sometimes a whole palm , and more ; so that when they are all gathered together , these impediments amount to more than seven , or possibly than eight palms . there concurreth for a third most potent cause of the waters continuing high in the evacuating , or draining chanel , and consequently on the plains ; the great abundance of water that issueth from fiume sisto , the waters of which do not keep within its banks when they are abundant ; but encreasing above its chanel , they unite with those of the evacuator , and dispersing thorow the fens are raised with great prejudice , and much greater than is conceived , according to what hath been demonstrated in the second consideration upon the lake of venice . nor is it to any purpose to say , that if we should measure all the waters that disimbogue from fiume sisto , and gather them into one summe , we should not finde them to be such , as that they shall be able to make the waters of the fens to increase , by reason of the great expansion of them , over which that body of water is to distend : for to this instance we answer with that which we have given notice of in the first consideration touching the lake of venice , treating of the abatement that is caused by the brent let into the lake . and moreover , if i shall adde thereto that which i write in the second consideration , it will be very apparent how greatly harmfull and prejudicial these excursions of waters from fiume sisto may be , which are not kept under , and confined within the river : therefore , proceeding to the provisions , and operations that are to be accounted principall , i reduce them to three heads . in the first place it is necessary to throw down those weares , and to take the pisciaries quite away , observing a maxime , in my judgment , infallible , that fishing and sowing are two things that can never consist together ; fishing being on the water , and sowing on land . secondly , it will be necessary to cut under water in the bottome of the river those weeds and plants that grow and increase in the river , and leave them to be carried into the sea by the stream ; for by this means these reeds shall not spring up and distend along the bottome of the river , by means of the beasts treading upon them ; and the same ought to be done often , and with care , and must not be delaied till the mischief increase , and the champain grounds be drowned , but one ought to order matters so , as that they may not drown . and i will affirm , that otherwise this principal point would become a most considerable inconvenience . thirdly , it is necessary to make good the banks of fiume sisto on the left hand , and to procure that those waters may run in the chanel , and not break forth . and it is to be noted , that it is not enough to do one or two of those things , but we are to put them all in execution ; for omitting any thing , the whole machine will be out of tune , and spoiled . but proceeding with due care , you shall not only drain the pontine fens , but by means of this last particular the current of fiume sisto shall scowr its own chanel of its self , even to the carrying part of it away : and haply with this abundance of water that it shall bear , the mouth della torre may be opened , and kept open into the sea. and it would , last of all , be of admirable benefit to cleanse fiume sisto from many trees and bushes wherewith it is overgrown . and with this i conclude , that the improvement or drain possible to be made consisteth in these three particulars . first , in taking away the fishing weares , leaving the course of the waters free . secondly , in keeping the principal rivers clear from weeds and plants . thirdly , in keeping the water of fiume sisto in its own chanel . all which are things that may be done with very little charge , and to the manifest benefit of the whole country , and to the rendering the air wholsomer in all those places adjoyning to the pontine fens . a consideration upon the draining of the territories of bologna , ferrara , and romagna . by d. benedetto castelli , abbot of s. benedetto aloisio , mathematician to p. vrban viii . and professor in the university of rome . the weghty businesse of the draining of the territories of bologna , ferrara , and romagna having been punctually handled and declared in writing from the excellent memory of the right honourable and noble monsignore corsini , who was heretofore deputed commissary general , and visitor of those waters ; i am not able to make such another discourse upon the same subject , but will only say somewhat for farther confirmation of that which i have said in this book upon the lake of venice , upon the pontine fens , and upon the draining of those plains of pisa , lying between the rivers arno and serchio ; whereby it is manifest , that in all the aforementioned cases , and in the present one that we are in hand with , there have , in times past , very grosse errours been committed , through the not having ever well understood the true measure of running waters ; and here it is to be noted , that the businesse is , that in venice , the diversion of the waters of the lake , by diverting the brent was debated , and in part executed , without consideration had how great abatement of water might follow in the lake , if the brent were diverted , as i have shewn in the first consideration upon this particular , from which act there hath insued very bad consequences , not only the difficulty of navigation , but it hath infected the wholsomnesse of the air , and caused the stoppage of the ports of venice . and on the contrary , the same inadvertency of not considering what rising of the water the reno , and other rivers being opened into the valleys of bologna and ferrara , might cause in the said valleys , is the certain cause that so many rich and fertile fields are drowned under water , converting the happy habitations and dwellings of men into miserable receptacles for fishes : things which doubtlesse would never have happened , if those rivers had been kept at their height , and reno had been turn'd into main-po , and the other rivers into that of argenta , and of volano . now there having sufficient been spoken by the above-named monsig . corsini in his relation , i will only adde one conceit of my own , which after the rivers should be regulated , as hath been said , i verily believe would be of extraordinary profit , i much doubt indeed that i shall finde it a hard matter to perswade men to be of my mind , but yet nevertheless i will not question , but that those , at least , who shall have understood what i have said and demonstrated concerning the manners and proportions , according to which the abatements and risings of running waters proceed , that are made by the diversions and introductions of vvaters , will apprehend that my conjecture is grounded upon reason , and although i descend not to the exactnesse of particulars , i will open the way to others , who having observed the requisite rules of considering the quantity of the waters that are introduced , or that happen to be diverted , shall be able with punctuality to examine the whole businesse , and then resolve on that which shall be expedient to be done . reflecting therefore upon the first proposition , that the risings of a running water made by the accession of new water into the river , are to one another , as the square-roots of the quantity of the water that runneth ; and consequently , that the same cometh to pass in the diversions : insomuch , that a river running in height one such a certain measure , to make it encrease double in height , the water is to be encreased to three times as much as it ran before ; so that when the water shall be quadruple , the height shall be double ; and if the water were centuple , the height would be decuple onely , and so from one quantity to another : and on the contrary , in the diversions ; if of the 100. parts of water that run thorow a river , there shall be diverted 19 / 100 , the height of the river diminisheth onely 1 / 10 , and continuing to divert 17 / 100 , the height of the river abateth likewise 1 / 10 , and so proceeding to divert 15 / 100 and then 13 / 100 , and then 11 / 100 , and then 9 / 100 , and then 7 / 100 , and then 5 / 100 , and then 3 / 100 , alwaies by each of these diversions , the height of the running water diminisheth the tenth part : although that the diversions be so unequal . reflecting i say upon this infallible truth , i have had a conceit , that though the reno and other rivers were diverted from the valleyes , and there was onely left the chanel of navigation , which was onely the 1 / 20 part of the whole water that falleth into the valleys ; yet nevertheless , the water in those same valleyes would retain a tenth part of that height that became conjoyned by the concourse of all the rivers : and therefore i should think that it were the best resolution to maintain the chanel of navigation ( if it were possible ) continuate unto the po of ferrara , and from thence to carry it into the po of volano , for besides that it would be of very great ease in the navigation of bologna , and ferrara , the said water would render the po of volano navigable as far as to the very walls of ferrara , and consequently the navigation would be continuate from bologna to the sea-side . but to manage this enterprize well , it is necessary to measure the quantity of the water that the rivers discharge into the valleys , and that which the chanel of navigation carryeth , in manner as i have demonstrated at the beginning of this book ; for this once known , we shall also come to know , how profitable this diversion of the chanel of navigation from the valleys is like to prove ; which yet would still be unprofitable , if so be that all the rivers that discharge their waters into the valleys , should not first be drained , according to what hath been above advertised . abbot castelli , in the present consideration referring himself to the relation of monsig . corsini , grounded upon the observations and precepts of the said abbot ; as is seen in the present discourse . i thought it convenient for the compleating of the work of our authour , upon these subjects , to insert it in this place . a relation of the waters in the territories of bologna and ferrara . by the right honourable and illustrious , monsignore corsini , a native of tuscany , superintendent of the general drains , and president of romagna . the rheno , and other brooks of romagna , were by the advice of p. agostino spernazzati the jesuite , towards the latter end of the time of pope clement viii . notwithstanding the opposition of the bolognesi , and others concerned therein , diverted from their chanels , for the more commodious cleansing of the po of ferrara , and of its two branches of primaro , and volano ; in order to the introducing the water of the main-po into them , to the end that their wonted torrents being restored , they might carry the muddy-water thence into the sea , and restore to the city the navigation which was last , as is manifest by the brief of the said pope clement , directed to the cardinal san clemence , bearing date the 22. of august , 1604. the work of the said cleansing , and introducing of the said po , either as being such in it self , or by the contention of the cardinal legates then in these parts ; and the jarrings that hapned betwixt them , proved so difficult , that after the expence of vast summs in the space of 21. years , there hath been nothing done , save the rendring of it the more difficult to be effected . interim , the torrents with their waters , both muddy and clear , have damaged the grounds lying on the right hand of the po of argenta , and the rheno those on its banks ; of which i will speak in the first place , as of that which is of greater importance , and from which the principal cause of the mischiefs that result from the rest doth proceed . this rheno having overflowed the * tennency of sanmartina , in circumference about fourteen miles given it before , and part of that of cominale given it afterwards , as it were , for a receptacle ; from whence , having deposed the matter of its muddiness , it issued clear by the mouths of masi , and of lievaloro , into the po of primaro , and of volano ; did break down the encompassing bank or dam towards s. martino , and that of its new chanel on the right hand neer to torre del fondo . by the breaches on this side it streamed out in great abundance from the upper part of cominale , and in the parts about raveda , pioggio , caprara , ghiare di reno , sant ' agostino , san prospero , san vincenzo , and others , and made them to become incultivable : it made also those places above but little fruitful , by reason of the impediments that their draines received , finding the conveyances called riolo and scorsuro , not only filled by la motta and la belletta , but that they turned backwards of themselves . but by the mouths in the inclosing bank or dam at borgo di s. martino issuing with violence , it first gave obstruction to the ancient navigation of la torre de la fossa , and afterwards to the moderne of the mouth of masi , so that at present the commerce between bologna and ferrara is lost , nor can it ever be in any durable way renewed , whilst that this exceeds its due bounds , and what ever moneys shall be imployed about the same shall be without any equivalent benefit , and to the manifest and notable prejudice of the * apostolick chamber . thence passing into the valley of marzara , it swelleth higher , not only by the rising of the water , but by the raising of the bottome , by reason of the matter sunk thither after land-floods , and dilateth so , that it covereth all the meadows thereabouts , nor doth it receive with the wonted facility the drains of the upper grounds , of which the next unto it lying under the waters that return upwards by the conveyances , and the more remote , not finding a passage for rain-waters that settle , become either altogether unprofitable or little better . from this valley , by the trench or ditch of marzara , or of la duca by la buova , or mouth of castaldo de rossi , and by the new passage it falleth into the po of argenta , which being to receive it clear , that so it may sink farther therein , and receiving it muddy , because it hath acquired a quicker course , there will arise a very contrary effect . here therefore the superficies of the water keeping high , until it come to the sea , hindereth the valleys of ravenna , where the river senio , those of san bernardino where santerno was turned , those of buon ' acquisto , and those of marmorto , where the idice , quaderna , sellero fall in , from swallowing and taking in their waters by their usual in-lets , yet many times , as i my self have seen in the visitation , they drink them up plentifully , whereupon , being conjoyned with the muddinesse of those rivers that fall into the same , they swell , and dilate , and overflow some grounds , and deprive others of their drains in like manner as hath been said of that of marrara , insomuch that from the point of s. giorgio , as far as s. alberto all those that are between the valleys and po are spoiled , of those that are between valley and valley many are in a very bad condition , and those that are some considerable space above not a little damnified . in fine , by raising the bottom or sand of the valleys , and the bed of reno , and the too great repletion of the po of primaro with waters , the valleys of comacchio ( on which side the banks are very bad ) and * polesine di s. giorgio are threatned with a danger , that may in time , if it be not remedied , become irreparable , and at present feeleth the incommodity of the waters , which penetrating thorow the pores of the earth do spring up in the same , which they call purlings , which is all likely to redound to the prejudice of ferrara , so noble a city of italy , and so important to the ecclesiastick state. which particulars all appear to be attested under the hand of a notary in the visitation which i made upon the command of his holinesse , and are withall known to be true by the * ferraresi themselves , of whom ( besides the request of the bolognesi ) the greater part beg compassion with sundry memorials , and remedies , aswell for the mischiefs past , as also for those in time to come , from which i hold it a duty of conscience , and of charity to deliver them . pope clement judged , that the sufficient means , to effect this was the said introduction of the main po into the chanel of ferrara ; a resolution truly heroical , and of no lesse beauty than benefit to that city , of which i speak not at present , because i think that there is need of a readier and more accomodate remedy . so that i see not how any other thing can be so much considerable as the removal of reno , omitting for this time to speak of * inclosing it from valley to valley untill it come to the sea , as the dukes of ferrara did design , forasmuch as all those ferraresi that have interest in the polesine di s. giorgio , and on the right hand of the po of argenta do not desire it , and do , but too openly , protest against it ; and because that before the chanel were made as far as the sea , many hundreds of years would be spent , and yet would not remedy the dammages of those who now are agrieved , but would much increase them , in regard the valleys would continue submerged , the drains stopped , and the other brooks obstructed , which would of necessity drown not a few lands that lie between valley and valley ; and in fine , in regard it hath not from san martina to the sea for a space of fifty miles a greater fall then 19 , 8 , 6 , feet , it would want that force which they themselves who propound this project do require it to have , that so it may not depose the matter of the muddiness when it is intended to be let into volana . so that making the line of the bottome neer to vigarano , it would rise to those prodigious termes that they do make bigger , and they may thence expect those mischiefs , for which they will not admit of introducing it into the said po of volana . amongst the wayes therefore that i have thought of for effecting that same remotion , and which i have caused to be viewed by skilful men that have taken a level thereof , ( with the assistance of the venerable father , d. benedetto castelli of casina , a man of much fidelity and honesty , and no less expert in such like affairs touching waters , than perfect in the mathematick disciplines ) two onely , the rest being either too tedious , or too dangerous to the city , have seemed to me worthy , and one of them also more than the other , to offer to your lordship . the one is to remit it into the chanel of volana , thorow which it goeth of its own accord to the sea. the other is to turn it into main-po at stellata , for , as at other times it hath done , it will carry it to the sea happily . as to what concerns the making choice of the first way , that which seemeth to perswade us to it is , that we therein do nothing that is new , in that it is but restored to the place whence it was removed in the year 1522. in the time of pope adrian , by an agreement made in way of contract , between alfonso , duke of ferrara , and the bolognesi ; and that it was diverted for reasons , that are either out of date , or else have been too long time deferred . in like manner the facility wherewith it may be effected , letting it run into the divided po , whereby it will be turned to ferrara , or else carrying it by torre del fondo , to the mouth of masi , and from thence thorow the trench made by the ferraresi , along by panaro , where also finding an ample bed , and high and thick banks , that will serve at other times for it , and for the waters of po , there may a great expence be spared . that what ever its fall be , it would maintain the same , not having other rivers , which with their floods can hinder it ; and that running confined between good banks , without doubt it would not leave la motto by the way ; but especially , that it would be sufficient if it came to codigoro , where being assisted by the ebbing and flowing of the sea , it would run no hazard of having its chanel filled up from thence downwards . that there might thence many benefits be derived to the city , by means of the running waters , and also no mean navigation might be expected . on the contrary it is objected , that it is not convenient to think of returning this torrent into the divided po , by reason of the peril that would thence redound to this city . and that going by torre del fondo , through sanmartina to the mouth de masi by the chappel of vigarano unto the sea , it is by this way 70. miles ; nor is the fall greater than 26. 5. 6. feet , so that it would come to fall but 4. inches & an half , or thereabouts in a mile ; whereas the common opinion of the skilfull ( to the end that the torrents may not depose their sand that they bring with them in land-floods ) requireth the twenty fourth part of the hundredth part of their whole length , which in our case , accounting according to the measure of these places , is 16. inches a * mile ; whereupon the sinking of the mud and sand would most certainly follow , and so an immense heightning of the line of the bottom , and consequently a necessity of raising the banks , the impossibility of maintaining them , the danger of breaches and decayes , things very prejudicial to the islets of this city , and of san giorgio , the obstruction of the drains , which from the tower of tienne downwards , fall into the said chanel ; to wit , those of the sluices of goro , and the drains , of the meadows of ferrara : and moreover , the damages that would arise unto the said islet of s. giorgio , and the valleys of comachio , by the waters that should enter into the goro or dam of the mills of belriguardo , thorow the trenches of quadrea , which cannot be stopt , because they belong to the duke of modena , who hath right of diverting the waters of that place at his pleasure to the work of turning mills . the greater part of which objections , others pretend to prove frivolous , by saying , that its running there till at the last it was turned another way , is a sign that it had made such an elevation of the line , of its bed as it required ; denying that it needeth so great a declivity as is mentioned above ; and that for the future it would rise no more . that the said dra●ns and ditches did empty into the same , whilst po was there ; so that they must needs be more able to do so when onely reno runs that way . that there would no breaches follow , or if they did , they would be onely of the water of reno , which in few hours might be taken away ( in those parts they call damming up of breaches , and mending the bank , taking away the breaches ) and it s a question whether they would procure more inconvenience than benefit , for that its mud and sand might in many places , by filling them up , occasion a seasonable improvement . now omitting to discourse of the solidity of the reasons on the oneside , or on the other , i will produce those that move me to suspend my allowance of this design . the first is , that although i dare not subscribe to the opinion of those that require 16. inches declivity in a mile to reno , to prevent its deposing of mud ; yet would i not be the author that should make a trial of it with so much hazard , for having to satisfie my self in some particulars caused a level to be taken of the rivers l'amone , senio , and santerno , by bernardino aleotti , we found that they have more declivity by much than artists require , as also the reno hath from la botta de ghislieri to the chappel of vigarano , for in the space of four miles its bottom-line falleth five feet and five inches . so that i hold it greater prudence to depend upon that example , than to go contrary to a common opinion , especially since , that the effects caused by reno it self do confirm me in the same , for when it was forsaken by the po , after a few years , either because it had choaked up its chanel with sand , or because it s too long journey did increase it , it also naturally turned aside , and took the way of the said po towards stellata . nay , in those very years that it did run that way , it only began ( as relations say ) to make breaches , an evident sign that it doth depose sand , and raise its bed ; which agreeth with the testimony of some that were examined in the visitation of the publique notary , who found great benefit by having running water , and some kind of passage for boats , and yet nevertheless affirm that it for want of running water had made too high stoppages and shelfes of sand ; so that if it should be restored to the course that it forsook , i much fear that after a short time , if not suddenly , it would leave it a-again . the second i take from the observation of what happened to panaro , when with so great applause of the feraresi , it was brought by cardinal serra into the said chanel of volana ; for that notwithstanding that it had running waters in much greater abundance than reno ; yet in the time that it continued in that chanel it raised its bed well neer five feet , as is to be seen below the sluice made by cardinal capponi to his new chanel ; yea , the said cardinal serra who desired that this his undertaking should appear to have been of no danger nor damage , was constrained at its overflowings , to give it vent into sanmartina , that it might not break in upon , and prejudice the city ; which danger i should more fear from reno , in regard it carrieth a greater abundance of water and sand. thirdly , i am much troubled ( in the uncertainty of the success of the affair ) at the great expence thereto required ; for in regard i do not approve of letting it in , neer to the fortresse , for many respects , and carrying it by la torre del fondo to the mouth de masi , it will take up eight miles of double banks , a thing not easie to be procured , by reason that the grounds lie under water ; but from the mouth de masi unto codigoro , it would also be necessary to make new scowrings of the chanel ; to the end , that the water approaching ( by wearing and carrying away the earth on both shores , might make a bed sufficient for its body , the depth made for panaro not serving the turn , as i conceive ; and if it should suffice , when could the people of ferrara hope to be re-imbursed and satisfied for the charge thereof ? fourthly , it serves as an argument with me , to see that the very individual persons concerned in the remotion or diversion of the said torrent , namely , the bolognesi do not incline unto it , and that the whole city of ferrara , even those very persons who at present receive damage by it , cannot indure to hear thereof . the reason that induceth these last named to be so averse thereto , is , either because that this undertaking will render the introduction of the water of main-po more difficult ; or because they fear the danger thereof ; the others decline the project , either for that they know that reno cannot long continue in that course , or because they fear that it is too much exposed to those mens revengeful cutting of it who do not desire it should ; and if a man have any other wayes , he ought , in my opinion , to forbear that , which to such as stand in need of its removal , is lesse satisfactory , and to such as oppose it , more prejudicial . to conclude , i exceedingly honour the judgment of cardinal capponi , who having to his natural ability and prudence added a particular study , observation , and experience of these waters for the space of three years together , doth not think that reno can go by volana ; to which agreeth the opinion of cardinal s. marcello , legate of this city , of whom , for his exquisite understanding , we ought to make great account . but if ever this should be resolved on , it would be materially necessary to unite the quick and running waters of the little chanel of cento , of the chanel navilio , of guazzaloca , and at its very beginning those of dardagna , which at present , is one of the springs or heads of panaro , that so they might assist it in carrying its sand , and the matter of its muddiness into the sea ; and then there would not fail to be a greater evacuation and scowring ; but withall the proprietors in the islet of san giorgio and of ferrara must prepare themselves to indure the inconveniences of purlings or sewings of the water from the river thorow the boggy ground thereabouts . i should more easily incline therefore to carry it into main-po at stellata , for the reasons that cardinal capponi most ingeniously enumerates in a short , but well-grounded tract of his : not because that indeed it would not both by purlings and by breaches occasion some inconvenience ; especially , in the beginning : but because i hold this for the incomodities of it , to be a far less evil than any of the rest ; and because that by this means there is no occasion given to them of ferrara , to explain that they are deprived of the hope of ever seeing the po again under the walls of their city : to whom , where it may be done , it is but reason that satisfaction should be given . it is certain that po was placed by nature in the midst of this great valley made by the appennine hills , and by the alps , to carry , as the master-drain to the sea , that is the grand receptacle of all waters ; those particular streams which descend from them . that the reno by all geographers , strabo , pliny , solimas , mella , and others is enumerated among the rivers that fall into the said po. that although po should of it self change its course , yet would reno go to look it out , if the works erected by humane industry did not obstruct its passage ; so that it neither is , nor ought to seem strange , if one for the greater common good should turn it into the same . now at stellata it may go several waies into po , as appeareth by the levels that were taken by my order ; of all which i should best like the turning of it to la botta de' ghislieri , carrying it above bondeno to the church of gambarone , or a little higher or lower , as shall be judged least prejudicial , when it cometh to the execution , and this for two principal reasons : the one because that then it will run along by the confines of the church p trimony , without separating ferrara from the rest of it ; the other is , because the line is shorter , and consequently the fall greater ; for that in a space of ten miles and one third , it falleth twenty six feet , more by much than is required by artists ; and would go by places where it could do but little hurt , notwithstanding that the persons interressed study to amplifie it incredibly . on the contrary , there are but onely two objections that are worthy to be examined ; one , that the drains and ditches of s. bianca , of the chanel of cento , and of burana , and all those others that enter into po , do hinder this diversion of reno , by the encreasing of the waters in the po. the other is that po rising about the transom of the pilaster-sluice , very near 20 feet , the reno would have no fall into the same ; whereupon it would rise to a terrible height , at which it would not be possible to make , or keep the banks made , so that it would break out and drown the meadowes , and cause mischiefs , and damages unspeakable and irreparable ; as is evident by the experiment made upon panaro , which being confined between banks , that it might go into po , this not being neither in its greatest excrescense , it broke out into the territories of final , and of ferrara . and though that might be done , it would thereupon ensue , that there being let into the chanel of po , 2800. square feet of water ( for so much we account those of reno and panaro , taken together in their greatest heights ) the superficies of it would rise at least four feet , insomuch that either it would be requisite to raise its banks all the way unto the sea , to the same height , which the treasures of the indies would not suffice to effect ; or else there would be a necessity of enduring excessive breaches . to these two heads are the arguments reduced , which are largely amplified against our opinion ; and i shall answer first to the last , as most material . i say therefore , that there are three cases to be considered : first , po high , and reno low . secondly , reno high , and po low . thirdly , reno and po both high together . as to the first and second , there is no difficulty in them ; for if po shall not be at its greatest height , reno shall ever have a fall into it , and there shall need no humane artifice about the banks : and if reno shall be low , po shall regurgitate and flow up into the chanel of it ; and also from thence no inconvenience shall follow . the third remains , from which there are expected many mischiefs ; but it is a most undoubted truth , that the excrescencies of reno , as coming from the adjacent appennines and rains , are to continue but seven , or eight hours at most , and so would never , or very rarely happen to be at the same time with those of po , caused by the melting of the snowes of the alps , at least 400. miles distance from thence . but because it sometimes may happen , i reply , that when it cometh to pass , reno shall not go into po , but it shall have allowed it one or two vents ; namely , into the chanel of ferrara , as it hath ever had ; and into sanmartina , where it runneth at present , and wherewith there is no doubt , but that the persons concerned will be well pleased , it being a great benefit to them , to have the water over-flow their grounds once every four or five years , instead of seeing it anoy them continually . yea , the vent may be regulated , reserving for it the chanel in which reno at present runneth ; and instead of turning it by a dam at la betta de ghislieri , perhaps , to turn it by help of strong sluices , that may upon all occasions be opened and shut . and for my part , i do not question but that the proprietors themselves in sanmartina would make a chanel for it ; which receiving , and confining it in the time of the vents , might carry the sand into the po of primaro : nor need there thence be feared any stoppage by mud and sand , since that it is supposed that there will but very seldom be any necessity of using it ; so that time would be allowed , upon occasion , to scowr and cleanse it . and in this manner all those prodigies vanish that are raised with so much fear from the enterance of the water of reno swelled into po , when it is high , to which there needeth no other answer ; yet neverthelesse we do not take that quantity of water , that is carried by reno , and by panaro , to be so great as is affirmed : for that p. d. benedetto castelli hath no lesse accutely than accurately observed the measures of this kind , noting that the breadth and depth of a river is not enough to resolve the question truly , but that there is respect to be had to the velocity of the waters , and the term of time , things hitherto not considered by the skilful in these affairs ; and therefore they are not able to say what quantity of waters the said rivers carry , nor to conclude of the risings that will follow thereupon . nay , it is most certain , that if all the rivers that fall into po , which are above thirty , should rise at the rate that these compute reno to do , an hundred feet of banks would not suffice , and yet they have far fewer : so that this confirmes the rule of r. p. d. benedetto , namely , that the proportion of the height of the water of reno in reno to the height of the water of reno in po , is compounded of the proportion of the breadth of the chanel of po to that of reno , and of the velocity of the water of reno in po to the velccity of the water of reno in reno ; a manifest argument that there cannot in it , by this new augmentation of waters follow any alteration that necessitates the raising of its banks , as appeareth by the example of panaro , which hath been so far from swelling po , that it hath rather asswaged it , for it hath carried away many shelfs and many islets that had grown in its bed , for want of waters sufficient to bear away the matter of land-floods in so broad a chanel ; and as is learnt by the trial made by us in panaro with the water of burana ; for erecting in the river standing marks , and shutting the said sluice , we could see no sensible abatement , nor much less after we had opened it sensible increasment ; by which we judge that the same is to succeed to po , by letting in of reno , burana having greater proportion to panaro than reno to po , considering the state of those rivers in which the observation was made . so that there is no longer any occasion for those great raisings of banks , and the danger of the ruptures as well of reno as of po do vanish , as also the fear lest that the sluices which empty into po should receive obstruction : which if they should , yet it would be over in a few hours . and as to the breaches of panaro which happened in 1623. i know not why , seeing that it is confessed that the po was not , at that time , at its height , one should rather charge it with the crime , than quit it thereof . the truth is , that the bank was not made of proof , since that the same now continueth whole and good , and panaro doth not break out ; nay , there was , when it brake more than a foot and half of its banks above the water , and to spare ; but it broke thorow by a moles working ; or by the hole of a water-rat , or some such vermine ; and by occasion of the badness of the said banks , as i finde by the testimony of some witnesses examined by my command , that i might know the truth thereof . nor can i here forbear to say , that it would be better , if in such matters men were more candid and sincere . but to secure our selves neverthelesse , to the utmost of our power , from such like breaches which may happen at the first , by reason of the newnesse of the banks , i presuppose that from po unto the place whence reno is cut , there ought to be a high and thick fence made with its banks , so that there would be no cause to fear any whatsoever accessions of water , although that concurrence of three rivers , which was by some more ingeniously aggravated than faithfully stated by that which was said above were true ; to whom i think not my self bound to make any farther reply , neither to those who say that po will ascend upwards into reno , since that these are the same persons who would introduce a small branch of the said po into the chanel of ferrara , that so it may conveigh to the sea , not reno onely , but also all the other brooks of which we complained ; and because that withal it is impossible , that a river so capacious as po should be incommoded by a torrent , that , as i may say , hath no proportion to it . i come now to the businesse of the ditches and draines ; and as to the conveyance of burana , it hath heretofore been debated to turn it into main-po , so that in this case it will receive no harm , and though it were not removed , yet would it by a trench under ground pursue the course that it now holdeth , and also would be able to dis-imbogue again into the said new chanel of reno , which conforming to the superficies of the water of po , would continue at a lower level than that which panara had when it came to ferrara , into which burana did neverthelesse empty it self for some time . the conveyance or drain of santa bianca , and the little chanel of cento may also empty themselves by two subterranean trenches , without any prejudice where they run at present , or without any more works of that nature , they may be turned into the said new chanel , although with somewhat more of inconvenience ; and withall , the chanel of ferrara , left dry , would be a sufficient receptacle for any other sewer or drain whatsoever , that should remain there . all which operations might be brought to perfection with 150. thousand crowns , well and faithfully laid out ; which summ the bolognesi will not be unwilling to provide ; besides that those ferraresi ought to contribute to it , who shall partake of the benefit . let me be permitted in this place to propose a thing which i have thought of , and which peradventure might occasion two benefits at once , although it be not wholly new . it was in the time of pope paul v. propounded by one crescenzio an ingineer , to cut the main-po , above le papozze ; and having made a sufficient evacuation to derive the water thereof into the po of adriano , and so to procure it to be navigable , which was not at that time effected , either by reason of the oppositions of those , whose possessions were to be cut thorow , or by reason of the great sum of money that was necessary for the effecting of it : but in viewing those rivers , we have observed , that the sedge cutting might easily be made below le papozze , in digging thorow the bank called santa maria , & drawing a trench of the bigness that skilful artists shall judge meet unto the po * of ariano , below the secche of the said s. maria ; which as being a work of not above 160. perches in length , would be finished with onely 12000. crowns . first ; it is to be believed , that the waters running that way , would not fail to open that mouth into the sea , which at present is almost choakt up by the shelf of sand , which the new mouth of ponto virro hath brought thither ; and that it would again bring into use the port goro , and its navigation . and haply experience might teach us , that the superficies of po might come to fall by this asswagement of water , so that the accession of reno would questionless make no rising in it : whereupon , if it should so fall out , those princes would have no reason to complain ; who seem to question , lest by this new accession of water into po , the sluices might be endangered . which i thought not fit to omit to represent to your lordship ; not , that i propose it to you as a thing absolutely certain , but that you might , if you so pleased , lay it before persons whose judgements are approved in these affairs . i return now from where i degrest , and affirm it as indubitable , that reno neither can , nor ought to continue longer where it at this day is ; and that it cannot go into any other place but that , whither cardinal capponi designed to carry it , and which at present pleaseth me better than any other ; or into volana , whence it was taken away ; the vigilance of men being able to obviate part of those mischiefs , which it may do there . but from its removal , besides the alleviation of the harm which by it self is caused , there would also result the diminution of that which is occasioned by the other brooks , to the right hand of the po of argenta ; forasmuch as the said po wanting all the water of reno , it would of necessity come to ebb in such manner , that the valleys would have a greater fall into the same , and consequently it would take in , and swallow greater abundance of water ; and by this means the ditches and draines of the up-lands would likewise more easily fall into them ; especially if the scouring of zenzalino were brought to perfection , by which the waters of marrara would fall into marmorta : and if also that of bastia were enlarged , and finished , by which there might enter as much water into the said po of argenta , as is taken from it by the removal of reno ; although that by that meanes the water of the valleys would asswage double : nor would the people of argenta , the isles of s. giorgio , and comacchio have any cause to complain ; for that there would not be given to them more water than was taken away : nay sometimes whereas they had muddy waters , they would have clear ; nor need they to fear any rising : and furthermore , by this means a very great quantity of ground would be restored to culture ; for the effecting of all which , the summ of 50. thousand crowns would go very far , and would serve the turn at present touching those brooks , carrying them a little farther in the mean time , to fill up the greater cavities of the valleys , that we might not enter upon a vaster and harder work , that would bring with it the difficulties of other operations , and so would hinder the benefit which these people expect from the paternal charity of his holiness . to the right honourable , monsignore d. ferrante cesarini . my treatise of the mensuration of running waters , right honourable , and most noble sir , hath not a greater prerogative than its having been the production of the command of pope vrban viii . when his holiness was pleased to enjoyn me to go with monsignore corsini , in the visitation that was imposed upon him in the year 1625. of the waters of ferrara , bologna , romagna , and romagnola ; for that , on that occasion applying my whole study to my service and duty , i published in that treatise some particulars till then not rightly understood and considered ( that i knew ) by any one ; although they be in themselves most important , and of extraordinary consequence . yet i must render thanks to your lordship for the honour you have done to that my tract ; but wish withal , that your esteem of it may not prejudice the universal esteem that the world hath of your honours most refined judgement . as to that point which i touch upon in the conclusion , namely , that the consideration of the velocity of running water supplyeth the consideration of the * length omitted in the common way of measuring running waters ; your lordship having commanded me that in favour of practise , and for the perfect discovery of the disorder that commonly happeneth now adayes in the distribution of the waters of fountains , i should demonstrate that the knowledge of the velocity serveth for the finding of the length : i have thought fit to satisfie your command by relating a fable ; which , if i do not deceive my self , will make out to us the truth thereof ; insomuch that the rest of my treatise shall thereby also become more manifest and intelligible , even to those who finde therein some kinde of obscurity . in the dayes of yore , before that the admirable art of weaving was in use , there was found in persia a vast and unvaluable treasure , which consisted in an huge multitude of pieces of ermesin , or damask , i know not whether ; which , as i take it , amounted to near two thousand pieces ; which were of such a nature , that though their breadth and thickness were finite and determinate , as they use to be at this day ; yet nevertheless , their length was in a certain sense infinite , for that those two thousand pieces , day and night without ceasing , issued out with their ends at such a rate , that of each piece there issued 100. ells a day , from a deep and dark cave , consecrated by the superstition of those people , to the fabulous arachne . in those innocent and early times ( i take it to have been , in that so much applauded and desired golden age ) it was left to the liberty of any one , to cut off of those pieces what quantity they pleased without any difficulty : but that felicity decaying and degenerating , which was altogether ignorant of meum and tuum ; terms certainly most pernicious , the original of all evils , and cause of all discords ; there were by those people strong and vigilant guards placed upon the cave , who resolved to make merchandize of the stuffes ; and in this manner they began to set a price upon that inestimable treasure , selling the propriety in those pieces to divers merchants ; to some they sold a right in one , to some in two , and to some in more . but that which was the worst of all , there was found out by the insatiable avarice of these men crafty inventions to deceive the merchants also ; who came to buy the aforesaid commodity , and to make themselves masters , some of one some of two , and some of more ends of those pieces of stuff ; and in particular , there were cetain ingenuous machines placed in the more secret places of the cave , with which at the pleasure of the guards , they did retard the velocity of those stuffs , in their issuing out of the cave ; insomuch , that he who ought to have had 100. ells of stuff in a day , had not above 50 , and he who should have had 400 , enjoyed the benefit of 50. onely ; and so all the rest were defrauded of their rights , the surplusage being sold , appropriated , and shared at the will of the corrupt officers : so that the business was without all order or justice , insomuch that the goddess arachne being displeased at those people , deprived every one of their benefit , and with a dreadful earthquake for ever closing the mouth of the cave , in punishment of so much impiety and malice : nor did it avail them to excuse themselves , by saying that they allowed the buyer the breadth and thickness bargained for ; and that of the length , which was infinite , there could no account be kept : for the wise and prudent priest of the sacred grotto answered , that the deceit lay in the length , which they were defrauded of , in that the velocity of the stuffe was retarded , as it issued out of the cave : and although the total length of the piece was infinite , for that it never ceased coming forth , and so was not to be computed ; yet nevertheless its length considered , part by part , as it came out of the cave , and was bargained for , continued still finite , and might be one while greater , and another while lesser , according as the piece was constituted in greater or lesser velocity ; and he added withall , that exact justice required , that when they sold a piece of stuff , and the propriety or dominion therein , they ought not only to have ascertained the breadth and thicknesse of the piece , but also to have determined the length , determining its velocity . the same disorder and confusion , that was represented in the fable , doth come to passe in the history of the distribution of the waters of conduits and fountains , seeing that they are sold and bought , having regard only to the two dimensions , i mean of breadth and height of the mouth that dischargeth the water ; and to remedy such an inconvenience , it is necessary to determine the length in the velocity ; for never shall we be able to make a guesse at the quantity of the body of running vvater , with the two dimensions only of breadth and height , without length . and to the end , that the whole business may be reduced to a most easie practice , by which the waters of aqueducts may be bought and sold justly , and with measures alwayes exact and constant . first , the quantity of the water ought diligently to be examined , which the whole principal * pipe dischargeth in a time certain , as for instance , in an hour , in half an hour , or in a lesse interval of time , ( for knowing which i have a most exact and easie rule ) and finding that the whole principal pipe dischargeth v. g. a thousand tuns of water in the space of one or more hours , in selling of this water , it ought not to be uttered by the ordinary and false measure , but the distribution is to be made with agreement to give and maintain to the buyer ten or twenty , or a greater number of tuns , as the bargain shall be made , in the space of an hour , or of some other set and determinate time . and here i adde , that if i were to undertake to make such an adjustment , i would make use of a way to divide and measure the time with such accuratenesse , that the space of an hour should be divided into four , six , or eight thousand parts without the least errour ; which rule was taught me by my master sign . galilaeo galilaei , chief philosopher to the most serene grand duke of tuscany . and this way will serve easily and admirably to our purpose and occasion ; so that we shall thereby be able to know how many quarts of water an aqueduct will discharge in a given time of hours , moneths , or years . and in this manner we may constitute a cock that shall discharge a certain and determinate quantity of water in a time given . and because daily experience shews us , that the springs of aqueducts do not maintain them alwayes equally high , and full of water , but that sometimes they increase , and sometimes decrease , which accident might possibly procure some difficulty in our distribution : therefore , to the end that all manner of scruple may be removed , i conceive that it would be convenient to provide a cistern , according to the occasion , into which there might alwayes fall one certain quantity of water , which should not be greater than that which the principal pipe dischargeth in times of drought , when the springs are bare of water , that so in this cistern the water might alwayes keep at one constant height . then to the cistern so prepared we are to fasten the cocks of particular persons to whom the water is sold by the reverend apostolique chamber , according to what hath been observed before ; and that quantity of water which remaineth over and above , is to be discharged into another cistern , in which the cocks of the waters for publick services , and of those which people buy upon particular occasions are to be placed . and when the businesse shall have been brought to this passe , there will likewise a remedy be found to the so many disorders that continually happen ; of which , for brevity sake , i will instance in but four only , which concern both publique and private benefit , as being , in my judgment , the most enormous and intolerable . the first inconvenience it , that in the common way of measuring , dispensing , and selling the waters of aqueducts , it is not understood , neither by the buyer nor seller , what the quantity truly is that is bought and sold ; nor could i ever meet with any either engineer or architect , or artist , or other that was able to decypher to me , what one , or two , or ten inches of water was . but by our above declared rule , for dispensing the waters of aqueducts we may very easily know the true quantity of water that is bought or sold , as that it is so many tuns an hour , so many a day , so many in a year , &c. the second disorder that happeneth , at present , in the distribution of aqueducts is , that as the businesse is now governed , it lieth in the power of a ●ordid mason to take unjustly from one , and give undeservedly to another more or lesse water than belongeth to them of right : and i have seen it done , of my own experience . but in our way of measuring and distributing waters , there can no fraud be committed ; and putting the case that they should be committed , it s an easie matter to know it , and amend it , by repairing to the tribunal appointed . thirdly , it happens very often , ( and we have examples thereof both antient and modern ) that in dispensing the water after the common and vulgar way ; there is sometimes more water dispended than there is in the register , in which there will be registred , as they say , two hundred inches ( for example ) and there will be dispensed two hundred and fifty inches , or more . which passage happened in the time of nerva the emperour , as giulio frontino writes , in his 2. book , de aquaductibus vrbis romae , where he observeth that they had in commentariis 12755. quinaries of water ; and found that they dispensed 14018. quinaries . and the like errour hath continued , and is in use also modernly until our times . but if our rule shall be observed , we shall incur no such disorder , nay there will alwayes be given to every one his share , according to the holy end of exact justice , which dat unicuique quod suum est . as on the contrary , it is manifest , that his divine majesty hateth and abominateth pondus & pondus , mensura & mensura , as the holy ghost speaketh by the mouth of solomon in the proverbs , chap. 20. pondus & pondus , mensura & mensura , utrumque abominabile est apud deum . and therefore who is it that seeth not that the way of dividing and measuring of vvaters , commonly used , is expresly against the law of god. since that thereby the same measure is made sometimes greater , and sometimes lesser ; a disorder so enormous and execrable , that i shall take the boldness to say , that for this sole respect it ought to be condemned and prohibited likewise by human law , which should enact that in this business there should be imployed either this our rule , or some other that is more exquisite and practicable , whereby the measure might keep one constant and determinate tenor , as we make it , and not , as it is now , to make pondus & pondus , mensura & mensura . and this is all that i had to offer to your most illustrious lordship , in obedience to your commands , reserving to my self the giving of a more exact account of this my invention , when the occasion shall offer , of reducing to practice so holy , just , and necessary a reformation of the measure of running waters and of aqueducts in particular : which rule may also be of great benefit in the division of the greater waters to over-flow grounds , and for other uses : i humbly bow , your most devoted , and most obliged servant , d. benedetto castelli , abb. casin . finis . a table of the most observable matters in this treatise of the mensuration of running waters . a a batements of a river in different and unequal diversions , is alwaies equal , which is proved with 100. syphons . page 75 arno river when it riseth upon a land-flood near the sea one third of a brace , it riseth about pisa 6. or 7. braces . 82 b banks near to the sea lower , than far from thence . corollary xiv . 16 brent river diverted from the lake of venice , and its effects . 64 brent supposed insufficient to remedy the inconveniences of the lake , and the falsity of that supposition . 67 brent , and its benefits in the lake . 70 its deposition of sand in the lake , how great it is . 78 , 79 bridges over rivers , and how they are to be made . appendix viii . 20 burana river , its rising , and falling in panaro . 110 c castelli applyed himself to this study by order of urban viii . 2 chanel of navigation in the valleys of bologna , and its inconveniences . 99 carried into the po of ferrara , and its benefits ibid. ciampoli a lover of those observations of waters . 3 d difficulty of this business of measuring waters . 2 disorders that happen in the distribution of the waters of aqueducts , and their remedies . 113 distribution of the waters of fountains , and aqueducts . appendix x. 22 distribution of water to over-flow grounds . appendix xi . 23 , 69 , 70 diversion of reno and other brooks of romagna , advised by p. spernazzati to what end it was . 100 drains and ditches , the benefit they receive by cutting away the weeds and reeds . appendix ix . 21 drains and sewers obstructed , in the diversion of reno into main po , and a remedy for the same . 110 e engineers unvers'd in the matters of waters . 2 erour found in the common way of measuring running waters : 68 , 69 errour in deriving the water of acqua paola . appendix ii. 17 , 18 errour of bartolotti . 86 , 87 errours of engineers in the derivation of chanels . corollary , xii . 12 errour of engineers in measuring of reno in po. appendix iii. ibid. errour of other engineers ; contrary to the precedent . appendix iv. ibid. errour of giovanni fontana in measuring waters . corollary xi . 9 errour of giulio frontino in measuring the waters of aqueducts . appendix i. 17 errours committed in cutting the bank at bondeno , in the swellings of po : corollary xiii . 81 f fenns pontine , drained by pope sixtus quintus , with vast expence . 92 the ruine and miscarriage thereof . 93 tardity of the principal chanel that drains them , cause of the drowning . ibid. they are obstructed by the fishing-wears , which swell the river . 94 waters of fiume sisto , which flow in great abundance into the evacuator of the said fenns . 94 , 95 remedies to the disorders of those fenns . 95 , 96 fontana giovanni , his errours in measuring waters . corollary xi . 9 fiume morto , whether it ought to fall into the sea , or into serchio , 79 let into serchio and its inconveniences . 79 , 80 the dangerous rising of its waters : when to be expected . 81 its inconveniences when it is higher in level than serchio , and why it riseth most on the sea-coasts , at such time as the winds make the sea to swell . 83 g galilaeo galilaei , honourably mentioned . page 2 , 28 his rule for measuring the time . 49 h height , vide quick heights different , made by the same stream of a brook or torrent , according to the divers velocities in the entrance of the river . corollary i. 6 heights different , made by the torrent in the river , according to the different heights of the river . corollary ii. ibid. k knowledge of motion how much i● importeth . 1 l lake of perugia , and , be observation made on it . appendix xii . 42 lake of thrasimenus and considerations upon it , a letter written to sig. galilaeo galilaei . 28 lake of venice , and considerations upon it . 63 , 73 low waters which let the bottom of it be discovered . 64 the stoppage and choaking of the ports , a main cause of the disorders of the lake , and the grand remedy to those disorders what it is . 66 lakes and meers along the sea-coasts , and the causes thereof . 65 length of waters , how it is to be measured . 70 m measure and distributions of waters . appendix v. 18 measure of rivers that fall into others difficult . coroll . x : 9 measure of the running water of a chanel of an height known by a regulator of a measure given , in a time assigned . proposition i. problem i. 50 measure of the water of any river , of any greatness , in a time given . proposition v. problem iii. 60 measure that shewes how much water a river dischargeth in a time given . 48 mole-holes , motion the principal subject of philosophy . 1 mud. vide sand. n navigation from bologna to ferrara , is become impossible , till such time as reno be diverted . 101 navigation in the lake of venice endangered , and how restored . 65 , 70 p perpendicularity of the banks of the river , to the upper superficies of it . 37 perpendicularity of the banks to the bottom . 37 perugia . vide lake . pontine . vide fenns . ports of venice , malamocco , bondolo , and chiozza , choaked up for want of water in the lake . 65 proportions of unequal sections of equal velocity , and of equal sections of unequal velocity . axiome iv. and v. 38 proportions of equal and unequal quantities of water , which pass by the sections of different rivers . proposition ii. 39 proportions of unequal sections that in equal times discharge equal quantities of water . proposition iii. 41 proportion wherewith one river falling into another , varieth in height . proposition iv. 44 proportion of the water discharged by a river in the time of flood , to the water discharged in an equal time by the said river , before or after the flood . proposition v. 44 proportion of the heights made by two equal brooks or streams falling into the same river . proposition vi. 45 proportion of the water which a river dischargeth encreasing in quick-height by the addition of new water , to that which it dischargeth after the encrease is made . proposition iv. theor. ii. 54 proportion of a river when high , to it self when low . coroll . i. 55 q quantity of running waters is never certain , if with the vulgar way of measuring them , their velocities be not considered . 32 quantities of waters which are discharged by a river , answer in equality to the velocities and times in which they are discharged . axiome i , ii , iii. 38 quick-height of a river , what it is . definition v. 48 r reason of the proverb , take heed of the still waters . coroll . vi. 7 reasons of monsignore corsini against the diversion of reno into the po of volano . 105 reasons of cardinal capponi and monsig . corsini , for the turning of reno into main po. 106 two objections on the contrary , and answers to them . 104 & 105 what ought to be the proportion of the heights of reno is reno , and of reno in po. 110 regulator what it is . definition iv. 48 relation of the waters of bologna and ferrara , by monsignore corsini . 100 reno in the valleys , and its bad effects . 100 , 101 two wayes to divert it . 103 the facility and utility of those wayes . ibid. the difficulties objected . 104 reply to bartolotti touching the dangers of turning fiume morto into serchio . 83 retardment of the course of a river caused by its banks . appendix vii . 19 risings made by flood-gates but small . appendix xiii . 26 rivers that are shallow swell much upon small showers , such as are deep rise but little upon great floods . corollary iii. 6 rivers the higher they are , the swifter . ibid. rivers the higher they are , thelesse they encrease upon floods . 49 rivers when they are to have equal and when like velocity . ibid. rivers in falling into the sea , form a shelf of sand called cavallo . 65 five rivers to be diverted from the lake of venice , and the inconveniences that would ensue thereupon . 74 , 75 a river of quick-height , and velocity in its regulator being given , if the height be redoubled by new water , it redoubleth also in velocity . proposition ii. theorem i. 51 keepeth the proportion of the heights , to the velocities . corollary 52 s sand and mud that entereth into the lake of venice , and the way to examine it . 76 seas agitated and driven by the winds stop up the ports . 64 , 65 sections of a river what they are . definition i. 37 sections equally swift what they are . definition ii. ibid. sections of river being given , to conceive others equal to them , of different breadth , height and velocity . petition . 38 sections of the same river , and their proportions to their velocities . coroll . i. 42 sections of a river discharge in any whatsoever place of the said river , equal quantities of water in equal times . proposition i. 39 sile river what mischiefes it threatneth , diverted from the lake . 74 spirtings of waters grow bigger the higher they go . coroll . xvi . 16 streams of rivers how they encrease and vary . coroll . i. 6 streams retarded , and the effects thereof . coroll . ix . 8 t table of the heights , additions , and quantities of waters , and its use . 56 thrasimenus . vide lake . time how it s measured in these operations of the waters . 49 torrents encrease at the encreasing of a river , though they carry no more water than before : coroll . iv. 6 torrents when they depose and carry away the sand. coroll . v. 7 torrents and their effects in a river . 6 , 7 torrents that fall into the valleys , or into po of volano , and their mischiefs prevented , by the diverting of reno into main po. 100 tyber and the causes of its inundations , coroll . viii . 8 v valleys of bologna and ferrara , their inundations and disorders , whence they proceed . 97 velocity of the water shewn by several examples . 3 its proportion to the measure . 5 velocities equal , what they are . 47 velocities like , what they are . 47 , 48 velocities of water known , how they help us in finding the lengths . 113 a fable to explain the truth thereof . ibid. venice . vide lake . vse of the regulator in measuring great rivers . consideration i. 60 w waters falling , why they disgross . coroll . xvi . 16 waters , how the length of them is measured . 70 waters that are imployed to flow grounds , how they are to be distributed . 19 , 53 , 54 waters to be carryed in pipes , to serve aquaducts and conduits , how they are to be measured . 115 , 116 way to know the rising of lakes by raines . 28 way of the vulgar to measure the vvaters of rivers . 68 wind gun , and portable fountain of vincenzo vincenti of urbin . 11 windes contrary , retard , and make rivers encrease . coroll . vii . 8 the end of the table of the second part of the first tome , notes, typically marginal, from the original text notes for div a31214-e200 a nella continuatione dell nuntio ●iderio . b lettera al p. abbate d. b. castelli d'arcetro ; li. 3. decemb. 16●9 . c de motu aquarum . lib. 2. prop. 37. p. 191. notes for div a31214-e2430 * * and as is at large demonstrated by that most excellent and honourable personage mr. boile in the industrious experiment of his pneumatical engine . * * artesia . * * commentarius beareth many senses , but in this place signifieth a certain register of the quantities of the waters in the several publique aquiducts of rome ; which word i find frequently used in the law-books of antient civilians : and by errogation we are to understand the distribution or delivering out of those stores of water . * * a coyn of pope julius worth six pence . notes for div a31214-e6940 * * or sluice . * * in pregadi , a particular council , the senators of which have great authority . * * a venice brace is 11 / 1● of our yard . * * a river of that name . * * i. savii dell ' acque , a particular council that take care of the lakes and other aquatick affairs . * * he here intends the demonstrations following , at the end of the first book * * deeper . * * lib. 1. * * the countrey or province lying round the city , heretofore called lati 〈◊〉 * * or lordship . * * the popes exchequer . * * polesine is a plat of ground almost surrounded with bogs or waters , like an island * * people of ferrara . * * in chanels made by hand . * * the inch of these places is somewhat bigger than ours . * * of adriano . notes for div a31214-e16870 * larghezza , but misprinted . 