Substantia. An International Journal of the History of Chemistry 6(1): 77-105, 2022

Firenze University Press 
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ISSN 2532-3997 (online) | DOI: 10.36253/Substantia-1423

Citation: Kenndler E. (2022) Capillary 
Electrophoresis (CE) and its Basic 
Principles in Historical Retrospect. 
Part 3. 1840s –1900ca. The First CE 
of Ions in 1861. Transference Num-
bers, Migration Velocity, Conductivity, 
Mobility. Substantia 6(1): 77-105. doi: 
10.36253/Substantia-1423

Received: Oct 01, 2021

Revised: Dec 15, 2021

Just Accepted Online: Dec 16, 2021

Published: Mar 07, 2022

Copyright: © 2022 Kenndler E. This is 
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Supporting Information files.

Competing Interests: The Author(s) 
declare(s) no conflict of interest.

Historical Articles

Capillary Electrophoresis (CE) and its Basic 
Principles in Historical Retrospect. Part 3. 
1840s –1900ca. The First CE of Ions in 1861. 
Transference Numbers, Migration Velocity, 
Conductivity, Mobility

Ernst Kenndler

Institute for Analytical Chemistry, Faculty of Chemistry, University of Vienna, Währin-
gerstrasse 38, A 1090, Vienna, Austria
E-mail: ernst.kenndler@univie.ac.at

Abstract. Since electrophoresis is a physical phenomenon – it is the movement of dis-
persed charged particles relative to a liquid under the influence of a spatially uniform 
electric field – its history is not limited to its use as a separation method. The history 
of capillary electrophoresis in particular, i.e. electrophoresis in capillary-sized open 
tubes, therefore does not begin in the 1960s, as is commonly assumed, but already a 
century earlier, if one refers to its principles. Capillary electrophoresis of ions was first 
performed by the French physicist Edmond Becquerel in 1861, about the same year as 
that of colloidal particles. Becquerel owns therefore the priority. It was subsequently 
performed on three other occasions in the Long Nineteenth Century, by Wilhelm Beetz 
in 1865, by Wilhelm Ostwald and Walther Nernst in 1889, and by Friedrich Kohl-
rausch and Adolf Heydweiller in 1895. All of these experiments were carried out in 
the context of research on conductivity and ion migration. Based on the theories of 
Grotthuß, Davy, and Faraday, it was believed until the 1840s that both the anions and 
the cations of a dissolved strong electrolyte – to which this review refers – migrate at 
the same velocity or speed in an electric field, but experimental observations in the 
mid-1840s cast doubt on this view. Wilhelm Hittorf was the first to show that these 
ions could migrate at different speeds, still consistent with Faraday´s laws. He was able 
to prove his hypothesis with experimental data and determined the migration veloc-
ities of the two types of ions in an electrolyte relative to the sum of their velocities, 
which he termed “Überführungszahlen” (transference or transport numbers). How-
ever, they did not initially yield the absolute velocities of the ions. This was achieved 
later by F. Kohlrausch, who devoted four decades of his research life, namely from the 
end of 1860 to about 1910, to the study of the conductivity of electrolyte solutions and 
the migration of ions. He discovered in 1879 that ions move independently from each 
other in solution (1st Kohlrausch law). It is remarkable that until the late 1880s it was 
generally believed that free ions do not exist in solutions in the absence of an external 
electrical force, but that ions were always tightly bound to their counterions. This belief 
dated back to Grotthuß in 1805. Although Rudolf Clausius hypothesized in 1857 that 
free ions are actually present in solutions as result of their thermal motion, this did not 
find further resonance. It is also remarkable that during this whole period under con-
sideration no attempt was ever made to separate ions with the same charge, although 
their different migration properties were already known. Continuing his research, 

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78 Ernst Kenndler

Kohlrausch found empirically in 1900 that at extremely low concentrations the molar conductivity of ions, i.e. the conductivity relat-
ed to their concentration, is a function of the square root of their concentration and approaches a certain limit at infinite dilution 
(2nd Kohlrausch law). As a precursor to this law, he derived in 1885 for larger concentration ranges the little-known relationship of 
molar conductivity as a function of the cubic root of concentration. He calculated the migration velocities of ions from their con-
ductivities and characterized the migration behavior by their mobility, which is a central property in electrophoresis. Kohlrausch 
was certainly a formative investigator of the electrophoretic properties of ions, but his work focused mainly on strong electrolytes. 
This review covers the research results in the field of mainly this class of electrolytes in the period from 1840 to about 1910; but it 
also reports on the personal background of some researchers who, despite important contributions, have been unjustly forgotten, as 
well as on researchers who were active outside the scientific community. Mention is made, for example, of Gustav Theodor Fechner, 
who was the first to prove the fact, indispensable for electrophoresis, that Ohm´s law also applies to electrolyte solutions. However, 
in contrast to the generally applied results of his investigations, he himself was rather ignored by later researchers. The conduc-
tivities and electrophoretic properties of weak electrolytes, which were known to Kohlrausch and his contemporaries but hardly 
explicable to them, at least until 1884, are not discussed in detail in this review. In that year, Svante Arrhenius published his ground-
breaking theory of electrolyte dissociation as his dissertation. This theory and the resulting consequences for the whole subject of 
electrolyte solutions require, however, a separate historical retrospect.

Keywords: first capillary electrophoresis, ions, strong electrolytes, Hittorf, Clausius, Kohlrausch.

INTRODUCTION

Although the motion of dissolved charged particles 
by electrophoresis1 during electrolysis was the topic of 
Part 2 of this series[4] the magnitude of their migration 
velocities was not subject of discussion.2 That part cov-
ered the period from the first observations of electrolysis 
and the inextricably linked electrophoresis in 1800, and 
the assumption that electrical forces from the electrodes 
exert on the ions by action at a distance. This concept 
was superseded in the mid-1830s by Michael Faraday’s 
pioneering theory that ions move at electric lines of 
force, which led to James Clerk Maxwell’s field theory.
[5] At the time when the action at a distance was widely 
accepted, the migration velocity of the ions was believed 
to vary with their distance from the electrodes, while 
as consequence of the field theory the assumption of a 
constant velocity prevailed. In no case, however, was the 
magnitude of the velocity of ion migration addressed. 
This will be the subject of this Part 3.

In short, and just for the sake of historical complete-
ness, we mention the first attempt to measure the migra-

1 To avoid misunderstandings, we indicate how we define electrophore-
sis. It is not just the migration of particles in an electric field, which, 
like colloids, have an electric double layer. Nor is it just the powerful 
separation method in use today, whose overwhelming importance, for 
example, for genomics, proteomics, metabolomics, and numerous other 
important areas we highlighted in Part 1.[1] It is in principle, as Hanns 
Lyklema most generally defined it, “the movement of dispersed particles 
relative to a fluid under the influence of a spatially uniform electric field”.
[2][3] We therefore have every reason to call such migrations electropho-
retic (see also Part 2 of this series).[4]
2 It should be noted in advance that the present part of our historical 
review deals mainly with single pure strong electrolytes in free solu-
tions.

tion velocity by Peter Mark Roget,3 which he already 
undertook in 1807. Roget tried to determine the migra-
tion speeds of oxygen and hydrogen generated by the 
electrolysis of water,4 but without success, as described 
in refs. [6, 7], Chapter Galvanism, p. 30. Michael Faraday 
then took up the subject only in 1833 in the Fifth Series 
of Experimental Researches (refs. [8, 9]; 524. – 535.). In the 
Eighth Series[10] from 1834 he explicitly argued that both 
the anions and the cations of an electrolyte travel at the 
same speed in opposite directions at the electric lines of 
force, and based this assumption on the law of the defi-
nite electrochemical action. He argued that equal chemi-
cal equivalents of oppositely charged ions are required 
at their respective electrodes at the same time, other-
wise electrolysis cannot happen. We discussed this point 
already in Part 2.[4]

Faraday briefly returned to the subject of migration 
velocities of particles in solution in 1838 in the Thir-
teenth Series.[11] At the end of this article he reviewed 
earlier attempts to measure the speed of electricity in 
metallic conductors, which had been unsuccessfully car-
ried out by William Watson in London in 1747 and 1748.
[12, 13] That of light was carried out (with some success) 
by Charles Wheatstone in 1834.[14] Faraday himself spec-
ulated on an approximate velocity of the ions in solu-

3 The British physician Peter Mark Roget (1779, London – 1869, West 
Malvern, Worcestershire) was Fullerian Professor of Physiology an der 
Royal Institution from 1834 till 1837.
4 Roget tried to measure the time interval between the closing of the 
electric circuit and the appearance of the gases on the separate elec-
trodes, which were 46 inches (i.e., ca. 117 cm) apart. After the com-
pletion of the circuit, however, no measurable interval could be deter-
mined; a result which was predicable taking into account the already 
known theories of Grotthuß and Davy.



79Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

tion, (ref. [11], pp. 164, 165) but only vaguely.5 In none of 
his contributions, however, Faraday reported on values 
of the migration velocities.

The assumption of equal ion velocities was chal-
lenged by Frederic Daniell and William Allen Miller by 
contradictory results of the electrolysis of copper and of 
zinc sulfate solutions in a double membrane cell, i.e., a 
cell divided by two diaphragm. After electrolysis, they 
found the same amount of copper in the cathode com-
partment as was initially put in. The amount of reduced 
copper plus the quantity that remained dissolved was 
exactly that as before electrolysis. From this, they con-
cluded that the copper ions do not migrate and only 
sulphate traverses the entire distance between the elec-
trodes. They hypothesized that the flow of the electro-
phoretic current6 was mainly by the anions, while the 
cations contributed little.[15, 16]

Claude Servais Pouillet observed a similar effect in 
1845 when he electrolyzed a solution of gold chloride.7 
He used a U-shaped tube with one of the electrodes in 
each arm. After passing the current, he found almost 

5 The English apothecary, physician and natural philosopher Sir William 
Watson (London, 1715 – 1787) charged wires with electric machines 
in London in 1747 and 1748.[12][13] However, differences in the time 
of appearance of the discharges at the two extreme ties of a wire of 4 
miles in length could not be determined visually. Charles Wheatstone 
attributed this miscarriage to the laggardness of the observing eye. He 
therefore constructed a device with rapidly rotating mirrors with which 
time intervals for the occurrence of electrically generated sparks could 
be measured beyond a millionth of a second. The measured velocity of 
light was either 576000 or 288000 miles per second, depending on the 
experimental circumstances assumed.[14] If we take the English mile, 
standardized in 1592 by the English Parliament as 1609 m, the latter 
velocity is about 460000 km.s-1. Faraday himself attempted to derive an 
approximate value for the velocity of ions in solution, not of the action 
of electricity (nrs. 1651. and 1652. in the Thirteenth Series). It just ended 
with a hypothetical comparison of the quantity of electric power equal 
to the effect appearing instantly at the distance of 576000 miles from its 
source, on the one hand, with the effect which is obtained by the move-
ment of hydrogen and oxygen after electrolysis of water through a cer-
tain distance of one tenth of an inch within an hour and a half, on the 
other hand.
6 Our justification for coining the term electrophoretic current for the 
flow of charges carried by ions is given in detail in Part 2.[4] We empha-
size that by electrophoresis we mean the movement of charged particles 
under direct current conditions, but not under alternating current con-
ditions. Under both conditions the electrical conductivity nevertheless 
has the same values.
7 Claude Servais Mathias Pouillet (1790, Cusance, Doubs – 1868, Par-
is) was a French physicist, and politician until the February revolution 
from 1848. His research comprised optics, photometry, thermody-
namics and electricity. His main publications were, among others, the 
book “Élémens de physique expérimentale et de météorologie”, published 
in 1827,[17] and “Mémoire sur la chaleur solaire, sur les pouvoirs rayon-
nants et absorbants de l’air atmosphérique et sur la température de l’es-
pace“(Memoir on the solar heat, on the radiating and absorbing powers of 
atmospheric air and on the temperature of the space) in 1838.[18] Claude 
Pouillet must not be confused with his brother Marcellin Pouillet, who 
was chemist at Conservatoire des Arts et Métiers.

no gold in the arm with the negative electrode, but 
gold in its initial content in the one with the positive 
electrode. Pouillet concluded from this result that the 
negative electrode took up the gold, while the chlo-
ride was transported to the positive electrode through 
a series of decompositions and recombinations and 
was set free there. Like Daniell and Miller, Pouillet 
concluded that the migration velocities of the anions 
and the cations are not the same, contrary to previous 
belief.[19, 20] Alfred Smee8 had a different point of view. 
He assumed that the primary process is the decompo-
sition of water when a metallic solution (i.e., a solution 
of a salt of a metal) is subjected to galvanic action. The 
following reduction is a secondary process caused by 
the hydrogen produced first by the metal from its salt 
solutions.[21, 22] In summary, all experiments reported 
so far have led to different and contradictory assump-
tions about the electrophoretic migration velocities of 
ions but none has contributed to the central question 
of their magnitude.

However, before continuing the discussion of fur-
ther approaches to determining the ion speeds, initi-
ated by Wilhelm Hittorf and his concept of the trans-
ference number, the author will not fail to show that 
theories long believed to have been overcome still had 
ardent supporters in the middle of the Long Nine-
teenth Century, albeit rarely. At that time, it came as 
a surprise that established theories, e.g., those of M. 
Faraday, were still rejected by staunch proponents of 
the Phlogiston Doctrine. One of these advocates was 
William Ford Stevenson (1811 – 1852), after all Fel-
low of the Royal Society, who in 1846 published a 
book whose title already fully reveals its content. It 
reads “Most important errors in chemistry, electricity, 
and magnetism, pointed out and refuted: and the phe-
nomena of electricity, and the polarity of the magnetic 
needle accounted for and explained by a Fellow of the 
Royal Society”.[23] Moreover, Stevenson was so violently 
provoked by the award of the Gold Medal of the Royal 
Society to the noted physico-chemist William Robert 
Grove9 in 1847 that he wrote a second conspicuously 
polemical book in 1849 entitled “The Composition of 
Hydrogen and the Non-Decomposition of Water incon-

8 Alfred Smee (1818, Camberwell – 1877, Finsbury Circus) was an 
English electro-scientist, metallurgist, chemist and surgeon.
9 Sir William Richard Grove (1811, Swansea, Wales – 1896, London) 
was a Welsh advocate. He did not practice this job; instead he became 
interested in electrical phenomena, and published his first paper on this 
topic in 1838.[24] Grove improved the Voltaic battery and invented a fuel 
cell battery what he reported in 1839,[25][26] and which is named after 
him. A basically similar cell[27][28] was invented by the German-Swiss 
physicist and chemist Christian Friedrich Schönbein (1799, Metzingen 
– 1868, Baden-Baden).



80 Ernst Kenndler

trovertibly established, in answer to the award of a med-
al by the Royal Society whereby the Contrary Doctrines 
are absolutely affirmed, also the Absurdity of the exist-
ing Systems of Electricity and Magnetism demonstrated 
and the True One Given.”[29] In this book, which, like 
his earlier one, was published by the author himself 
because all journals had refused to accept it, he again 
vehemently rejected all previous theories about the 
effect of electricity on liquids because they did not 
agree with the Phlogiston Doctrine. He was going so 
far as to accuse the Committee of the Royal Society, 
which awarded Grove the Golden Medal, of complete 
incompetence. We briefly quote verbatim one of his 
numerous attacks on the Committee, for example that 
on pp. 22-23.

Every body must know that the appreciation of a paper 
upon a special subject, such as Chemistry, must finally 
depend upon the opinions and report of those gentlemen 
who are presumed to be specially acquainted with the 
subject. My observation must therefore be understood to 
apply exclusively to the COMMITTEE of Chemistry, and 
to no other portion of the Royal Society. Of the names 
of the gentlemen composing this committee I am at this 
moment ignorant, and I have no motive whatever to 
induce me to make the inquiry.
I must, however, remark, that a TOTAL ABSENCE OF 
INFORMATION (a fact which will be elicited from a 
perusal of these pages) in a conclave of scientific men 
upon a subject on which they were voluntarily about to 
pronounce, and actually did pronounce, a most important 
opinion (an erroneous one, as may be supposed) pregnant 
with vast consequences is, I believe and trust without a 
parallel in the annals of science.10

To remind the readers of the state of science at that 
time, we mention that already more than four decades 
ago, viz. in 1804, the last prominent supporter of the 
phlogiston theory died, John Priestley, who defended 
this doctrine as late as 1803 with the book “The Doctrine 
of Phlogiston Established and that of the Composition of 
Water refuted”.[30] We refer, on the other hand, to some 
contemporary works, e.g., those of Michael Faraday 
in 1846,[31] of James Clerk Maxwell ś first paper also in 
1846,[32] of Rudolf Clausius and of James Prescott Joule 
in 1850,[33, 34] to name only the best known, and come to 
the works of Wilhelm Hittorf, who raised the knowledge 
of ion migration to a next level.

10 The capital letters and italics correspond to the original text.

W. HITTORF: RELATIVE MIGRATION VELOCITIES 
AND TRANSFERENCE NUMBERS OF IONS OF AN 

ELECTROLYTE

From 1853 to 185911 Wilhelm Hittorf developed a 
promising attempt to measure the migration velocities 
of ions.12 He described his basic idea in 1853 in a first 
paper out of four, entitled “Ueber die Wanderung der 
Ionen während der Elektrolyse. Erste Mittheilung.”[36] (On 
the migration of ions during electrolysis. First Notice.)13 
This concept was still based on the traditional view that 
a cation, C, and an anion, A, are tightly bound in solu-
tion in the absence of an electric field, forming a single 
macroscopically uncharged unit or molecule CA. Conse-
quently, free ions were believed not to exist. Note that in 
Hittorf ś conception the distance between the molecules 
was much larger than the moleculeś  size. This differed 
significantly from the theories of Grotthuß, Davy and 
Berzelius, in which the molecules in the chains to which 
they arrange were in direct contact (see Part 2 of our 
series). This greater distance between the molecules is a 
precondition for Hittorf ś theory.

Hittorf based his concept on the relationship 
between the velocity of ions to their respective elec-
trodes and the change in their concentrations there 
before and after electrolysis. Hittorf believed, in contrast 
to the established assumption of equal velocities, that 
ions migrate at different speeds, and postulated that this 
hypothesis can be confirmed by determining the change 
of their concentrations in their solutions at the electrodes 
by chemical analysis. He assumed that more of faster-
moving cations must be found at the cathode and fewer 
of slower-moving anions at the anode, and vice versa.

In Hittorf ś concept the molecules CA with cations 
C and anion A are initially aligned under the influence 
of the electric potential, so that the ions are directed 
towards their respective electrodes, as shown in Fig. 1, 
row a (anions are depicted as black semicircles, cations 

11 On November 24th of the same year 1859 Charles Darwin published 
his seminal book “On the Origin of Species by means of Natural Selec-
tion, or the Preservation of favoured Races in the Struggle for Life”.[35]
12 Johann Wilhelm Hittorf (1824, Bonn – 1914) studied mathematics 
und natural sciences in Bonn. After receiving his doctorate in 1848, he 
was given the position of a university lecturer in the following year. In 
1856 he became professor of physics and chemistry at the University of 
Münster (Westphalia) and director of laboratories from 1879 to 1889. In 
the 1850s Hittorf contributed significantly to electrochemistry with the 
introduction of the transference numbers of ions, and constructed the 
instrumentations for their determination. Hittorf directed his research 
further to the passage of the electric current through gases and to the 
emitted spectra, and discovered the electron rays, later called cathode 
rays.
13 The Engl. translation was published in Harper’s Scientific Memoirs 
from 1899, ref. [37], pp. 49-80.



81Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

as open semicircles; single-charged ions are considered). 
Next, the assembled ions of molecule CA separate from 
each other and move to the nearest oppositely charged 
ion,14 with which they combine to form a new molecules 
AC (row b). Note that the ion travels as a free ion during 
the movement over this distance. Prior to the next step, 
this newly formed molecules AC had to rotate by 180° 
from AC to CA in order to get their proper position, 
that is to say, to be aligned with the respective electrodes 
(row c). Then, this process of decomposition and recom-
bination continues as long as the electric potential is 
applied and the ions are finally decomposed electrolyti-
cally. The number of cations and anions decomposed by 
electrolysis is the same, independent of their velocities 
and in accordance with Faraday ś law of definite electro-
chemical action (see Chapter 3.1.4. in Part 2).

In order to prove the validity of his concept experi-
mentally, a vessel of a measuring device was first filled 
with a solution with a given initial concentration of the 
electrolyte. In contrast to Daniell ś instrument, the ves-
sel was not separated by a membrane, a diaphragm or 
another porous boundary. In Figure 1 the ions of the 
molecules are depicted as full and empty semicircles. 
If we suppose that the velocities of both ion species are 
equal, the ions reassemble into new molecules in the 

14 We called it counterion in previous Part 2, and will use this term in 
our publications. It is customary in modern phraseology.

middle of their distance, and both travel along the same 
distance in a given time. Therefore, the change of their 
concentrations in their respective electrode compart-
ments would be the same.

In the general case, when the two types of ions have 
different velocities, they travel different distances within 
a certain time before reuniting to form the next mol-
ecule. Then, eventually, more ions of the faster species 
reach the solution near the respective electrode, and few-
er ions of the slower species reach the oppositely charged 
electrode. Thus, the number of ions of the two species 
in their electrode compartments is unequal. We empha-
size again that this argument is valid even if, according 
to Faraday’s above-mentioned law, the same number of 
both ions is electrolytically decomposed in their com-
partments.

The question arises as to how Hittorf solved the 
problem of separating the vessel into an anode and cath-
ode compartment without inserting a porous boundary. 
Hittorf ’s solution, which circumvented this problem is 
shown schematically in Figure 2.15 There, the electro-
lyte solution is separated not by a real boundary but by 
an imaginary one, indicated by the vertical line, which 
can be placed anywhere. The cathode is on the left side, 

15 In this figure, the representation of the molecules in the vertical direc-
tion and in direct contact to each other is as in Berzelius’ paper, ref. [38], 
p. 278, is in discrepancy with Hittorf´s own assumption on p. 180, ref. 
[36] “Der Zeichnung liegt die Annahme zu Grunde, daß die Entfernung 
zwischen den benachbarten Atomen des Elektrolyten größer als diejenige 
ist, in welcher die chemisch verbundenen Ionen jedes Atoms von einanan-
der abstehen“ (The drawing is based on the assumption that the distance 
between the neighboring atoms of the electrolyte is greater than the 
distance between the chemically bonded ions of each atom.) This require-
ment is satisfied in Figure 1. However, the deviation in Figure 2 has no 
consequence for Hittorf´s conclusions. [The author].

Figure 1. Hittorf´s concept and determination of the relative 
velocities and the transference numbers for the case that anions 
and cations have equal migration velocities. Anions: black semi-
circles; cations: open semicircles. In solution, the ions are present 
in pairs as macroscopically uncharged molecules, since all ions 
unite with their oppositely charged ions by electrostatic attraction. 
There are no free ions present. Row a: When an electric potential is 
applied, the molecules are aligned in the direction of their respec-
tive electrodes. Row b: The molecules are split into their ions, which 
migrate towards their corresponding electrodes, but reassemble 
with the oppositely charged ions in their immediate vicinity to form 
new molecules. Row c: The molecules rotate 180° to take the proper 
position in the field. Details can be found in the text. The figure is 
reproduced from Hittorf´s publication from 1853 (ref. [36], Plate II, 
after p. 352).

Figure 2. Hittorf´s concept and determination of the relative veloci-
ties and transference numbers for the case that anions and cations 
have different migration velocities. Anions: black full circles; cations 
open circles. Cations migrate in direction of the arrows to the left, 
anions to the right. Details are described in the text. (From ref. [36]).



82 Ernst Kenndler

the anode on the right side. The cations are depicted 
as open circles, the anions as black circles. The trans-
fer mechanism involving the 180° rotation is the same 
as described above. In the present example, the initial 
number of each ion type or equivalent is 18 (top row), 
The fictitious cathode compartment (left) contains 8 
molecules, the anode compartment 10.

After completing the circuit, the ions migrate with 
velocities, v. In the case depicted in Figure 2 the cations 
cross the fictitious boundary faster than the anions. We 
assume, for example, that the anions travers ⅓, the cati-
ons ⅔ of their distance after their dispartment and the 
following recombination. But how can these different 
distances be determined? Hittorf turned this problem 
from the molecular to the molar scale, and developed 
the following method, for which we select at random the 
conditions in the anode compartment. He considered 
the change of the numbers (or equivalents) of anions 
and cations there. He recognized that from the begin of 
the electrolysis, shown in the top row, to its end (in the 
bottom row) the number of cations is reduced from 10 to 
6, that is, 4 cations traversed the boundary and migrated 
towards the cathode. The number of anions in the anode 
compartment changed from 10 to 12, that is, it increased 
by 2. In the solution, 6 from the 12 anions remained and 
6 were electrolytically decomposed; this decomposition 
applies to the cations as well. Thus, 2 anions crossed 
the boundary and moved into the anode compartment. 
To conclude, in the anode compartment a reduction of 
cations from 10 to 6 happened, equals 4, and the change 
of the number of anions is from 10 to 12, equals two. It 
follows that the change in equivalents in the anion com-
partment for the anions and for cations is ⅓ and ⅔. This 
result which would be obtained by experiment is identi-
cal to our input assumption.

Generally speaking, if the one ion traverses 1/n of 
the distance, the other (n-1)/n, after electrolysis the com-
partment of the former ion contains 1/n equivalent more 
of the one, and (n-1)/n equivalents less of the other ion. 
Hittorf termed these numbers “Überführungszahlen” 
(transference or transport numbers) which we symbolize 
by τ. Their sum (τ++τ–) equals one. As mentioned above, 
they can be derived by quantitative chemical analysis of 
their concentrations.

The transference numbers express the migration 
velocity of the one ion relative to the counterion in a 
given electrolyte. The smaller the transference number 
of the ion, the slower is its migration velocity relative to 
its counterion. In the above example τ– was ⅓, τ+ was ⅔, 
which is consistent with our initial assumptions about 
the different distance the two ions travel before forming 
a new molecule, or that the cation migrates at twice the 

speed of the anion. In general, the ratio of the transfer-
ence numbers is equal to the inverse ratio of the veloci-
ties by τ+/τ–=v–/v+. It should be noted that one does not 
obtain the absolute migration velocity of an ion, but only 
that relative to the counterion of the same electrolyte.

It is also mentioned that the transference num-
ber expresses the fraction of current, i, transported by 
one type of ion in relation to the total current, i.e., the 
sum of the currents of both types of ions. It reads, for 
example, for the cation τ+=i+/(i++ii). To get the currents 
Hittorf used a Poggendorff silver electrometer to simul-
taneously measure the total amount of current flowing 
during electrolysis and obtained (i++ii). Then, he recal-
culated i+ from the number of equivalents of the cation 
which he determined by chemical analysis in the anode 
compartment, and received the fraction of the current 
which was transported by the cation, and which is equal 
to its transference number τ+. Since (τ++τ–)=1, the trans-
ference number, τ–, of the anion can be calculated with-
out measuring it. It is therefore sufficient to measure the 
concentration, and thus the value of τ, of only one ion 
in one compartment, and neither both in the same com-
partment, nor all four in the two compartments.

For the experimental determination of the concen-
trations of the ions after electrolysis, Hittorf modified 
the cell of Daniell and Miller by omitting the mem-
branes. Readers interested in details are referred to the 
comprehensive description in Hittorf ś First Notice of 
1853[36] which after all covers the three pages 187-189. 
The schematic drawing of the device is given in Fig. 4 in 
Plate II, after p. 352.

In this First Notice Hittorf examined different cop-
per and silver salts. He found that their transference 
numbers were independent of the (low) current. Their 
changes, within the investigated temperature range 
between 4°C and 21°C proved to be unreliable.16 Rel-
evant for future research, especially for that of Friedrich 
Kohlrausch, was his observation that the transference 
numbers can depend significantly on the concentration 
of the electrolyte.

16 Note that we are discussing transference numbers, not conductivities. 
The German physicist Gustav Heinrich Wiedemann (1826, Berlin – 
1899) observed that the electric conductance (or resistance) of electrolyte 
solutions depends on their viscosity. He varied the viscosity of the solu-
tion by varying the temperature and/or the salt concentration, and sup-
posed a relation between the electric behavior and the mechanistic prop-
erties of the solutions. However, Wiedemann found that these conclu-
sions were based on imperfect and preliminary experiments (see ref. [39], 
pp. 169, 170). Wiedemann´s conclusions nonetheless preceded Walden´s 
rule or Walden´s product (named after Paul Walden, a Russian-Latvi-
an-German chemist), which he formulated in 1906,[40] sixty years after 
Wiedemann´s assumptions. Walden´s rule states that the product of the 
conductivity of an electrolyte solution at limiting conditions and the vis-
cosity of the solvent is constant and independent of the solvent.



83Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

Hittorf also speculated on possible sources of error, 
primarily with respect to the role of water, since he 
assumed, contrary to popular belief, that instead of the 
cation of the salt, H+ from the water could be reduced 
directly. However, he found that this primary, direct 
reduction of H+ to gaseous hydrogen could be neglected. 
To support his opinion, he used solvents that were not 
decomposed electrolytically and measured the transfer-
ence numbers in absolute ethanol and, in later Notes, 
in amyl alcohol. His results made it clear that water did 
not contribute to the current; it acted only as an electro-
chemically inactive solvent of the salts.

For the Second Notice from 1856 Hittorf construct-
ed an improved device, again without membrane, and 
investigated whether or not electroosmotic flow affected 
the transference numbers.[41] He compared the results 
measured in devices with and without a membrane, and 
obtained the same transference numbers.

History showed that it is not uncommon for a front 
of critics and opponents to form when a new theory or 
method is introduced.17 This also happened with Hittorf, 
and so he began his Third Notice in 1859[42] with a reply 
to Wiedemanń s critique.[39] Then a comprehensive reply 
to the derogatory reproaches [43, 44] of Gustav Magnus18 
followed, whom he called ”Hauptgegner meiner Arbe-
iten“ (main opponent of my works). In ref. [42], p.342, 
Hittorf wrote

Magnus hatte in seiner ersten Abhandlung, §9, meiner elek-
trischen Arbeiten erwähnt und angegeben, daß dieselben 
mit der Zersetzung, welche die Elektrolyte durch den Strom 
erfahren, nichts zu thun hätten und über die Daniell śche 
Theorie … nichts lehren. (Magnus had mentioned my elec-
trical work in his first paper, §9, noting that it had nothing 
to do with the decomposition of electrolytes by the current 
and that it taught nothing about Daniell’s theory.)

The rigor with which Hittorf rejected this criticism 
is evident in the fact that it extended over twenty print-
ed pages. The remaining part of this Third Notice dealt 
with the transference of compounds that Hittorf had not 
examined in the Second Notice.

A paragraph in the Fourth and last Notice[45] worth 
noting comprised, beyond the determination of transfer-

17 Svante Arrhenius, for example, was even lampooned when he present-
ed his dissociation theory. Ironically, 25 years later he was awarded the 
Nobel Prize. We will tell this episode in the next Part 4 of our historical 
review series.
18 Heinrich Gustav Magnus (1802, Berlin – 1870) was an influencing 
German chemist and physicist. In 1845 he became professor of physics, 
chemistry and technology at the University in Berlin. His students or 
coworkers were, among others, A. von Baeyer, E. Du Bois-Reymond, R. 
Clausius, P. von Groth, H. von Helmholtz, G. Kirchhoff, A. Kundt, E. 
Sarasin, J. Tyndall and E. Warburg. 

ence numbers, Hittorf ś critique of Clausiuś  theory.[46] 
We will return to this theory below. Contrary to estab-
lished opinion, Clausius postulated that free ions do 
exist in solution even in the absence of an electric poten-
tial due to their motion caused by their thermal energy. 
Hittorf strictly rejected this theory and commented on 
p. 584

Der Schluß, zu den Hr. Clausius aus seinen Prämis-
sen gelangt, steht meinen Erfahrungen nach mit der 
Wirklichkeit im Widerspruch, … Es sind bloß die letzt-
genannten Zersetzungen, welche die Theorie der Elektro-
lyse von Hrn. Clausius brauchen kann. Bis jetzt ist kein 
Chemiker so kühn gewesen, sie anzunehmen, … (The 
conclusion Mr. Clausius draws from his premises is, in my 
experience, at odds with reality, … Only the latter decom-
positions can use Mr. Clausius’ theory of electrolysis. 
Until now, no chemist has been so bold as to accept it.)

We see that Hittorf was not only the target of criti-
cism, but was himself a critic. The last part of this paper 
dealt with the determination and discussion of the 
transference of complex ions, and what he called “double 
salts”.19 Salts of cadmium and iodine, for example, which 
contain complex anions will play an important role in 
Arrheniuś  dissociation theory.

At the time of Hittorf publications transference 
numbers by his method were also determined by G. 
Wiedemann[47] and by A. Weiske.[48] These and Hittorf ś 
data were later used by Friedrich Kohlrausch in his stud-
ies of conductivities.

We already pointed out that a given ion has different 
transference numbers in electrolytes of different compo-
sition, depending on the counterion. For example, Hit-
torf determined τ+ of 0.63 for Ag+ as acetate and of 0.47 
as nitrate (ref. [36], p. 206).20 From these data it follows 
that the silver ion velocity is 1.7 times higher than that 
of acetate, and about 10% lower than the nitrate velocity. 
Regrettably, the method provided only the relative ion 
velocities, but not the absolute values of the individual ion 
species. The decisive advance towards the solution of this 
problem was initiated by Kohlrausch’s work on the con-
ductivities of electrolyte solutions, in particular by his law 
of independent ion migration. We will discuss it below.

19 It can be assumed that the majority of readers have little interest in 
details. We have therefore included them in this footnote. These double 
salts consisted, for example, of K, Ag, and CN, or Na, Pt, and Cl. Their 
number was rather limited, since most were not stable when dissolved 
in water. Hittorf measured and discussed the transfer, for example, of 
the complex salts consisting of cadmium and iodine, which he was able 
to dissolve undecomposed in absolute ethanol and in amyl alcohol.
20 These values are in good agreement with current transference num-
bers, at 25°C, e.g., of 0.624 for Ag+ (0.01 mol.L-1) as acetate and of 
0.4648 as nitrate.[49]



84 Ernst Kenndler

The reader may wonder that this historical review 
does not even mention a certain empirical law which – 
as generally assumed – Friedrich Kohlrausch had con-
firmed by careful measurements in 1869.[50] It had, how-
ever, already been applied earlier, namely in the 1830s by 
Michael Faraday and in the 1850s by Wilhelm Hittorf 
in their investigations of the electrophoretic current in 
solutions of ions. It was also an indispensable law in fur-
ther research on this subject and is still daily practice. 
What is meant is the law about the connection between 
electrical potential difference, resistance and current 
strength, which Georg Simon Ohm had found empiri-
cally in the middle of the 1820s, albeit for metallic wires, 
i.e., for 1st class conductors.[51-56] That it also applied to 
2nd class conductors, that is to say, to solutions of ions, 
was by no means a foregone conclusion because of the 
fundamental difference in the nature of conduction. So 
how did it come about that Ohm’s law proved to be valid 
also for solutions of ions?

A LEAP IN TIME, BACK TO 1831: G. TH. FECHNER´S 
PROOF THAT OHM´S LAW APPLIES TO SOLUTIONS 

OF ELECTROLYTES

Before we get to Kohlrausch ś above-mentioned 
conductivity measurements, we have to realize that he 
did, in principle, measure the resistance or the specific 
resistance of the electrolyte solution, a property that we 
have yet not even addressed in this historical retrospect. 
To do this, we have to go back to the 1820s, to the time 
when Faraday made experiments in organic chemistry in 
Davy ś laboratory. At that time Georg Simon Ohm pio-
neered the research in electric resistance of 1st class con-
ductors.

Ohm was not affiliated with the scientific community 
at the time of his research. He was a school teacher at the 
Jesuit Gymnasium in Cologne when he derived his law in 
mid-1820s. He performed his experiments in the labora-
tory of this college with wires made of different metals 
and various lengths and diameters. He published his pre-
liminary results initially in two treatises in 1825.[51, 52] As 
he was not satisfied with his work,21 he developed a new 
theoretical approach, which led to the law named after 
him. This well-known law says that the current strength 
is directly proportional to the electric potential difference 

21 In the last two sentences at the end of his second paper from 1925,[51] 
Ohm complained about the lack of support for his research: “Meine Arbe-
it·fängt allmählig an, sich zu einem Ganzen zu runden. Nur bedaure ich, 
daß ich häufig aus Mangel an Mitteln, Untersuchungen abbrechen muß, die 
ich so gern weiter verfolgt hätte“ (My work gradually begins to round off 
into a whole. My only regret is that I often have to abandon investigations 
that I would have liked to pursue further, due to lack of funds.)

and indirectly proportional to the resistance of the con-
ductor. Ohm published his new theory in 1826.[53-55] In 
his opus magnum “Die galvanische Kette, mathematisch 
bearbeitet” (The galvanic chain, mathematically processed)
[56] he summarized in 1827 the results together with a 
comprehensive mathematical treatment.

Ohm ś work did not attract much attention, but the 
interest changed when French physicists claimed prior-
ity of the law for Claude Servais Mathias Pouillet,22 who 
rediscovered Ohm ś law years later and published his 
results in 1837[57] (German version in ref. [58]; the editor, 
Johann Christian Poggendorff, added a critical comment 
to this version, cited in footnote 23). Pouillet derived the 
according relations rather from experimental results 
which was considered as being superior to Ohm ś merely 
theoretical approach.

His assertion of priority provoked a heated debate, 
led primarily by Jean Claude Eugène Péclet, who pub-
lished a harsh rebuff of Pouillet’s claim in an essay enti-
tled “Lettre touchant un passage de la dernière édition du 
Traité de Physique de M. Pouillet” (Letter concerning a 
passage in the last edition of the Traité de Physique by M. 
Pouillet)[61] stating

C’est seulement en 1837 que M. Pouillet a publié son 
Mémoire dont toutes les formules se déduisent de celles 
de M. Ohm par de simples transformations, comme M. 
Henrici l’a démontré (Annales de Poggendorff tomes 
LIII[62] et LIV[63] ), … (It was not until 1837 that M. Pouil-
let published his Memoir, all the formulas of which can 
be deduced from those of M. Ohm by simple transforma-
tions, as M. Henrici has shown (Pogg. Annal. LIII and 
LIV),…)24 

Finally and at last Ohm’s priority was recognized 
internationally, and in 1841 he received the prestigious 
Copley Medal from the Royal Society in London. Nev-
ertheless, in Germany it lasted until 1852 that he became 
professor for experimental physics at the University in 
Munich, at the age of 63, two years before his death.

22 We quoted Pouillet already in the Introduction of this review.
23 Poggendorf commented: „Wiewohl die Resultate dieser Abhandlung 
zum Theil nur Bestätigungen der von Ohm („Die GaIvanisehe Kette” und 
Schweigg. Journ. Bd. XXXXVI S. 137),[59] entdeckten, auch von Fechner 
(Maaßbestimmung über die galvanische Kette) und früher von Pouillet 
selbst (Annal. Bd. XV S. 91)[60] beobachteten Gesetze sind, so schien doch 
die unverkürzte Mittheilung derselben,schon weil sie so wenig berücksich-
tigt wurde sind, nicht überflüssig. P.” (Although the results of this trea-
tise are partly only confirmations of the laws discovered by Ohm (“Die 
GaIvanisehe Kette” and Schweigg. Journ. Bd. XXXXVI p. 137),[59] also 
by Fechner (Maaßbestimmung über die galvanische Kette) and earlier by 
Pouillet himself (Annal. Bd. XV p. 91)[60] so the unabridged communica-
tion of them seemed not superfluous, already because they were so little 
considered. P.) [citations added by the author].
24 Complete literature sources added by the author.



85Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

Initially regarded of minor importance, his law was 
later recognized as highly significant for the technology 
of ever-widening electrical telegraphy, especially after 
the mid-1850s with the introduction of the single-wire 
system by Samuel Morse.

We have mentioned above that after his publication 
in 1827 Ohm ś work was widely ignored, and only few 
scientists recognized its importance, with Gustav Theo-
dor Fechner25 as Ohm ś main supporter (his portrait is 
shown in Figure 3).

25 Gustav Theodor Fechner (1801, Groß-Särchen, now Żarki Wielkie, 
near Muskau in Lower Lusitia – 1887, Leipzig) attended the Academy 
of Arts in Dresden from 1814, and studied medicine there from 1817 
and in Leipzig from 1818, where he graduated in 1823. However, he 
left the field of medicine and completed his habilitation in 1823 at the 
Philosophical Faculty. He was appointed professor of physics in 1834; 
his research focused on galvanism and optics. Due to a severe eye com-
plaint from 1840 to 1843, he retired. In 1860 he expanded Weber´s law 
to Weber-Fechner law. This law expresses the non-linear relationship 
between psychological sensation, S, and the physical intensity, I, as S = 
K ln I.

Fechner’s scientific merits should not be underesti-
mated, although they were, because he extended Ohm’s 
theory of the 1st to 2nd class conductors. His work is 
therefore indispensable for electrophoresis. He is also 
worth noting because, in addition to his scientific inter-
ests, he had a penchant for writing satirical pseudo-sci-
entific works. In 1821 he published his first paper ever; 
it was entitled “Beweis, daß der Mond aus Jodine beste-
he” (Proof that the moon consists of iodine),[65] published 
under his pseudonym Dr. Mises. It is a humorous pam-
phlet against materialistic medicine. Of similar kind was 
his scientific satire from 1825 “Vergleichende Anatomie 
der Engel” (Comparative anatomy of angels).[66]

In these early 1820s, Fechner prepared the transla-
tion of Jean-Baptiste Biot ś textbook “Précis élémentaire 
de physique expérimentale”[67, 68] into German, which 
appeared in 1824 and 1825, but he found the descrip-
tion of electricity and of the theory of galvanism in this 
book highly out of date. In order to raise these themes 
to the contemporary level, he decided to upgrade it by 
Ohm ś theory. At this occasion, he found keen interest 
in this topic, and expanded his research from the hith-
erto investigated metallic conductors to liquids, pio-
neering in this way the quantitative context of electric 
potential difference, current and resistance in ion solu-
tions.26 After two years of extensive experimental work, 
Fechner presented his results and conclusions in the 
book “Massbestimmungen über die galvanische Kette” 
published in 1831.[69]

Fechner demonstrated that Ohm ś law not only 
applies to metallic conductors, but also to electrolyte 
solutions. He gave a résumé of these findings (amongst 
others) by stating on pp. 235-236 of his book

… (i) Der Leitungswiderstand der Flüssigkeiten ist dem 
Abstande der Erregerplatten darin direct proportional… 
(ii) Der Widerstand der Flüssigkeit steht im umgekehrten 
Verhältnisse des Querschnittes der Flüssigkeit… .(iii) Der 
Widerstand der Flüssigkeit ist unabhängig von Beschaf-
fenheit der Plattenpaare… (iv) Der Widerstand der Flüs-
sigkeit nimmt ab mit der Quantität saurer oder salziger 
Bestandtheile, die man in dieselbe hinzufügt. (v) Durch 
fortgehends gleiche Zumischungen gleicher Antheile Säu-
re wird der Widerstand des Brunnenwassers auch fortge-
hend um gleiche Quantitäten verringert…“ ((i) The elec-
tric resistance of the liquids is directly proportional to the 
distance of the excitation plates therein. (ii) The resistance 
of the liquid is in inverse proportion to the cross section 
of the liquid … (iii) The resistance of the liquid is inde-
pendent of the nature of the plate pairs … (iv) The resist-

26 The water Fechner used in his experiments can be considered rather 
as a dilute electrolyte solution. Water with the highest purity which was 
available for him was well water, which certainly contained a relatively 
high amount of ions. All the more his results are to be appreciated.

Figure 3. Portrait of Gustav Theodor Fechner (1801 – 1887). Date 
and author unknown. Source, ref. [64], public domain.



86 Ernst Kenndler

ance of the liquid decreases with the quantity of acidic or 
salty components are added to it. (v) By continuously add-
ing equal amounts of acid, the resistance of the well water 
is also continuously reduced by equal quantities…)

If we convert these formulations into a modern 
notation, we get for a given solution that (i) R=prop l; (ii) 
R=prop(1-A); (iii) R≠f(U); (iv) and (v) R=prop(-S.c). Sym-
bol R stands for the electrical resistance of the liquid, l is 
the distance between the electrodes, A is the cross sec-
tional area of the electrodes, U is the electrical potential 
difference, and c is the concentration of acidic or salty 
additives to water; S is a factor of proportionality. It is 
seen that these findings actually represent the first evi-
dence that Ohm ś law also applies to liquid conductors.27 
It is worth noting that the combination of (i) and (ii) 
leads to equation R=prop(l/A), in accordance with mod-
ern notation as R=ρl/A, in which ρ is termed electrical 
resistivity or specific electrical resistance.

After his retirement, Fechner focused mainly on 
philosophy and topics of psychophysics and psycho-
logical aesthetics. During this time he published works 
mainly based on Natur Philosophie and religious-mysti-
cal ideas.28

R. CLAUSIUS’ THEORY: FREE IONS ARE PRESENT 
IN ELECTROLYTE SOLUTIONS EVEN WITHOUT AN 

APPLIED ELECTRIC FIELD

Coming back now from Fechner ś time to 1852, 
when Rudolf Clausius29 turned his interest on 2nd 
class conductors after publishing his paper about the 
work done on 1st class conductors and the heat gener-
ated thereby30,[84-86] In “Ueber die Elektricitätsleitung 

27 It is clear that points (iv) and (v) do not have counterparts in pure 
metals, but the observations were nevertheless correct and preceded at 
least within a small concentration range the measurements of the con-
ductivities by F. Kohlrausch.
28 Fechner published, for example, poems,[70] a book about the soul 
life of plants,[71] 3 vol. about things of heaven and the hereafter,[72][73][74] 
about psychophysics,[75][76][77][78] a book with the mysterious title “the 
day view versus the night view”,[79] but also a paper in Pogg. Ann. Phys. 
Chem. “Ueber die Bestimmung des wahrscheinlichen Fehlers eines Beob-
achtungsmittels durch die Summe der einfachen Abweichungen” (On the 
determination of the probable error of an observation mean by the sum of 
the simple deviations.)[80]
29 Rudolf (Julius Emanuel) Clausius (1822, Köslin, province of Pomer-
ania in Prussia, now Koszalin, Poland) -1888, Bonn] is one of the first 
theoretical physicist of the Nineteenth century and a central founder 
of thermodynamics (2nd law of thermodynamics), and the kinetic gas 
theory. He created the concept of entropy and contributed significant-
ly to fundamental concepts of statistical mechanics. Less known is his 
work on free ions in solutions, which he carried out mainly during his 
research activities as professor at the ETH in Zürich in the 1850s.
30 In this paper Clausius derived the theoretical basis of the empirical 

in Elektrolyten” from 1857[46] (Engl. vers., On the Work 
performed and the Heat generated in a Conductor by a 
Stationary Electric Current,[87] French vers., Mémoire 
sur la Chaleur dégagée par les courants électriques.[88]), 
Clausius expressed his rejection of the established view 
of the transport of electric charges through electrolyte 
solutions, a theory that was going back to Theodor von 
Grotthuß. Even in Clausiuś  time (and later), it was gen-
erally assumed that the electrolyte molecules, called the 
complete molecules by him, were composed of atoms or 
groups of several atoms, which he called partial mol-
ecules.31 Each molecule consists, as was believed, of two 
tightly bound partial molecules of opposite charge (i.e., 
ion and counterion). We recall that in the theories of 
Grotthuß and Davy the molecules form a continuous 
chain that extends without gaps from one electrode to 
the other. Only the terminal molecules of this chain are 
in direct contact with the electrodes and are the first to 
be decomposed during electrolysis. Then, an instantane-
ous recombination of the ions with the counterions of 
the neighboring molecules, and the decomposition of the 
newly formed molecules happens along the entire chain. 
We will not repeat this mechanism of the flow of elec-
tricity as we discussed it in detail in the previous Part 2 
of our series.[4] Important to emphasize is that the estab-
lished theories of Grotthuß and Davy exclude the pres-
ence of free ions in solution in the absence of an electric 
potential, because an electric force would be mandatory 
to separate the tightly bound ions of a molecule.

In his said paper from 1857 Clausius radically broke 
with this conventional view[46, 87, 88] He first considered a 
liquid that contains “electrolytic molecules”, i.e., electro-
lytes. Clausius’ basic condition for all further considera-
tions was that electric neutrality had to be in every vol-
ume element of the liquid. If there was no external elec-
tric force, the molecules were dispersed in an arbitrary 
order and possibly vibrated around a certain equilibrium 
position. He further assumed that in the same molecule 
the attraction between ion and counterion, which are 
close to each other, is greater than the attraction of one 
ion to the counterion of another molecule.

Clausius assumed, in analogy to his paper “Ueber 
die Art der Bewegung, welche wir Wärme nennen”[90] 
(The nature of the motion which we call heat)[91] from 

results of J. P. Joule,[81] M. E. Lenz, the father of Robert Lenz[82] and 
Edmond Becquerel.[83]
31 Clausius did not use the terms ion, anion and cation in this paper, 
although they have been known since 1834, when Michael Faraday intro-
duced them.[89] Clausius differentiated the neutral “Gesamtmolecüle” 
(complete molecules), which were combinations of the oppositely charged 
ions, which he called “Theilmolecüle” (partial molecules). For the sake of 
simplicity, we name Clausius´ “complete molecule” as molecule, and, “par-
tial molecules” as ions, and cations and anions if appropriate.



87Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

the same year that – in absence of an electric field – the 
electrolyte molecules do not remain permanently in the 
liquid in an equilibrium position around which they 
oscillate. On the contrary, they are moving and their 
motion is irregular. Moreover, an ion can be disconnect-
ed from its molecule due to its thermal energy and then 
moves randomly between the other molecules in the 
solution. It can happen that this ion attracts the counter-
ion of another molecule more strongly than the ion and 
counterion of this molecule attract themselves. In this 
case, this ion and the counterion of the molecule form 
a new molecule and the parent ion is set free. It then 
moves in the solution between the other molecules and 
reacts with one of them in the manner just described; 
then the whole process continues.

A second possibility for the formation of free ions 
assumed by Clausius was that two different molecules 
interact with each other. In this case, it can happen that 
the ion of one molecule takes a preferred position over 
the counterion of the other molecule and these two ions 
combine to form a new molecule. This process releases 
two ions, which either combine to form a new molecule 
or disperse between the other molecules in the solution 
and act there as described above. We emphasize again 
that we have described the situation in the absence of an 
external electric force. It was considered by Clausius as 
the natural state of electrolytes in solution.

When an external electrical force acts, the first reac-
tion of the molecules would be to rotate into the proper 
position towards their respective electrodes (what Davy 
and Berzelius did not take into account, but Hittorf 
did). Then the force would separate ion and counterion 
of a molecule and drive them in opposite directions. In 
this case the ion of one molecule may combine with the 
counterion of the other. However, this can only happen 
if the attractive force between the ion and the counte-
rion of the one molecule is overcome. Clausius argued 
that the influence of the external electric force not only 
starts from a certain strength, but that even the slightest 
force acts in the manner described above. The magnitude 
of the effect increases with the strength of the force. That 
is, the effect fully complies with Ohm’s law. He wrote (we 
reproduce verbatim the Engl. version, ref. [87], p. 99-100)

But in order to separate the already combined partial 
molecules, the attraction which they exert upon each oth-
er must be overcome, for which a force of a certain inten-
sity is necessary; hence we are led to the conclusion, that 
so long as the force acting within the conductor does not 
possess this requisite intensity, no decomposition what-
ever can take place; but that, on the other hand, as soon 
as the force has attained this intensity, a great many mol-
ecules must be simultaneously decomposed, inasmuch 

as all are exposed to the influence of the same force, and 
have almost the same relative positions to each other.

and continued

So long as the moving force acting within the conductor is 
below a certain limit, it causes no current whatever; so soon 
as it attains this limit, however, a very strong current is sud-
denly produced. This conclusion, however, is in direct contra-
diction to experiment. The smallest possible force gives rise 
to a current accompanied by alternate decompositions and 
recombinations, and the intensity of this current increases 
in proportion to the force, according to Ohm’s law.

However, in the original paper written in German, 
this passage has another meaning; it reads (ref. [46], p. 
346-347)

So lange die im Leiter wirksame treibende Kraft unter 
einer gewissen Gränze ist, bewirkt sie gar keinen Srom, 
wenn sie aber diese Gränze erreicht hat, so entsteht plöt-
zlich ein sehr starker Strom. Dieser Schluß widerspricht 
aber der Erfahrung vollkommen. Schon die geringste Kraft 
bewirkt einen durch abwechselnde Zersetzungen und 
Wiederverbindungen geleiteten Strom, und die Intensität 
dieses Stromes wächst nach dem Ohm’schen Gesetze der 
Kraft proportional. [The reader’s attention is drawn to 
footnote 32].

If an external electric force acts, the cations and 
the anions in the solution do not move randomly, but 
are driven in opposite directions. In addition, the force 
facilitates the decomposition of the molecules, and the 
detachment of an ion from its molecule occurs more 
frequently than without such electric force. Clausius 
assumed that the number of positive and negative ions 
which move in opposite direction is not necessarily 
equal, it depends on their activity of molecular motion, 
which can be different for different ions. The counter-
directed movement of both types of ions represents the 
galvanic current33 in the liquid. Its strength is given by 
the sum of the flows of both ions.

32 The author would like to add a note here. He refers to the mislead-
ing or even wrong translation of Clausius’ original work in the English 
version, which he has marked in italics in the main text. Clausius wro-
te verbatim: “Dieser Schluß widerspricht aber der Erfahrung vollkom-
men.” The English version reads: “This conclusion, however, is in direct 
contradiction to experiment.” The term Erfahrung is translated here by 
experiment, but the correct translation is experience – in fact a crucial 
difference. In the French version the sentence is correctly translated as 
“… En d´autres termes, aussi longtemps que la force est au-dessous d´une 
certaine limite, il n´y a pas de courant, et dès que cette limite est dépassée, 
il nait subitement un courant intense. Cette conclusion est évidement con-
traire à l´expèrience.”, ref. [88], p. 254.)
33 We call it, as defined in the previous parts of our review, the electro-
phoretic current. It is not the flow of charges carried by electrons. The 



88 Ernst Kenndler

This theory also offers the explanation why the 
conductivity of a 2nd class conductor increases with 
increasing temperature: it is because the greater the 
activity of motion of the particles due to their thermal 
energy in the solution, the more the decomposition of 
the molecules is facilitated.

Although Clausius’ innovative theory of the per-
manent presence of free ions offered new explanations 
for the properties of electrolyte solutions and became 
widely known, it is noteworthy that the majority of the 
scientific community (but not its elite) did not replace 
the theory published by Grotthuß half a century ago in 
1805. This lack of scientific acceptance was criticized, to 
quote an arbitrarily chosen example, in an 1879 publi-
cation, another two decades after Clausius’ work. Franz 
Exner,34 professor of physics at the University of Vienna 
and teacher of two Nobel Laureates, pointed out in his 
publication “Ueber die Electrolyse des Wassers” (On the 
electrolysis of water), ref. [92], p. 350)

… dass die Clausius’sche Hypothese über die Constitution 
der Flüssigkeiten der Theorie der Electrolyse… mit den 
bekannten Thatsachen nicht nur nicht im Widerspruche 
steht, sondern durch dieselben auf das Entschieden-
ste bestätigt wird. Unter allen Umstânden aber ist es 
an der Zeit, die jetzt noch fast ausschliesslich citirte 
Grotthuss’sche Theorie der Electrolyse endgültig fallen 
zu lassen; denn seit wir … einen klarern Einblick in das 
Wesen dieser Vorgänge erlangt haben, erscheinen die von 
der Grotthuss’schen Theorie geforderten, von Molecül zu 
Molecül fortschreitenden Zersetzungen und Wiederver-
einigungen als eine absurde Vorstellung. (… that Clausius’ 
hypothesis of the constitution of liquids does not contra-
dict the theory of electrolysis … not only with the known 
facts, but is most decidedly confirmed by them. Under all 
circumstances, however, it is high time to finally abandon 
Grotthuß´ theory of electrolysis, which is almost exclu-
sively cited; for since we … have gained a clearer insight 
into the nature of these processes, the decompositions 
and reunifications which progresses from molecule to 
molecule, as required by Grotthuß´ theory, appear to be 
an absurd notion.)

It took nevertheless another decade before the 
existence of free, non-associated ions, as formulated in 
Svante Arrheniuś  seminal theory, was accepted, albeit 
reluctantly and against fierce opposition.

charges are carried – notabene – by ions, which is the unique feature of 
electrophoresis.
34 Franz Serafin Exner (1849, Vienna – 1926) was an Austrian physi-
cist. In 1891 he became professor of physics at the University of Vienna 
and succeeded J. J. Loschmidt. His best-known students were the Pol-
ish physicist Marian Smoluchowski, and the Austrian physicists Erwin 
Schrödinger (Nobel Laureate for physics 1933), and Victor Franz Hess 
(Nobel Laureate for physics 1936).

F. KOHLRAUSCH’S FUNDAMENTAL CONTRIBUTIONS 
TO ION CONDUCTIVITY, VELOCITY AND MOBILITY

Friedrich Kohlrausch,35 who coined the subject of 
ion conductivity and ion migration (of strong elecro-
lytes) in the next decades, concluded his habilitation in 
1863, not in electrochemistry, but “Ueber die elastische 
Nachwirkung bei der Torsion“[93, 94] (Elastic aftereffects 
during torsion) at the University of Göttingen, where 
he became private docent in 1866 and in 1867 associate 
professor. During the four years in Göttingen from 1866 
to 1870 he was mainly, though not exclusively, engaged 
in research on geomagnetic and electrical measure-
ments, and in investigations of the resistance and con-
ductivity of electrolyte solutions.36

Kohlrausch’s Entry into Electrochemical Research in 1868

Together with his coworker and former doctoral 
student Wilhelm August Nippoldt37 Kohlrausch pub-
lished his first contributions to electrochemistry in 1868 
and 1869 in various versions.[50, 105-107] The overarch-
ing subject of these papers was ”Ueber die Gültigkeit der 
Ohmschen Gesetze für Elektrolyte und eine numerische 
Bestimmung des Leitungswiderstandes der verdünnten 
Schwefelsäure durch alternierende Ströme“ (On the valid-
ity of Ohm’s laws for electrolytes and a numerical deter-
mination of the electric resistance of dilute sulfuric acid 
by alternating currents).[106, 107] In this paper, Kohlrausch 
and Nippoldt posed three questions: (1) How can the 
influence of the polarization of electrodes be exclud-

35 Friedrich Kohlrausch (1840, Rinteln-on-Weser – 1910) was a Ger-
man physisist. He studied physics in Erlangen and Göttingen, where 
he received his doctoral degree in 1863. In 1867 he was appointed to 
a professorship in Göttingen. Famous for his exact experimental work, 
his accurate measurements and his outstanding level in research, Kohl-
rausch became professor at ETH Zurich in 1870, at Technical University 
Darmstadt in 1871, at the University of Würzburg 1875, and at the Uni-
versity of Strasbourg as from 1888. He was successor of H. von Helm-
holtz at the Physikalisch-Technischen Reichsanstalt in Berlin, where he 
was director between 1895 and 1905. The Reichsanstalt was founded in 
1887 and was the first government-financed research institution world-
wide, where their staff members – in contrast to the Universities – were 
not committed to teach. Prominent members were Walther (Hermann) 
Nernst (1864 – 1941), Emil (Gabriel) Warburg (1846 – 1931), Walther 
(Wilhelm Georg) Bothe (1891 – 1957), Albert Einstein (1879 – 1955) 
and Max (Karl Ernst Ludwig) Planck (1858 – 1947).
36 Beside these main topics he also dealt, e.g., with the construction of 
an apparatus which serves for room cooling,[95]. the speed of propa-
gation of the stimulus in the human nerves,[96] elastic effects after tor-
sion,[97][98] geomagnetic observations in Göttingen,[99][100][101][102] the 
amount of electricity generated by an influence machine,[103] and others. 
37 The title of Nippoldt´s dissertation was “Untersuchungen über den 
galvanischen Widerstand der Schwefelsäure bei verschiedenen Konzentra-
tionsgraden” (Studies on the galvanic resistance of sulfuric acid at various 
degrees of concentration.)[104]



89Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

ed when determining the electrical resistance of liq-
uids? (2) Does Ohm’s law also apply to decomposable 
conductors?38 And connected with this: How can Clausi-
us’ postulate be proven that Ohm’s law still holds for the 
smallest possible electromotive forces? (3) How does the 
electrical resistance of decomposable conductors depend 
on their concentration?39

Clausius explicitly pointed out in his paper about 
free ions from 1858, discussed above, that “The smallest 
possible force gives rise to a current accompanied by alter-
nate decompositions and recombinations, and the inten-
sity of this current increases in proportion to the force, 
according to Ohm’s law.” Since Clausius gave no experi-
mental results for this “smallest possible force”, and did 
not cite any sources in which this force was given,40 we 
find this central argument vague and indefinite and 
a weak point in Clausius’ chain of reasoning (see also 
footnote 32).

However, Kohlrausch and Nippoldt took up this 
challenge and attempted to measure a critical value of 
this force. Unable to achieve a sufficiently low alternat-
ing current, they applied thermoelectric current instead, 
generated by a pair of Cu-Fe wires. And indeed, Kohl-
rausch and Nippoldt were able to spectacularly deter-
mine the lowest electromotive force at which the elec-
trolytic decomposition of the zinc vitriol solution still 
occurred, i.e., they measured whether or not current and 
emf were in direct proportion.41 Their results led them to 
conclude that ”… die Gültigkeit des Ohmschen Gesetzes 
… bis zu einer elektromotorischen Kraft von 0,00000233 

38 Kohlrausch and Nippoldt called here electrolyte solutions, i.e., 2nd 
class conductors, as opposed to metals, “decomposable conductors”.
39 Kohlrausch, of course, was not the first to research the conductivi-
ty or resistance of electrolyte solutions. Such earlier investigations had 
been discussed and compared in G. Wiedemann`s “Galvanismus”(ref. 
[108], pp. 191-208). Wiedemann reported on A. de la Rive (1830); G. T. 
Fechner (1831), see the Chapter “Leap in Time” above; C. S. M. Pouillet 
(1837); M. E. Lenz (1838); F. C. Henrici (1845) W. G. Hankel (1846); 
E. Becquerel (1846); E. N. Horsford (1847); E. Becker (1850, 1851); 
G. Wiedemann (1856); A. Saweljew (1856); W. Schmidt (1859). None 
of these researchers, however, has systematically studied this topic for 
about four decades and none of them has contributed with such fun-
damental findings. In this respect, the justification that Kohlrausch has 
coined the topic seems appropriate.
40 In a letter to the Chairman of the Deutschen Bunsengesellschaft, W. 
Nernst, from May 24, 1908, Kohlrausch himself wrote about Clausius’ 
argumentation and his and Nippolt´s measurement: “Nach  den von 
Clausius entwickelten Vorstellungen dürfte dies wohl als wahrschein-
lich gelten, war jedoch niemals an der Erfahrung gepriüft worden. Diese 
Lücke wurde ausgefüllt.“ (According to the ideas developed by Clausius, 
this is very likely, but had never been tested on experience. This gap was 
filled.).[109], p. 385. Note that Kohlrausch insisted on a test.
41 The solution of zinc vitriol (i.e., zinc sulphate) electrolyzed by amal-
gamated zinc electrodes to exclude polarization contained 16.6 g of 
the salt in 100 g solution. This solution was filled into a tube with 2400 
mm2 cross-sectional area and had a length of 83 mm. The current was 
measured with Nobili’s astatic galvanometer.

oder 1/429000 Grove hierdurch als bewiesen ansehen 
kann“ (… the validity of Ohm’s law … down to an electro-
motive force of 0.00000233 or 1/429000 Grove can thus be 
regarded as proven). This emf in Grove is equivalent to 
4,2.10-6 V. Referring to the work of H. Buff from 1855,[110] 
Kohlrausch and Nippoldt deduced that this weak electri-
cal force which decomposed their electrolyte was greater 
than the force of its chemical affinity. Thus they agreed 
with Clausius’ theory, but their conclusion was based 
on factual data (p. 379). They ended the paper with the 
nonetheless qualifying remark

Die Prüfung des Ohmschen Gesetzes für Elektrolyte auf 
noch kleinere Kräfte als die obigen auszudehnen, darf 
weder als überf lüssig noch als unmöglich bezeichnet 
werden. (To extend the test of Ohm’s law for electrolytes 
to even smaller forces than the above may be said to be 
neither superfluous nor impossible.)

The first and third questions posed above related to 
one of the main sources of errors in measuring the elec-
trical resistance and conductivity of liquids, namely the 
polarization of the electrodes. Two options were known 
to minimize polarization. To use alternating instead of 
direct current; and to measure with amalgamated zinc 
electrodes, that were not polarized. Kohlrausch and Nip-
poldt opted for alternating current, which they generated 
in their laboratory using a rather elaborate device they 
built themselves.42 They mounted, in addition, large-area 
platinum electrodes to reduce the current density there.

Sulfuric acid as the test substance was diluted in 
water at different percentages[106, 107] and the resistances 
were determined.43 Their reciprocals, the “relative con-
ductivities”, are plotted in Figure 4. They were in accord-
ance with earlier contributions by other authors, but 
were more accurate.

The curve of the relative conductivity of the solu-
tion vs. the specific weight of the sulfuric acid diluted 
in steps of ten (percentage of acid) increased at low con-
centrations, but then reached a maximum at 1.233 spe-
cific weight which equals 31.5 weight % of sulphuric acid 
hydrate (the “hydrate theory” is addressed in the follow-
ing Part 4 of our historical reviews).

42 In their first electrochemical experiments, Kohlrausch and Nippoldt 
used a rather complicated apparatus to generate alternating current, 
which was later replaced by one that was much easier to handle. They 
produced equal but oppositely directed currents of short duration and 
rapid succession by induction with a rotating magnet using large-area 
platinum electrodes (later, a small induction coil was used). The number 
of revolutions of the magnet was determined by means of a siren fixed 
in the axis of the magnet and its pitch was compared with a set of organ 
pipes. The induction currents were observed with a sensitive Weber bifi-
lar dynamometer, which was later replaced by a Wheatstone bridge.
43 The resistance was related to that of mercury.



90 Ernst Kenndler

Kohlrausch ś finding that the conductivity depends 
on the concentration of the dissolved electrolyte initi-
ated one of his major research activities. He carried out 
analogue measurements, also with alternating current,44 
and published the results in 1875 with Otto Grotrian,[111, 
112] and in 1876 in a paper with a similar content, but 
with an improved experimental set-up.[113] In the same 
year he published the preliminary version of the law of 
independent ion migration,[114] the subject of the follow-
ing chapter.

The Law of Independent Ion Migration: 1st Kohlrausch Law

Around the 1850s several authors, to name Wil-
helm Hankel,[115] Gustav Wiedemann[39, 47] and Wilhelm 
Beetz[116] investigated the relationship between the elec-
trical resistance of electrolyte solutions and their vis-
cosity.45 In 1856 Wiedemann came to the preliminary 
conclusion that under the conditions of his experiments 
(ref. [47], p.229) “ … würde … der Leitungswiderstand der 
Zähigkeit der Flüssigkeiten direct … proportional seyn. 
(…would … the resistivity be directly proportional to the 
viscosity of the liquids.)46 

44 The salt content in the solutions was between ca. 3% and 30% (w/w). 
It seems perhaps superfluous to nearly always indicate the concentra-
tions of the electrolytes in the respective measurements. However, this 
is not the case, since they play a central role in the migration properties 
of the ions.
45 The device to measure the viscosity was based on the findings of the 
German hydraulics construction engineer Gotthilf Ludwig Hagen[117]  
and the French physiologist and physicist Jean Léonard Marie Poi-
seuille.[118][119][120] The device resembled the nowadays used standard 
U-tube viscometer.
46 See also refs. [39], pp. 169, 170; [108], pp. 421-426; [121], pp. 632-634, and 
[122]

The German physicist Georg Quincke47 modeled 
in 1871 the resistance to the motion of “Theilmolecüle” 
(partial molecules), the ionic constituents of a “Gesammt-
molecül” (complete molecule) in a thin thread of a liquid 
solution and brought into play not only the viscosity of 
the liquid but also the mutual attraction and repulsion 
of the ions.[123] He argued that this electrical interaction 
is compensated by the corresponding effect of the neigh-
boring counterion and is therefore irrelevant, and con-
cluded that

Die specifisches Leitungsfähigkeit der gesamten Flüssig-
keit ist gleich der Summe der partiellen specifischen Lei-
tungsfähigkeiten der einzelnen Bestandtheile. (The specif-
ic conductivity of the entire liquid is equal to the sum of 
the partial specific conductivities of the individual com-
ponents.)

This reads in eq. (26) on p. 16 that λ= λ1+λ2+…λr. 
Here, λ is the specific conductivity of the solution, and λi 
are those of the individual ionic constituents, the partial 
molecules, with i ranging from 1 to r.48

In the second half of the 1870s Otto Grotrian found 
a striking connection between electric resistance and 
mechanic frictional resistance.[124, 125] Rudolf von Lenz, 
in the same years, investigated a relationship between 
the resistance of haloïd salt solutions and their density 
(not of their viscosity).[126, 127] All researches agreed that 
the liquid of the solution decelerates the motion of the 
ions and thus increases the resistance of the current. By 
the way, this is a prerequisite for a constant migration 
velocity of an ion driven by a constant force in the theo-
ry of electric lines of action of Michael Faraday (see Part 
2, Chapter 3.1.6.).

This point of view was shared by Kohlrausch, who 
supposed that the source of the frictional resistance 
and thus the influence on the migration velocity of the 
ions in dilute aqueous solutions can only come from 
the water molecules due to their large excess over all 
other constituents. Taking into account this connection 
between electrical force and mechanical resistance in ion 
transport, Kohlrausch came up with the key idea that 

47 Georg Hermann Quincke (1834, Frankfurt/Oder – 1924, Heidelberg) 
studied physics, chemistry and mathematics, and presented his doctoral 
thesis on “Kapillarerscheinungen bei Quecksilber“ (Capillary phenomena 
with mercury) at the Humboldt-University in Berlin in1858. In 1875 he 
became successor of Gustav Kirchhoff at the University of Heidelberg, 
where he retired in 1907. Interesting for the present subject are his sci-
entific activities in capillarity, in the electric properties of colloidal par-
ticles and in electroosmosis (we will come back to these important con-
tributions in a later review).
48 Note that Quincke used Clausius´ phraseology, and that this equation 
has some similarity with Kohlrausch´s law of independent ion migra-
tion.

Figure 4. “Relative Leitfähigkeit” (relative conductivity) vs. specific 
weight (also density) of dilute sulphuric acid. The resistance was 
measured with alternating current as described in the main text. 
Abscissa: specific weights of the acid solution at 18.5°C from 1.0504 
to 1.5025, corresponding to a content of the acid from 8.3 to 60.3%. 
The curve depicts the “Leitungsvermögen” at 22°C. From ref. [107], 
p. 386.



91Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

the extent of this mutual influence is most likely differ-
ent for different ions, which would lead to their unequal 
migration velocities. He communicated his hypothesis in 
1876 – the preliminary version of the law of independent 
ion migration – and confidently stated (ref. [114], p. 215)49

Ist nun die Lösung sehr verdünnt, so wird diese Reibung 
vorwiegend an den Wassertheilchen stattfinden. Demnach 
wird man weiter zu schließen versucht sein – und dies ist 
ein Schluß, der meines Wissens noch nicht gezogen worden 
ist – daß jedem elektrochemischen Elemente (z. B. dem 
Wasserstoff, Chlor oder auch einem Radicale wie NO3) 
als solchem ein bestimmter Widerstand in verdünnter 
wässeriger Lösung zukommt, gleichgültig, aus welcher 
Verbindung es elektrolysirt wird. (If the solution is very 
dilute, this friction will mainly take place on the water 
particles. Accordingly, one will be tempted to conclude 
further – and this is a conclusion which, to my knowledge, 
has not yet been drawn – that every electrochemical ele-
ment (e.g., hydrogen, chlorine or even a radical like NO3) 
as such has a certain resistance in dilute aqueous solution, 
regardless of the compound from which it is electrolyzed.)

He argued, on the one hand, that the current is 
related to the sum of the velocities (v–+v+) of the two 
oppositely charged ions.50 The current is, according to 
Ohm’s law, also in inverse proportion to the resistance, 
that is to say, it is proportional to conductivity Λ. Hence 
the conductivity is proportional to (v–+v+).51 He pointed 

49 In this early paper he took values for electrolyte concentrations in the 
low weight percent range.
50 In the following discussion electrolytes with two single-charged ions 
are considered for the sake of simplicity (for other electrolytes the cor-
responding equations have to be extended by the numbers of ions, v, 
and the charge numbers, z. Since electrolytes with v–=v+ and z+=|z–|=1 
are regarded, the molar and the equivalent concentrations and the 
respective conductivities are the same.
51 We point out that at the time of Kohlrausch there was no standard-
ized terminology, nor were the symbols of the physical and chemi-
cal quantities unified. Kohlrausch, for example, used the terms “Lei-
tungsvermögen” or “Leitfähigkeit” of the solution, which is “conduct-
ibility” or “conductivity” in English, and ascribed it in some papers 
by symbol k, in others by Λ. More misleading is Kohlrausch´s usage 
of the term “Beweglichkeit”, with symbols l+ and l-, in other papers u 
and v, which is translated into English as “mobility” (a point that has 
been mentioned in the English translation of Kohlrausch´s paper from 
1876[114] in Harper’s Scientific Memoirs from 1899 (ref. [128], footnote at 
p. 89). In Kohlrausch’s paper from 1876 “Beweglichkeit” is a dimension-
less number, which is the velocity of migration of an ion related to that 
of hydrogen. The latter has the arbitrarily chosen value of 1. Kohlrausch 
initially formulated in his hypothesis of independent ion migration that 
the conductivity is the sum of the “Beweglichkeiten” of the ions, which 
he expressed by Λ=(l++l–) or by k=(u+v) (comp. with the different nota-
tions given in the main text). In later papers, Kohlrausch used the term 
“Wanderung” (Engl. migration) instead. Somewhat problematic for the 
reader of Kohlrausch’s original works may be that he often changed 
terms during the four decades of his scientific activity. This is under-
standable, because, as we mentioned above, there was no standardized 
nomenclature. However, since this review is not intended to be a text-

out that, on the other hand, Hittorf ś transference num-
ber expresses the ratio of the velocity of an ion to the 
sum of the velocities of both ions, e.g., for the anion 
by τ–=v–/(v–+v+). For two electrochemically equal elec-
trolytes, (1) and (2), with a common anion and with 
cation velocities of v+(1) and v+(2), respectively, he set  
Λ(1)/Λ(2)=(v–+v+)(v–(1)+v+(2)), expanded the equation by 
v–, and obtained the relationship Λ(1)/Λ(2)=τ–(2)/τ–(1). The 
corroboration of his hypothesis required that the ratio 
of the conductivities of the solutions of two electrolytes 
with a common ion had to be equal to the inverse ratio 
of the transference numbers of the common ion (it was 
already noted above that the transference number of an 
ion in an electrolyte depends on its counterion).

Kohlrausch scrutinized his hypothesis on the basis 
of transference numbers of about a dozen electrolytes 
from monobasic acids52 (salts of alkalis and earth alka-
lis as chlorides, bromides, iodides, nitrates, perchlorates 
and acetates), and actually found a good agreement with 
his theoretical prediction. Thus he concluded on p. 219

Die Annahme von der unabhängigen Beweglichkeit der 
Ionen läßt sich zweitens durch die Überführungszahlen 
allein prüfen und hierdurch auch an Körpern, deren Lei-
tungsvermögen noch nicht bekannt ist, bestätigen oder 
widerlegen. (Secondly, the assumption of the independent 
migration of the ions can be proved by the transfer num-
bers alone and thus confirmed or disproved on bodies 
whose conductivity is not yet known.)

To this end, Kohlrausch took four compounds, 
which were composed of two pairs of ions, and related 
their resulting eight transference numbers to one anoth-
er. In fact, he was able to calculate “Beweglichkeiten” 
(verbatim “mobilities”), the velocities relative to that of 
hydrogen. This hypothesis must not be confused with 
the final law of independent ion migration Kohlrausch 
published three years later.[130] 

At the end of his 1876 paper (on p. 222) he came 
nevertheless to the conclusion that further experimen-
tal investigations were necessary to decide whether this 
aforementioned statement applies also in general or not. 
He began to examine systematically and with exception-
al accuracy numerous aspects of the influence of various 

book of physical chemistry, we usually adopt the terms as Kohlrausch 
used it in the respective paper, unless they are completely misleading. 
In the cases where it could lead to confusion, we will use the modern 
terminology and symbols.
52 It is hardly known that acids with 1, 2 and 3 H+ ions and bases with 
corresponding OH- ions were called mono-, di- and triatomic until 
1853, when Faustin-J. (also Faustino) Malaguti (1802 – 1878) proposed 
in his “Leçons élémentaires de Chimie” (ref. [129], p. 331) to call them 
mono-, di- and tribasic acids and mono-, di- and triacidic bases, respec-
tively. It is still modern nomenclature.



92 Ernst Kenndler

experimental variables on the conductivity of electrolyte 
solutions till around 1910 (that is, please note, still in the 
Long Nineteenth Century). During this time period, he 
published almost 145 papers on this subject.

But first he continued work on his above-mentioned 
hypothesis for the next three years and published his 
results in 1879 on 120 pages of an ample paper that con-
sisted of three parts.[130, 131] In theoretical Part III[130] he 
derived in detail the law of independent ion migration, 
which is also named 1st Kohlrausch law. In § 15 of this 
Part III he defined the quantity m, which he called the 
molecular content, as the number of electrochemical 
molecules per unit volume.53 He defined the “molecu-
lares Leitungsvermögen” (the molecular, later also molar 
conductivity), k/m, of the electrolyte in aqueous solution 
as conductivity, k, related to the molecular content, m. 
This quantity will be used by him in his future papers. 
Then, in § 18, he reported the remarkable finding of the 
similar difference in the molecular conductivities of two 
single-charged salts with a common ion. To give some 
examples: the difference for the pair K and Li is 274 for 
the chlorides, and 272 for the iodides; it is 160 for K and 
Na as chlorides, and 185 for their iodides; for the chlo-
rides of K and NH4 it is 21, and 14 for their iodides (all in 
the measure he used). These results encouraged him to 
formulate the final version of the law of independent ion 
migration in § 21, p. 168.[130] This derivation, expressed 
in modern notation, begins with the fact that the molar 
conductivity Λ of an electrolyte solution is the sum of 

53 We have already mentioned that, tedious for the current reader, Kohl-
rausch often changed the nomenclature and the phraseology during the 
long time of his researches. In this § 15 on p. 146 of ref. [130] he defi-
ned m as “Die Anzahl der …. electrochemischen Molecüle, welche in der 
Volumeneinheit enthalten sind, werde ich kurz die Molecülzahl oder den 
Moleculargehalt der Lösung nennen und durch m bezeichnen.“ (The num-
ber of …. electrochemical molecules contained in the unit volume, I will 
briefly call the molecule number or the molecular content of the solution 
and denote it by m) It is a relative quantity, which is calculated “Aus 
dem Procentgehalt und dem specifischen Gewicht bei 18° berechnet man 
die in 1 ccm Lösung enthaltene Milligrammzahl des Electrolytes und theilt 
letztere Zahl durch das electrochemische Moleculargewicht der Substanz.“ 
(From the content in percent and the specific weight  at 18°, one calculates 
the milligrams of the electrolyte contained in 1 ccm of solution and divides 
the latter number by the electrochemical molecular weight of the sub-
stance). It clarifies the matter by Kohlrausch´s statement on pp. 172-173 
in ref. [132] “Die untersuchten Flüssigkeiten sind bezeichnet nach ihrem 
Gehalte an ,,electrochemischen Molecülen” (Aequivalenten) in der Volu-
meneinheit. Der ,,Moleculargehalt” m bedeutet …. die in 1 L der Lösung 
enthaltene Menge in Grammen, getheilt durch das Aequivalentgewicht 
A des Körpers. m = 1 bedeutet also die bei der Titriranalyse sogenannte 
,,Normallösung.“ (The liquids examined are designated according to their 
content of “electrochemical molecules” (equivalents) in the unit of volume. 
The “molecular content” m means … the quantity in grams contained in 
1 L of the solution, divided by the equivalent weight A of the compound. 
m = 1 therefore means the “normal solution” as it is known in titration 
analysis.) Later Kohlrausch called m the equivalent concentration (what 
Faraday named electrochemical equivalent concentration).

the molar ion conductivities, λ+ and λ–, of the two ions, 
i.e., Λ=(λ++λ–).54 To obtain the conductivity of the indi-
vidual ions, Kohlrausch combined Λ, as indicated above, 
with the transference number, τ, what led to the quested 
ion conductivity, e.g., for the anion as λ–=τ–Λ, in which 
both, Λ and τ–, are experimentally determinable measur-
ands. Analogously, the cation conductivity is λ+=(1-τ–) or 
τ+Λ, because (τ++τ–)=1.

On p. 168, ref. [130] Kohlrausch formulated this law 
of independent ion migration (reproduced verbatim; note 
the almost identical wording of his 1876 hypothesis, that 
we quoted above, but which was, in contrast, formulated 
in subjunctive) as

Hiernach muß also jedem elektrochemischen Elemente 
– z.B. dem H, K, Ag, …, Cl, J, NO3,… – in verdünnter 
wäßriger Lösung ein ganz bestimmter Widerstand 
zukommen, gleichgültig aus welchem Elektroly te der 
Bestandteil abgeschieden wird. Aus diesen Widerständen, 
welche für jedes Element ein für allemal bestimmbar 
sein müssen, wird sich das Leitungsvermögen jeder (ver-
dünnten) Lösung berechnen lassen. (According to this, 
every electrochemical element – for example H, K, Ag, 
…,. Cl, J, NO3,… – must feature a very definite resistance 
in dilute aqueous solution, regardless of which electrolyte 
the component is deposited from. From these resistances, 
which must be determinable for every element once and 
for all, the conductivity of each (dilute) solution will be 
calculable.)

He tested the validity of this theory by calculating 
the equivalent conductivity of the salts55 by summariz-
ing the tabulated conductivities of their ions (he complet-
ed his data with those from Robert von Lenz.)[126, 136],56 
Even after taking into account electrolytes with double-

54 We shall discuss in the following section that, taking into account the 
results of his research on the concentration dependence of conductiv-
ities, the modern notion of this equation reads Λ0=(λ+0+λ–0); super-
script 0 indicates limiting conditions, that is, when the concentrations 
approach zero; see also, e.g., refs. [133][134][135]
55 The concentrations of the salts were between around 5 weight % and 
their solubility limit, which reached for some salts about 80 weight %.
56 The little-known Baltic-Russian physicist Robert von Lenz (1833, St. 
Petersburg -1903), son of the  German-Baltic physicist Heinrich Frie-
drich Emil Lenz (1804, Dorpat, now Tartu, Estonia – 1865, Rome) 
known for Lenz’s law in electrodynamics, was professor of physical 
geography at the University of St. Petersburg from 1865 to 1899. He 
published a paper in 1877, read in 1876, about conductivities of haloïd 
salts. Lenz´s conclusions there resembled Kohlrausch´s law of indepen-
dent ion migration.[126][127] In 1879 he published conductivities of aque-
ous alkali salt solutions in the concentration ranges from about 10-1 to 
10-3 equ.L-1.[136] Notably, Lenz was the first who systematically deter-
mined transference numbers, conductivities and diffusion coefficients of 
ions in mixed aqueous-ethanolic solutions up to ethanol concentrations 
of about 94% (v/v). He confirmed the proportionality of conductivity 
and diffusion rate,[137] which was later expressed quantitatively (for lim-
iting conditions) by the Nernst-Einstein equation.



93Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

charged ions, Kohlrausch found that the calculated val-
ues were in satisfactory agreement with the measured 
ones, considering the limited reliability of the transfer-
ence numbers.57 Eventually, Kohlrausch concluded 

In diesen Beispielen sehen wir unsere Vermuthung, dass 
die Beweglichkeit eines Jons in verschiedenen Verbind-
ungen die gleiche ist, mit grosser Annäherung bestätigt. 
(In these examples we see our conjecture confirmed with 
great approximation that the mobility of an ion is the 
same in different compounds.)

Kohlrausch ś finding that ions migrate in the elec-
tric potential independent of the counterions was a mile-
stone for the further development of the theories of ion 
migration.

The Concentration Dependence of the Conductivity, and 
the Conductivity at Limiting Conditions

In the above chapter we have described Kohlrausch’s 
first experiments in 1869 and 1870 on the conductivity 
of electrolyte solutions. This subject fascinated him so 
much that he introduced his next paper of July 1874 (the 
precursor of refs. [111, 112]) with the prophetic sentence: 
“Diese in Gemeinschaft mit Hrn. Grotrian ausgeführte 
Arbeit soll den Anfang einer geordneten Experimental-
Untersuchung über die Strom-Arbeit im Inneren der 
Elektrolyte bilden “ (This work, carried out in collabo-
ration with Mr. Grotrian, is to form the beginning of an 
orderly experimental investigation of the work of the cur-
rent inside electrolytes). This undertaking then actually 
extended over four decades. Following this stated inten-
tion, in 1875 and 1876 he investigated the resistance or 
conductivity of a large number of solutions of salts, bas-
es, organic and inorganic acids and their dependence on 
the electrolyte content.[111-113, 144]

Their electrolyte concentrations ranged from full 
saturation down to a few percent by weight. Kohlrausch 
found a steady increase in conductivity with increasing 
concentration, with some electrolytes having a maxi-
mum at a particular concentration. For the discussion 

57 Transference numbers with higher accuracy and with much less 
experimental effort than those by Hittorf´s method were later deter-
mined by the moving boundary method. This method will be discussed 
in a future paper together with electrophoretic separation methods in 
free solution. It was introduced in 1886 by Oliver Lodge,[138] and was 
further developed by W. C. D. Whetham,[139]. by O. Masson,[140] by A. 
Noyes,[141] by B. D. Steele and R. B. Denison,[142] and by others. It was 
theoretically clarified, in addition to other methods, in 1897 by Fried-
rich Kohlrausch with his “beharrliche Funktion” (the “persistent func-
tion”, better known as “regulating function”).[143] We will, however, not 
go into the details here.

and comparison of the conductivities of the various elec-
trolytes, he considered the indication of the concentra-
tion in percent by weight to be inappropriate. The con-
ductivities of sulfuric acid and acetic acid, for example, 
could be determined at 100 %, while oxalic acid reached 
only 7 %, both (w/w). Note that also in 1876 he pub-
lished the preliminary version of the law of independ-
ent ion migration (ref. [114], see previous section). These 
measurements were also carried out with solutions with 
electrolyte concentrations not lower than a few weight 
percent.58

The “Cubic-Root” Relation, the Precursor of the “Square-
Root Law”

In his paper from 1885 “Ueber das Leitungsvermö-
gen einiger Electrolyte in äusserst verdünnter wässer-
iger Lösung” (On the conductivity of some electrolytes in 
extremely dilute aqueous solution)[132] Kohlrausch pre-
sented his measured conductivities in the low electrolyte 
concentration range between 10-5 and 1.0 mol.L-1. He 
completed the actual data with those for molecular con-
centrations larger than 1 mol.L-1 by his earlier ones and 
by those published by Long,[147] and obtained equivalent 
conductivities for concentrations up to nearly 10 mol.L-1. 
Since it was not meaningful to plot the molar or equiv-
alent concentration, m, in a linear scale over a range of 
about 6 orders of magnitude, he chose the cubic root of 
m as the abscissa.59 The resulting k/m vs m1/3 curves are 
shown in Figure 5.

Two shapes of these curves were clearly discrimina-
ble for Kohlrausch. He distinguished therefore two class-
es of electrolytes. Alkali salts of the type A+B- were typi-
cal representatives of the 1st class. For these electrolytes, 
the k/m values decreased only slightly by a few ten per-
cent with increasing concentration in the low concentra-
tion range (Figure 5, upper scale). In contrast, 2nd class 
electrolytes like acetic acid and NH3 exhibited a very low 
molar conductivity at high concentrations (pure ace-
tic acid behaved as non-conductor). They remained at a 
low level when diluted over a wide concentration range, 
but rose steeply to values in the same range as those of 
the strong electrolytes when the solution became highly 

58 In 1868/69 also A. Paalzow measured the resistance of diluted salts 
and acids down to the low % range.[145][146] Rudolf Lenz reported con-
ductivities of haloïd salts in 1877.[126][127] Later, experimental results 
and theoretical discussions about ion conductivities and their concen-
tration dependence were published in 1880 by J. H. Long,[147] in 1884 
by E. Bouty,[148][149][150] by Svante Arrhenius in his doctoral thesis,[151][152] 
which Kohlrausch provided with some pointed remarks, and by W. Ost-
wald.[153]
59 Kohlrausch followed the suggestion of R. Lenz in 1878 to relate con-
ductivity to the amount of electrolyte molecules in the solution.[136]



94 Ernst Kenndler

diluted (see the two lowest and concave curves in the 
bottom scale of Figure 5.)

Kohlrausch recognized from the curves that the 
molar (or equivalent) conductivities of both classes of 
electrolytes nevertheless reached a certain limit at con-
centrations approaching zero.[132] He expressed k/m as a 
function of m for dilute solutions of strong electrolytes 
by the equation k/m=A-Bm1/3. This relationship stated 
that the equivalent conductivity is proportional to the 
cubic root of the concentration, and under limiting con-
ditions it is equal to constant value A. For salts from 
single-charged ions, if only for these, the curves were 
approximately linear up to the concentration range of 1 
mol.L-1 (see, for example, that for KClO3 in the figure). 
Kohlrausch interpreted this dependence by the assump-
tion that m1/3  corresponds to the reciprocal mean dis-
tance between the electrolyte molecules. For the 2nd 
class electrolytes he had no coherent explanation. This 
cubic root equation, which applied to a relatively large 
range of concentration, preceded Kohlrausch ś “square-
root” equation for extremely dilute solutions which will 
be discussed in the following.

After the investigations in 1885 Kohlrausch was 
aware of the insufficient accuracy of the data measured 
so far, as he assessed their quality as too low for the 
formulation of a sound and general theory, especially 
with regard of the values at very low concentrations. He 

therefore tried to identify and reduce the possible sourc-
es of errors. This was the goal of his comprehensive and 
elaborate studies over the next years.

In Figure 6 a photograph of Friedrich Kohlrausch ś 
group at the University in Würzburg in 1887 is shown. It 
was taken when Kohlrausch was visited by Svante Arrhe-
nius, who published in this year his seminal dissociation 
theory “Ueber die Dissociation der in Wasser gelösten Stof-
fe” (On the dissociation of substances dissolved in water).
[155],60 Although Arrhenius’ theory provided the explana-
tion for the deviating dependence of the 2nd class elec-
trolytes such as acetic acid, Kohlrausch was skeptical of 
it. He continued to focus on strong electrolytes at limiting 
conditions, preferably on those with single-charged ions.

In strict chronological order we had now to pro-
ceed with Arrhenius’ dissociation theory from 1884.[151, 
152]. However, we prefer to continue systematically with 
Kohlrausch’s electrochemical work after 1887,61 and will 

60 Arrhenius completed his doctoral thesis in 1884. It was published 
in two parts of “Recherches sur la conductibilité galvanique des électro-
lytes.”[151][152] In 1887, his dissociation theory was published in the first 
volume of Zeitschrift für physikalische Chemie, Stöchiometrie und Ver-
wandtschaftslehre,[155] founded by Wilhelm Ostwald and Jacobus Hen-
ricus van `t Hoff. In 1928 its title was changed to Zeitschrift für physi-
kalische Chemie. Arrhenius’ theory fundamentally changed the previous 
conception of the behavior of electrolytes in solutions, and was a deci-
sive step in the development of modern physical chemistry. In 1903 he 
became the first Swedish Nobel laureate.
61 It should be noted that in 1889 and 1890, due to adverse circumstanc-
es, Kohlrausch did not publish a single paper.

Figure 5. Equivalent conductivity (“specific molecular conductiv-
ity”) as function of the cubic root, m1/3  , of the equivalent concen-
tration, m. The figure shows the left sectors of the total plot, that 
between zero and 1 equ.L-1 concentrations. The curves were drawn 
exactly through the measured values. Upper scale, strong electro-
lytes, e.g. KCl, KClO3, etc. Lower scale, concave two lowest curves: 
weak electrolytes acetic acid, NH3. Modified; from ref. [132], Plate II, 
after p. 648.

Figure 6. Photograph of Friedrich Kohlrausch´s research group at 
the Physical Institute of the University in Würzburg in winter semes-
ter 1886/87, taken in February 1887. Standing from left, Adolf Hey-
dweiller, Ewald Rasch, Svante Arrhenius (research visit in Würzburg 
in 1886/1887), Walther Nernst. Sitting from left, Wilhelm Kohl-
rausch, Friedrich Kohlrausch, Samuel Sheldon (postgraduate; 1887-
1888). Source of photograph: Ernst H. Riesenfeld. Svante Arrhenius. 
Akademische Verlagsgesellschaft, Leipzig, 1931. Public domain.[154]



95Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

return to Arrhenius’ theory and its pioneering conse-
quences in the following, separate Part 4 of our series.

The “Square-Root” Law: 2nd Kohlrausch Law

In order to achieve the proverbial high accuracy 
of his experimental results, for which Kohlrausch was 
famous, he examined step by step the effects of pos-
sible causes of errors. He tried to reduce the total sys-
tematic error at conductivity of solution with molecular 
concentration of 0.0001 which required errors in con-
ductivity one magnitude lower in each individual step 
at molecular concentrations of 0.00001. We list a part 
of the subjects of these studies in condensed form in 
footnote 62, along with the articles in which they were 
published. It turned out that two sources of errors were 
most problematic. One was the well-known polariza-
tion of the electrodes, a problem Kohlrausch solved, as 
he had done earlier, by using alternating rather than 
direct current. He used, in addition, an improved appa-
ratus, the Wheatstone bridge, for the measurement of 
the resistance.63

The second problem was that the water used as a 
solvent had to be of very high purity. Kohlrausch’s co-
worker Adolf Heydweiller countered this problem in 
1894 with cumbersome and time-consuming purifica-
tion processes.[158, 172]

In their paper from 1900, Kohlrausch and his co-
worker E. M Maltby published very accurate conductivi-
ties of alkali halides and nitrates in highly dilute solu-
tions in a comprehensive report which covered eighty 

62 (▪) Influence of solubility of glass ware in contact with the solutions 
on the conductivity; ascertaining threshold level of conductivity of pure 
water used as solvent.[156][157][158] (▪) Corrections taking into account 
temperature coefficients of water and of solutions, comparison with pre-
vious measurements.[132][159] (▪) Estimation of deviations of electrolyte 
concentrations upon contraction by mixing of solutions and by evapo-
ration of solvent.[160] (▪) Measurement of resistance of electrolyte solu-
tions with direct and alternating current.[161][162]163]164] (▪) Density mea-
surements of dilute electrolyte solutions.[160][165] (▪) Determining and 
improving the properties of rheostat, capacitor and Wheatstone bridge.
[166]. (▪) Specification and improvement of quality of resistor cells and 
electric wiring.[167] (▪) Investing effect of polarization of platinized elec-
trodes in measuring cell.[168][169] (▪) Calibration of thermometer to 0.01° 
instead of common 0.1° (§ 15) and of the volumina of graduated mea-
suring glassware (§ 16, volumetric flasks; § 18, pipets) in ref. [133]
63 The principle of the device called Wheatstone bridge was initially 
described by the British mathematician and physicist Samuel Hunter 
Christie (1784, London – 1865, Twickenham, London) and reported in 
1833 in his Bakerian Lecture “Experimental Determination of the Laws 
of Magneto-electric Induction in different masses of the same Metal, and 
of its Intensity in different Metals.“[170] It was not noted until Charles 
Wheatstone presented it ten years later, mind you, as Christie’s inven-
tion, in his Bakerian lecture “An Account of Several New Instruments 
and Processes for Determining the Constants of a Voltaic Circuit.”[171]

printed pages and summarized the results of their 
elaborate investigations.[133] Taking the data at lowest 
m between 1.10-5 and 4.10-5 equ.L-1 (out of a set over a 
range of up to 1 equ.L-1) Kohlrausch expressed the 
dependence of the equivalent conductivity, here symbol-
ized by Λ, on m by the equation Λ0-Λ=Pm1/2; Λ0 and P 
are electrolyte-specific constants.[133],64. He called this 
equation “Quadratwurzel Gesetz” (literally “square root 
law”, better known in English literature as 2nd Kohl-
rausch law).65 The equation signifies the linear depend-
ence of the equivalent conductivity of the electrolyte 
on the square root of its equivalent concentration, and 
again applied especially for strong electrolytes with sin-
gle-charged ions. The intercept Λ0 represents the limit-
ing equivalent conductivity of the electrolyte at concen-
trations m→0. Constant P, the slope of the line, depends 
mainly on the stoichiometry of the respective electrolyte. 
Note that the concentration to the power of ⅓ in the 
equation in his paper from 1885[132] is substituted here by 
the power of ½, because the former applied for a much 
larger concentration range. The decisive factor for the 
better agreement of the m1/2 – relationship was not the 
lower measurable concentration of the electrolytes, it 
was the higher accuracy of the conductivity data at these 
extremely low concentrations. We illustrate this excellent 
relationship in Figure 7,[135] when Kohlrausch had avail-
able a larger number of more accurate data.66

The following paper of 1907 is a kind of résumé of 
Kohlrausch ś electrochemical contributions; in it he 
reconfirmed his earlier works. He subjected his theories 
of independent ion migration and those of conductance 
and mobility at limiting conditions to his own criti-
cism. Moreover, he reaffirmed the validity of his square 
root law from 1900[133] not without emphasizing that 
this law applies only to salts of single-charged ions, and 
to concentrations not higher than a few 10-5 mol.L-1. For 
higher concentrations this dependence is represented 
– as described in the above chapter – by the cubic root 
equation.[133] Kohlrausch also mentioned the alternative 
equations by Max Rudolphi[173] and J. H. van t́ Hoff,[174] 
which read in his version (Λ0-Λ)/Λp=Cη1/2. Exponent 
p was taken as 2 by the former, and 3/2 by the latter 
author; η is here the equivalent concentration. Kohl-
rausch pointed out that these equations, however, apply 
only to individual cases. In 1908 he published three 

64 In this concentration range the conductivity of water (purified by up 
to 40 to 50 distillations under vacuum from a quartz apparatus)[158] was 
about one order of magnitude lower than those of the highest diluted 
electrolyte solutions.
65 Remember that the 1st Kohlrausch law is the law of independent ion 
migration.
66 The data were taken from sources Kohlrausch cited in footnote 3, p. 
336, ref. [135]



96 Ernst Kenndler

more papers on electrochemistry, mainly on temperature 
effects of electrolyte solutions, and on January 4, 1910 
he submitted a paper on “Practical Rules for Number 
Corrections, Namely for the Transition to Other Atomic 
Weights”.[175] He died on January 17, 1910.

Migration Velocity and Mobility of ions

The question about the absolute migration veloci-
ties of the ions, not only about their relative values, has 
been systematically treated by Kohlrausch in several 
papers. [114, 130, 159, 176] In 1893 he had available improved 
values of the conductivity in dilute solutions, a valuable 
addition of Hittorf ś transference numbers, more reli-
able values for the electrochemical equivalents and the 
absolute resistance of mercury. Therefore, he was able 
to calculate more accurate data “Ueber die Geschwindig-
keit elektrolytischer Ionen” (On the velocity of electrolytic 
ions).[159] He limited the following calculation to strong 
electrolytes, from which he could be convinced that the 
molecules completely decompose to ions (we recall that 
Arrhenius dissociation theory was published as journal 

article in 1887). We place his derivation into footnote 67 
and add only the result after transformation into mod-
ern system of units and terminology.

Kohlrausch derived an equation for the migration 
velocities at unit field strength, that is to say, at 1 V.cm-1,  
which he called “Beweglichkeiten” (mobilities), and which 
are, after multiplied by the according factor, the migration 
velocities in cm.s-1. By transformation this mobility reads 
μi=λi/F, at limiting conditions μi0=λi0/F, and is today also 
called mobility of ion, i. Here λi is the molar ion conduc-
tivity, and F the Faraday constant. The velocity v in cm.s-1 
at field strength E is accordingly vi= μi.E.68

Ion mobilities μi are of decisive importance in all 
variants of capillary electrophoresis in free solution. 
They are ion specific parameters that are independent of 
the potential. They depend on temperature, on electro-
lyte concentration (more precisely, on ion strength, what 
was unknown at that time) and on the solvent.69

Since the migration velocity can be derived from the 
known ion conductivity and the chosen field strength, 
the question posed in this Part 3 about its magnitude 
can be regarded as answered.

However, the reason for its dependence on experi-
mental variables, especially on their concentration, was 
still unknown at that time.

The reader will probably note that we have not yet 
addressed the main question of whether or not electro-
phoresis experiments in free solution were performed in 
devices of capillary format in the years under considera-
tion. For this reason, we conclude the present essay by 
describing the first use of capillaries in electrophore-
sis and additionally mention that all experiments cited 
below were performed with direct current.

67 Kohlrausch derived the velocities for single-charged 1:1 electrolytes, 
that is, the molar and equivalent concentrations are the same. He con-
sidered a solution with molar concentration m of the electrolyte, which 
has the conductivity, k, and the “molecular conductivity” k/m, which is 
the sum of the molar conductivities of anions and cations. He derived 
the migration velocities of the ions at a potential difference of 1 V.cm-1.  
He first changed conductivity k from its relationship to mercury to 
Ohm. He calculated the current in Amp. at 1 V.cm-1 in 1 cm3 of elec-
trolyte solution with m mol.L-1 concentration, and derived the number 
of moles electrolyzed by this current. This quantity is released at the 
electrodes at a distance of 1 cm. From this he derived the sum of the 
mean velocities of cations and anions and obtained those of the two ion 
species using Hittorf´s transference numbers. The resulting equation 
expressed the ion migration velocity in cm.s-1, mind you, at a poten-
tial difference of 1 V.cm-1, as a function of the molar ion conductivity. 
Readers who are interested in the specific numerical data in this deriva-
tion are referred to pp. 402-403 in ref. [159]
68 In modern notation the migration velocity v is in cm.s-1, the mobility  
μ in cm2.V-1.s-1 or S.cm2.A-1.s-1, and the molar ion conductivity in S.cm2.
mol-1.
69 Other researchers determined migration velocities of ions in the time 
period under consideration as well by the moving boundary method. 
We mentioned them in footnote57.

Figure 7. Dependence of the equivalent conductivity on the square 
root of the equivalent concentration according to the 2nd Kohl-
rausch law, the square-root law (termed “Quadratwurzel Gesetz” by 
Kohlrausch) for 1st class electrolytes. The straight lines of electro-
lytes with the same stoichiometry run parallel, most pronouncedly 
for salts with 1:1 single-charged ions. They are highlighted in blue. 
Since the letters in the illustrations of that time were mostly very 
small and hardly legible, we give the formulas of these salts in the 
order from top to bottom as follows: CsCl; KBr; KCl; KNO3; KSCN; 
KClO3; AgNO3; NaCl; NaF; LiCl; KJO3; NaJO3; LiJO3; LiNO3. Ordi-
nate, equ. conc.; abscissa, equ. conductivity. Modified, from [135].



97Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

THE FIRST CAPILLARY ELECTROPHORESES OF IONS

At the outset of this particular chapter in the histo-
ry of electrophoresis, it should be made clear again that 
electrophoresis is not limited to the separation process 
as which it is generally regarded today, as already stated 
in footnote 1 in the introduction to this article. The his-
tory of capillary electrophoresis must therefore be con-
sidered from this point of view. To maintain continuity 
with the preceding narrative, we follow up the previous 
section with Kohlrausch’s research around 1900 and 
address the topic in reverse chronological order.

1895. F. Kohlrausch and A. Heydweiller

In the course of their investigations on pure water 
in 1894[158] Kohlrausch and his coworker Adolf Heyd-
weiller observed that after applying direct current the 
electrical resistance of water decreased rapidly. Changes 
in resistance were also observed in normally distilled 
and in highly distilled water and in some dilute aqueous 
salt solutions. Switching the current off and on resulted 
in some cases first in a decrease, after some time in an 
increase of the conductivity; in other cases, the reverse 
sequence was observed. One can follow their explana-
tions of the reasons for these effects70 in their paper 
“Ueber Widerstandsänderung von Lösungen durch con-
stante electrische Ströme” (On the change of resistance 
of solutions at constant electric currents)[163] published in 
1895. But this is of minor interest here.

Much more relevant to the issue at hand, they con-
ducted their experiments in narrow open tubes of capil-
lary dimensions because the zone boundaries described 
in footnote 70 were much sharper there than in tubes of 
larger diameters. They therefore used U-shaped capillar-
ies with lengths of a few cm and inner cross-sectional 
areas of 1 mm2 and 0.6 mm2, that is, with radii of 560 
and 440 µm. Kohlrausch and Heydweiller thus per-
formed capillary electrophoresis – mind you – of ions. 
But they were far from being the first to introduce this 
method.

70 They related it, for example, to the reaction of the solutions at the 
electrodes and the migration of boundaries of H+ or OH- formed by 
electrolysis from the one to the other electrode. Such effects were called 
by G. Wiedemann “Ausbreitung der freien Säure vom positiven Pol aus” 
(Propagation of the free acid from the positive pole), ref. [39], p. 167, 
and by H. Buff “Ausbreitung der Säure gegen den negative Pol ” (Prop-
agation of the acid towards the negative pole), ref. [177], p. 171. When 
both boundaries meet one another, neutralization takes place, water is 
formed, and the conductivity of the solution decreases. Kohlrausch and 
Heydweiller could visualize the motion of the boundaries by adding 
acid/base indicators.

1889. W. Ostwald and W. Nernst

We recall that Clausius’ theory of free ions from 
1858 was proved by Kohlrausch’s 1869 experiment using 
thermoelectricity[107] as described in the chapter above. 
In 1888, Wilhelm Ostwald had theorized that free ions 
must be present in an electrolyte solution, otherwise the 
principles of electricity would be violated.[178] In 1889, 
together with Walter Nernst, he caught up with the 
experimental confirmation of his theoretical paper and 
described it in “Ueber freie Ionen” (On Free Ions).[179]

Ostwald and Nernst used an apparatus similar to 
Lippmann’s capillary electrometer.71 They modified the 
simplest version of this instrument, which is depicted 
in Fig. 3 on p. 503 of ref. [180]. In short, they took a tube 
of several tens of centimeters in length and reduced its 
lumen at one end to a capillary of 3,7.10-3 cm inner radi-
us. They fixed the tube vertically, poured mercury into 
it, and immersed the tip of the capillary in dilute sul-
furic acid. Then they sucked the mercury together with 
the acid into the middle of the capillary length. A plati-
num wire served for connection with the mercury. Next, 
they took a glass flask, covered with tin foil and filled 
with dilute sulfuric acid. This solution was connected to 
the acidic solution in the capillary via a wet thread. The 
mercury was grounded, and the positive pole of a small 
electrifying machine was connected to the outer tin foil 
of the flask. As soon as the machine was set in motion, 
the mercury meniscus promptly raised, indicating a 
potential difference between the two electrodes.

Remarkably, gas bubbles were formed, dividing the 
mercury in the capillary at several points. The authors 
explained this effect as follows. When the tin foil of the 
flask becomes positively charged, the negative sulfate 
ions are attracted, while the positive hydrogen ions are 
repelled. The latter travel through the wetted threat to 
the solution in the capillary and then through the plati-
num wire from the mercury to ground. The hydrogen 
transfers its electricity to the mercury in the capillary 
and appears as hydrogen gas.

71 Lippmann’s capillary electrometer enabled the measurement of very 
small numbers of electrical charges, and of potential differences down 
to a few tens of µV. Its main part consisted of a capillary half filled 
with liquid mercury in direct contact with a dilute solution of sulfuric 
acid. Both are connected with wires that serve as electrodes. Its prin-
ciple is based on the relationship between the surface tension, the sur-
face charge density of the mercury and the potential difference of the 
electrode points. Expressed by the Lippmann-Helmholtz equation, the 
surface tension of mercury is directly related to its surface charge densi-
ty. A change in the potential difference leads to a change in the surface 
charge density, which in turn changes the surface tension. This caus-
es the mercury meniscus in the capillary to rise or fall, which can be 
accurately measured using a microscope and, after calibration, gives the 
potential difference between the two electrode points.



98 Ernst Kenndler

Ostwald and Nernst argued that the motion is caused 
by influence, also known as electrostatic induction, and 
the formation of hydrogen on the mercury is clear evi-
dence that decomposition has occurred. Since electrolysis 
does not occur without electrophoretic ion migration, the 
authors claimed that it was free ions that were moving. 
They also argued that only their explanation was consist-
ent with the laws of thermodynamics (p.125 ff.). Taking 
this explanation as fact, Ostwald and Nernst performed 
capillary electrophoresis – again, mind you – of ions, six 
years before Kohlrausch and Heydweiller.

1865. W. Beetz

The German physicist Wilhelm Beetz72 had already 
done research in this field in 1862, albeit with wider 
tubes, namely one with 13.4 mm i.d. and 297 mm length, 
the other with 6.2 mm i.d. and 207 mm length;[116] num-
bers rounded by us. His attention was drawn to the 1861 
work of Edmond Becquerel on the conductivity of elec-
trolyte solutions in capillaries,[181] which we will discuss 
in the next section. Beetz recognized that the conclusions 
in his work differed in part from Becquerel’s. Doubting 
Becquerel’s results, he decided to extend his measure-
ments in 1865 from wide tubes to capillaries.[182] Thus, for 
comparison, he measured the resistances and calculated 
their reciprocal, the “Leitungsfähigkeiten” of electrolyte 
solutions in these capillaries.

For this purpose, Beetz constructed a device 
equipped with two Grove elements and determined the 
conductivities of zinc sulfate solutions with non-polariz-
ing amalgamated zinc electrodes, and in six capillaries. 
The capillaries were between 77.7 and 161.2 mm long 
and had cross-sectional areas between 28.10-3 and 89.10-2  
mm2 (derived from the weights of the mercury-filled 
tubes), corresponding to inner diameters between 190 
and 690 µm; all numbers rounded by us. Beetz found 
that the resistances are directly proportional to the 
lengths of the capillaries, and are inversely proportional 
to the cross-sectional area of the capillaries.

1861. The Priority: Edmond Becquerel

In 1846 and 1847, the French physicist Edmond Bec-
querel73 published the result of his investigations of the 

72 Wilhelm von Beetz (1822, Berlin – 1886, Munich) studied physics and 
chemistry in Berlin from 1840. From 1850 he was professor of physics at 
the Cadet Corps and at the Artillery and Engineering School in Berlin, 
from 1855 professor in Bern, from 1858 in Erlangen and from 1868 pro-
fessor at the Technical University in Munich. His main field of research 
was electricity, especially topics of electrical conductivity of liquids.
73 Edmond Becquerel, together with his father Antoine-César Becquer-

conductivity of electrolyte solutions that were filled in 
tubes with centimeter dimensions of inner diameter and 
length. In these works[184-186] he tested whether the rela-
tions of lengths and cross sections, as he had found in 
metal wires, also applies in electrolyte solutions.74

In the April 1861 issue of Annales du conservatoire 
des arts et des métiers, he published an essay with the 
designative title “Études sur la conductibilité des liquides 
dans les tubes capillaires rhéostat destiné à la comparai-
son des grandes résistances” (Studies on the conductivity 
of liquids in capillary tubes; rheostat for the comparison 
of large resistances”.[181] In this paper he reported con-
ductivities of liquids, but measured in capillaries of dif-
ferent inner diameters for comparison with resistances 
of metallic wires.

The device Edmond Becquerel constructed and used 
for his measurements in capillaries is presented in Fig-
ure 8. We describe in the following only the right one 
of the two glass tubes shown, because the other, simi-
lar measuring system had the same characteristics and 
was installed only for control and comparison. And it 
is described in more detail because – to the best of the 
author’s knowledge – it was the first instrument ever 
used to perform capillary electrophoresis of ions in free 
solution.

The device consisted of a glass tube (AB) closed at 
the bottom and open at the top, with a diameter of 2 to 
3 cm and a height of 50 to 60 cm. It was placed vertically 
in a larger glass vessel (MN) with 20 cm diameter and 
a height approximately equal to that of the tube. Water 
was filled into the large vessel to maintain the test solu-
tion, an aqueous solution of an electrolyte, at constant 
temperature. The tube was filled with the solution whose 
conductivity was to be determined. A capillary (GH) 
with a constant inner diameter and open on both ends, 
scaled in half-mm increments, was inserted in the axis 
of the tube and fixed there. The test liquid was filled into 
the tube and penetrated into the capillary, forming a 
narrow column of the electrolyte solution inside. Then a 
metal wire, (cd), made from copper, zinc, silver, or plati-
num, the type of which depended on the test solution, 

el, discovered in 1839 a variant of the photoelectric effect, later called 
the Becquerel effect. His main areas of research were phosphorescence 
of light and its chemical effects. He also investigated topics in optics 
and electricity. He is the father of Nobel Laureate (Antoine) Henri Bec-
querel. For a detailed biography of Alexandre-Edmond Becquerel (1820, 
Paris – 1891) see C. Blondel, ref. [183].
74 It is remarkable that all authors discussed so far completely ignored 
Gustav Theodor Fechner´s comprehensive contribution about the valid-
ity of Ohm´s law for electrolyte solution, which he reported in his book 
“Massbestimmungen über die galvanische Kette”.[69] He published the 
same findings already in 1831, see his conclusions formulated in points 
(i) and (ii) in Chapter “Leap in Time” above. Fechner, however, did not 
carry out his measurements in capillaries.



99Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

were inserted into the tube (AB). The end of the wire 
in the tube was placed near the bottom of the capillary 
(GH). The diameter of the other wire, (ab), which was 
inserted into the capillary from its upper opening, was 
very close to the inner diameter of the capillary, and act-
ed like a piston. By pressing this wire, the length of the 
liquid column of the test solution in the capillary could 
be varied and its position could be measured on the cali-
brated scale with a magnifying glass.

The metal wires, (cde) and (ab), were connected to a 
Bunsen battery consisting of one to ten elements.75 With 

75 A Bunsen element was invented by Robert Bunsen in 1841.[188][189] It 
is an electrochemical zinc-carbon cell with zinc as anode in dilute sulfu-
ric acid, which is separated from a carbon cathode in nitric or chromic 

this arrangement, the current was forced to flow through 
the test solution inside the capillary, the length of which 
could be varied by hand by the wire. The current was 
measured with an astatic galvanometer. By using capil-
laries with different cross sections the resistance and the 
conductivity of the electrolyte solution in dependence on 
the liquid length and its diameter could be determined. 
Five different capillaries were used with lumen radii of 
929, 478, 238, 229 and 183 µm. Polarization was mini-
mized by using wires of the same metal as the cations of 
the test solutions.

Becquerel found that the resistance of such a liquid 
thread in a capillary is in direct proportion to its length, 
which is consistent with theory. However, he found that 
the product of resistance and the square of the inner 
diameter varied with decreasing diameter (of capillaries 
with the same length), and differed from that calculated 
for the given diameter (see Plate on p. 741).

On the one hand, Beetz agreed with Becquerel ś 
first conclusion. In contrast to Becquerel, however, Beetz 
found the resistances to be inversely proportional to the 
cross-sectional area of the capillaries, that is, the product 
of resistance and cross-sectional area is constant for cap-
illaries of a given length. Beetź s results were in agree-
ment with the present theory, and also with Fechneŕ s 
early findings (see Chapter “Leap in Time”). Beetz’s 
conclusions were plausible, and he had good reasons to 
explain the deviations from Becquerel’s results, which he 
attributed to improper experimental conditions.

We note that Edmond Becquerel measured the con-
ductivities, no matter whether right or not, and thus 
the migration properties of dissolved ions in an electric 
field, i.e., he actually performed electrophoresis. Even 
more, he was (as far as we know) the first to apply elec-
trophoresis in capillaries – again, mind you – of ions.

It is noteworthy that the first capillary electropho-
resis of colloidal or coarse-grained particles was per-
formed around the same years, 1860 and then 1861, a 
fact we highlighted in the introduction to Part 1 of our 
series.[1] We will report in detail on this first capillary 
electrophoresis of colloidal particles in a later article. 
However, perhaps surprisingly, this will not be the work 
of either Nicolas Gautherot or Ferdinand Friedrich von 
Reuß, as they did not use capillaries in their discoveries.

SUMMARY

Around 1840, it was generally believed that the ions 
of strong electrolytes, like those of salts, migrate in solu-

acid by a porous pot. A single element delivers an electric potential of 
about 1.9 V.

Figure 8. The rheostat constructed by Edmond Becquerel in 1861 for 
the first capillary electrophoresis of ions.[187] Explanations are includ-
ed in the main text. Reproduced from Cnum – Conservatoire numé-
rique des Arts et Métiers – http://cnum.cnam.fr with permission.



100 Ernst Kenndler

tions at the same electrophoretic velocity toward their 
respective electrodes, a view shaped by the theories of 
Th. von Grotthuß, H. Davy, and M. Faraday. However, 
this view was challenged by the results of recent experi-
ments, which had shown that the solutions of some 
strong electrolytes after electrolysis had different con-
centrations near the two electrodes, in the so-called elec-
trode compartments. These findings were incompatible 
with the established theory. Wilhelm Hittorf drew his 
conclusions from these observations and argued that the 
earlier view was based on a fallacy. Instead, he derived a 
hypothesis according to which anions and cations actu-
ally move electrophoretically at different speeds. In his 
opinion, concentrations can only differ if one type of 
ion migrates faster than the other. He related the change 
in concentration in the electrode compartments to the 
current that an ion type transports relative to the total 
current which flows during electrolysis. He termed this 
fraction of the current, which is equal to the ratio of the 
velocity of a particular ion to the sum of the velocities of 
both ion species ”Überführungszahl”, i.e., transference 
or transport number of an ion in a given electrolyte. 
Regrettably, the transference number expressed only the 
velocity of an ion relative to its counterion, but did not 
give the magnitude of the absolute velocity.

At the end of the 1860s, Friedrich Kohlrausch began 
researching the conductivity of electrolytes, a topic that 
would subsequently occupy him throughout his life. He 
found that conductivity decreased with decreasing con-
centration of the electrolyte, but more relevant to him 
were the conductivities normalized to their concentra-
tions. He observed that the ratio k/m of conductivity, 
k, and the equivalent or molar concentration, m, of the 
electrolyte increased with increasing dilution. He quoted 
k/m as the equivalent and molar conductivity, in modern 
notation, Λ,76 the quantity which turned out to be cen-
tral for his further research.

Kohlrausch found that two types of electrolytes can 
be distinguished. With strong electrolytes, such as neu-
tral salts, the value k/m decreased only slightly with 
increasing concentration. With weak electrolytes such as 
acetic acid and ammonia, on the other hand, there was 
no such dependence, since k/m remained at low values 
at low dilutions but rose steeply within a certain narrow 
range of decreasing concentration.

He subsequently focused his research on strong 
electrolytes in very dilute solutions, preferably but not 
exclusively on those consisting of single-charged ions. 

76 For the sake of better readability, we replace the written terms by 
symbols and restrict ourselves to strong 1:1 electrolytes with sin-
gle-charged ions. The molar conductivity of the electrolyte solution is Λ, 
that of the ion species λ. The molar concentration is symbolized by m.

He was able to show that ion and counterion of an elec-
trolyte migrate independently of each other and that an 
ion, regardless of which electrolyte it comes from, always 
has the same “molecular” – now molar – ion conduc-
tivity. This was the law of independent ion migration, 
also quoted as the 1st Kohlrausch law, which he derived 
in 1879. In determining Λ at different concentrations, 
Kohlrausch formulated an empirical law which stated 
that Λ decreases linearly with m1/2 for very dilute solu-
tions. It is known as the 2nd Kohlrausch law and was 
called by him the “Quadratwurzel Gesetz (square root 
law). The extrapolation of the ion concentration to limit-
ing conditions, i.e., to concentrations approaching zero, 
led to an ion-specific and concentration-independent 
variable, the limiting ion conductivity. It is little known 
that the 2nd Kohlrausch law was preceded by the rela-
tionship between Λ and the cubic root, m1/3, which 
applied to a larger concentration range.

The ion velocities and their mobilities, that is, their 
drift speed at a unit field strength, could be calculated 
by Kohlrausch by combining Hittorf ś transfer numbers 
with conductivity data and the law of independent ion 
migration. However, their knowledge did not contrib-
ute to a deeper understanding of the form in which ions 
exist in solutions.

It also did not indicate how they drift in the electric 
field trough the solution, although a connection with the 
viscosity of the solution and with the frictional resist-
ance has already been assumed. It must be remembered 
that the generally accepted concept before the late 1880s 
was not very different from the one introduced by von 
Grotthuß about eight decades ago. It was still based on 
the conjecture that an ion only exists in solution in an 
electrically neutral assembly with a counterion, which 
needs an electric field to divide. Rudolf Clausius, on the 
other hand, argued in 1857 that ions in solutions exist 
in free form as a result of their thermal energy even in 
the absence of an external electric force, although, as he 
assumed, only to a small extent.77

We do not wish to diminish the significant contri-
butions of many other scientists to ion migration, but 
it would not be appropriate to quote names selective-
ly. Certainly we must cite the early contributions of G. 
Fechner, but also refer to the later measurements of ion 
migration velocities by those mentioned in footnote 57 
who mainly used the moving boundary method for their 
determinations.

77 This latter aspect of Clausius´ theory, the low fraction of free ions, 
was retrospectively disproved in 1889 by Wilhelm Ostwald and Walter 
Nernst in their paper entitled “Über freie Ionen” (On free ions) by the 
conflictive consequences to the law of thermodynamics and by subtle 
experiments.[179]



101Capillary Electrophoresis (CE) and its Basic Principles in Historical Retrospect. Part 3

However, we consider Kohlrausch a key figure in the 
field, having done pioneering work for more than four 
decades, longer than others, although his greatest achieve-
ments in the field of electrophoretic properties were ulti-
mately in the area of strong electrolytes. At the end of 
Kohlrausch’s research, which lasted until about 1910, two 
questions remained unanswered for him. The first ques-
tion was why the values of strong electrolytes increase 
with increasing dilution to a limit at concentrations close 
to zero. Kohlrausch hypothesized that under the limiting, 
but only under these conditions, possible ion-counterion 
interactions tend to cease completely. But the second 
open question, namely why compounds of the 2nd class, 
weak electrolytes like acetic acid, deviate so much from 
the usual behavior of the strong electrolytes, could by no 
means be answered conclusively with this assumption.

The answer to the first question was given at the 
begin of the Short 20th Century78 by Lars Onsager,[190, 191] 
based on the theories of Peter Debye and Erich Hückel.
[192, 193] But Kohlrausch could have seen the solution to 
the second problem as early as the 1890s, if he had not 
been so skeptical of the theory of electrolyte dissociation 
Svante Arrhenius published in 1887. In fact, this disso-
ciation theory not only provided the plausible answer 
to this second question but moreover, represented the 
next, major step toward the modern physical chemistry 
of electrolyte solutions. This pioneering theory and its 
consequences in the last decades of the Long Nineteenth 
Century, or, as we term it, the “1st period of electropho-
resis,” which ended in 1914 with the first utilization of 
electrophoresis as a method for separating compounds 
in mixtures will be the subject of the following Part 4.

We attach great importance to close this chapter of 
scientific research not without pointing out that electro-
phoresis of ions in free solutions in capillaries was per-
formed for the first time in its history in the second half 
of the Long Nineteenth Century, in four times between 
1861 and 1895. The last time this happened was in 1895, 
when F. Kohlrausch and A. Heydweiller applied direct 
current instead of alternating current to liquids filled 
in glass capillaries and observed the movement of the 
boundaries of ion zones caused by unexpected resistance 
changes. One could speculate whether this phenomenon 
led him to derive his important “beharrliche Funktion” 
in 1897, the “regulating function”. In 1889, W. Ostwald 
and W. Nernst investigated whether free ions are present 
in solutions according to Clausius’ theory. They used the 

78 The “Short Twenties Century,” popularized by the noted British histo-
rian Eric Hobsbawm (1917 – 2012) in his book The Age of Extremes, 
covers the period between the beginning of World War I in 1914, i.e., 
at the end of the Long Nineteenth Century, until the beginning of the 
collapse of the USSR in 1989. For details, see Part 1 of our review series.

capillary of a Lippmann electrometer for their experi-
ments. In 1865, W. Beetz investigated ion migration in 
capillaries because he doubted the results of Edmond 
Becquerel, who wanted to compare the conductivities 
of liquids in capillaries with those of metal wires. In 
any case, it is recognized that the priority is owned by 
Edmond Becquerel, since he first performed capillary 
electrophoresis of ions as early as 1861.

ACKNOWLEDGEMENT

The author would like to thank Peter Frühauf for his 
valuable support in the realization of this paper.

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