The father of Charles Soret was Jacques-Louis Soret (30/06/1827 – 13/05/1890), professor of physical medicine at the University of Geneva. Among other things, Jacques-Louis Soret in 1865 proved that the formula of ozone was O3 by indirect measurements of its density, in 1878 discovered a new chemical element called “holmium” and in 1883 an intense absorption band in the blue region of the spectrum of porphyrins called today “The Soret band”, see e.g. . But the most important thing for the E.G.R.T. (European Group of Research in Thermodiffusion) is that he got married with Clémentine Odier (1831-1889), and that they had a son Charles SORET, born in Geneva on the 23rd of September 1854. From his earliest childhood, Charles was continuously educated by his parents Jacques-Louis and Clémentine. Due to long and various discussions with his father, Charles Soret was very soon introduced to the scientific method, developing his taste for mathematical and physical sciences. Charles studied at the College, next at the old University College of Geneva. He became Bachelor in Arts in 1872 and two years later he got his diploma of Bachelor in Mathematical Sciences. Charles Soret was against a too early specialisation, and despite the fact that he above all liked more mathematics, he took a lot of courses in physical and natural sciences. But his native town Geneva could not offer him more than this general education. He went to Paris to continue his studies at the Sorbonne. Convinced that a good physicist had to be first an excellent mathematician, he got in 1876 a Master degree in Mathematical Sciences. The story says that the examinations were so hard that year that only two candidates received their degree : Charles Soret and the brilliant French mathematician Henri Poincaré. Next he focused on physics and in 1878 he received a Master degree in Physics. He was really delighted at his teachers and among them, Alfred Cornu et Emile Sarreau famous for their works in optics, electricity, astronomy and geodesy. In the meantime Charles Soret left Paris to spend one semester in Germany. In Heidelberg he spent some time to study chemistry with Bunsen ; this trip in Germany was followed by a second short stay in Paris. But he definitively left Paris because in 1879 the chair of crystallography and mineralogy was offered to him at the University of Geneva, first as a lecturer, next as full professor what he became on the 26th of July 1881. Charles Soret was not only very modest but also timorous and he took a lot of time before accepting these teaching duties, because what he liked overall was original research, and without the advices of his father and his friends it is hard to believe that he would have become university professor. For Soret, the courses that he had to teach were totally new, including the setup of labs. For teaching purposes Soret designed, cut and constructed himself a lot of crystallographic models. The only room he had was used for chemical manipulations, optical measurements and crystallographic determinations. Even in such imperfect conditions Soret started high level research, demonstrating that human being cannot be stopped by difficult circumstances. After his first lectures, Soret published in 1879 the first note on thermodiffusion entitled : “Etat d’équilibre des dissolutions dont deux parties sont portées à des températures différentes (On the equilibrium state of solutions with two parts kept at different temperatures)” . Experiments were performed with NaCl and KNO3 solutions, contained in tubes of two types: straight tubes and U-shaped tubes. The extremities of these tubes were dipped one into a hot chamber (78°C) with circulating hot water, the other in cold water (15 to 18°C). In this first note, the duration of an experiment was rather short for tubes having a length L=30 cm: 10 to 25 days. By cutting the extremities of the tubes and collecting the flowing solution in three parts (the lower, the middle and the upper part) Soret demonstrated that the salt concentrated at the cold end of the tube, in accordance with a result obtained by C. Ludwig more than 20 years before . Soret was probably not aware of the work of Ludwig. He knew the classical experiments of Gay-Lussac and Graham demonstrating that in isothermal conditions a salt solution will become uniform in composition after some sufficiently long time independently of the initial salt distribution. And in the introduction of his 1879 paper he wrote (original text in French): “I propose to investigate if the final equilibrium state is the same when the temperature is varying from one point to another in the liquid. In other words, considering an initially homogeneous solution placed in a container, for example a vertical cylindrical tube with the upper part maintained at a high temperature and a lower part at a low temperature, the question arises to know if the concentration will remain uniform everywhere, or will increase in some part at the expenses of another part? This question was, to my knowledge, never treated before and a priori the answer cannot be given and could be important for the still obscure theory of diffusive phenomena of solutions”. At that time, Fick’s law was already 20 years old and Soret was aware of that law, that he recalled on p.56 of his paper . Using his notations:
where q is the concentration and k some “constant of diffusion”. By the way, it seems that there is a problem with a sign in Eq.(1) unless k is defined negatively. In steady state conditions and taking into account boundary conditions Soret wrote that the final equilibrium state should be of uniform concentration provided that the temperature is constant in the liquid. He tried to extend the theory of Fick when the temperature is varying from one point to another by considering that k is a function of space k(x) since it is a function of the temperature. He reached at the same conclusion: “The solution must tend to the same equilibrium state as if the temperature were constant, i.e. a state of uniform concentration”. And later: “... we have seen that my experiments do not confirm this consequence and show the existence of a phenomenon not contained in the equation of Mr. Fick, but not incompatible with this equation”. For Soret there was a term missing in the theory of Fick when the temperature was not uniform. In view of this scientific approach, it is hard to believe that Soret knew the results of Ludwig and simply tried to reproduce and to explain the findings. Quoting once again the original 1879 paper of Soret, let j be the weight of salt crossing during a time interval dt a unit surface on a plane perpendicular to the diffusion direction x (p.57 of the paper) ; Soret postulates that this weight j depends on “ the state of the solution on both sides of this plane”, that is to say, using the notations of Soret, on q, t, dq/dx and on dt/dx, where q is the salt concentration and t the temperature. “ The function j continuously varies with dq/dx et dt/dx, and should change sign at the same time as dq/dx=0 and dt/dx=0”. Starting with this statement Soret expands j as
Moreover, stating that j has to change sign with dq/dx and dt/dx simultaneously, Soret dropped the quadratic terms.
and in a first approximation he neglected the cubical and higher order terms Therefore
where a and β remain function of q and τ. Thus following Soret the equation describing the phenomenon is:
giving back Eq.(1) when d τ/dx = 0 with a=k. Therefore for Soret there was one term missing in the theory of Fick for nonisothermal conditions and (p.59 of ) he wrote in steady state conditions:
This is precisely the equation that we use today with the following changes in notations (Soret called u the salt mass fraction)
; and (7)
By repeating the same experiment twice, analysing the concentrations after 10 and 19 days, Soret demonstrated that Δq, the difference in concentration between cold and hot parts (qcold-qhot), increased with time, but it seems that in this first paper he did not recognize that the steady state was not reached. Also by repeating the experiment with different initial concentrations, and analysing Δq after 23 days, he was able to show that Δq increases with initial concentration q0. Thus due to Soret’s deep insight into the phenomenon, also revealed in subsequent papers, it is totally justified to attach his name to thermodiffusion even if Ludwig was the first to report in a one page paper the existence of thermodiffusion.
The second paper of Soret “ Influence de la température sur la distribution des sels dans leurs solutions (Influence of the temperature of the distribution of salts in their solutions)” was published one year later . Besides KNO3 and NaCl, he used two other salts, KCl and LiCl. He arrived at the same conclusion that salt concentrates at the cold part of the tube. In order to propose that the separation was proportional to the initial salt concentration, Soret used only data obtained after 50 days for KCl and 56 days for NaCl. He discarded results obtained after 15 and 25 days because “the dissolutions were far reaching reaching their equilibrium sate” .Since salt solutions are usually dilute, u0<<1 and from Eqs.(6) and (7)
and this explains that the separation increases with initial concentration. Soret used tubes having a length L = 30cm. If we evaluate the relaxation time q = L2/(π2D) for this length with a diffusion coefficient D = 2 x 10-5 cm2/sec (valid for dilute NaCl solutions) we find q = 4500000 sec or 52 days. Not too bad! Unfortunately Soret did not give in his paper the values of the initial concentrations, nor the concentrations of the middle part of the tubes (that could be assumed to be close to the initial values) “ in order not to lengthen the paper”, but only the concentrations of the cold and hot parts of the tubes. Nevertheless I plotted in the graph below the difference Δq =(qcold-qhot) as a function of the mean value (qcold+qhot)/2 supposed to be close to q0 for the four experiments with NaCl after 56 days: the linearity is surprisingly excellent
There is also another important conclusion in the same paper: based on the study of different salts Soret concluded that for the same initial concentration the difference of concentration between the two parts was an increasing function of the molar mass. He did not really explain this, but because the separation dq/dx is proportional to β/a ( Eq. 6) or to DT/D, and since the isothermal diffusion coefficient a or D decreases for solutes of increasing molar mass, we understand easily Soret’s finding.
The third paper on thermodiffusion is from 1881 . The experimental results reported for KCl, NaCl, LiCl and CuSO4 are quite similar to those published in . It is in that paper that Soret wrote for the first time that “the dissolutions were far from reaching their equilibrium sate after 23 days” and that the result after 56 days are probably steady “even if I could not immediately check the fact, because I could not heat simultaneously a sufficient number of tubes in order to devote some to a kinetic study of the phenomenon”. There is also an important footnote in the same paper : “ I stopped to employ the U-shape tubes that I used previously, because they produce an irregular temperature distribution resulting in internal convective currents; therefore I could not get reproducible values”. Clearly Soret recognised the role of convection, the necessity to heat from above and to have a temperature gradient aligned with the gravity. And as a final verification that all what he described was not due to some artefact, he suspended in air the same tubes but without heating the upper part and still waited 56 days: he did not found any significant difference in concentration between the upper and the lower parts of the tube. This type of verification is often forgotten nowadays!
Very quickly the Soret effect had a huge influence in petrography. As noted by Davis A. Young : “The theory of differentiation dominated igneous petrology between 1880 and 1902. During this period, petrologists eagerly applied insights from the burgeoning field of physical chemistry to account for differentiation. Acceptance of the Soret effect, a mechanism applicable to differentiation of magma in purely liquid condition, prevailed in the early 1890s”. And we know today all the interest of the oil industry for the Soret effect. One could even say that this interest was at the foundation of these IMT conferences .
The interest of Charles Soret for the thermodiffusion phenomenon seems to be limited in time to a few years, even if he published in 1884 a last additional note on thermodiffusion, working this time with KI, KBr, K2Cr2O4, Na2SO4 , NaNO3, CuSO4 and Cu(NO3)2 solutions, confirming with these new salts the earlier experiments. But there were no new conclusions.
As already said, Soret became in 1881 full professor and devoted himself almost entirely to studies in optics, in the properties of crystals and in chemical mineralogy, his favourite branches. Since the European Group of Research in Thermodiffusion is not particularly interested in these branches, we do not intend to describe in details all what Soret did; however a short survey follows to fully appreciate the vastness of his work and scientific knowledge.
In 1883, he wrote two very important preliminary papers [8,9,10] (one was translated into German by Prof. Groth in Zeitschrift für Krystallographie) on a new refractometer to measure the refraction and the dispersion in crystallized bodies. Indeed since Soret was back at the University of Geneva, he undertook a huge work on alums, which are double sulphates of the form M2SO4,M’2(SO4)3,24H2O, where M is an alkali metal (like Na, K, Rb, Cs, but also NH4) and M’ a trivalent metal (Al, Fe or Cr) and he arrived quickly at the conclusion that only methods based on the total reflection could give an important insight into the properties of these bodies. He was convinced that all existing apparatus were unable to do the projected work and therefore he invented a very ingenious new refractometer, showing all his knowledge in purely mechanical work. With this new refractometer he could determine the indices of all the Fraunhofer spectral lines in a very big work published in1884 . And one of the difficulties of the work was to obtain the “pure” chemical compounds. But Soret was a sufficiently good chemist and he could not be discouraged by the difficulty of the chemical synthesis. In 1884 appeared a work on optical rotation in which Soret obviously showed the relation of the phenomenon with enantiomorphism . In 1887, at the death of Elie Wartmann (who studied electric currents in vegetables  and gave in 1843 an exemplary survey of daltonism) the chair of general physics at the University of Geneva was free and offered to Soret. He became full professor of physics on March 11, 1887. He was not really happy, because his teaching duties as professor of mineralogy allowed him to take a lot of time for research. Being chair-holder of general physics at the University of Geneva, (with students in different fields, from medicine to physics!), this new job required much more teaching duties, mainly for the development of students labs and almost no time was left for personal work. Anyway, in 1888 (September 11) he resigned from the chair of crystallography and mineralogy, but he wanted to summarize his lectures given during 10 years at the Faculty of Sciences and started to write a textbook on these subjects. This huge book of 654 pages, containing 538 figures, entitled “Eléments de cristallographie physique” appeared in1893 . This is a very clear and precise presentation of the principles of geometrical and physical crystallography, still cited today. Thus Soret started to organise labs for the fresh students in the different fields of physics, and later research labs for Ph.D. students. During that time he studied a gas (air) thermometer in collaboration with Le Royer and published two notes in the Archives , the first in 1888 and the second one year later. 1889 is also the year of the death of his mother. In 1989 Charles published with his father Jacques-Louis some considerations on the Brewster neutral point . Jacques-Louis Soret was not only a father, but a friend, a colleague at the University and finally a co-worker of Charles. We understand that the death of Jacques-Louis Soret on the 13th of May 1890 was a sad blow to Charles. Nevertheless in 1892 he published two theoretical papers, the first in April  on the thermal conductivity of crystals and the second in October  on the polarization of dielectrics. Experiments on the thermal conductivity of crystals followed in 1893 and 1894 . With Charles-Eugène Guye, his first Ph.D. student who became the successor of Charles Soret at the University of Geneva, he studied the rotary polarization of quartz down to -70°C, using solid CO2 for the cooling and the Soret-Le Royer gas thermometer for measuring the temperature . Fizeau, and also his father Jacques-Louis showed that the rotatory power of quartz slightly increases with temperature. Charles operated down to -70°C in order to know if this remains true at low temperatures. Between 1896 and 1899, Soret devoted himself to several subjects. Let us cite: the refraction of blue and green solutions of alums of chromium , the influence of waves on the light reflected by aqueous layers , research on crystals of sodium chlorate in order to determine the reasons of producing right-handed or left-handed crystals .
Between 1898 and 1900, Soret became Rector of the University of Geneva but he continued to supervise his students. He was a tactful rector, even with the public authorities of his country. He belonged to the minority class of rectors regretted by all. Due to all these multiple tasks, Soret became very tired; gradually the idea grew in his mind to stop teaching and it became a firm decision a few months later, despite all the efforts of his colleagues. On July 10, 1900 Soret resigned from his teaching duties and became honorary professor. Tired and ill, he also stopped all research activities, a situation which was hard to suffer. After three years of long rest, as his health was improving and he came back to work on the refraction of tourmalines . On March 22, 1904, Soret attended for the last time the meeting of the board of editors of the “Archives” (a member of which he had been for more than 20 years). On March 24, he greatly suffered from digestive tracts with violent pains and was successfully operated on March 28, but a few days later,on the 4th of April 1904, at 4 am, Charles Soret deceased. The scientific community lost a strenuous worker and as well as a great physicist, even if he did not reach the reputation of those which were at the foundation of some branches of physics.
During his scientific career Charles Soret directed 7 Ph.D thesis from 1889 to1903, and among these thesis, that of Charles-Eugène GUYE (“Sur la polarisation rotatoire du chlorate de soude”) who became later specialist in relativity and, according to Einstein, gave the best experimental verification of the variation of the mass of an object as a function of its velocity.
 Govindjee and D. Krogmann, Photosynthesis Research, 80, p.15 (2004)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève] ,t.II, p. 48-61.(1879)
 C. Ludwig, Sitz. Ber. Akad. Wiss. Wien Math.-Naturw. Kl., 20, p. 539 (1856)
 Ch. Soret, C.R. Acad. Sci.,Paris, 91(5), p. 289-291 (1880).
 Ch. Soret, Ann. Chim. Phys., 22, p. 293-297 (1881)
 Davis A. Young, Earth Sciences History, 18(2), p. 295 (1999)
 F. Montel, Entropie (Proceedings of IMT1), 184-185, p.83 (1994)
P. Costesèque et al., Entropie (Proceedings of IMT1), 184-185, p.94 and 1001 (1994)
B. Faissat and F. Montel, Entropie (Proceedings of IMT2), 198-199, p.107 (1996)
A. Firoozabadi et al., Entropie (Proceedings of IMT2), 198-199, p.109 (1996)
P. Costesèque and Ph. Jamet, Entropie (Proceedings of IMT3), 217, p.51 (1999)
A. Shapiro and E. Stenby, Entropie (Proceedings of IMT 3), 217, p.55 (1999)
P. Costesèque et al., Thermal Nonequilibrium Phenomena in Fluid Mixtures (Proceedings
of IMT4), Lecture Notes in Physics, 584, p. 389 (2001)
B. Wilbois et al., Phil. Mag. (Proceedings of IMT5), 83(17-18), p.2209 (2003)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.IX, p.5 (1883)
 German translation of  by Groth, Zeitsch. f. Kryst., t.VII, p. 6 (1883)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.X, p.300 (1883)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.XI, p.51 (1884), and t.XII, p.553 (1884)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.XI, p.412 (1884)
 E. Wartmann, Archives des Sciences Physiques et Naturelles de Genève, t.XV, (1850)
 Ch. Soret, Eléments de cristallographie physique, Geneva and Paris, Georg. & Gauthiers-Villars (1893) ; available from www.antiqbook.com.
 Ch. Soret and M.A. Le Royer, Archives des Sciences Physiques et Naturelles de Genève, t. XX, p.584 (1888) and t. XXI, p.89 (1889)
 Ch. Soret and J.-L. Soret, Archives des Sciences Physiques et Naturelles de Genève, t. XXI, p.28 (1889)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.XXVII, p.373 (1892)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.XXVIII, p.347 (1892)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.XXIX, p.355 (1893) and t.XXXII, p.630 (1894)
 Ch. Soret and Ch.-E. Guye, Archives des Sciences Physiques et Naturelles de Genève, t.XXIX, p.242 (1893)
 Ch. Soret et al., Archives des Sciences Physiques et Naturelles de Genève, t.II, p.180 (1896) and t.III, p.736 (1897)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.IV, p.461 and p. 530 (1897)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.VII, p.80 (1899)
 Ch. Soret, Archives des Sciences Physiques et Naturelles de Genève, t.XVII, p.263 and 563 (1904)
This small biography is mostly based on the very extensive biography of Charles Soret written by Louis Duparc his colleague at the University of Geneva, and which appeared a few months after the death of Soret in “Archives des Sciences Physiques et Naturelles de Genève”, t.XVIII, p. 5-24 (July 1904). The analysis of his work on thermodiffusion is based on the original papers.