326 PROCEEDINGS OF THE AMERICAN ACADEMY. 



which I communicate in this paper have been made on the simplest 

 form of ternary mixtures, that where all three substances are liquids. 

 The subject has been very little studied, the only researches known to 

 me being by Tuchschmidt and Folleuius,* Berthelot and Jungfleisch,t 

 Duclaux, t Nernst, § and PfeiiFer. || Of these, all except the first and 

 last deal with the equilibrium between two liquid phases ; the paper 

 of Tuchschmidt and Follenius contains but one series of measurements, 

 while Pfeiffer remarks, apropos of his own extended investigations, 

 that " there is very little to be made out of them." In this he does 

 himself an injustice, for, as I shall show, his results are very satisfac- 

 tory and astonishingly accurate when one remembers how they were 

 made. 



The simplest case of three-liquid systems is when one has two prac- 

 tically non-miscible liquids, and a third with which each of the others 

 is miscible in all proportions; for then any complication due to the 

 mutual solubility of the two dissolved liquids is avoided. It is pos- 

 sible to say something a priori about the law which governs these 

 saturated solutions. Let A and £ be two non-miscible liquids, S the 

 common solvent with which A and B are miscible in all proportions 

 when taken singly, and let the quantity of S remain constant, so that 

 we are considering the amounts of A and B^ namely x and y, which 

 will dissolve simultaneously in a fixed amount of S. It is known, 

 experimentally, that the presence of A decreases the solubility of B, 

 and vice versa ; it is required to find the law governing this change of 

 solubility. This, being a case of equilibrium, must come under the 

 general equation of equilibrium. 



where dx and dy denote the changes in the concentrations of A and 

 B respectively. 



This equation, though absolutely accurate, is of no value practically 

 so long as the differential coefficients are unknown functions. In re- 

 gard to them we may make two assumptions. Tlie decrease in tlie 

 solubility of A may be proportional to the amount of B added, and inde- 

 pendent of the amounts of A and B already present in the solution. 

 The differential equation expressing this is : 

 (2) a dx + b y = 0, 



* B. B., IV. 583. 1871. 



t Ann. chim. pliys., [4.], XXVI. 396. 1872. | Ibid., [5.], p. 264. 1876. 



§ Zeitschr. f. pli. Chein., VI. 16. 1890. || Ibid., IX. 469. 1892. 



