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L. The Thermodynamics of Cryohydrates. By J. Pap.ker, 

 B.A., late Scholar of St. John's College, Cambridge*. 



DK, GUTHEIE has found that when a dilute saline solu- 

 tion, formed by dissolving a salt in water or any other 

 liquid, is subjected to reduction of temperature, the ice 

 formed is perfectly fresh, until a certain temperature is 

 reached, which depends only on the natures of the salt and 

 liquid employed, and not on their relative proportions. The 

 solution then freezes, without further reduction of tempera- 

 ture, into a solid homogeneous brine. Dr. Guthrie has also 

 found that the final solution thus obtained, which he calls a 

 " cryohydrate," is of the same strength whatever may have 

 been the strength of the dilute solution with which we started. 



Again, he has found that the lowest temperature obtainable 

 by means of a " cryogen," i. e. a freezmg mixture of salt and 

 ice, is the freezing-point of the corresponding cryohydrate. 



These experimental results have been obtained at atmo- 

 spheric pressure, but we shall suppose them to be true at 

 any pressure. 



We at once infer that at the freezing-point of the cryohy- 

 drate, the salt and pure ice are neutral to each other ; in 

 other words, a saturated solution is then in stable equilibrium 

 with pure ice. There is, therefore, only one stable solution 

 possible at this temperature, viz. the cryohydrate itself. 



At any temperature above the freezing-point of the cryohy- 

 drate, and below the freezing-point of the pure liquid, there 

 may be any number of stable solutions, the strongest being 

 a saturated solution, and the weakest in stable equilibrium 

 with pure ice. 



Analytically, let 9, yjr be the thermodynamic potentials at 

 constant pressure of unit weights of the salt and ice, re- 

 spectively, at any temperature between the freezing-points of 

 the cryohydrate and of' the pure liquid. 



Also let the weakest stable solution contain a weight m x of 

 the salt, and a weight m 2 of the liquid. Its thermodynamic 

 potential will be 



®= m ifi + ™ 2 A, 



where f 1, f 2 are homogeneous in rn 1 and m 2 and of degree 0. 



But the solution is in stable equilibrium with pure ice, and 

 not with the salt; hence; 



A <</>, / 2 =f. 



* Communicated by the Author. 



