132 Day and Allen — Isomorphism and Thermal 



curve of solid A. Now if a small quantity of B is added and 

 the solid phase which crystallizes out contains the same pro- 

 portions of A and B as the liquid mixture in which it formed, 

 the vapor tensions of the liquid and solid phases must have 

 been lowered equally and the solidifying point will fall at y 2 

 with the same temperature as the pure solvent. (Equality of 

 vapor tension in the solid and liquid phases determines the 

 temperature of change of state.) If A crystallizes alone from 

 A + B, the vapor-tension curve will continue on to 2 2 and the 

 temperature of solidification fall to £ 2 ; while if the solid phase 

 contains both components but is richer in A than the liquid 

 phase, solidification will occur at an intermediate point. ' 



Fig. 13. 



IOOA «— Composition— * IOOB 



Fig. 14. 



Fig. 14 will serve to show the crucial character of the issue 

 raised. The ordinates represent temperatures, and the abscis- 

 sas percentages of A and B. Kiister finds his solid and liquid 

 phases identical in composition within the limits of experi- 

 mental error and the solidifying temperature on the line AB 

 at a point which can be determined from the proportions of 

 the components — at d for example. But the laws of dilute 

 solutions tell us that if the phases are identical in composition, 

 the solidifying point of A 4- B must fall at c, i. e. must remain 

 the same as for pure A. 



The temperatures at which Krister's observations were made 

 and their painstaking character leave no doubt as to the valid- 

 ity of the experimental fact. Neither can it be objected that 

 Kiister's solutions were not sufficiently dilute to reveal the true 

 relation, for the observations upon naphthaline and /3-naphthol 

 have been repeated by Brum* with very dilute solutions of 

 one of the components in the other, and completely verified. 



Now the laws of solutions hold for solid solutions even for 

 moderately high concentrations (Bodlander) when the com- 

 ponents are not isomorphous, and on the other hand even 

 liquid crystals, when isomorphous, follow Kiister's Rule more 

 nearly than the law of solutions. 



* G. Bnini, Atti della Reale Accademia dei Lincei, series 5, vii, p. 138, 

 1898. 



