﻿232 Mr Bernard Cavanagh on 



greatly preponderates, it is a matter of mathematical 

 necessity that the " molecular expression for \jr " should take 

 (in the limit) a linear form, and it was to this type o£ 

 " dilute solution " that Planck confined himself, arriving 

 readily at the Raoult-van't Hoff " laws of dilute solution." 

 Dilute solutions in a liquid paraffin would be of this 

 type. 



Van Laar * took the linear expression as the criterion of 

 " perfect solution 5 ' in general, and not making the approxi- 

 mations which Planck, considering very low concentrations, 

 had made, was able to show that the Raoult-van't Hoff 

 laws formed too restricted a criterion when the solution was 

 very dilute. 



He, however, considered only solutions in which the 

 solvent was of the same type as that of Planck, viz. : a 

 single molecular species. 



In view of the fact that the Raoult-van't Hoff laws have 

 been found to hold for dilute solution in our common and 

 useful solvents, which are certainly not of the type considered 

 by Planck and Van Laar, the present author was led to the 

 problem of " complex solvents," which will be the first illus- 

 tration of the theoretical problem outlined above. A 

 preliminary treatment appeared in the first of these papers, 

 but a more complete and rigorous treatment is now presented. 



The second illustration will be the problem of partially 

 " solvated " solutes, a discussion of which will follow that of 

 " complex solvents." 



The first result is that the Raoult-van't Hoff laws have 

 been rigorously predicted for extreme dilutions in such 

 solutions. It is shown, in fact, how the " experimental " 

 expression for i/r simulates, in the limit, the " molecular " 

 expression in form. 



But farther the way is prepared for the thorough investi- 

 gation of middle and high concentrations in such solutions. 

 To this end the "linear" terms in the experimental 

 expression for i|r, which simulate and replace the simple 

 linear terms in the molecular expression, have been treated 

 with some thoroughness and rigour, these being the terms to 

 which the expression reduces when the solution is " perfect." 



When the quite practical criteria thus provided are applied, 

 the belief that " perfect solution " always ceases in these 

 "complex" solutions at quite low concentrations may be 

 largely dispelled. 



In simple solutions of the kind considered by Planck and 



* Z.f. Phys. Chem., several papers, 1903 etc. 





