Molecular Thermodynamics. 627 



len obviously for dilute solution [cf. (55)] we shall 



^ = M [(/)M4-2R C ]+2;i(</,~Illog C )-RMo(/) , c*, (68) 



where 



y du 



and 



~dcf>' _ v[_ 



or 







_3_ 



(£'T) = f+*-=K'+f^. . . . (70) 



From (6S) we derive 



so that for a small osmotic pressure P [cf (35)] 



R^=' 2+J 3^ ^ 



Now Milner, applying his thermodynamic demonstration, 

 with the form of ''viriaL'' we have assumed would obtain 



H^r*-i£*.. ■ • • • <") 



Comparing (71) and (72) we see that this would mean 



4>'+Y=0, (73) 



i. e., by (70), 



^-{*T)=0, (74) 



3 > r («') = (75) 



. «.,by(73), 



^Now Milner's thermodynamic demonstration will apply to 

 the form (65) if u'/p & is independent of temperature, i. e. if: 



so that rigorous thermodynamics roughly bears out his 

 demonstration in this simplest case, making nearly the same 

 demand in order to arrive at the "virial" equation. But 



2 S 2 



