( 5i9 ) 



the simplifications in (he considerations and calcidations — tliat tliese 

 cases may l)e adopted as the normal ones, from vvhicli all the other 

 cases are to he considered as devialions in greater or smaller degree. 

 In our case the consideration of the limiting- case « = 0, «' ^ 

 otfers another advantage, viz. that much of what will be deduced 

 in ^^•llal follows, may he transferretl with some restrictions to the 

 hoilingpohit-Une.s for ideal liquid and gaseous phases. For the thermo- 

 dynamic relations of equilibrium agree perfectly, when the distinguish- 

 ing feature between Ihe two kinds of equilibrium, viz. the degree of 

 the mutual influence of the two components in each of the phases has 

 vanished. The difference consists only in this, that for the processes 

 of melting the pure latent heat of melting may be assumed to be inde- 

 pendent of the tempei-ature, whereas for the processes of boiling the 

 latent heat of evaporation will decrease with increasing temperature. 

 Only in those cases, therefore, in Avhich the boiling points of the two 

 components do not differ much, the following considerations may be 

 transferred to boilingpoint-curves of liquids, where « may be put 

 = 0. When the difference betweeii the boiling points is larger, this 

 cannot be done any more. 



II. The fundamental equations (2) of my first paper ') become 



fa , a' \ 



/? = -=0, /?'=:- =zO simply: 

 \ 9i li J 



1 H log 1 -I log 



It is now possible to eliminate x', and to express cc explicitly in 

 7, and in the same Wi,iy to express the quantity x' explicitly in T 

 after eliminating x. 



In the first place we find: 



1 iV ' ,v 



(2) 



so that, when for shortness we put: 



we get, in consequence of (1 — x')-\-x'=zl, the relation: 



(1 — ,v) e ^ -\- xe ' ^=--\. 



1) These Proc. VI, .June 27, 1903, p. 151. 



