an 



Pressures in Liquid Mixtures. Ill 



d s$r); but u k =ln P K for x K = I, that is, by (3), 

 for &i = A' 2 = #3 = ••• =t \-i ~ 



or for z r = -ir(r = 1, 2, 3,". . . ,*-l). 



Substituting these values of the s's in (41), we have 

 g 



In P) . =2/- if- j^9 a • ' ' • • (r = X ' 2 ' 3 ' • • • ' K ~ l] 

 and 



in p k =2 j-K^^L. ; 



* ^(« — I) 1 ' 

 that is, if 2 denotes the same summation as ^ with the 

 omission of the term for which G = 0, 

 a^==lnP r ~2(-lf ( ^^^. ) ... (r = l,2,3....,*-l) (55) 

 and 



a?=lnV.-g~^<>«... ■ • • -j ■ • (56) 



Substituting the expressions for a ( r! ... (1<G) from (53) 



in (55), using 2 to denote the same summation as ^ with 



the omission oF the terms for which G = or 1, and taking 



account of (50), we find 



(K-2) 9r r *®-9r Or 



+ 



(*£-*) (G-1)J 



=ln p - + ^- 1)3r («-V(ft-i) c -- (r=1 ' 2 ' 8 ' -' K ~ 1} - (57) 



Substituting the expressions for a^ ... (1<G) from (52) in 

 (56), taking account of (50), we find 



=lnP - + ^(«-i) tt («-i) c • ■ • (58) 



