( 455 ) 



If we moreover put 



^— - = »«; -^- = y'; -^—' = X; -^'- = 0'; . (27) 

 «1 ^1 «1 61 



we find easily from (1), (2) and (3) for (lie equation of the new 

 surface : ^) : 



n»' = - (1+0 % 3^ {f>.'-{-v') - ~~^ + {l-]-t')l,doij.v + {l-.v) log {l-.v)l (28) 

 where 



«-^•' = Y + T'''*'~y^^'''~'^'^*'' ^^^^ 



further : 





16. For investigations in tlie neiglibourhood of the sides it is 

 desirable to develop tlie expression foi" if/ so fai' as {possible according 

 to tlie powers of .c. We write tlicrefore: 



tp' = (l^-0.^•%.■P + Xo + Xl•*'• + X.'^' + (32) 



where in finite form ^) 



X„ = -(l+0%^(2 + 3i'')---^ (33) 



8(l-l-v) 



/ 2y' ^ Qx' 



(1+0 



- 2y'' 2y'— d' 1 



("2 + 3^1^ ~ 2 + 37 '^ Y 



8(1 + ??) 



1) If we wanted lo consicier ctx as funclion of the temperature, tlic simplest way 



of doing this would be hy writing the second term of the second member : 



«'^. (1 +fj i' + f„ «"* + .. .) , ^ 8 a, 



1 — , — , . The formula Ti = ~~^r-- ,,,, would continue to 



I -j- V 11 h^ MR 



hold unmodified for the critical temperature of the principal com|)oiU'nl. j)rovided 

 we take for Oi the value it has at that critical temperature. With Clausius' Iiypolliesis 

 that ciz is inversely proportionate to 2', we should get =i = — 1; £0 = +!. Also 

 (!29) continues to hold and the modifications in the developments into series and 

 in the formulae derived from them would be easy to apply. 



*) hi this form they may be used for investigations concerning I he conditions 

 ;il the side of the ({/-surface at temperatures greatly diO'eriug from Ihe critical tem- 

 perature of the principal comi)onent, as are made by Ki:i:som : Confribulions lo the 

 knowledge of the j/surfacc of van dku Waai.s. VI. Tlu! increase of pressure al 

 condensation of a substance with small admixlures. I'roc. I'lOyal Acad. IV, p. G,j'.J — 

 668; Leiden, Gomm. phys. Lab. N^. 79. 



