120 On Partial Pressures in Liquid Mixtures. 



and the z^ z 2 , p^ p 2 , pz that belong to any one observation. 

 Finally, P l5 P 2 , P 3 are determined by (57' ) and (58"). 



If wanted, c is calculated from ((53 /; ). 



The most laborious part of the calculation is the deter- 

 mination of the 47 sums that enter into the normal equations. 

 This is best effected according to the following scheme. 



For each observation, find 



z h z 2 , ln.r 1? In # 2 , In #3, In-, In—, In—, In—, 



°°\ iV 2 Pi P'A 



next, by successive multiplications by z h 



.2 Z Z ~4 ~o .6 T+p^f -6 _ -3 v *&\ 

 *1» *1* ~V> *V *1 L^o 1 "*! ~~ ~1 X ~1_|» 



Vl *ft> * [test^, = 4xy, 

 ~r2' s r2» 2 r2 [test c : / 2 = 4 x / 2 J ; 

 then, by successive multiplications by z 2 , 



~2 .3 .4 .5 , 

 •"2' ~2' ~2' *2» " 



.6 

 '2 



[test 4 =4x4], 



» y ~ /~2 », ^,3 

 1 2» ^l^' *1*2» 



*Z 4 

 ~1*2' 



Vi [test ^4=^x4], 



-2- ^2^2 ^2~3 

 1^2' x, l~2^ ~1~2' 



~2„4 

 -2^ 2 



[test 44=^x^4], 



*3- .3-2 ^3~3 

 ~\~2> ~l~2» *\*% 





Tfpst * 3 ~ 3 = ^ X ^ 3 1 



Z 4 Z * 4 ^ 2 





[test .-}*»=«,>< 4$), 



*fc 





1 test ~n^o —^ ^j x z,z 2 1* 



*2U> ^21' *2 1 





[test4^ 1 =4x/ x ], 



2 rVl' *1*2^1 





[test z^J,^ z x xz\l^ 



Z 2 ~ I 





[test^Z^^x^j], 



~ / -27 ^37 

 "2 2* *2 2f ~2 l 2 





[test 4l 2 =4x/ 2 ], 



Z \ Z 2 2' ^\ Z 2 2 





[test ^^^^x^y, 



z\z 2 t 2 





[tesU?* 2 Z 2 = z Y xz x zJ^ 



If the calculation of these numbers is carried out in 

 tabular form, like functions in one column and functions 

 belonging to the same observation in one line, the 



