956 Dr. S. A. Shorter : Contribution to tlie 



The equilibrium equation is 



where <f>i is the chemical potential of C; in the pure state. 

 We may regard this equation as determining the osmotic 

 difference of pressure p — p as a function of s 1} s 2 , p , anc ^ 0* 

 If we write 



p-p =n i (s 1 , s 2 , p , 6), 



we have 



<t>i(Po,0)=fi(si,S2,Po + &i,0)- . • . (49) 

 By differentiation we obtain the equations 



S»;(«l, S 2 ,2> -f ni,<9)=:— Pi(5 1? 5 2 ,p + ^', #) ^-Ht(*l, s 2 ,p , 0) 



QSj 



...(8=0,1,2:^=1,2). . . (50) 



:From these equations we see that the addition to the mixture 

 of the component to which the membrane is permeable 

 always lowers the osmotic pressure, but that the addition of 

 one of the other components may either raise or lower the 

 osmotic pressure. If the addition of one of these latter com- 

 ponents lowers the osmotic pressure, the addition of the other 

 must raise it. 



By the use of one kind of membrane, only two of the 

 quantities St/ may be evaluated. The use of the three mem- 

 branes gives the value of all six of these quantities. Since 

 these six are connected by the three equations (9), (10), and 

 (11), w r e have the following relations between the different 

 osmotic pressures : 



P ^ n ° _i_cP ^ii« P ^° 2 n /*i\ 



Fo ^ +SlPl o^ +52P2 ¥ 1 =0 * '. s (51) 



Po^ + ^P^+^,^0 . . . (52) 

 OS 2 ds 2 ds 2 7 



os 2 d*i 



Equation (48) may be regarded as determining 2 } ~Po as a 

 function of s ly s 2 , p, and 6. If we write 



p— p = Ti(s l9 8 9j p, 0), 

 we have 



</>*( p— r*, o)=fi(s u s 2 ,p, 6), 



so that 



s v (*!, s„ p, 0)=- Vi { p - a ., e ) ^ r< 5l , S2 , P) 6) , (54) 



