

the Theory of Solutions. 601 



p is the pressure- on the same side of the membrane as the 

 solution. In order to apply these equations to our particular 

 case, we must remember that we have to place the solution 

 under this pressure. If equation (13) is differentiated with 

 regard to c, we get 



_ a/i('S/?.T) = I/StA 



(S— ) means the change of osmotic pressure per unit of 



concentration change, when the temperature and the pressure 

 in the solution are kept constant. If this is introduced into 

 equation (11 6), the result is 



(|t)|£ = p? c(1+c) 3p k< . . . (llc) 



It must be noticed that this equation holds good for all 

 concentrations. 



If the value of ^- is introduced into equation (2) : 

 on 



rfc== _ep<i±£)|e d u (Ma) 







The quantities I ^- J, ~ } and p are certain continuous 



functions of c, p, and T for the fluid mixture considered. 

 As we have considered the fluid as incompressible, and as 



(^— ) is approximately independent of the pressure, we may 

 OC/p 



consider the three quantities as functions of c and T. Term 

 (11 a) is then an exact differential ; and by integration, we 



get 



\ 





PoKl + 0|; 



ic=U. .... (146) 



The expression to the left, when integrated, gives a 

 function of the concentration, which however contains the 

 temperature as a parameter but not the pressure. By 

 equation (14 b) the concentration is determined as a function 

 of the coordinates. 



