596* Mr. L. Vegard : Contributions to 



Then we get 



Jcidiii + k 2 dn 2 = 0. 



Or as dn y and dn 2 are variations corresponding to the same 

 variation dx : 



^+^=0 (8a) 



^X Q^ 



If now -=r- - is eliminated between equations (7a) and (Sa\ 

 Ox u y 



we get 



:© + 



[(M l/ ;-|M 2 /;)g 1 + M li!l (^ + -f)pK]^ (7», 



The thermodynamic potential for both elements taken 

 together will be 



a,' + « B = 2 ,4(M l/l -|M 2 / 2 )g + M 1 n 1 g| + C |>K]^. 



In order to find the condition for equilibrium, we must 

 carry out a small variation, which consists in the masses 

 M^eTi! and M 2 e/i 2 being carried from the first to the second 

 element. These variations en x and en 2 are not, however, 

 independent of each other but are connected by the equation 



Vicni + v 2 en 2 = (8^) 



This equation (85) can with complete mathematical exact- 

 ness only be applied on the supposition that the molecular 

 volumes do not vary with the concentration. As, however, 

 we shall see later on, the result must also, on account of the 

 continuity of nature, approximately be applicable to such solu- 

 tions for which the concentration is quite small ; and this is 

 really the case with most solutions. And furthermore, the 

 actual change of concentration in the state of equilibrium is 

 a very small quantity. 



The thermodynamic potential after the variation of our 

 two elements, can now be found by calculating the potential 

 of each element separately. 



The thermodynamic potential after the variation will then 

 be for the first element, 



co^co-^f.-'-'M^eny; 



v 2 



