the Theory of Solutions. 597 



for the second. 



<-.+ [( Ml/l - 1 m,^ + m^^ + , ||>k]</. 



On a superficial view, one would have thought that also p, 

 as a function of the concentration, would have varied here. 

 We must, however, remember that p is the average density 

 between the centres of the elements ; and by this relative 

 exchange of masses nothing will be carried away from the 

 whole double element. The average density keeps its value 

 unaltered, and change of pressure between the centres is not 

 influenced by the variation. 



The above term for <»/ can be considerably simplified, 

 since 



Vj\ + Vf% c _ d /B/i t C d/ 9 \_Q 

 "d&p "dcdp dp\dc Be/ 



As will be seen later, 



h 1 =v 1 , Jc 2 = v 2 -\ 



Ml M-M 2 5p = (9) 



op v s dp ■> 



The term for as{ will then appear as follows : 

 B/= ^(M l/l -^e )ll + (MV 1 _^^ eA . 



By the aid of equations (5), (8a), (85), and (9) we get : 



V*l v 2 n 2 J 



/ 1 i'i 1\ 

 ec =— c(- — W 



and consequently 



If this is introduced into the equation for ©/, we get at 

 last for the whole variation of the thermodynamic potential : 



8 w =(« 1 + « 1 0-(« + «0=(M 1 ^ 1 -^M 2 ^ > )|^€n 1 ^. (10a) 



\ 0'' r 2 d r /O'' 



