754 



as for the cathode holds : 



do ■=z e 



-ƒ■•'-. 



4. We must fiirtlier consider the change of ihe ''non-magnetic" 

 part of the free energy ; as we saw above the \alues must l)e 

 assigned to tlie variables which they will have in the magnetic held. 



The only change which is involved in this, is the change of con- 

 centration of the solution. If the free energy of the unity of mass 

 of this is If', then that of the volume of solution to of density (,> is 



d •ƒ 'j = ^ . to . i|; , 

 when W^ is the free energy of the solution. When we make use of 

 (17) and (18), and further of the relation : 



;* = -p (21) 



which follows from (7), the variation of this will amount to : 



ödW, — 6v 



p oil' 1 — mc , 

 tf, + ^ + / . to . . (22) 



^ 06' VI 



For the free energy of the unity of mass of the sohition we shall 

 use the well-known equation : 



tp z=; tfjg -f «c -f- ,?o' + . . . . + liTc log , . . . . (23) 

 in which \]\ means the free energy for c = 0. 



In this we must give to the variables c and v the values which 

 they possess in the magnetic lield in the state of equilibrium. 



On the other hand we can, however, also imagine that different 

 concentrations can permanently exist in the different volume elements 

 of the solution, in such a way that no change can be brought about 

 in this by the magnetic field. Thus we shall obtain the potential 

 difference between the electrodes on arbitrary distribution of the 

 concentration. The supposition made is a fiction; the more so as 

 we have assumed also the resistance equal to zero; in general the 

 velocit}' of diffusion will namely increase as the resistance decreases, 

 with which permanent concentration differences are in contradiction. 

 This supposition, however, must always be made for such problems, 

 in order to be able to apply the laws of the reversible processes; 

 hence we also make them here. 



With the aid of (22) we get from (21) 



p Rl ^ a' 



(hi '/; — (Iv t|,^ + ^ 4- — (1 -f log c) — RTc -\- - 

 Q m m 



U\ — öv\\ 



When we use here the expressions (11) and (12). and integrate 



