75Ó 



in the second circuit in which the electrolyte is found, we think 

 inserted an electromotive force — E, which is in equilibriutn with 

 the electromotive force E existing eventually in consequence of the 

 presence of the magnetic tield; we shall assume that sense of circuit 

 which is directed inside the electrolyte towards the magnetised 

 electrode, to be positive. We shall assume also the resistance of this 

 second circuit to be zero. 



We shall subject this whole system to an infinitesimal variation. 

 Let this variation consist in the passage of an infinitely small 

 quantity of electricity e through the second circuit, and that in that 

 sense that is directed inside the electrolyte towards the magnetized 

 electrode. We shall moreover assume that in this variation the 

 magnetic induction remains unchanged in all the points of the 

 system. We shall further assume that the surface that bounds the 

 second circuit, does not change its position. 



In the first place we shall consider the work of the external 

 forces, 'fliese forces consist of: 1. the electromotive forces in «he 

 first circuit (that of the electromagnet); 2. the electromotive force 

 — E in the second circuit; 3. the external pressure p. As we have 

 supposed ^ to remain constant in all the points of the system, the 

 value of 



ƒ 



^N 'da 



which represents the tlux of ^^ through the first circuit will not 

 change either. It follows from this that no electromotive force is 

 active in this circuit, so that the work of this force is zero. The 

 electromotive force —E in the second circuit will perform work 

 equal io —E. e, when a quantity of electricity e passes. The whole 

 volume of the second circuit being supposed constant, the w^ork of 

 the external pressure will amount to zero. 



In all the work performed by the system is therefore 



öW=E.e (10) 



Let us then consider the change of the free energy of the system. 

 For this purpose w^e shall examine what are the consequences of 

 the passage of the quantity of electricity e through the electrolyte 

 in the direction of the non-magnetized electrode towards the mag- 

 netized one. We shall call the former the anode, the latter the 

 cathode. 



If u and V represent the absolute values of the velocities of cation 



