FARADAY'S SECOND LAW. 245 



254. SUCCESSIVE CHEMICAL ACTIONS OF THE CURRENT. 

 FARADAY'S SECOND LAW. Let us suppose that several Grove's 

 cells and voltameters are arranged in series in one and the same 

 circuit. Let n be the number of cells, ri the number of voltameters, 

 R the total resistance of the circuit, and I the strength of the 

 current which flows through it. In each unit of time the work 

 done by the whole of the cells is n]apl' } that expended by the 

 voltameters is ri]ap\. Lastly, a quantity of work RI 2 is converted 

 into heat in accordance with Joule's law. If there is neither 

 positive nor negative external work, the sum of the positive works 

 must be equal to the sum of the negative works, which gives 



from which 



The product IR is necessarily positive ; the current can only exist 

 therefore provided that 



n>n'. 



The numbers n and n' are whole numbers if the polarization is a 

 maximum in all the cells ; if the polarization was incomplete in 

 one of them, the corresponding electromotive force would only be a 

 fraction of H, and n should then be considered as a fractional 

 number. In all cases, the necessary and sufficient condition for 

 the existence of the current is that n shall be greater than *ri. 



When the permanent state has been attained, the polarization 

 being supposed complete in the cells as well as in the volta- 

 meters, the same work is done during the same time, positive in the 

 one, and negative in the others. In other words, for each unit of 

 electricity which traverses the system, the same quantity of water is 

 found in the couples, and is decomposed in the voltameters. 



255. Faraday's second law holds even when the polarization is 

 not complete at all points of the circuit in question. Suppose, for 

 instance, that in one of the couples the thickness of the layer of 

 gas has fallen below its limiting value, and that at a given moment 

 the electromotive force has only the value H', which is less than H ; 

 the transport of a unit of electricity no longer represents the same 

 work as in the others, but the relation H' = ]a'p is still satisfied, if by 

 ct we represent the heat of formation of unit weight of water with 



