INSULATED BATTERY. 253 



shall have therefore for the ends A and B, or the two poles, 

 and accordingly 



V.-V. 



Suppose that we give an extra charge M' to the battery; this 

 charge will distribute itself as it would on an ordinary conductor 

 of the same shape, and will produce a constant potential V in the 

 interior, such that if P is the capacity of the battery, 



The potential V being added everywhere to the original potential 

 will not affect the law of contacts. Hence, at the top A we shall 

 have 



and, on the mth couple from the bottom, 



V 



Let us now suppose that we connect the mih couple of an 

 insulated battery, whose total charge is zero, with a conductor whose 

 capacity is C. This will take a charge M ; there will be a fall of 

 potential V in every point of the battery, so that if V m is the new 

 potential of the couple in question, we shall have 



from which we get 



v =_ v __ -- 



a 2 "~2 P 2 P 



We have, moreover, 



