254 ENERGY OF CURRENTS. 



Eliminating the intermediate potential V m from these two equa- 

 tions, we get 



P n 



If the mth couple is connected with the earth, we clearly have 



The distribution of potentials on any given battery, symmetrical 

 or not, would be determined in the same way. In the latter case, 

 the neutral point of the insulated and uncharged battery is no longer 

 in the middle. 



267. REPRESENTATION OF POTENTIALS IN THE INTERIOR OF 

 THE BATTERY. Let us represent the battery by a straight line such 

 that each portion of the length is proportional to the resistance 

 of the part which it represents, and at each point draw an ordinate 

 proportional to the potential at this point. Let us suppose the case 

 to be that of a battery of Volta's couples, the potential increases 

 by a constant quantity at each zinc-copper contact ; the curve will 

 show then at the corresponding points a sudden change of the 

 ordinate, which is always the same. If the battery is open, the 

 potential is constant in the battery from one contact to the 

 following; the curve representing the potentials will be formed of 

 a series of equidistant steps like those of a ladder. The line of 

 zero potential passes through the middle, if the battery is insulated, 

 or it passes through any given point which is connected with a 

 conductor of some capacity or with the ground. 



Three cases may present themselves in the case of a closed 

 battery : 



i. The interpolar conductor has a resistance which may be 

 neglected in comparison with that of the battery. The two poles 

 are sensibly at the same potential, and each contact produces the 

 same variation of potential ; but from one contact to the following 

 there is a progressive fall of precisely equal amount. If n is the 

 number of couples, and r the resistance of each of them, Ohm's law 

 gives 



the current is the same as with a single couple. 



