82 WORK OF ELECTRICAL FORCES. 



than that of a single jar; but for a given potential it would be p 

 times less. It is the exact opposite of charge by quantity. 



All the laws relating to the discharge of batteries have been 

 experimentally established by M. Riess. 



On the whole, then, in working at a constant potential that is 

 to say, with a constant source of electricity, the best combination 

 that can be made with a given number of jars, so as to obtain the 

 maximum energy in the discharge, is to join them in quantity, pro- 

 vided always that the jars can sustain the maximum potential of the 

 source. If, on the other hand, only a limited supply of electricity is 

 available, it is best to arrange them in cascade. 



The first is the case most frequently met with in electrical 

 machines; but as they usually produce very high potentials, it is 

 often advantageous to select a suitable combination of the jars by 

 which these high potentials may be used and at the same time the 

 charge be economized. 



96. ELECTRICAL WORK IN THE DISPLACEMENT OF INSULATED 

 CONDUCTORS. Conductors with a Constant Charge. The value of 

 the potential energy of a system of conductors is 



When the relative position of these conductors is changed, with- 

 out in any way connecting them, a positive or negative work of the 

 electrical forces is, in general, produced, and therefore the energy of 

 the system is altered. If the conductors are left to themselves they 

 obey the electrical actions which urge them ; the work of these forces 

 is positive and corresponds to a loss of energy in the system. If, 

 by any external work, the system experiences a deformation in a 

 direction contrary to that of the electrical actions, the energy 

 increases to a corresponding extent. 



Hence, calling </T the work of the electrical forces, and dW the 

 corresponding variation of energy, we have at each moment 



(i) </w+dnr=o. 



The energy of conductors which are left to their reciprocal actions 

 tends therefore towards a minimum. 



We have, moreover, the general expression, 



1 T 



2 2 



