ENERGY OF A SYSTEM OF CONDUCTORS. 79 



to reach the state in question we started from the neutral state, we 

 have simply 



W = -(M 1 V 1 + M 2 V 2 + ) = MV. 



We thus see that the energy of a system of conductors is equal to 

 the half -sum of the products of each mass by the corresponding potential. 



91. A conductor which remains insulated during the charge is 

 merely electrified by induction, and its total charge is zero ; there is 

 no term, therefore, in the sum of the products, which corresponds to 

 an insulated conductor. 



In like manner, a conductor kept in connection with the earth 

 remains at zero potential, and does not enter into the expression for 

 the energy. 



It must however be remarked that these two kinds of conductors 

 affect the value of the energy, by modifying the influence of the 

 capacities, and therefore the potentials, of the electrified bodies. 



Lastly, the same formula holds for the case of insulating bodies, 

 however electrified. Each of the volume elements of an insulating 

 body may, in fact, be considered as an infinitely small conductor on 

 which the corresponding electrical mass is distributed. In this case 

 the preceding sum becomes an integral; calling p the electrical 

 density, and V the potential on the volume element dv, the energy of 

 the system is expressed by 



The energy accumulated by electrification on a system of con- 

 ductors is expended when the system is discharged, and may be 

 transformed into mechanical work, or into an equivalent effect : 

 disengagement of heat, chemical action, etc. 



92. If electricity were a material substance, the masses consti- 

 tuting the electrical layers would acquire a certain vis viva during 

 the discharge, in virtue of which they would, like a pendulum, pass 

 beyond their position of equilibrium, so as to restore to the system a 

 fraction of its initial energy ; a succession of discharges alternately 

 in opposite directions would be produced, until the heat disengaged 

 upon the conductors had exhausted the whole of the available 

 energy, and final equilibrium would only be reached after a certain 

 number of oscillations. Experiment shows, indeed, that under 



