140] SYSTEMS OF CONDUCTORS. 271 



outside and the equation (5) can no longer be used, but in place of 

 it we have, by (4), 



*-- 



The system now tends to move so as to increase the energy, and 

 the increase of energy is exactly equal to the work done by the 

 electrical forces. For 



(7) 



We accordingly see that the system is analogous to a cyclic 

 system. The forces <> s correspond to the negative values of the 

 positional forces P s , for the latter are denned as the forces that 

 must be applied from outside in order to equilibrate the reactions 

 of the system. Comparing equations (5) and (6) with (i) and (3) 

 of 69, we obtain the analogous results 



P- i _<- 



fy. ' 8*. ' 



The electrical energy W plays the role of the kinetic energy T 

 in the cyclic system. In order to determine which of the variables 

 e or V are to be assimilated to velocities and which to momenta, 

 we must recall that in an adiabatic motion work is done through 

 the positional coordinates at the expense of the energy T. This 

 corresponds to the case of constant charges (2). The charges are 

 accordingly the analogues of the momenta, and the potentials of 

 the velocities. Accordingly to an isocyclic motion will correspond 

 a motion in which the potentials are maintained constant. We 

 have already seen that in this case electrical energy must be 

 supplied from without, and since this must not only do work but 

 also increase the energy of the system by an equal amount we 

 have the analogue of the Theorem I of 70 : In any motion 

 of a system of conductors in which the potentials of the conductors 

 are maintained constant, an amount of electrical energy must 

 be supplied from without equal to twice the amount of work done 

 by the electrical forces during the motion. 



The equations for the cyclic forces P s ~ are here not 



cat 

 applicable. 



