TO THE THEORY OF ELECTRICITY. 71 



by conceiving, that whilst the body moves forward through the 

 infinitely small angle da, the electricity within it shall remain 

 fixed, and then be permitted to move, until it is in equilibrium 

 with the coercive force. 



Now the value of the potential function at p, arising from 

 the body itself, after having moved through the angle da* (the 

 electricity being fixed), will evidently be obtained by changing 

 VT into CT dco in the expression just given, and is therefore 



dV 



br sin 6 cos tzr + V '+ br sin 6 sin w dw 7 dco. 



din- 



adding now the part bx = br sin 6 cos r, due to the exterior 

 bodies, and restoring x, y, &c. we have, since 



dV_ dV dV 

 <fa~ y dx 4 x dy ' 



y dx dy) 



for the value of the total potential function at the end of the 

 next instant, the electricity being still supposed fixed. We have 

 now only to determine what this will become, by allowing the 

 electricity to move forward until the total forces acting on points 

 within the body, which may now exceed the coercive force by 

 an infinitely small quantity, are again reduced to an equilibrium 

 with it. If this were done, we should, w T hen the initial state 

 of the body was given, be able to determine, successively, its 

 state for every one of the following instants. But since it is 

 evident from the nature of the problem, that the body, by re- 

 volving, will quickly arrive at a permanent state, in which the 

 value of Fwill afterwards remain unchanged and be independ- 

 ent of its initial value, we will here confine ourselves to the 

 determination of this permanent state. It is easy to see, by 

 considering the forces arising from the new total potential func- 

 tion, whose value has just been given, that in this case the 

 electricity will be in motion over the whole interior of the body, 

 and consequently 



