GENERAL PRELIMINARY RESULTS. 39 



It is evident from art. 5, that our preceding arguments will 

 be equally applicable to the space exterior to the surfaces of any 

 number of conducting bodies, provided we introduce the con- 

 dition, that the potential function F, belonging to this space, 

 shall be equal to zero, when either p or p shall remove to an in- 

 finite distance from these bodies, which condition will evidently 

 be satisfied, provided all the bodies are originally in a natural 

 state. Supposing this therefore to be the case, we see that the 

 potential function belonging to any point p of the exterior space, 

 arising from the electricity induced on the surfaces of any num- 

 ber of conducting bodies, by an electrified point in p, is equal to 

 that which would have place at p, if the electrified point were 

 removed to p'. 



What has been just advanced, being perfectly independent 

 of the number and magnitude of the conducting bodies, may 

 be applied to the case of an infinite number of particles, in 

 each of which the fluid may move freely, but which are so 

 constituted that it cannot pass from one to another. This is 

 what is always supposed to take place in the theory of mag- 

 netism, and the present article will be found of great use to 

 us when in the sequel we come to treat of that theory. 



(7.) These things being established with respect to electrified 

 surfaces ; the general theory of the relations between the den- 

 sity of the electric fluid and the corresponding potential func- 

 tions, when the electricity is disseminated through the interior 

 of solid bodies as well as over their surfaces, will very readily 

 flow from what has been proved (art. 1). 



For this let V represent the value of the potential function 

 at a point p', within a solid body of any form, arising from the 

 whole of the electric fluid contained in it, and p be the density 

 of the electricity in its interior; p being a function of the 

 three rectangular co-ordinates x, y, z : then if p be the density at 

 the surface of the body, we shall have 



T7 ,_ [dx dy dz p [clcrp 



~r~^~ + )~> 



r being the distance between the point p whose co-ordinates are 



