30 GENERAL PRELIMINARY RESULTS. 



Hence it appears, that there exists a value of />, viz. 

 _ - 1 (fdV\ ' (dV'\\ 



p ~- = + 



which will give Fand F 7 , for the two potential functions, within 

 and without the surface. 



Again, ( -w J = force with which a particle of positive 



electricity p, placed within the surface and infinitely near it, is 

 impelled in the direction dw perpendicular to this surface, 



and directed inwards; and (~^~ T ) expresses the force with 



which a similar particle p placed without this surface, on the 

 same normal with p, and also infinitely near it, is impelled 

 outwards in the direction of this normal : but the sum of these 

 two forces is equal to double the force that an infinite plane 

 would exert upon p, supposing it uniformly covered with elec- 

 tricity of the same density as at the foot of the normal on which 

 p is ; and this last force is easily shown to be expressed by 2-Trp, 

 hence by equating 



4?r . _(?r **n 



and consequently there is only one value of p, which can pro- 

 duce F and V as corresponding potential functions. 



Although in what precedes, we have considered the surface 

 of one body only, the same arguments apply, how great soever 

 may be their number ; for the potential functions F and F' would 

 still be given by the formulae 



the only difference would be, that the integrations must now ex- 

 tend over the surface of all the bodies, and, that the number of 



