TO THE THEORY OF ELECTRICITY, 61 



we shall have R* = y* -f z*, and by neglecting quantities of the 



8 Z 

 order - compared with those retained, we have successively 



a -.8, = |, and tan0~0 = i0' 

 Thus the value of ' becomes 



In the same way, it is easy to show from the equation (11) 

 of this article, that />", the value of the density on an element 

 da-" of the exterior surface of the shell, corresponding to the 

 element da-' of the interior surface, will be 



which, on account of the smallness of p for every part of the 

 surface, except very near the orifice s, is sensibly constant and 



W 



equal to - , therefore 



p" 37T.E 3 ' 



which equation shows how very small the density within the 

 shell is, even when the orifice is considerable. 



(11.) The determination of the electrical phenomena, which 

 result from long metallic wires, insulated and suspended in the 

 atmosphere, depends upon the most simple calculations. As an 

 example, let us conceive two spheres A and B, connected by a 

 long slender conducting wire; then pdxdydz representing the 

 quantity of electricity in an element dxdydz of the exterior 

 space, (whether it results from the ground in the vicinity of the 

 wire having become slightly electrical^ or from a mist, or even 

 _a passing cloud,) and r being the distance of this element from 

 A's centre; also r' its distance from Z?'s, the value of the 



