TO THE THEORY OF ELECTRICITY. 55 



f being the distance P, dcr. This substituted in the general 

 equation (6), art. 5, gives 



In the same way we shall have, when the point P is exterior to 

 the sphere, 



-* , } 



fa 

 } 



f 



The use of these two equations will appear almost immediately, 

 when we come to determine the distribution of the electric 

 fluid, on a thin spherical shell, perforated with a small circular 

 orifice. 



The results just given may be readily obtained by means of 

 LAPLACE'S much admired analysis (Mec. Ce'l. Liv. 3, Ch. n.), 

 and indeed, our general equations (9), flow very easily from the 

 equation (2) art. 10 of that Chapter. Want of room compels 

 me to omit these confirmations of our analysis, and this I do 

 the more freely, as the manner of deducing them must im- 

 mediately occur to any one who has read this part of the Me'- 

 canique Celeste. 



Conceive now, two spheres S and /S", whose radii are a and 

 a, to communicate with each other by means of an infinitely 

 fine wire : it is required to determine the ratio of the quantities 

 of electric fluid on these spheres, when in a state of equilibrium ; 

 supposing the distance of their centres to be represented by b. 



The value of the potential function, arising from the elec- 

 tricity on. the surface of S, at a point ^?, placed in its 

 centre, is 



da- being an element of the surface of the sphere, p the density 

 of the fluid on this element, and Q the total quantity- on the 

 sphere. If now we represent by JF", the value of the potential 

 function for the same point p, arising from S f , we shall have, 

 by adding together both parts, 



