

GENERAL PRELIMINARY RESULTS. 



(1.) THE function which represents the sum of all the elec- 

 tric particles acting on a given point divided by their respective 

 distances from this point, has the property of giving, in a very 

 simple form, the forces by which it is solicited, arising from the 

 whole electrified mass. We shall, in what follows, endeavour 

 to discover some relations between this function, and the density 

 of the electricity in the mass or masses producing it, and apply 

 the relations thus obtained, to the theory of electricity. 



Firstly, let us consider a body of any form whatever, through 

 which the electricity is distributed according to any given law, 

 and fixed there, and let x, y\ z', be the rectangular co-ordinates 

 of a particle of this body, p the density of the electricity in this 

 particle, so that dx'dydz being the volume of the particle, 

 p'dxdy'dz shall be the quantity of electricity it contains : more- 

 over, let / be the distance between this particle and a point p 

 exterior to the body, and V represent the sum of all the par- 

 ticles of electricity divided by their respective distances from 

 this point, whose co-ordinates are supposed to be cc, y, z, then 

 shall we have 



r' * V(*' - xf + (y' - y)* + (z' - z}\ 

 and 



[p 1 dx'dydz' 

 -) r ; 



the integral comprehending every particle in the electrified mass 

 under consideration, 



22 



