14 INTRODUCTORY OBSERVATIONS. 



If an electrical jar communicates by means of a long slender 

 wire with a spherical conductor, and is charged in the ordinary 

 way, the density of the electricity at any point of the interior 

 surface of the jar, is to the density on the conductor itself, as the 

 radius of the spherical conductor to the thickness of the glass in 

 that point. 



The total quantity of electricity contained in the interior of 

 any number of equal and similar jars, when one of them com- 

 municates with the prime conductor and the others are charged 

 by cascade, is precisely equal to that, which one only would receive, 

 if placed in communication with the same conductor, its exterior 

 surface being connected with the common reservoir. This method 

 of charging batteries, therefore, must not be employed when any 

 great accumulation of electricity is required. 



It has been shown by M. PoiSSON, in his first Memoir on 

 Magnetism (Mem. de 1'Acad. de Sciences, 1821 et 1822), that 

 when an electrified body is placed in the interior of a hollow 

 spherical conducting shell of uniform thickness, it will not be 

 acted upon in the slightest degree by any bodies exterior to the 

 shell, however intensely they may be electrified. In the ninth 

 article of the present Essay this is proved to be generally true, 

 whatever may be the form or thickness of the conducting shell. 



In the tenth article there will be found some simple equa- 

 tions, by means of which the density of the electricity induced 

 on a spherical conducting surface, placed under the influence of 

 any electrical forces whatever, is immediately given ; and thence 

 the general value of the potential function for any point either 

 within or without this surface is determined from the arbitrary 

 value at the surface itself, by the aid of a definite integral. The 

 proportion in which the electricity will divide itself between 

 two insulated conducting spheres of different diameters, con- 

 nected by a very fine wire, is afterwards considered ; and it is 

 proved, that when the radius of one of them is small compared 

 with the distance between their surfaces, the product of the 

 mean density of the electricity on either sphere, by the radius of 

 that sphere, and again by the shortest distance of its surface 

 from the centre of the other sphere, will be the same for both. 

 Hence when their distance is very great, the densities are in the 

 inverse ratio of the radii of the spheres. 



