154 Troceedings of Philosophical Societies. [Feb, 



applies equally to the case of any number of conductors acting 

 mutually upon each other. It will furnish in each case as many 

 equations as we consider of conductors ; and these equations 

 will serve to determine the variable thickness of the coating 

 which envelopes these different bodies. 



M. Poisson satisfies himself for the present, with giving these 

 equations for two spheres of different diameters, formed of a mat- 

 ter which is a perfect conductor, and placed at any distance from 

 each other. When the two spheres touch, the equations may 

 be integrated in a very simple manner by definite integrals. 

 They show us that the thickness is nothing at the point of 

 contact, that is to say, that if tvvo spheres of any diameters are 

 placed in contact and excited in common, there will be no clec* 

 tricity at their point of contact. In this particular the calculus 

 agrees exactly with the experiments of Coulomb. (Acad, des 

 Sciences 1787-) 



In the neighbourhood of this point, and to a considerable dis- 

 tance from it, the electricity is very weak upon the two spheres. 

 When it begins to become sensible, it is at first most intense on 

 the largest of the two spheres ; after this it increases at the great- 

 est rate upon the smallest sphere, so that upon the point diame- 

 trically opposite the point of contact it is always greater on the 

 smaller sphere than in the corresponding point of the greater 

 sphere. 



When the spheres are separated, each carries off the whole 

 quantity of electricity with which it was covered, and as soon as 

 they are removed beyond all mutual action, this electricity is 

 distributed uniformly on each sphere. But the ratio of the mean 

 thickness is given by this analysis in a function of the ratio of the 

 two radii. Thus the formula of M. Poisson includes the solu- 

 tion of this physical problem: To find in what ratio electricity 

 is divided, between two globes that touch, and whose radii are 

 given. This ratio is always less than of the surfaces ; so 

 that after separation the thickness is always greater on the 

 smaller of the two globes. The ratio between these two thick- 

 nesses tends towards a constant limit which is equal to the 

 square of the ratio of the circumference to the diameter, divided 

 by six, which is very nearly 5 to 3. Thus when a very small 

 sphere is placed upon an excited sphere of considerable size, the 

 electricity divides itself between the two bodies in the ratio, of 

 about five times the surfaces of the small sphere, to three times 

 the surface of the greatest. 



Coulomb had endeavoured to determine this ratio by experi- 

 ment. He had always found it below the number 2, or 6 to 3, 

 from which he concluded that the number two ought to be its 

 limit. It is easy to see that such a limit could not be experi^ 

 mentally determined with much precision. Therefore, instead 



