i6o 



PARTICULAR CASES OF EQUILIBRIUM. 



The first case corresponds to the electrification of an uninsulated 

 sphere under the influence of an external mass; the second gives 

 the influence of an electrified mass on an uninsulated spherical surface 

 which surrounds it. 



The density o- of the layer at each point should satisfy the 

 ratio 



F= 47TCT. 



At the point P, on the surface (Fig. 47) the force is directed along 

 PO ; it is the resultant of the forces /and/', one aeting from A and 



Fig. 47- 



the other directed towards A'. The triangle formed by the three 

 forces F,/ and/' is similar to the triangle APA'; we have then 



AA' r' r 



and, consequently, 



/ m m 20, m 



I = 20. = 2a = 2ak i = . . 



From this we have 



m 



m 



CT = 



The force and density at a point on the surface S are therefore 

 inversely as the cube of the distance, either from the point A, or 

 from the point A'. 



This density is positive if the mass m be replaced by a layer dis- 

 tributed on the spherical surface S ; this is the case of the inductive 

 action of a mass - m', placed inside an uninsulated spherical surface. 



