ELECTRIFICATION OF A SPHERE BY A POINT. l6l 



The density is negative if the action of this layer be substituted 

 for that of the mass - m' t which corresponds to the problem of an 

 uninsulated sphere S under the influence of the mass m at A. 



In these two cases, the sphere is given as well as the position and 

 magnitude of one of the masses. 



Knowing the mass m, the radius of the sphere R, and the dis- 

 tance AO = </, we get directly 



= > 

 Jx 



and, consequently, 



a* yJ- m 



(T= - 



4 7TR 



173. If, after having insulated the sphere, we superpose on the 

 layer - m any uniform layer M, equilibrium still holds, and the 

 potential of the sphere, which was zero, becomes 



If we make M = m', the total charge of the sphere is zero, and 

 its potential is 



This is the case of an insulated sphere, originally in the neutral 

 state, electrified under the influence of an external point. As the 

 mass is null, the potential at the centre only depends on the external 

 mass. We must then have 



m ' 



The density of this new layer being 



m m 



r - 



