44 GENERAL THEOREMS. 



The layer M, developed by induction on the surface S, is equal 

 and of opposite sign to the algebraical sum of the masses comprised 

 within the cavity. This layer absorbs the flow of force emanating 

 from the internal masses. The system of this layer, and of the 

 masses which it comprises, gives a potential zero, and its action 

 is zero at every outside point. 



If the conductor A is in connection with the earth, its potential 

 is zero ; if then there are no other acting masses than those con- 

 tained within the cavity, the external surface S' is in the neutral 

 state, and the potential is everywhere zero outside the cavity. 



An electrical mass M', placed on the insulated surface S', acquires 

 there a distribution independent of the internal masses. It will 

 produce a constant potential V throughout the whole extent of the 

 conductor A, and of the cavities which it encloses ; and this potential 

 will add itself at each point to the potential already existing. The 

 mass M' will not exert there any influence on the equilibrium of 

 the internal masses. 



58. If there are no other acting masses than those comprised 

 within the cavity, and if the conductor A were originally in the 

 neutral state, its total charge should remain zero ; simultaneously 

 with the layer M on the inner surface S, it will develop an equal 

 and opposite layer M' on the exterior surface S', and we shall have 



M' = -M = 



This layer M', equal to the algebraical sum of the internal masses, 

 and of the same sign, is of itself in equilibrium whatever be the 

 position of the internal masses. 



We get thus Faraday's law : The quantity of electricity induced by 

 an electrical system on a conductor, which surrounds it, is equal to the 

 quantity of inducing electricity. 



59. The action which given electrical masses exert on the exterior 

 of any closed surface, is the same as that of a layer of the same mass 

 spread on this surface according to a certain law. 



Let m, m', m" , .... or JVz, be the given masses, which we will 

 suppose fixed as if they belonged to non-conducting bodies ; a surface 

 S of any given form envelopes them. Suppose that, for a moment, 

 we replace this surface by a material sheet, forming an infinitely 

 thin conductor in connection with the earth ; the internal surface 

 of this sheet will become covered with a mass - M = m, whose 

 potential, for all external points, is equal and of opposite sign to 



