MEASUREMENT OF MASSES OF ELECTRICITY. 173 



to this distance ; hence it is very useful to arrive at more accurate 

 expressions. 



802. Applying Murphy's method to the case of two equal 

 spheres A and B, whose centres are O and O', we shall assume that 

 the electrical images (176) produced by successive influence, instead 

 of being at different points, are all on the conjugate points P and P' 

 of the centres O and O' with respect to the two surfaces that is to 

 say, on the principal electrical images due to the influence on each 

 of the spheres of a homogeneous layer spread over the other. If x 

 denote the distance OP or O'P', and d' the distances OP' and O'P, 

 we have 



x = , and d' = d-x. 

 d 



As the charge for unit potential is equal to the radius r of 

 the spheres, we easily find, for the values of the capacities C a 

 and C a (86), 



C.--77- ' 



r 



'f 



If m and m' are the two masses, V and V the corresponding 

 potentials, the expression for the mass m is 



and by interchanging the values V and V we obtain the value of the 

 mass m. 



Consider the total mass m as made up of two parts, one m l = rV, 

 of which the distribution is uniform, and which we may suppose 

 concentrated at the centre of the sphere ; the other m 2 = m- m v 

 which arises from the induced layers, and which we shall assume 

 concentrated in> the point P. 



The reciprocal action of the two spheres is the sum of the 

 actions exerted by the masses m l and - m 2 of one of the spheres 



