Trof. Thomson, On the Electric Theory of Gravitation. 67 



lines of force by k(P — Ny where k is a constant. If we dis- 

 criminate between the effect of positive and negative lines we 

 must replace this expression by 



aP^+^N'-2yPN, 



where a, yS, 7 are not necessarily equal to each other. On this 

 assumption let us calculate what would be the attraction between 

 two slabs of matter A and B. Suppose that for each unit of 

 surface of A there are Pi units of positive electricity, N-^ of 

 negative, while Pg and N2 are the corresponding qua,ntities for B. 



iPi 



A B 



iNi 



*R, 



Fig. 1. 



If P is the number of positive lines of electric force through 

 unit area, iV the number of negative, then we see that between 

 the plates 



to the right of B, 



P = l{P, + P,\ N = ^{N, + N,), 

 to the left of A, 



P = -^{P^ + P.), i\r=-i(i\r, + i\r^). 



The force on unit area of B towards A will be the tension in 

 the region between A and B minus that in the region to the right 

 of B, i.e. it will be equal to 



{icc{P,-P,r+i^{N,-N,y-^,y(P,-P,)(N,-]!{,)} 

 - {\a{P, + P,y + i^{]^, + N,y - i7 (P, + P,) (N, + iV^)} 



= -aP,P,-fiN,N, + y{P,N, + P,N,) (1). 



Let us take the case when both A and B are electrically 

 neutral, i.e. when Pi = Ni, P2 = i\^2, then this force will be equal to 



{2y-{oi + ^)}P,P,. 



