90 ON DIELECTRICS. 



the surface S 2 ; and the resultants of these two systems of perpen- 

 dicular forces /X$>i and / 2 </S 2 are equal, and of opposite signs, as 

 they represent action and reaction. 



103. The real force which acts between the two electrified 

 surfaces Sj and S 2 may be regarded as arising from the elementary 

 actions, which are exerted directly and at a distance, between the 

 different electrical masses which cover them, taken in pairs. This is 

 the hypothesis which, up to the present, has formed the basis of all 

 our calculations. But it may also be assumed that this action is 

 transmitted through the surrounding medium in virtue of a special 

 elasticity, as Faraday believed. Regarding it from this point of view, 

 we shall proceed to investigate the mechanical conditions which the 

 intervening medium ought then to satisfy. 



For this purpose, let us consider an orthogonal tube between the 

 two surfaces S x and S 2 . The flow of forces issues from dS l (Fig. 23), 

 and is absorbed at ^S 2 , and the two elements dS-^ and </S 2 are exactly 

 in the same condition as if they were connected by elastic threads 

 parallel to the lines of force, and pulling the two elements towards 

 each other, with a force equal to / x for unit surface on </S, and to / 2 

 on ^S. 



Fig. 23. 



Let us take in this tube a volume-element bounded by two 

 infinitely near equipotential surfaces S and Sj at a distance of dn 

 from each other, and let us suppose this to become solidified. This 

 element must be regarded as subjected to two tensions pulling its 

 bases outwards, and the resultant of which is 



rfR =/</S' -pd = i (F VS' - FVS). 



57T 



As from the properties of tubes of force 



we have 



^ R== 8^ 



