70 ELECTRICAL EQUILIBRIUM. 



there by an antagonistic force; this surface will have a uniform 

 electrical layer, and the force P, necessary to resist the electrical 

 attraction, is expressed by 



Sir W. Thomson has made use of this property in the construction 

 of his absolute electrometers ; that portion of the surface S which 

 surrounds the movable part to keep it at a constant density is called 

 the guard-plate. 



82. Let us now suppose that a conducting plate A, at potential 

 Vj (Fig. 20), is placed between two conductors B and B', terminated 

 by surfaces parallel to those of the plate, one at the distance <?, and 

 potential V 2 , the other at the distance e' and potential V 2 . 



to 



Fig. 20. 



The density on the conductor A, at a great distance from 



V V V V 



the edges, is -^ 2 for the upper face, and L ^ for the lower 



face, so that the charge which corresponds to unit surface of the 

 plate is 



_ /tr ir tr 17' ' 



Disregarding the variation of density at the edges, the total 

 charge of the plate, of surface S, is thus 



S 

 M= 



If the potentials V 2 and V' 2 are equal, we have simply 



M= *"" 2 



47T 



