EFFECT OF INTERPOSING A DIELECTRIC. 105 



those which would be produced if this medium were a conductor, 

 and that the primitive charge of A had been replaced by M. 



The charges + M on A, - M and + M on C, and - M on B do, 

 in fact, establish constant potentials on the bodies A, B, and C ; on 

 the other hand, the equal and opposite layers, +M X and M 1? 

 produce constant potentials on the conductors A and B, so that 

 they are in equilibrium. The form of the equipotential surfaces 

 intermediate to the conductors A and B is not modified, and the 

 direction of the force remains everywhere the same. 



From the surface S 2 to the surface S' the increase of potential is 

 the same as if the layer C did not exist ; the variation also remains 

 the same from S to S r 



In order to establish the condition relative to the dielectric, let 

 us consider an orthogonal tube which cuts on the surfaces Sj and S, 

 the elements ^/Sj and ^/S, the densities on which have the absolute 

 values o-j and <r. The flow of force 4Tro- l ^S 1 which issues from the 

 element ^S x is partly absorbed on the element */S, and the fraction 

 lost is 



As this fraction should be equal to i (112), it follows that 



P 

 the ratio of the charges ov/S and o-^S-^ of the two corresponding 



elements is also i . The condition of equilibrium of the dielec- 



f 



trie is then satisfied if we have 



The force having become //, times less between the surfaces 

 S and S', the fall of potential has diminished in the same ratio, so 

 that the total increase of potential in going from B to A is now 



Calling U 15 the new potential of the conductor A, we have 



