

102 ON DIELECTRICS. 



which would give the force F x by the ordinary ratio 4fJ^-' a = F lf is 

 equal to the algebraical sum of the real density <r a of the conductor 

 and of the fictive density v l at the surface of the dielectrics ; from 

 this we get 





In like manner, on the conductor B we have 



If the surface S has a real layer of density o-', the fictive layer 

 having the density cr, the perpendicular forces on both sides satisfy 

 the equation 



We have further, in the two media respectively, 



Replacing the forces F x and F 2 by their values 47rcr' a and - 47rcr' 6 , 



0. 



This equation expresses that the algebraical sum of the apparent 

 charges of corresponding elements of the two conductors, is equal and 

 of opposite sign to the total charge of the corresponding element of the 

 bounding surface of the two dielectrics. 



120. ENERGY OF A SYSTEM IN THE CASE OF ANY GIVEN 

 DIELECTRICS. The general expression of energy is, as we have 

 seen (107), 



i i f 



-JVV = - 



2^ 2j 



- Vpdv. 



