198-202] Stresses in Dielectric Media 175 



200. This system of stresses has not been proved to be the only system 

 of stresses by which the mechanical forces can be replaced, and, as we have 

 seen, it is not certain that the mechanical forces must be regarded as arising 

 from a system of stresses at all, rather than from action at a distance. 



It may be noticed, however, that whether or not these stresses actually 

 exist, the resultant force on any piece of dielectric must be exactly the 

 same as it would be if the stresses actually existed. For the resultant 

 force on any piece of dielectric has a component X parallel to the axis 

 of x, given by 



= - (I (IP XX + mP xy + nP xz ) dS 



by Green's Theorem, and this shews that the actual force is identical with 

 what it would be if these stresses existed (cf, 193). 



Force on a charged conductor. 



201. The mechanical force on the surface of a charged conductor 

 immersed in a dielectric can be obtained at once by regarding it as 

 produced by the stresses in the ether. There will be no stresses in the 

 interior of the conductor, so that the force on its surface may be regarded 

 as due to the tensions of the tubes of force in the dielectric. The tension 

 is accordingly of amount 



STT STT dr 

 per unit area, an expression which can be written in the simpler form 



Force at boundary of a dielectric. 



202. Let us consider the equilibrium of a dielectric at a surface of 

 discontinuity, at which the lines of force undergo refraction on passing 

 from one medium of inductive capacity K l to a second of inductive 

 capacity K 2 . 



