186, 187] DIELECTRICS AND MAGNETIZABLE BODIES. 



363 



image P' we place a charge e'. Then we may determine the 

 charge e f so that on the left the potential will be the same as 

 that due to charges e and e placed at P and P' in a uniform 

 medium, while on the right we shall have V the same as would be 

 produced by a charge e + e placed at P. For if we put 



e e 



on the left F= - + , 

 r r 



dV 



e dr e' dr e- e 



cos#; 



on the right F = 



e 4- e 

 r 



dV e + e' dr e + e 



cos 0. 



But at the surface these must satisfy the equation 



dV dV , , ,. , x1 



= ^ + ^^ = {^(e-e)-^(e + e>)} 



Consequently if we put 



FIG. 72. 



