198 Methods for the Solution of Special Problems [OH. vm 



Thus the conditions of the problem are completely satisfied by giving 

 e', e" values such as will satisfy relations (129) and (130) ; i.e. by taking 



, K-, 



- 



225. The pull on the dielectric is that due to the tensions of the lines of 

 force which cross its boundary. In air these lines of force are the same as 

 if we had charges e, e' at P, P' entirely in air, so that the whole tension 

 in the direction P'P of the lines of force in air is 



ee 



e 2 (jfiT-1) 

 or j= ^. 



This system of tensions shews itself as an attraction between the dielectric 

 and the point charge. If the dielectric is free to move and the point charge 

 fixed, the dielectric will be drawn towards the point charge by this force, and 

 conversely if the dielectric is fixed the point charge will be attracted towards 

 the dielectric by this force. 



INVERSION. 



226. The geometrical method of inversion may sometimes be used to 

 deduce the solution of one problem from that of another problem of which 

 the solution is already known. 



Geometrical Theory. 



227. Let be any point which we shall call the centre of inversion, and 



Q' 



FIG. 67. 



let AB be a sphere drawn about with a radius K which we shall call the 

 radius of inversion. 



