64 



EEPOBT 1891. 



forecast the result. Especially is this true of such problems as 

 deal with the nature of the held when two or more different 

 dielectrics in juxtaposition are strained by electrical charges : 

 problems which, by the ordinary method, are most difficult to 

 grasp completely. 



In the case of a charged sphere placed 

 on one side of a lai'ge conducting plate 

 put to earth, it is obvious that there is 

 — as represented in the figure — a bulge 

 of the dielectric into the plate ; and it 

 may bo readily proved that the dis- 

 placement at P is perpendicular to the 

 plate and the same as if there were no 

 plate, only uniform dielectric, and the 

 strain were due to a charge Q at 

 and — Q at the point Q, which is the 

 image of in the plate. The amount 

 of the displacement is therefore 

 ^ Q OB 

 " ■ 477 . OP- ■ OP ■ 



Let us consider a more difficult problem, the strain arising 

 from a charge Q placed on one side of a plane which separates 

 dielectric of elasticity E^ from dielectric of elasticity Eg. Sup- 

 pose E. < El. Evidently there is a bulge in this case also. 



Now, if Eo were equal to Ei, i.e., if the medium were 

 homogeneous throughout, the displacement of P perpendicular 

 to the plane v/ould be 



Q OB 



4^.'OP2 ■ OP 



If E., were equal to zero, the displacement would be 



2 Q 2?- 



■ 47r . OP^ ■ OP ' 



i.e., it would just be doubled: the bulge would be exactly 

 similar, but twice as big. 



It is natural to guess, then, that when E. is <E and >0, 

 the displacement of P is equal to 



