TRANSACTIONS OF SECTION A. 65 



n , N Q OB 



where yx is < 1 and > 0, and is the same for every position of P. 

 If this be SO, the state of strain of the medium to the left of 

 the plane is that due to a charge Q at O, and a charge — fiQ 

 at the point Q (the medium being for the moment supposed 

 uniform) . 



Consequently the pressure at P 



_Ei ^ El /xQ ,. . 



~47r"OP" ~47r'QP" ■■■ ■" ^'^ 



And the state of strain of the medium to the right of the 

 plane is that due to a charge (1 + z^) Q at O, the medium being 

 again supposed uniform. 



Consequently the pressure at P 



^E, (1+/^) Q (--s 



47r* OP ■ ■■■ ■■■ ^ '^ 



Hence for equilibrium, equating (i.) and (ii.) : 



E,(1-/..) = E.(1+^) 

 _ El — Eg 



'^ ~ Ei+E.; 



This value of /x is independent of the position of P : so the 

 state of strain, of the nature guessed at, and having this par- 

 ticular value of jji, is one which gives complete equilibrium, and 

 is therefore the solution of our problem. 



Since the strain of the medium to the left of the plane is 



that due to a charge Q at 0, and a charge —~^ — ~^ . Q at the 



El + E.J 



point Q, the pressure at the surface of the sphere at is very 

 nearly 



El (Q Ei-E, Q] 



47r U Ei + Ea 2&) 



where a is the radius of the sphere, and b the distance of the 

 centre from the plane. 



The energy of the strain is therefore 



Ei.Q2 ( 1 _ Ei-E, J^) . 

 Stt \a Ei+E,"2^f' 

 and there is a force of attraction towards the plane equal to 

 El . Q" El — E, 

 IGtt . b'' ' Ei+E, ■ 



The advantage of being able to form a mental picture of 

 one's problem is, I think, specially evident in the determina- 

 tion of the effect of placing in a held of uniform force — i.e., 



