in Conducting Sheets and Solid Bodies. 9 



The general solution of this equation is 



**0#&ij2g, W 



in which the L term vanishes at the centre, and the M term 

 vanishes at infinity. 



In the case of a shell, the values of L, M are to be deter- 

 mined by means of two sets of boundary conditions. 



In the case of a solid sphere, M = 0, and L is to be deter- 

 mined. But it is better for our purpose to proceed as 

 follows : — 



Write Qx=CH 



and the equation, wanting the right-hand side, becomes 



of which the solution for this case, when Qi is to be finite at 

 the origin, is 



QisssAiJ flB+ i(Xf'). 



Hence 



Q=-jJ» +i (Xr), 



or, say, 



Thus the solution is 



P= {- A r n + A 1 r"*J n+4 (Xr)}Y n 6 urf 

 inside the sphere, and 



P= { -A a» + A.a-iJ^Xa^Qj^Y^, 

 outside the sphere, where 



-nA a n -> +A 1 j^{a-iJ n+i {\a)} 



= (n + l)A «»-»- (n + l)A 1 a- f J„ +i (\«); 

 or 



Ai= <*+}?:•*. . . (5 ) 



{(»+i)o-'+ij{«-u, +( (x«)) 



