]\[(VicJiestcr Mcntoirs, J'o/. h. (191 1), No. 20. 9 



Also since and 6^ are both to vanish when ,r = o, X must 

 have the form 



1 



where // and 7< are functions of r and .r. 



On substitution in the general equations of ecjuilibrium 

 we obtain the further equations 



if 



C U YT ^X. X / -ir T - 1 



?'--— + 2 U= -::-- - ^( A - i ) , 



cr ix I - .V" 



whence 



Fr= j'r{X+ Y)dr, 



Ur"- = i- / \xdr - --— „ 1 V(A' - Y )dr . . . (4) 

 cx.l I - .r'.' 



Since C/ must vanish when x = a, we still have to 

 impose a further condition in this last case. 

 Taking ,- ., /"' , 



it appears to be necessary that 



I nivdr + — ^ — „ I vYdr 



shall vanish when .v = t(, or that 



i,v^~-^~,Y 



I - x'- 



shall have a form similar to that of A'. 



[We are also enabled to complete the set of equations 



(2) by finding \Prdi\ and Un/r, say /^ and [/. 



Thus 



P= - j'r log ?iX+ Y)dr 



and 



i?= - fVlog r ^^dr + -^1 / "?■ lotr r{X - Y)dr \ 

 J ex I - X [J ' J 



