140 Prof. P. J. Daniell on the 



Let us denote T ^^ by \. 



r «) 

 Then 



-"• )i 0« owl 15 15 7 14 14 39 



+ C ! iv / 3,r 



"-]••• (") 



^ r(|)r(i) 2*- r(§) -arj.» (1 yj rf ^ 



Put ,-=.-, then UAj, Ty^p- 



— 1 — ~ cos (b 



Put #=1 + x/ 3 1 -? so that 6 lies between and 7r. 



1 + cos cj> r 



i _ 3 .j_ r* d$ 



where k 2 = —. — = sin 2 15°, 



1 3 3 / 4 

 or" £=%-F(i,i,M 2 ) 



will give the value o£ X. 



In the region II. a solution of Laplace's equation will be 

 given by 



r 



This satisfies the proper conditions ; for near the end 

 z = — L we have 



while at the boundary -57 = 1, 



On 

 or J 1 (k r ) = 0r 



Thus the &,.'s must be chosen so as to satisfy this equation. 

 Then / BV\ . v , T ,, . 



\ O^ /r=0 r 



