00 = 



440 Mr. K. Hargreaves on 



results for reference. We have 



S=^(l-^ 0! T=^, 2 (<£ + N (1 c 2 ), 



for volume distribution, denominator 12 for conductor; 

 ] a?cdX 



T — M — I cPcdX 



l (a 2 +\){c 2 +A.(l-^)}3/2- 

 (i.) For a 2 (l-7- 2 )>c 2 , and 7 2 =a S(i_,.2)_ c a 



^ =^tan-^, L = M =i|^ (l-^)-^J. N =l(2« 2 -<fc,) ; 



(ii .) for a 2 ( 1 - r 2 ) < e 2 , and 7 2 = c 2 - a 2 ( 1 - r 2 ) 



(110) 



7 ~c — y 7* 



This includes the sphere for which 



1 + r 1-r 2 ' 1 + r , 1 AT 1. 1 + r 2 



0o=- lo Si^' 1J o-^o 



with Q q l-r\ 1 + r Q fl+f 1 , 1+r 



E = s/ilog^-l} 3 s.= ^ 



>•-? 



peer pea 

 or r — 

 b 



(iii.) Forc s = a 8 (l-r 9 ), </> =2a 2 , L =M = N (l-r2) = .,. 



o 



It may also be mentioned that we get the case for two 

 dimensions by putting c — in the original notation (100), viz. 



l + X{a(i-p*) + b(l.-q 2 )}+X 2 au{l--f-qZ) 



= ax 1 {I + U ( 1 - <f) } + bif{ 1 + Xa (1 -?) } + 2abpg\ay, 



which is independent of r. 



When (pqr) are all small quantities, the general case is 

 much simplified. Using (104), 



n_P<? C™ abcdXr 1^ 2 1^ « 2 /r -i 



!■ (in) 



and then 



E = s -^f=^oM i+ H + ^' 2L J 



