Induction in Spheroids. 



463 



.*. Subtracting, 



-Jn = VV-1 • (2^-l)P n __ l + (7Z-l) 2 _ 1 I n _ 2 + . . 



= V^I [<2n-l)P*-i + ( ~^ 2 (8n-3) P„- 3 + . . . .]. 



J VI— /* 2 



= - VT^{(2n-l)P w . 1 + g^(2«-5)P ll _3 + ...} 



= n 2 J w (say). 



■'• n n" 1 fir • (1 ~ ^^ = Pn ^ rz ^ + - J * - 1 from (0) 



= Jin (say). 

 (3) 



r <^,-r -^io g ^^-ffc i p,_ 1+ ... + ..i--^ = 



J Vf 2 -1 2 J V^ 2 -l ^~ 1 JL-l.n T J V^-l. 



i t t r + 1 1 I <^r f , _ ., N _. 



= i._J„log^ I + -,.J- 7 - J:ri . {(2»-l)P,, 



= i_JJog^ + i. [(2n-l)_,I._,+ . .. + ...] 

 (where the argument of the I's is r and not //). 



= Q„v/«" :i ^I-j^=* from (D) 



= Q , A /^I-[|- 1 I„- 1 logg| + ( ^ I? {(2n-?,)_J„. 2 + ..} 

 f 2»-3 T 7-1 



= iX H (say). 



2 12 



