Mutual Induction of a Circle and a Coaxal Helix. 59 

 Hence we may write 



A + a^^ ' 2.4.6 ... 2»i 2ni+l\K + a} "" 

 where x = kn'ay. 

 Or, writing down the first few terms of the series, 



A + a L " 2 3\A + aJ ^ 

 ^"^ ' ^ U + aK^ 



2.4 5 



1.3.5 1 ' - ^ « 



.6 7 \A + a; 



2.4 

 1.3.5.7 1 



P. 



, 1.3.5.7 1/ X \° 

 ■^2.4.6.8'9\A + aj ^ 



— &c. 1 



It now remains to indicate how Vq, Pj, Pg, &c. may be 

 calculated. 

 Let 



Then 

 and 



Q..= P 'E 



-^0 n- 



(l-c^sin^^)"^ 



(2\ 2 



c d 



2m-ldc 



With the help of these two formulge, observing that 

 Qo =F(c), 

 Q-i = E(c), 

 and using the relations 



dY{c) ^ E(c) F(c) 

 rfe c(l - c^) c 



and 



fZE(c) _ E(e)-F(c ) 



de G 



