466 Prof. D. N. Mallik on Magnetic 



From these the constants can be determined, viz., 



since A n P n (R) = B w Q n (R). 



13. For a very prolate spheroid, R is very nearly equal 

 to 1. 



In this case the effect of all but the first term is negligible 

 in the present problem (of induction). 



To prove this, we notice that 



4 7^ C "ZrT 



Qn(R) dU v J dii 



Hence if M re =: the part of magnetic induction due to the 

 Q» term, 



_ + 4**0 au> 



where U = JJo + Vi-h . .. 



= Y + V 1 . 



* * Jln ~ A* R V An dR U dii ) FnW 



f P„(R) dQ n dF n *} 



_ p (1 + 47T&) dQn J Q,(R) ' 



-A 2 ' R ^dtti pTRWQT 



rfR dR 



iQn 7Qn } 



LQ»(R)'dR ^ + j 6/R J 

 But 



Q„w=|p»io g ^;-[ 2 ^.p„_ 1+ ... + ...] 



rfQ« _ 1 tfP n , r+1 _ _Pn_ [277-1 (7P,,,! ,1 



" dr "~2 dr g r-l r 2 -l Ll-rc' rtr J' 



p rfQn n ^P«_ P«' r^-1/ dP,,^ p ^Pn\ 1 



" ln ¥/" Wn ^-""^^l""Ll-n\ rM dr ^"arT 'J 



