Induction in Spheroids. 459 



series o£ confocal spheroids, we have 



pdp — cdc, (c = the major axis) 



= h Q ~rdr, . 



where p is the perpendicular on the tangent plane at any 

 point from the centre, and 



dp = dn. 



=^-ki-§- 



But 



1 = |S(2n+l)P Il ( A *)P»(^)Q 1 ,(r)Q»(r'), 



+ terms depending on <£, 



where r\ yJ refer to the point P. 



Als ° 1 1 [" sin 2 cos 2 01 



p 2 ~PL^-l + r 2 J 



or , 7 



P ~ aA 2 -cos 2 ; 

 and dS = A 2 vV 2 -cos 2 \/?~-l . sin # . <J0. 



remembering that <f> terms disappear on integration between 

 limits to 2tt. 

 Finally, since 



dr t*-V 



d =2.|Q (^-i) + 2;|^p„(,oQ4of:. , J(^-i)(i-^)[.; 



Or the potential due to a current i circulating in the wire is 

 7. To calculate the potential due to several turns of wire, 



