of an Electrified Ellipsoid. 



339 



Now in fig. 4 let the ellipsoid PQ be determined by A, nnd 

 the ellipsoid RS by h + dh. Let the angular coordinate of 



Eur. 4. 



P and S be (/>, and let that of Q and R be (p +dcf>. Then the 

 area PQRS 



d(x,p) „. , . / dxdp dx dp\ „ ,, 



7i 2 — I 2 cos 2 6 7J , 



- T dk dd>. 



Va \//?-l 2 



Now if the area PQRS revolve about the axis Ox the volume 

 of the ring traced out is 



2,. #?£ dh # = toW-no**)*'* dh # . 



r d(n,(p) a. 



Thus for the magnetic part of the energy we have 



ixqhi? 



CC A 2 sin 3 dh d<f> 

 J J {h 2 -t 2 ){h 2 -P cos 2 <(>)' 



Since \ goes from to co A goes from a to co . The limits 

 of </> are and nr. 



Now 



J A 2 -/ 2 cos 2 c/> ~ ~~ P L C0S <f> ~~Jhf g A-/cos</J 



Hence 



1 f' A 2 -/?, A + H 



= K 2 aT^a^I./' 



MvVr, a 2 +/ 2 , A+zr 

 = 4F L 7i 2T lo S"/7=7J • 



