248 Mr. S. H. Burbury on the 



axis is vty/l — k 2 , we obtain easily a quadratic equation in 

 r, the solution of which is 



.,- 9N *rcos#±l 



v 7 1 — K 2 COS 1 



and taking the upper sign, which is sufficient, 



, 1-16" 



1 — kcos 

 also , . l + /r — 2/c cosO 



1—K cos 

 whence, neglecting k 2 and higher powers, 



r = vt(l-\-tccos0), r'=?;^(l — /ecos 0). 



12. Our integral for the ellipsoidal shell then becomes 



X=-C"~2Tr 2 i*sm0d0vdt{l + H:cos0)^^; . (A) 



or substituting for r 9 r 1 , and 0' their values above given, 



X=— 1 — - 27r 2 -g -■ v^(l-j-#ccos0) 



Jo ^ r ° 



= -{ ^^27r 2 Wi(l + 7/ecos6Osin 2 0rf<9. 



Jo dt 



13. Before proceeding further with this integration we have 



j Ti- 

 to give to —j- its value according to the nature of the problem 



to be considered. I will take two cases. 



Case 1. — The change of magnetic force -y- is due simply 



to the motion of the charged sphere, u being maintained 



. , T , w dR d/zine\ 



constant. In this case -,, =zeu ^li\~~2 / 



_ sin dr cos d0 



= — zeu — 5 =- + eu . — 5— -y- . 



r dt ir dt 



But, due to the motion with constant u. 



Therefore 



dr . . d0 u sin 



dU __ 2 sin cos 

 dt ~ m ? 



