10 Prof. A. Schuster's EUt -kat Notes. 



current, and becomes : T_ an;l — Y inside the sphere 



and outside respectively. The vector B is determined by the 



condition that it most be continnons with its first derive. 

 at the surface of the sphere, and most satisfy the condition 



V 2 Bi= — #*-j- -~r- Y„= —pW* inside the sphere, 

 and 



V 2 B : = —^— —^ Y v = — /* 1 l r, _ m _i ontside the sphere. 



¥'„ and SP"_ r ,-: are solid harmonics of degree n— 1 



— . — - respectively. ILt : :i_ ..::;; us ar'e saris:: e a :.y 



and 



B- = - — — ^^ — -- . ? inside :~_r sphere. 



The complete vector-] >tential ::" the moving sphere is rhere- 

 fore io the ooisi . ace 



A- = ^-"- -^ *-te , 



1 2 rfs .... 2«-l 2n + oj " "- 



- .,- ,2n-l -.-.-roy * _1? 



The expressions for the inside space are obtained by writiug 

 ¥„ for >!*_»_,, and interchanging r and a. 



In the calcolations for the magnet:: forces the last term of 

 A.: is the Mily me which produces an effect, and, conse- 

 quently. 



- a -'■• t- 



Let ^ represent the harmonic of dr.::: and type 7. 

 -:. with the usual notation 



/■" 1*1 



— — - : :s 73 sin"^ — . 

 a" +1 r ^ ' 



ana 'I'' the sories] Hiding harmonic 



/•" . . 2*P. 



sin crc sin" .-- 



---.= 



a' - - dfi c 



