Put 

 and 



Prof. A. Schuster on Magnetic Precession. 31^ 



east respectively are expressed by 



^ s = 2//,&m E cos 6/t 



"^E = — 2(Jt,Q)li S cos 0/t, 

 or 



2fta> cos 6 d<$> (&x 



2/i&) cot rf4> , ' 



^ E= r~d$ (fa) 



a d& d 2 , , TT ,„, 



C0S ^ = -"^W 2 * +H ' • • • • (7) 



cot ^!=*^* +K ' w 



where /e is a constant and H and K functions of (f> and 6 7 

 which are to be determined. 



If an operation is performed with the equations (7) and (8), 

 which may be represented by the symbol 



d<t> sm ° de ' 



the left-hand side of the resulting equation becomes 

 d n d® d „d<& . „d<£> 



df cose w-de oos0 dj =m '% ; 



on the right-hand side we have 



d» d . n d 2 i , . dE dKsin0 



r d° , d_ . # a* "| 



G> + -rr — 



</</> 3 dS dOdfl d<j> dd 



Hence 



dH _ <ZK sin 6 • a± f <** . <* • ^ A . Il d> 



dc\>~ d6 K Sm " d<£ Lsin 2 &W + sin 0af0 sU1 ° dd k J * 



The right-hand side vanishes, if <E> is a surface harmonic of 

 degree //, provided that n{n + 1) =l/tc. 

 Hence we may put in that case, 



d6' sin dd<l> 



Equations (7) and (8) will now become 



S_ t \n. n + 1 sin 8d<f> 2 dd )' ' K > 



E * \*. ■ » + 1 </&ty sin 6W0 1 ^ ^ 



