THE THEORY OF TERRESTRIAL MAGNETISM. 459 



When Wj=n 2, the coefficient of a n _ 2 in the final equation for ft n is 



n-m 



, 



when ^ n + 2, the coefficient of a n+2 vanishes. 



The coefficient of /S (li in the same final equation for ft n is 



2) f l R 



J-i 

 Hence the coefficient of /?_., is 



and the coefficient of /B n+ ,, is 



2 w + m+2)!(n-m + 



The coefficient of a, ( in the final equation for a n is 



(n + 111) \ (n m)\ 



X ~f~ 



{1.3.5 ... 

 11. Hence the final equation for a n becomes 



\ (n m)\ 



(1.3.5 ...(2n -l)} 2 



-3m 2 ] (n + m)\ (n-m)\ 

 " 



~- (2n-l)(2n+l)(2n+"3) {T .3 . 5...(2n- 



, 



a " +i> ' 



, 2w (n + l)(2n-3) (n + m)! (ro-m)! 

 e ~2n + l" ~{l.3.5...(2n-l)} 2 



582 



