420 THE THEORY OP TERRESTRIAL MAGNETISM. 



Hence on a sphere of radius 1 we have 



X; =n- 



Also, as above, 



Hence p F" - Z,; = (i + m) 



and (l-/* s )* 



Also we have 



^- 



From these formulae we find 



and 



We have also 



( ) +( ) 2 



-1 J -1 J -1 



+ \ (n - 

 (n-m)l (n + m)l [I , 



2 T7^75T^2^ (n ~ m+ 



2 



+ - (w m) (w + mi + 1 ) + m 3 



(n m)l (n + m}\ 

 = 



. 3. 5 ...2n- 



(11). 



