422 THE THEORY OF TERRESTRIAL MAGNETISM. 



Also we have 



y( Y:J - (x:)*} d^ 



= _ ( n + m ) ( _ m ) P 



)!(n + m)l , . 



.....-l)}'(2+l)* W 

 and 



! n m! 



Adding we get 



(n - m) ! (w + m) ! rw^ij+l) _ "I 

 ^ {1.3.5...(2n-l)Y 2 L 2n+ 1 



{1.3. 5.'..(2n-l)} ! 

 Combining this with 



ri ri 



L ( Y > d>J - = 2 {f73 . 5 . . . (2n -1)}* 



we have 



"n(n+l) 



Also 



P (r; 

 | 1 i ( / ,r;+^;)( / ,F re ':-^)^+| 1 i ( jt tr:-j:;)( / ,r n :+. 



(\ / \ I T7"m4-l T7"wi 1 7 i / \ / \ I 



w mlfWi + m) //: , .n au + (w + m) (%, m) j 



J-i J-i 



or 



(n-m)l (n 1 



_ 



1.3. 5...(2w-l) 1.3.5 ...(2^-1)' 



