THE THEORY OF TERRESTRIAL MAGNETISM. 423 



Also 

 therefore 



14. We have seen above that 





2 



V ~2+l{l.3.5...(2-l)} 2 ' 



and that ( 1 /i 2 )* F = mH ; 



/i tjj^Y 7 If 1 / T^ m x, , 1 (n-m)\(n + m}\ 

 j-il^it**-*)-^ ^ = m{T.TT5 72^1) 



2 _ (#r) 2 



Also since 





f 1 ^(H:)\ 7 n 2 \ (w-m)!(n + 7n)! 



it follows that ~- du. = ( -- -} r -5 e r /7> -- TvTa 



J _! 1 /i 2 \m 2n+l/ {1 . 3 . 5 ... (2n I)} 2 



We have also seen that, when n, is less than n, 



* 



hence, under the same condition, 



P #:#, 1 Jn-mjl^ + m)^ 



J _! 1 -^ ^~m 1 . 3 . 5 ... (2- 1) 1 . 3 . 5".".. (2n : - l) ' 



fl ..2 77-1" Um fl TTm TTm n 



also f t^d^- r^r^- ^;^^ 



j -i -^ j -i i ~^ j -i 



where n and %! must evidently be both even or both odd, in order that 

 the integral may have a finite value. 



When in these equations we are only concerned with the same 

 value of m, we may conveniently write H n for H and H Ht for H^, for 

 the sake of simplification. 



