THE THEORY OF TERRESTRIAL MAGNETISM. 421 



And since Z? = (n+l)H, we have 



12. Also we have 





(n-m)\ (n + m)\ |~1 . 1 



(n w)! (w + ra)! m 

 {fr^75T.r(2ra -T)} 2 2n~+ 



Also since 



and 



we have 





r- - z;;) + fa Y: + x?) fa r- + z;;) + ( i - ^ 2 ) r - r; 



= ( + m) (n, + m) H^H^ + (n - m) (, - -m) H^H^ + m*H?HZ ; 



hence j^ A7^c^+ |^ 17^^ = ..................... (12), 



since all the integrals on the right-hand side of the equation vanish. 



f 1 f 1 



Also we have ZZ,' l n d l j. = 0, since H?H?du = 0. 

 J-i J-i 



13. Also 



: + x?) fa Y: 4 JT-) 



I* Hr'H^ dp. -~ 

 J -i J -i 



r;)^ = o ..................... (13). 





