424 THE THEORY OP TERRESTRIAL MAGNETISM. 



15. From the differential equation for H n we have 



alld 



Multiply by H ni and H n respectively and add, then 



r <PH n #H ni -] r dff <*#,-! 



- ** } I/** ^ 2 + " v \ ~ ^ t H *> -^ + H -^r J 



9m 2 



1 



But ( 1 - M -) - , 



7 dp ' p. p. p. p. 



therefore 



or 



dH. 



' dp, dp. 



[9m- 1 

 n(n+l) + n, (n, + 1) - ^- 8 J ^^ = 0. 



Integrating from /,= -! to /*=!, we get 



When w = 1( this gives the value of 



(!",) fc-n(n+ 1)/* (fin 



J _i 



-i J -i 



as we have seen elsewhere. 



