ARE EMPLOYED IN THE THEORY OF TERRESTRIAL MAGNETISM. 249 

 In the case when m 0, 



n 3 

 ffn _ rro _ _ ^_ rro 



'^"^ " (2w - 1) (2n + !)"-' 

 Differentiating equation (8) with respect to /i, we have 



9. From equation (l) we get 



Differentiating m 1 times with regard to /A, we have 



Multiplying by (1 /r) 2 we get 



<?r ' - 2/*m ( 1 - /r)"- + (n -m+l) (n + m) Qr 1 = ............ (10). 



Also we get from the same equation by multiplying by (l jn')'"*" 1 , 



Jm p 

 \-I _J_ 



~ 



/I 



' 



d m ~ i p 



+ (n-m+l) (n + m) (l -/rT - = 0, 



or 



Hence integrating with respect to //,, we get 



Giving to m the several values 2, 3, &c. we get by integration : 



) &c. 



A. II. 32 



