ARE EMPLOYED IN THE THEORY OF TERRESTRIAL MAGNETISM. 255 



16. Differentiating the expressions for P n+1 and P lt _j (with respect to /A) 

 m times, we get 



'" m 1 *- 1 P 



d m P n . d'"P n 

 - 



Multiplying by (1 /i 2 ) 2 we have 



and 



or +I 



and Q:-^^Q:-(n-m+ 1) (1 -/tf <?r'- 



Hence, combining these two equations, we get 



2n+l m n + m 



whence the quantities <? +1 , &c., may be successively determined. 



17. putn g 



in equation (13), we have 



- ..2n-l) , , 

 V M 



1.2. 3 ... (n-m) 



1 1.3.5 ... (2n-l) 



2' 1.2. 3 ... (n-m-1) " 



I/ 1W x 1.3.5 ... (2ft- 1) 



n 



, . 



