426 THE THEORY OF TERRESTRIAL MAGNETISM. 



Now integrate from fj.= I to /u, = 1 . and we get 



/ n\n (v-L-l-n ^-"-n 7 * I TT TT 7 



(1 a) -j " 7 du. + m ti n rL n ap. 

 J-i dp dp J_i 



f 1 ! If 1 - f 1 



~[_2 ^ 2 l(l J J-i J-i " "' 



2 

 Multiplying the equation obtained in Art. 15 by - and subtracting 



from this, we get 



H,, ff n , 



-i 



......... (16). 



17. We have seen above (p. 420) that 







hence (1 -/*) (^.-) + (1 -/*')( r." 



= ( 1 - ^) (n + m) 2 (fl.- 1 )' + (n - ) 2 (^T ')' + 

 l^ 



Multiplying by cZ^u, and integrating from 1 to + 1 , we have 



1 1 1 



_ o 



2 



;^ 2 + n + m 2 + 2m (n-m)(n + m+l) , 



f n s + n + w'- ~~ * 



m)! 



(2n- l)(2n+l)(2n + 3){l .3.5... (2n-l)} 2 

 x {[n (n + 1 ) + m (m 2)] (n a + n - m? + m) + (n 2 + n + n? + 2m) (ri' + n-m' m) 



