456 THE THEORY OF TERRESTRIAL MAGNETISM. 



Also the coefficient of ft ni in the same partial equation for y8 n is 



The coefficient of a n in the partial equation of condition for a n will be 

 found from the coefficient of a, (i in the same equation by putting n for ,. 



Similarly the coefficient of (3 n in any partial equation of condition for /3 n 

 will be found from the coefficient of /8 ni in the same equation by putting n 

 for j . 



Hence the coefficient of a,, in the partial equation of condition for a n 

 will be 



and the coefficient of /S n in the partial equation of condition for f$ n will be 



9. Since - = 1 + e~u,~, we have 



i 



1 - n, + 3 s 

 ^sr+.= -~2 --- e P> 



)j _ 911 -m '*' '*'l f ^ 



" " 3 = 



j 2 ., 

 and r n+ "' 2 = 1 -- -- r>y. 



Also the area of a small belt of the surface of the spheroid is 



8S= - 2777- 8/x' 



= - 2ir ( 1 - *y ) 8/t' = - 27r ( 1 - e- + 2e"/i') S/x. 



If we assume the weight of the observations in any belt of latitude 

 to be proportional to the area of the belt, then to form the final 



