THE THEORY OF TERRESTRIAL MAGNETISM. 461 



coefficient of a n> ; see Art. 8) will be 



J 



' 



Hence we see from the investigations of these integrals on pp. 421 and 

 427, that the coefficient of a n in the final equation for a n> arising from 

 combining X, Y and Z, will be 



(n-m)! , , 



'- 2 



Similarly the coefficient of j3 n in the final equation for /8 n is 



Hence the coefficient of /8 B in the combined final equation for yS n is 



If the polar radius instead of the equatorial radius be taken as the unit of 

 length, then we must multiply the coefficient of a n in the final equation for 

 a n by (1 e") n+1 or 1 (n+l)e*, and we multiply the coefficient of /8 re in the 

 final equation for $, by (l e 2 )~" or 1+ne 2 , and the equations are somewhat 

 simplified. 



