PREFACE TO PART II. xix 



since the coefficients of a Mi and all the other terms on the left-hand side 

 of this equation vanish when the integration is taken all over the Earth's 

 surface. 



Hence a n . n (n+l) (Htf dp ^ 





-i -i 



Similarly, by putting n t for n, we may get the value of a n . 

 In the same way the final equation for finding a n from the equations 



for Z would give us 



Z;Z dp + &c. = 



or 



n 

 since Z'Z dp = 



i.e. 



If we take into account separately the parts of the magnetic force at 

 a point due to the internal and external centres of magnetic force, the 

 general terms of the coefficient of cos m\ in the potential function will be 

 of the form 



+ fl r n H m 



n + i ~ Pn ' I -"n > 



and the corresponding coefficients in X, Y, and Z will be 



in X = (, + ft, r-') [I (n - m) H^ - \ (n + m) H^ ] ; 



n - 



r(w-MK fl ,-i , 



^+2 ~ n Pn1 -" 



in /j \ 



,,,ii.-ra 



L J , 



c2 



