PREFACE TO PART II. xiii 



internal forces, and n subscript to refer to external magnetic forces, 



whose origin is outside the Earth's surface, i.e. forces corresponding to 



negative powers of I 1 . 



The corresponding terms are : 

 in the value of X, 



(J TTm 



and r n ~ l ( I - ^ -j (#!' cos m\ + h H sin mX) 



in the value of Y, 



~ ( 1 - tf -* mH: (</;;' sin mX - h? cos wiX) 



and r"-' (1 -p.*)-* wiJ?" ($ sin m\-h'^ n cos wi 



in the value of Z, 



.H": (^ cos mX + /C sin mX) and - nr" - ' H^ (cj m n cos w^X + h' n sin mX). 

 It is also proved that 



and (1 _^ 



and these relations are often useful in expressing the terms in the value 

 of X. 



It is found convenient to employ the notation with n and n subscript 

 more generally to refer to internal and external forces respectively, and in 

 this sense the following notation is employed : 



Let 



TTm _ TTm _ n J T/m _ n TTm 



y n r n+l- [1 n anQ - ~ ? ""' 



and let 



*: = ^ Li ( - ) ^: 1+1 - K* + ) ^:r '] 



be the coefficient of (^' cos mX + h sin mX) in the expression for X, the 



