PREFACE TO PART II. xvii 



hence X'X d 



f X':X 

 J-i 



since we have seen that for any value of m and different values of n and 



n 1} the value of 



ri 



-1 



For the same reason 



-i 



Now let us consider the application of these formulae to the determination 

 of the numerical values of the magnetic constants of terrestrial magnetism. 

 For a given value of //, (i.e. for a given latitude) we have a series of 

 terms forming the coefficients of cos m\ and sin mX, in the values of the 

 magnetic potential and of the magnetic forces X, Y, and Z, which are of 

 the forms 



where a n , a, h , &c., are the magnetic constants to be determined. 



The numerical values of H, X, Y, and Z for different values of 

 n and m must be calculated, and in any belt of latitude of breadth corre- 

 sponding to the numerical value taken for S/t, these coefficients must be 

 equated to the values of the forces as derived from the magnetic observa- 

 tions taken in that belt of latitude. 



The values of the magnetic forces X, Y, and Z are derived for every 

 10 of longitude and every 5 of latitude from the declination (S), the 

 dip (i,), and the horizontal force (<u), as given in the charts from which the 

 observations are obtained. These values of the forces X, Y, and Z are 

 analysed for belts of latitude 5 in breadth around the Earth's surface by 

 a formula of the type + j cos X + 6, sin X + a, cos 2X + 6 2 sin 2X + &c. 



If we take x m to represent the coefficient of cosmX in the expansion 

 of the value of the force X for a given belt of latitude corresponding to the 

 colatitude 6 = cos ~ l p. : 



then a n X: + a n X',: + a^X' + &c. = x m , 



A. II. C 



