PREFACE TO PART II. xxvii 



And similarly the equations for A and h n will be found from the equations 

 for g and g n , when n m is odd, by substituting 



2 (&. + &/) for 2( a > + a !/ ) in tae e q uations for x > 

 - 2 (>-/) for (&,-&,') in the equations for Y, 



and n(bm b m ') f r o( a m~ a /) i n the equations for Z. 



2j 



Thus each equation for the determination of magnetic constants is 

 separated into two equations, each of which contains only one-half the 

 number of magnetic constants to be deteiTnined. 



In the first solution of the equations, the absolute terms (i.e. the terms 

 derived from the observed values of the magnetic elements) are taken from 

 Sabine's magnetic charts for the period about 1845, as published in the 

 Philosophical Transactions of the Royal Society. In the second solution, 

 the observed values of the magnetic elements are taken from the Admiralty 

 charts for 1880 prepared by Captain Creak, kindly lent by the Lords of 

 the Admiralty. 



The values of X, Y and Z are calculated for every 10 of longitude 

 and every 5 of latitude from the declination (8), the dip (t) and the 

 horizontal force () as given in the charts. Then the values of X, Y 

 and Z are analysed for belts of latitude 5 in breadth around the earth 

 by the formula 



a + ! cos X + 6, sin X + a a cos 2X + &. 2 sin 2X + , &c. 



The values of these coefficients for the different belts of latitude were 

 obtained and tabulated. Then if a m and b m denote the values of two of 

 these coefficients for a given northern latitude, and a m ', b m ' the correspond- 

 ing values for an equal southern latitude, then the values of -(a m + a m ')> 



LA 



-(a m -a m '), o(& m + &,'), 'and ^(b m b m f ) and of their logarithms are determined. 



22 ^ 



The values of these quantities are determined for each of the periods for 

 which the magnetic constants are required. 



The numerous tables contained in this work have been calculated with 

 the utmost care, under Professor Adams' minute supervision and instructions, 

 by Mr Graham, who has done a great part of the work, and by Mr Todd 



d2 



