SOLUTION OF THE EQUATIONS. 627 



In the north and south polar charts given at the end of this volume 

 the black curved lines indicate the values of the Total force as given in 

 Sabine's Arctic and Antarctic Magnetic Surveys (1840 1845), and the red 

 lines indicate the values of the Vertical and the Horizontal forces recorded 

 by Captain Creak for the period 1880. 



20. If we take into account the terms depending upon magnetic 

 forces outside the Earth, the equations of condition for the polar element 

 will include the following terms in addition to those which have been 

 already given on p. 614: 



- [9 -9985458] g_J - [9-7525993] g_J - [9-3773050] g_J - [8-9416945] g_J - [8-4709763] g_ 10 l = |(a + a), 



-g-! 1 - [9-9001816] g_ 3 1 - [9-5750539] </_ 5 ] - [9-1649975] ^_ 7 > -[8-7097914] f^ 1 = J(a-a'), 



- [9-9985458] h_* - [9-7525993] h_? - [9-3773050] h_J - [8-9416945] h_ s l - [8-4709763] /j.,,, 1 = (6 + V), 



- A., 1 - [9-9001 816] h_ 3 l - [9-5750539] A_ 5 ' - [9-1649975] h_ 7 > - [8-7097914] h_J =$(b- b'), 



- [ -1234845] 0_ 2 - [9-9567193] </_ 4 - [9-6113883] </_ 6 - [9-1915720] </_- [8-7306136] </_ = J (c + c'), 



- g-! - [ -0762729] </_ 3 - [9-7969026] g_ - [9 -4080355] g_ 7 " - [8-9650639] </_ 9 = i (c - c'). 



These terms have been added to make the equations complete, but 

 they have not as yet been employed in the determination of the magnetic 

 constants. 



Description of the following Tables. 



The following Tables give the several final equations which have 

 been employed in the determination of the magnetic constants for the 

 periods 1845 and 1880; they are derived from the equations given on 

 pp. 554 587 by combining the equations for X, for Y and for Z from 

 the several belts between 67 N. and 67 -JS. latitude, and are of the 

 type given as equation (4) of this section. 



Some of the more important final equations for the magnetic constants 

 with a negative suffix (g^) have been added to the tables, and their 

 solution would give the values of these constants for the same periods of 

 time. In some other cases the numerical values of the coefficients only of 

 the magnetic constants have been given in the tables, so that by supplying 

 the terms depending on the observed values of the magnetic elements for 

 any given period of time the values of the constants for that period may 

 be determined. 



792 



