SOLUTION OF THE EQUATIONS. 603 



10. Let us further illustrate the mode of solving these final equations 

 by taking the case of m = and n odd from the equations for X, and also 

 from the equations for Z, taken separately, for the period 1845. 



We will form the equations of condition taking into account the 

 data only up to 67^ N. and S. latitudes. The formation of the final 

 equations for g, g. and g will then be as follows : 



From equations for (A"), 



7'6331952</ 1 - '1138565 g, - "0886747 g= 53'575026, 

 1138565ry 1 +2-8880836^- -1765 1 12 0,= - 2'456863, 

 0880747(7,- '1765112^ + '3955108 & = - '4538875. 



And we have from equations for (Z), 



12-0636234 (/;>- 2'14134G9# :i - 7000106 # 5 = 85'065860, 

 2-1413469 </," + 27856531 #,"- '4744250 g = -16"292662, 

 7000106 &"- '4744250 g, + "4394974 g =- 4'6678164. 



Solving the equations for (A), we get 



y? = 7 "01229, g= - '56367, # 5 ='l7302. 



These values agree almost exactly with those found from the whole of the 

 equations for (A") up to latitude 77^. 



Solving the equations for (Z), we get 



g? = 6-951666, gf= -'524544, and g= -'11476. 



These values agree very closely with those found from the whole of the 

 equations for (Z) up to latitude 77^. 



The values of g and g. derived from the equations for (Z) agree fairly 

 well with those found from the equations for (A), but the values of g 

 have opposite signs. Probably the neglected term in g 7 " may have some 

 influence on this result. 



Taking the magnetic constants depending upon external forces into 

 account, let us find approximately what values of g_?, g_, g_ will bring 

 the two sets of results into harmony. This may be done by substituting 



YL 



9n+9-n f r 9n m the equations for (A), and g n a --.9-n f r <7 i n the 



fv ~i -L 



762 



