612 SOLUTION OF THE EQUATIONS. 



Formation of Equations for the Polar regions. 



14. To complete the investigation this polar area should be taken 

 into account by the addition of theoretical terms involving the magnetic 

 constants on the left-hand side of the equations of condition and the 

 final equations, and by the addition on the right-hand side of these equa- 

 tions of quantities derived from observations of the magnetic elements over 

 this polar area. In the absence or the uncertainty with regard to these 

 polar observations we can scarcely do more than prepare the way for the 

 time when our knowledge of these elements shall be more extensive by 

 making the equations as complete as possible. 



To find the values of X, Y, Z at the poles for m = and m 1 

 for the several values of n, we have r = (l e 2 )-, 



also X n " = 0, y n = 0, for all values of n, 



70 ^_ 7*^L y<>_^ 1 7<>_8 1 



'~" *- A ~ 5 ' *~"' 



_ 

 * ~ 21 



" 



161 yo = 7o = 7o__ 7o- 



33 r 8 ' 7 429 r" 715 r 10 ' 9 2431 r 1 " 10 ~4199r 12 ' 



Next let m=l, 

 then Y n l = -X n l = ^Z n \ for all values of n. 



For X these coefficients are to be multiplied by g,* cos X h n l sin X, and 

 for Y by g n l sin X - h n l cos X. Also Z n l = 0, for all values of n. 



To find the logarithms of the coefficients of g and h for the pole, 

 log (l-e 2 ) = 9-9970916, logr = 9'9985458, log^ = "0014542. 



