604 SOLUTION OF THE EQUATIONS. 



equations for (Z). Hence we get in the cases treated above 



0, = fi'971874, #_ 1 = -040416, 0,= - -541312, g_*= - "022358, 



g = '01605, and g_= '15697. 

 Hence the constant g_ seems to be of great importance. 



The values found for the two first of the above constants are in British 

 units by Gauss (1830) by Ermari (1829) 



g?= 7-0155 r/,= 6'9417 



g = - -1430 gf= - -4069. 



The values of these constants, derived from the above series of equations 

 for (X), (Y) and (Z) combined, for all latitudes from 67| S. to 67 N., are 



<// = 6-98081 and g= - '523986 

 for the period 1845 from Sabine's charts. 



The values derived for the above constants from the above equations of 

 condition, taking m from to 4 and n from 1 to 4 only, and neglecting the 

 other terms, i.e., taking those constants only which were determined by 

 Gauss, are 



&" = 6'9777 and </ s = -'5310 

 for the same period. 



11. The values of the constants given in the two following tables are 

 derived from the combined equations for (X), (Y) and (Z) to equations (e) 

 inclusive (i.e. between latitudes 67 S. and 67 N.), supposing the constants 

 corresponding to negative values of n to be non-existent. The equations for 

 the belts outside these latitudes have not been included because of the 

 scarcity of observations of the magnetic elements. 



The second of these tables gives the values of the constants when we 

 include in the equations only those 24 constants which are taken into account 

 by Gauss himself. This table also includes the values (in British units) of 

 these constants as determined by Gauss and by Erman. 



*The values of the Magnetic Constants are derived from 



(1) Sabine's Charts for 1845 in the Philosophical Transactions of the 

 Royal Society. 



(2) The Admiralty Charts for 1880. 



* (The values given in the British Association Report* for 1898 (p. 128) for A/, A 4 ' and A,' 

 for the period 1845 should be replaced by the values here given to those constants.) 



