600 FORMATION OF THE FINAL EQUATIONS. 



The final equations for some of the more important magnetic constants 

 are given at the end of this volume. We propose to solve the final 

 equations derived from the series for X, Y and Z combined, taking 

 into account the data obtained from magnetic observations over the 

 portion of the surface of the Earth between latitudes 67^ N. and 67 S., 

 taking only the equations of condition for belts between these latitudes, 

 and taking only those terms in these equations for values of m from 

 to G and for values of n from 1 to 6 inclusive. These equations will 

 give values for 48 constants, and no equation will contain more than 

 three unknown quantities. 



The Table on p. 605 gives the values of these 48 constants thus 

 obtained from observations of the magnetic elements for 1845 and for 1880. 



Solution of the Equations. 



8. The coefficients on the left-hand side of the equations of condition 

 (and therefore also on the left-hand side of the final equations) will be the 

 same for g% and for A, but the right-hand members of the equations or 

 the absolute terms will be different. Taking a to stand for either g or 

 A, the equations for solution may be conveniently arranged as follows : 



From the equations for (X) taken separately 

 X *:* < t S 



From the series of equations for (X) combined with those for (Y) we 

 may also solve the equations, of which the type will be as follows : 



{s [*':*>] + 2 [ Y": Y'I w-]} a ; 



Ac. = or 



the absolute terms being derived in this case from the series for (X) and for 

 ( Y ) combined. 



The values of the same constant derived from these equations taken 

 separately or taken together will differ somewhat from one another. 



