438 THE THEORY OF TERRESTRIAL MAGNETISM. 



If we combine all the equations of condition involving x, y and z, 

 the final equations for the determination of a,, will be 



J 1 1 



and similar equations for the other magnetic constants. 



since J 1 [(x:y + ( Y:Y] dp. -n(n+ 1) J 1 



and 



-i 

 we have 



From the above equations it appears that the weight of a determina- 

 tion of a magnetic constant from the observations of the horizontal force 

 is to the weight of its determination from the observations of the vertical 

 force as n to (n+l). 



24. If we take into account separately the parts of the magnetic 

 force at a point due to the internal and external centres of magnetic 

 force, the general terms of the coefficient of cos m\ in the potential function 

 will be of the form 



+ r 



i ' Pn' 



Jl+ 



and the corresponding coefficients in X, Y, and Z will be 



in Y, + ftX'- m ( 1 - ^ H?, 



If then, as before, we put r=l, we shall have the final equation for 

 a n as follows : 



