452 THE THEORY OF TERRESTRIAL MAGNETISM. 



6. The above equations may be combined so as to give the final 

 equations for a n and /3 n respectively. 



Multiplying the last equation by (n + 1 ) and adding to the former, 

 we get the final equation for a n : 



+ terms in e 2 involving other magnetic constants 



= P X n x m dp.+ \ Y n y m dn+(n+l)t H n z m d^ 

 J -i J-i J-i 



The principal term in a n has the coefficient 

 9 / w ix (n-m)\ (n + m)\ 



>{i.w75~.::i2n-i)y' 



as before found. We see that when n=l, and also when n(n+l) = 



i.e. when n 3 and m = 2, the term containing yS K disappears from this 



equation. 



In the same way by multiplying the last equation of Art. 5 by n 

 and subtracting it from the former, we get the final equation for yS n : 



j f/o (w 



^ |(2n + I ) nfi, + a, ( e- 



I n 1 



+ terms in e" involving other magnetic constants 



= X a x m dft+\ Y n y m diJ.-n\ H n z m dp. 

 )~\ J -i J -i 



7. The formulae for finding the numerical values of the coefficients 



Vf^-^H'f, and V n = r n H', 



fi -4- 1 



^T-=Srfl?, and Z = -nr'^H':, 



