460 THE THEORY OF TERRESTRIAL MAGNETISM. 



= a known quantity of the form 



where (w) dp represents the weight, and where x m ', y m ' and z m ' are derived 

 from the observations of the horizontal and vertical magnetic forces. 



Similarly the final equation for /3 n becomes 



2[(n+l)-37n a ]__ (n + m)\ (n-m)\ 

 2n-T)(2n+ l]T(2nT3) {l . 3T5T7(2rT-T) 



n _\ 4w (n-1) fl 



~ 1* 



3 / (2n 1) (2n + l) L3 



2 2 (n + m)! (w m)! 

 a "- 2 ' e ~ 2n + 1 1 . 3 . 5 T.T2n^T 



)! (n m)! 

 {T^ 3. 5 ... (2w-l)}' 



= a known quantity of the form 



-i -i J-i 



In the same way the other final equations for a n _ 2 , /S n+ . 2 , &c. may be 

 formed from the equations of condition, and the coefficients of the other 

 magnetic constants in all the final equations determined. 



Also it appears that in the final equation for each magnetic constant, 

 for a given value of m, there will only be five unknown magnetic constants 

 when the equations for X, Y and Z are combined, since the coefficients of 

 the other magnetic constants will severally vanish. 



12. The coefficient of a n in the final equation for a n (as found from the 



