xviii PREFACE TO PART II. 



where x m is derived from the observations. Similar equations, involving on 

 one side the magnetic constants a n , a ni , &c., and on the other the values 

 derived from the observations, must be formed for all the successive different 

 belts of latitude from the north pole to the south pole i.e., for all values 

 of p. between 1 and 1. 



The numerical values of X, X, &c., as well as the values of H (as 

 above defined), have been determined for every degree of latitude and recorded 

 for future use, but, in the actual determinations of the magnetic constants 

 which have been made, belts of latitude 5 in breadth have been taken, 

 or &0 has been taken as 5, and the area of the belt is proportional 

 to S/A. 



Supposing the observations equally distributed over the surface of the 

 globe, or supposing the weight of any determination proportional to the 

 surface of the corresponding element about the point of observation, then 

 the weight of each of the above equations is proportional to S/u., and 

 multiplying the equation in X for each value of p. by X", and summing 

 up the separate equations for the whole surface of the Earth, we get the 

 final equation 



Similarly, the final equation for a (li is found by multiplying the above 

 equations by X^, 7, and Z respectively, and we get 



( X> >^ d * + &c - = 



Similarly, if y m denote the coefficient of sin mX or cos iX in the value 

 of the force Y as derived from observations, we have 



2(aF B )=y m> 



and the final equations for finding a n and a n _ respectively will be 



and a f , Y: Y:<k + , f ( Y:Y ^ + & c . = f ' Y- y^. 



J - J-l J-l 



Combining the final equations for a,, from X and Y together, we have 



~ 



