66 ON MAGNETISM. 



cf 3 . 2AB + c," 5 . L = EB . sin & ; 

 ,~ 5 . L = J&?Z? . sin (f> . 



Substituting the numerical values of c x , C 2 , <,, and 

 <k,, we have here two simple equations for determination 

 of the two unknown quantities AB and L. Both will be 

 expressed as multiples of EB. The quantity L is of no 

 further use to us. But AB is now expressed by such a 

 formula as AB = Jc x EB : and therefore A = kxE: k 

 being a number given by the solution of the equations. 

 Thus we have the magnet-power of the Earth expressed 

 accurately as a multiple of the magnet-power of A. 



Having thus acquired the power of separating the 

 first term from the rest, in the expression for the angular 

 momentum produced by the action of one magnet upon 

 another, we may now conceive that first term only to be 

 retained, in an action of which the idea will be service- 

 able to us. If c is 1 (that is, the unit of measure, what- 

 ever it may be), then the angular momentum, caused 

 in B by the action of A broadside-on, is AB. Suppose 

 now that we have two magnets S and S', exactly similar 

 and equal, such that, using the letters for the magnet- 

 powers as defined in Article 20, paragraph (a), S= 1, 

 8' = 1 : and suppose the distance of their centers to be 

 = 1 ; then the angular momentum produced in S' by 

 S, broadside-on, as depending on the first term of the 

 formula, = 1. Such a magnet may well be conceived as 

 a standard magnet. And when we obtain a numerical 

 value A for the magnet-power of the needle A, it means 

 that its action on S' at distance 1 is A times as great 



