38 ON MAGNETISM. 



ax 3 is unaltered, and the integral throughout is a con- 

 tinual aggregation of quantities with the same sign: 

 and so for j3y and /3y 3 .) Then the expression for the 

 angular momentum is 



in which, when c is large, the second term is much 

 smaller than the first. Succeeding terms would be 

 multiplied by c~ m ~ 5 &c., and, by taking c large enough, 

 may certainly be made insensible. 



(b) Treating the result of Article 16 in the same 

 way, and putting L for the bracket which then presents 

 itself, we find that, with the disturbing magnet end-on 

 and the disturbed needle broadside-on, the expression 

 for the angular momentum is 



in which, when c is large, the second term is much 

 smaller than the first. 



(c) The reader's attention is particularly called to 

 the circumstance that the principal term in the second 

 case (disturbing magnet end -on) is m times as great as 

 that in the first case (disturbing magnet broadside-on) : 

 and that in both the successive powers of c are m 1, 

 m 3. Thus, if the law of attraction and repulsion 

 of magnetic masses be the inverse square of the dis- 

 tance, or m = 2, then the principal term in the second 

 case is double the principal term in the first case, and 

 the successive indexes of c are 3, 5. It will be 

 found that these remarks are of the utmost importance 



