NOTES ON MAGNETISM*. 



No. II. 



IN order to a distinct understanding of the results obtained 

 in the last number of the Journal, it will be desirable to con- 

 sider the established conventions with respect to the signs of the 

 symbols which we had occasion to employ. 



North magnetism is assumed to be positive ; hence, of course, 

 south magnetism must be considered as negative. 



The measure M of the magnetic power of a bar magnet is, 

 as we have seen, equal to fpsds, p being the magnetism of the 

 element ds, which is situated at a distance from the origin 

 equal to s. The limits of the integral are such as to include 

 the whole length of the magnet. 



The position of the origin is arbitrary : we may conveniently 

 place it at the centre of the magnet, but the value of f/jisds is 

 the same whether this be done or any other point be taken. 

 For let the origin be shifted through a distance a, so 

 that s = s' a, then 



fjjisds = ffi (s a) ds' = f/j,s'ds' a/fids' : 



and as all the integrals extend throughout the length of the 

 magnet f/^ds = 0, and therefore 



ffjLs'ds' or MM\ 



which was to be proved. 



But the value of ffjusds changes its sign if the direction in 

 which s is measured changes. Let I be the length of the magnet ; 

 then, s being measured in one direction, say from left to right, 

 we have 



= I /Jisds. 

 J o 



* Cambridge Mathematical Journal, No. XXI. Vol. iv. p. 139, May, 1844. 



