NOTES ON MAGNETISM. 187 



Now suppose that s = I s, then the limits are interchanged 

 and ds =-ds- } consequently 



= f V ( l ~ s '} ds> = - f W<&' = - M', 



M 



s being measured in the direction opposite to that of 5, or from 

 right to left. 



The magnetism of a magnet may thus be always represented 

 by a positive quantity. 



Any two points in the axis of a magnet may be taken as its 

 poles. But although the position of the poles is matter of con- 

 vention, yet relatively to one another, one is the north and the 

 other the south pole. 



The physical character by which they are distinguished is 

 this : if a particle of north magnetism be placed in the pro- 

 longation of the axis from south to north, it is repelled from 

 the magnet. Contrariwise, if it be placed in the prolongation 

 of the axis towards the south. Further, we must integrate 

 jjbsds from south to north, i. e. s must be taken as positive 

 when fjids lies to the north of the origin, in order that M may 

 be positive. This may be shown by supposing a particle of 

 north magnetism m placed in the prolongation of the axis 

 towards the north, and at a distance r from the centre of the 

 magnet. If we assume that from south to north is positive, 



the action of the magnet on m is ; and as this action is 



repulsive its expression will be positive, and therefore M is so. 

 If we had assumed from north to south to be positive, the 



action of the magnet would have been represented by -- 8 ~ , 



and as this is positive, M will necessarily be negative. So that, 

 in order to make the measure of the magnet's power positive, we 

 must take the direction S . . . N as positive. 



Consequently the angle 6 must be measured from it. We 

 suppose it measured in the usual manner, viz. in the unscrew 

 direction. 



The general expression for the moment of rotation due to the 

 action of one magnet on another is much simplified when the two 

 magnets are supposed to lie in one plane. 



