ELEMENTARY THEORY OF MAGNETISM. 9 



magnet and the direction of the field being as shown in Fig. 10. 

 By length of magnet is meant the distance between its poles. 

 The poles of the magnet are acted upon by the two opposite forces 



'difectionHf fteld 



Fig. 10. 



The equal and opposite forces which act upon the poles of the magnet consti- 

 tute a torque which tends to turn the magnet into the direction of the field. 



mH as shown, and the combined torque action of these forces 

 about an axis perpendicular to the plane of the paper is mlH 



sin 0. That is: 



T= - mlHsind (i) 



where T is the torque action of the forces mH in Fig. 10. The 

 negative sign is chosen because the torque T tends to reduce 

 6 which may be considered to be a positive angle. This equation 

 expresses T in dyne-centimeters. If the angle is always very 

 small then the value of in radians is sensibly equal to sin 0, 

 and in this case equation (i) becomes: 



T = - mlH-0 (2) 



This equation shows* that a suspended magnet when started 

 will perform harmonic vibrations about its axis of suspension 

 such that: 



(3) 



in which K is the moment of inertia of the steel bar (the magnet) 

 about the axis of suspension, and / is the period of one complete 



* See Arts. 42 and 66, Franklin and MacNutt's Mechanics and Heat. 



