74 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



that is to say, the magnet is in equilibrium. This equilibrium is 

 stable when the north pole of the magnet points in the direction 

 of the magnetic field (0 equal to zero), and it is unstable when 

 the south pole of the magnet points in the direction of the mag- 

 netic field (9 equal to 180). 



If the angle 6 is never large in value then 6 (in radians) 

 may be written for sin 6 in equation (21) giving 



(22] 



This equation shows * that a suspended magnet when started will 

 perform harmonic vibrations about its axis of suspension in such 

 a manner that 



in which K is the moment of inertia of the magnet about the 

 axis of suspension, and / is the period of one complete vibra- 

 tion. This equation is not even approximately true if 6 reaches 

 large values, that is, if the amplitude of the oscillations of the 

 magnet is large. 



42. Gauss's method for measuring the horizontal component of 

 the earth's magnetic field. A method was devised by Gauss in 

 1850 for determining the value of the horizontal component of the 

 earth's magnetic field. The details of this method are described 

 in Chapter X. 



43. Behavior of a magnet in a non-uniform magnetic field. 

 The forces which act upon the poles of a magnet in a non-uni- 

 form magnetic field tend in general to turn the magnet and also 

 to impart to it a motion of translation, because the force which 

 acts on the north pole of the magnet is in general not opposite 

 in direction and not equal in value to the force which acts on the 

 south pole of the magnet ; that is, the field at the north pole of 

 the magnet is in general different in intensity and in direction 

 from the field at the south pole of the magnet. This is shown 



* See discussion of harmonic motion in any good treatise on elementary mechanics. 



