POSITIONS OF EQUILIBRIUM OF A SUPPORTED MAGNET. 69 



always considered as less suitable for absolute measurements than the 

 unifilar balance, on account of its more complicated construction. 



It is however the only apparatus in which the torsion couple can 

 be directly determined from the dimensions themselves that is, the 

 length and distance of the wires without bringing into play the 

 moment of inertia of a body, or determining the times of oscillation. 

 It is true that the distances a and b of the points of support must be 

 known with great accuracy. As the thickness of the wire itself 

 introduces a cause of uncertainty into the measurement of these 

 distances, they should be rather large, which greatly diminishes the 

 sensitiveness. Prof. Kohlrausch has thus constructed a bifilar 

 suspension of exceptional dimensions, with wires two metres in 

 length, and in which the distance of the points of support, which is 

 several centimetres, may be directly measured by the aid of a 

 micrometric division. 



721. VARIOUS POSITIONS OF EQUILIBRIUM OF A MAGNET WHICH 

 is SUPPORTED BY A SYSTEM OF WIRES. If the suspended body has 

 of itself a directive force, as in the case of a magnet under the action 

 of the Earth, equilibrium may be obtained in several ways. 



Gauss says, that the magnet is in its natural position when its 

 magnetic axis is in the magnetic meridian, with the pole N turned 

 towards the north, and is in its inverse position when the. pole N is 

 turned towards the south. 



Let M be the magnetic moment of the bar, and H the horizontal 

 component of the Earth's magnetism. When the magnet is in its 

 natural position, the moment MH is added to the torsion couple of 

 suspension, so that the value of the directive couple of the system is 



and the equilibrium is always stable. 



If the magnet is in the inverse position, the directive couple of 

 the system becomes 



Q = C-MH. 



In this case the equilibrium of the system is stable or unstable 

 according as 



C>MH. 



With the bifilar the distance of the two wires can always be 

 regulated, so that the condition C>MH is realised. If then the 

 system is made to oscillate alternately in the two positions, the 



