70 MEASUREMENT OF COUPLES. 



numbers N and N' of infinitely small oscillations, or of equal 

 amplitude made during the same time, give the ratio 



N 2 C + 



from which we deduce the ratio of the two couples 



C 



(12) 



MH 



Suppose that while the bar is in its natural position and the wire 

 without torsion, the upper micrometer is turned through the angle w. 

 To attain the new state of equilibrium, the vertical plane passing 

 through the magnetic axis of the bar turns through an angle 0, and 

 with a unifilar suspension we have 



MH sin# = C (w-0). 

 A bifilar would give in like manner 



MH sin0 = C' sin (w-0). 



The direction of the magnet is then oblique to the magnetic 

 meridian. If the coefficients C and C' are known, the angles w and 6 

 would enable us to determine the product HM. 



The magnet is transverse when its magnetic axis is perpendicular 

 to the meridian. In this case the two previous equations become 



MH = C 



= C'cos (u. 



If the value of M remains constant, as well as the couple relative 

 to the suspension, the variations of the component H might be 

 determined by the changes of direction of the system in the vicinity 

 of its transverse position.* 



* GAUSS. Resultate aus den Beob. des Mag. Vereins. 1837. (Euvres, p. 137. 



