Bifilar or Horizontal Force Magnetometer. xxix 



for this reason, the following methods, which are independent of the angle of torsion, 

 were employed to determine the coefficient : — 



34. If the equation of equilibrium for the bifilar magnet at right angles to the 

 magnetic meridian be 



mX=F, (1.) 



and if a magnet whose magnetic moment is M be placed with its axis in the mag- 

 netic meridian passing through the centre of the bifilar bar, the centres of the two 

 bars being at a distance r, and the resulting angle of deflection be n scale divisions 

 = a v , the equation of equilibrium will be 



m 



{*+£0 + £**)}«*'=*- 



For a value of the earth's horizontal force X + aX, which would alone have pro- 

 duced the deviation a v, we have 



wfX + AXjcosA v=F' ; 

 whence 



aX 2M 



x IT 



G+M) « 



If the deflecting bar be now employed to deflect a freely-suspended unifilar magnet, 



M . . 



in order to determine the value of — , as in the ordinary observations for absolute 



.X. 



horizontal intensity ; u being the angle of deflection for a distance r we have 



2M 1 



= fj tan u 



x ' i+V* 4 



r l r l 



If the bifilar and unifilar bars are of the same dimensions p and q, which are quan- 

 tities depending upon the distribution of the magnetism in the bars, may be consi- 

 dered equal to p x and q h and if the deflections for both bars be made at the same 

 distances, or r—r x then 



aX 



-— -=tan u, 



.A. 



i , tan u /0 N 



and k= (3.) 



n 



If, however, the bifilar and unifilar magnets are of different dimensions, the value 



of —— should be obtained from the deflections of the unifilar at different distances, 

 X 



p± and ^i being eliminated ; that value being substituted in equation (2.), and deflec- 

 tions of the bifilar being obtained for different values of r, p and q also may be 

 eliminated. 



MAG. AND MET. OBS. 1844. h 



