54 MEASUREMENT OF RESISTANCES IN ABSOLUTE VALUE. 



The second, used by M. Dorn,* does not bring in the magnetic 

 moment of the bar, but the square of the component H' of the 

 terrestrial field appears in the formula, which doubles the relative 

 error of the result. 



M 



In the first case, the ratio is in general determined, as we 



11 



shall see, by the deflection which the bar produces on a tangent 

 galvanometer when it is put in a direction perpendicular to the 

 magnetic meridian. This bar is not then in the same condition 

 as during the experiments of oscillation, and we may have to allow 

 for the influence of the earth's field on the value of the magnetic 

 moment. 



In order to get over this difficulty, Professor Wildf places the 

 plane of the multiplier almost perpendicularly to the magnetic 

 meridian, and keeps the magnet there by a bifilar suspension (721). 

 A copper bar being brought into this position without torsion, it is 

 replaced by the magnetised bar, and the torsion 6 necessary to keep 

 it there is measured. 



Let C be the coefficient of the bifilar, a the angle which the bar 

 makes with the meridian if it were under the influence of the bifilar 

 alone, the angle (a - 6) being near 90. The condition of equi- 

 librium is 



Csin0-MHsin(a-0) = 0. 



When the bar makes small oscillations about its position of 

 equilibrium, the couple which tends to bring it there is expressed 

 by 



[C cos + MH cos (a - 0)] dO = MH [cot sin (a - 0) + cos (a - 0)] dO, 



or virtually 



[C cos + MH cos (a - 0)] dO = MH cot dO. 



Hence, in the equation for the motion (845), the couple MH 

 must be replaced by MH cot 0, or H by H cot that is to say, 

 divide the expression for R previously found, by cot 0. The value 

 of 8 determined by the equation of equilibrium varies moreover 

 with a that is to say, with the declination, and especially with H. 



* DORN. Wied. Ann., Vol. xvn., p. 773. 1882. 



t H. WILD. Memoires de VAcademie des Science de Saint Petersburg [7], 

 Vol. xxxii. 1884. 



