212 MEASUREMENT OF CURRENTS. 



meridian ; repeating this operation with a torsion 6 ', which gives a 

 deflection /?', the conditions of equilibrium are 



MH sin ?+? = c 



These three equations determine the angles and /3 , which, if 

 necessary, enable us to rectify the original position, and the ratio 



Q 



e = of the coefficient of the wire to the couple produced by 

 the field upon the needle. 



As the deflection is generally very small, we get from it 



sin /3 (i + cos /?') - sin ft'(i + cos /3) 



(6 - ft) (I + cos p) - (0' -/?')(! + cos ft) ' 

 If the initial torsion is zero, we have also /? = 0, and 



Lastly, if the deflections ft are themselves very small, as when 

 cocoon threads are used, this expression simply becomes 



A very simple means of producing torsion in a wire, when it is 

 not suspended to a torsion circle, consists in making the needle turn 

 through a whole circumference by means of an external magnet ; in 

 that case we have 



<9=27T. 



Allowing for this angle, and for the angle a, which the direction 

 of the field makes with the mean plane of the coil, the equations of 

 equilibrium for the direct and inverse directions of the current are 



IMG cos (8 + a - ft Q ) = HM sin (8 - ft Q ) + C (0 - ft + 8), 

 IMG cos (8' - a + /? ) = HM sin (ff + ft) - C (0 - ft - ?) ; 



