572 MAGNETIC FIELD. 



disappear in the difference of torsion, and the ratio of the fields 

 is still given by equation (6). 



More generally, if the directions of the fields F and F' and of 

 the terrestrial fields are very close, it will readily be seen that the 

 square of the error is simply of the order of the angle of deflection. 



A bifilar suspension would give similar results. The apparatus 

 being properly adjusted, we should have 



(7) C sin (co - 0) = M H sin . 



The defect of adjustment will be eliminated by taking the mean 

 of the readings of two observations right and left, with positions 

 of equilibrium which are sensibly opposed ; if the difference of the 

 angles is very small, we may replace the angles w and in equation (7) 

 by the means of two readings to the right and left. 



For a mean deflection 6 is 90, we get simply 



MH= -C cos co. 



In this case, if the mean torsion is co with the terrestrial field, 

 w and to' with the fields H + F and H + F', we have 



F' cos co - cos co' 



F cos co - cos co ' 



1143. Let us now assume that the apparatus is carefully adjusted 

 with a bifilar or unifilar suspension. For a small displacement d6, 

 starting from the position of equilibrium defined by equations (5) or 

 (7), the value of the couple which brings the needle into its position 

 of equilibrium is given by one of the expressions 





m 



and the corresponding numbers of oscillations N and N' give 



= M H cos O + ^~Q , 



sin w - 



