606 MAGNETIC FIELD. 



semi-difference of the readings gives the deflection a, and the con- 

 dition of equilibrium is 



F 2 M 



As the deflections are- not large, the influence of the induced 

 magnetisation on the deflecting magnet need not be taken into 

 account. The series of the observations is the same as in the 

 preceding case, with this difference that the sines, and not the 

 tangents, of the angles, come into the formulae. 



The distances R and R', from the centre of the stirrup to the 

 deflecting bar, have been determined once for all, by measuring with 

 a microscope, on the slide of a dividing machine, the distance from 

 the suspension-wire to the ends of the magnet placed on a stirrup, 

 and then turned over. As the bar cannot be placed on the other 

 side, to correct for the error of centering, the position of the wire 

 must remain unchanged; it is centred each time with the screws 

 B and B', so that the microscope, when turned through 180 about 

 the horizontal axis, sees the two fiducial lines of a bar without dis- 

 placing the arrangement. 



The change of side is possible when the rod T is replaced by 

 another rod, parallel to the movable magnet, and carrying stirrups 

 in which the deflecting bar may be placed, in a direction perpen- 

 dicular to the rod ; in this case, observations right or left eliminate 

 the want of centering of the wire. The declinometer is then in the 

 equatorial plane of the deflecting bar ; the deflections are almost 

 half what they are in the first case, and do not admit of the same 

 accuracy; but, when the construction of the apparatus permits, it 

 is useful to make the observations in the two positions, as a control. 



It has been assumed that the terrestrial field has remained the 

 same during the observation of the oscillations, and the series of 

 readings of the declinometer ; the data of an apparatus for variations 

 observed simultaneously will enable us to reduce all readings to the 

 same period. We ought, lastly, to ascertain whether the suspension- 

 wire has an appreciable torsion, and a correction is introduced for 

 the duration of the oscillations. 



1178. Gauss determined the directing couple MH by the 

 method of torsion (1142), with a unifilar or bifilar suspension, 

 and measuring the coefficient C for the system of suspension by 

 the ordinary methods. In this case the induced magnetisation 

 does not come in, if the deflection is near 90. 



