Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/127

Rh Next, hang the stirrup to the suspension fibre, and place the magnet in it, adjusting it carefully so that y may be vertical and upwards, then the moment of the force tending to increase α is

But if ζ is the observed azimuth of the line of collimation so that the force may be written

When the apparatus is in equilibrium this quantity is zero for a particular value of ζ.

When the apparatus never comes to rest, but must be observed in a state of vibration, the value of ζ corresponding to the position of equilibrium may be calculated by a method which will be described in Art. 735.

When the force of torsion is small compared with the moment of the magnetic force, we may put δ - ζ + l - λ for the sine of that angle.

If we give to β, the reading of the torsion circle, two different values, β1 and β2, and if ζ1 and ζ2 are the corresponding values of ζ, or, if we put and equation (7) becomes, dividing by M H sin m, If we now reverse the magnet so that y is downwards, and adjust the apparatus till y is exactly vertical, and if ζ' is the new value of the azimuth, and δ' the corresponding declination, whence