Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/128

Rh The reading of the torsion circle should now be adjusted, so that the coefficient of $$\tau^\prime$$ may be as nearly as possible zero. For this purpose we must determine $$\lambda$$, the value of $$\alpha - \beta$$ when there is no torsion. This may be done by placing a non-magnetic bar of the same weight as the magnet in the stirrup, and determining $$\alpha - \beta$$ when there is equilibrium. Since $$\tau^\prime$$ is small, great accuracy is required. Another method is to use a torsion bar of the same weight as the magnet, containing within it a very small magnet whose magnetic moment is $$\tfrac{1}{n}$$ of that of the principal magnet. Since $$\tau$$ remains the same, $$\tau^\prime$$ will become $$n \tau^\prime$$, and if $$\zeta_{1}$$ and $$\zeta_{1}^\prime$$ are the values of $$\zeta$$ as found by the torsion bar, Subtracting this equation from (11),  Having found the value of $$\beta + \lambda$$ in this way, $$\beta$$, the reading of the torsion circle, should he altered till  as nearly as possible in the ordinary position of the apparatus.

Then, since $$\tau^\prime$$ is a very small numerical quantity, and since its coefficient is very small, the value of the second term in the expression for $$\delta$$ will not vary much for small errors in the values of $$\tau^\prime$$ and $$\lambda$$, which are the quantities whose values are least accurately known.

The value of $$\delta$$, the magnetic declination, may be found in this way with considerable accuracy, provided it remains constant during the experiments, so that we may assume $$\delta^\prime = \delta$$.

When great accuracy is required it is necessary to take account ot the variations of $$\delta$$ during the experiment. For this purpose observations of another suspended magnet should be made at the some instants that the different values of $$\zeta$$ are observed, and if $$\eta, \eta^\prime$$ are the observed azimuths of the second magnet corresponding to $$\zeta$$and $$\zeta^\prime$$, and if $$\delta$$ and $$\delta^\prime$$ are the corresponding values of $$\delta$$, then Hence, to find the value of $$\delta$$ we must add to (11) a correction  The declination at the time of the first observation is therefore