Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/385

753.] The principal constants which we wish to determine are—

(1) The magnetic force at the centre of the coil due to a unit-current. This is the quantity denoted by $$G_1$$ in Art. 700.

(2) The magnetic moment of the coil due to a unit-current. This is the quantity $$g_1$$.

753.] To determine $$G_1$$. Since the coils of the working galvanometer are much smaller than the standard coil, we place the galvanometer within the standard coil, so that their centres coincide, the planes of both coils being vertical and parallel to the earth's magnetic force. We have thus obtained a differential galvanometer one of whose coils is the standard coil, for which the value of $$G_1$$ is known, while that of the other coil is $$G_1^\prime$$, the value of which we have to determine.

The magnet suspended in the centre of the galvanometer coil is acted on by the currents in both coils. If the strength of the current in the standard coil is $$\gamma$$, and that in the galvanometer coil $$\gamma^\prime$$, then, if these currents flowing in opposite directions produce a deflexion $$\delta$$ of the magnet, where $$H$$ is the horizontal magnetic force of the earth.

If the currents are so arranged as to produce no deflexion, we may find $$G_1^\prime$$ by the equation

We may determine the ratio of $$\gamma$$ to $$\gamma^\prime$$ in several ways. Since the value of $$G_1$$ is in general greater for the galvanometer than for the standard coil, we may arrange the circuit so that the whole current $$\gamma$$ flows through the standard coil, and is then divided so that $$\gamma^\prime$$ flows through the galvanometer and resistance coils, the combined resistance of which is $$R_1$$, while the remainder $$\gamma - \gamma^\prime$$ flows through another set of resistance coils whose combined resistance is $$R_2$$.