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

 

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,

$H\tan \delta =G_{1}^{\prime }\gamma ^{\prime }-G_{1}\gamma$

(1)

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

$G_{1}^{\prime }={\frac {\gamma }{\gamma ^{\prime }}}G_{1}$.

(2)

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 $R_{2}$.

of its various parts. Hence any concealed flaw in the continuity of the metal may cause the main stream of electricity to flow either close to the outside or close to the inside of the circular ring. Thus the true path of the current becomes uncertain. Besides this, when the current flows only once round the circle, especial care is necessary to avoid any action on the suspended magnet due to the current on its way to or from the circle, because the current in the electrodes is equal to that in the circle. In the construction of many instruments the action of this part of the current seems to have been altogether lost sight of.

The most perfect method is to make one of the electrodes in the form of a metal tube, and the other a wire covered with insulating material, and placed inside the tube and concentric with it. The external action of the electrodes when thus arranged is zero, by Art. 683.