Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/387

 

position of the circuits can be easily performed. In order to attain a sufficient degree of accuracy, it is necessary that the distance between the circuits should be capable of exact measurement. But when the distance between the circuits is sufficient to prevent errors of measurement from introducing large errors into the result, the coefficient of induction itself is necessarily very much reduced in magnitude. Now for many experiments it is necessary to make the coefficient of induction large, and we can only do so by bringing the circuits close together, so that the method of direct measurement becomes impossible, and, in order to determine the coefficient of induction, we must compare it with that of a pair of coils arranged so that their coefficient may be obtained by direct measurement and calculation.

This may be done as follows:

Fig. 61.Let $A$ and $a$ be the standard pair of coils, $B$ and $b$ the coils to be compared with them. Connect $A$ and $B$ in one circuit, and place the electrodes of the galvanometer, $G$, at $P$ and $Q$, so that the resistance of $PAQ$ is $R$, and that of $QBP$ is $S$, $K$ being the resistance of the galvanometer. Connect $a$ and $b$ in one circuit with the battery.

Let the current in $A$ be ${\dot {x}}$, that in $B$, ${\dot {y}}$, and that in the galvanometer, ${\dot {x}}-{\dot {y}}$, that in the battery circuit being $\gamma$.

Then, if $M_{1}$ is the coefficient of induction between $A$ and $a$, and $M_{2}$ that between $B$ and $b$, the integral induction current through the galvanometer at breaking the battery circuit is

$x-y=\gamma {\frac {{\frac {M_{1}}{R}}-{\frac {M_{2}}{S}}}{1+{\frac {K}{R}}+{\frac {K}{S}}}}$.

(8)

By adjusting the resistances $R$ and $S$ till there is no current through the galvanometer at making or breaking the galvanometer circuit, the ratio of $M_{2}$ to $M_{1}$ may be determined by measuring that of $S$ to $R$.