Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/391

759.] from $$A_2$$ and placed in a position in which the coefficient of mutual induction between $$A_1$$ and $$A_2$$ is zero (Art. 538), a current of induction is produced in both circuits, and the galvanometer needle receives an impulse which produces a certain transient deflexion.

The resistance of the wire, $$R$$, is deduced from a comparison between the permanent deflexion, due to the steady current, and the transient deflexion, due to the current of induction.

Let the resistance of $$QGA_{1}P$$ be $$K$$, of $$PA_{2}BQ$$, $$B$$, and of $$PQ$$, $$R$$.

Let $$L$$, $$M$$ and $$N$$ be the coefficients of induction of $$A_1$$ and $$A_2$$.

Let $$\dot{x}$$ be the current in $$G$$, and $$\dot{y}$$ that in $$B$$, then the current from $$P$$ to $$Q$$ is $$\dot{x}-\dot{y}$$.

Let $$E$$ be the electromotive force of the battery, then

When the currents are constant, and everything at rest,

If $$M$$ now suddenly becomes zero on account of the separation of $$A_1$$ from $$A_2$$, then, integrating with respect to $$t$$,

Substituting the value of $$\dot{y}$$ in terms of $$\dot{x}$$ from (3), we find

��x M

x~ R *

When, as in Kirchhoff's experiment, both $$B$$ and $$K$$ are large compared with $$R$$, this equation is reduced to

Of these quantities, $$x$$ is found from the throw of the galvanometer due to the induction current. See Art. 768. The permanent current, $$\dot{x}$$, is found from the permanent deflexion due to the steady current; see Art. 746. $$M$$ is found either by direct calculation from the geometrical data, or by a comparison with a pair of coils, for which this calculation has been made; see Art. 755. From