Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/202

170 (2) The induction of the circuit $$A$$ on the circuit $$X$$ is equal to that of $$X$$ upon $$A$$.

For if we put $$A$$ in the galvanometer circuit, and $$X$$ in the battery circuit, the equilibrium of electromotive force is not disturbed.

(3) The induction is proportional to the inducing current.

For if we have ascertained that the induction of $$A$$ on $$X$$ is equal to that of $$B$$ on $$Y$$, and also to that of $$C$$ on $$Z$$, we may make the battery current first flow through $$A$$, and then divide itself in any proportion between $$B$$ and $$C$$. Then if we connect $$X$$ reversed, $$Y$$ and $$Z$$ direct, all in series, with the galvanometer, the electromotive force in $$X$$ will balance the sum of the electromotive forces in $$Y$$ and $$Z$$.

(4) In pairs of circuits forming systems geometrically similar the induction is proportional to their linear dimensions.

For if the three pairs of circuits above mentioned are all similar, but if the linear dimension of the first pair is the sum of the corresponding linear dimensions of the second and third pairs, then, if $$A$$, $$B$$, and $$C$$ are connected in series with the battery, and $$X$$ reversed, $$Y$$ and $$Z$$ also in series with the galvanometer, there will be equilibrium.

(5) The electromotive force produced in a coil of $$n$$ windings by a current in a coil of $$m$$ windings is proportional to the product $$mn$$.

537.] For experiments of the kind we have been considering the galvanometer should be as sensitive as possible, and its needle as light as possible, so as to give a sensible indication of a very small transient current. The experiments on induction due to motion require the needle to have a somewhat longer period of vibration, so that there may be time to effect certain motions of the conductors while the needle is not far from its position of equilibrium. In the former experiments, the electromotive forces in the galvanometer circuit were in equilibrium during the whole time, so that no current passed through the galvanometer coil. In those now to be described, the electromotive forces act first in one direction and then in the other, so as to produce in succession two currents in opposite directions through the galvanometer, and we have to shew that the impulses on the galvanometer needle due to these successive currents are in certain cases equal and opposite.

The theory of the application of the galvanometer to the measurement of transient currents will be considered more at length in Art. 748. At present it is sufficient for our purpose to