Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/388

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756.] In the branch $$AF$$ of Wheatstone's Bridge let a coil be inserted, the coefficient of self-induction of which we wish to find. Let us call it $$L$$.

In the connecting wire between $$A$$ and the battery another coil is inserted. The coefficient of mutual induction between this coil and the coil in $$AF$$ is $$M$$. It may be measured by the method described in Art. 755.

If the current from $$A$$ to $$F$$ is $$x$$, and that from $$A$$ to $$H$$ is $$y$$, that from $$Z$$ to $$A$$, through $$B$$, will be $$x+y$$. The external electromotive force from $$A$$ to $$F$$ is

The external electromotive force along $$AH$$ is

If the galvanometer placed between $$F$$ and $$H$$ indicates no current, either transient or permanent, then by (9) and (10), since $$H-F=0$$,

Since $$L$$ is always positive, $$M$$ must be negative, and therefore the current must flow in opposite directions through the coils placed in $$P$$ and in $$B$$. In making the experiment we may either begin by adjusting the resistances so that which is the condition that there may be no permanent current, and then adjust the distance between the coils till the galvanometer ceases to indicate a transient current on making and breaking the battery connexion; or, if this distance is not capable of adjustment, we may get rid of the transient current by altering the resistances $$Q$$ and $$S$$ in such a way that the ratio of $$Q$$ to $$S$$ remains constant.

If this double adjustment is found too troublesome, we may adopt