Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/449

352.] with a mercury cup, into which one electrode of the galvanometer may be plunged.

The rest of the apparatus is arranged, as in Wheatstone's Bridge, with resistance coils or boxes $$A$$ and $$C$$, and a wire $$PR$$ with a sliding contact piece $$Q$$, to which the other electrode of the galvanometer is connected.

Now let the galvanometer be connected to $$S$$ and $$Q$$, and let $$A_1$$ and $$C_1$$ be so arranged, and the position of $$Q$$ so determined, that there is no current in the galvanometer wire.

Then we know thatwhere $$XS,\, PQ,$$ &c. stand for the resistances in these conductors.

From this we get

Now let the electrode of the galvanometer be connected to $$S'$$, and let resistance be transferred from $$C$$ to $$A$$ (by carrying resistance coils from one side to the other) till electric equilibrium of the galvanometer wire can be obtained by placing $$Q$$ at some point of the wire, say $$Q_2$$. Let the values of $$C$$ and $$A$$ be now $$C_2$$ and $$A_2$$, and let

Then we have, as before,

In the same way, placing the apparatus on the second conductor at $$TT'$$ and again transferring resistance, we get, when the electrode is in $$T'$$, and when it is in $$T$$,

We can now deduce the ratio of the resistances $$SS'$$ and $$T'T$$, for