Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/451

355.] Four conductors of great resistance may also be arranged as in Wheatstone's Bridge, and the bridge itself may consist of the electrodes of an electrometer instead of those of a galvanometer. The advantage of this method is that no permanent current is required to produce the deviation of the electrometer, whereas the galvanometer cannot be deflected unless a current passes through the wire.

354.] When the resistance of a conductor is so great that the current which can be sent through it by any available electromotive force is too small to be directly measured by a galvanometer, a condenser may be used in order to accumulate the electricity for a certain time, and then, by discharging the condenser through a galvanometer, the quantity accumulated may be estimated. This is Messrs. Bright and Clark's method of testing the joints of submarine cables.

355.] But the simplest method of measuring the resistance of such a conductor is to charge a condenser of great capacity and to connect its two surfaces with the electrodes of an electrometer and also with the extremities of the conductor. If $$E$$ is the diffference of potentials as shewn by the electrometer, $$S$$ the capacity of the condenser, and $$Q$$ the charge on either surface, $$R$$ the resistance of the conductor and $$x$$ the current in it, then, by the theory of condensers,

By Ohm's Law, and by the definition of a current,

Hence where $$Q_0$$ is the charge at first when $$t = 0$$.

Similarly where $$E_0$$ is the original reading of the electrometer, and $$E$$ the same after a time $$t$$. From this we find which gives $$R$$ in absolute measure. In this expression a knowledge of the value of the unit of the electrometer scale is not required.