Page:Elementary Text-book of Physics (Anthony, 1897).djvu/332

318 will equalize the potentials of two electrified conductors, if it be used to connect them. Manifestly this property of the substances forming a circuit will influence the strength of the current in the circuit. It was shown on theoretical considerations, in 1827, by Ohm that in a homogeneous conductor which is kept constant the current varies directly with the difEerence of potential between the terminals. If $$R$$ represent a factor, constant for each conductor. Ohm's law is expressed in its simplest form by The quantity $$R$$ is called the resistance of the conductor. If the difference of potential be maintained constant, and the conductor be altered in any way that does not introduce an internal electromotive force, the current will vary with the changes in the conductor, and there will be a different value of $$R$$ with each change in the conductor. The quantity $$R$$ is therefore a function of the nature and materials of the conductor, and does not depend on the current or the difference of potential between the ends of the conductor. Since it is the ratio of the current to the difference of potential, and since we know these quantities in electrostatic units, we can measure $$R$$ in electrostatic units. From the dimensions of $$I$$ and $$(V_{1} - V_{2})$$ we may obtain the dimensions of $$R.$$ They are in electrostatic units Since the difEerence of potential in equation (97) is the measure of the electromotive force in the conductor considered, it is natural to extend the relation therein expressed to the whole circuit, in which the current is maintained by the electromotive force $$E.$$ The expression of Ohm's law for the whole circuit is  This relation cannot in every case be experimentally verified, but in many cases in which the electromotive force may be directly and accurately calculated its validity has been demonstrated.