Page:Elementary Text-book of Physics (Anthony, 1897).djvu/387

§ 311] If we now insert a galvanometer in the fixed cross-piece, and suppose the resistance of all the circuit except the sliding piece to be negligible, and moye the sliding piece at such a rate that the current in the galyanometer is unity, we have the resistance of the sliding piece determined from the velocity with which it moves. For, by Ohm's law, $$i = \frac{e}{r},$$ and since $$i = 1$$ and $$e = v,$$ we have $$r = v.$$

Such an arrangement as that here described is of course impossible in practice, but it embodies the principle of the method actually used to determine the unit of resistance by the Committee of the British Association. In their method, a circular coil of wire, in the centre of which was suspended a small magnetic needle, was mounted so as to rotate with constant velocity about a vertical diameter. From the dimensions and velocity of rotation of the coil and the intensity of the earth's magnetic field, the induced electromotive force in the coil was calculated. The current in the same coil was determined by the deflection of the small magnet. The ratio of these two quantities gave the resistance of the coil.

311. Ratio between the Electrostatic and Electromagnetic Units.—When the dimensions of any electrical quantity derived from its electrostatic definition are compared with its dimensions derived from its electromagnetic definition, the ratio between them is always of the dimensions of some power of a velocity. The ratio between the electrostatic and electromagnetic unit of any electrical quantity is, therefore, some power of a velocity. If this ratio be obtained for any set of units, the number expressing it will also express some power of a velocity. This velocity is an absolute quantity or constant of Nature. Whatever changes are made in the units of length and time, the number expressing this velocity in the new units will also express the ratio of the two sets of electrical units.

This ratio, which is called $$v,$$ can be measured in several ways. The method which was first used, by Weber and Kohlrausch, depends upon the comparison of a quantity of electricity measured