Page:Elementary Text-book of Physics (Anthony, 1897).djvu/388

374 in the two systems. From the dimensions of current in the electromagnetic system we have the dimensions of quantity $$[q] = [iT] = M^{\frac{1}{2}}L^{\frac{3}{2}}.$$ The dimensions of quantity in the electrostatic system are $$[Q] = M^{\frac{1}{2}}L^{\frac{3}{2}}T^{-1}.$$ The ratio of these dimensions is $$\left[ \frac{Q}{q} \right] = LT^{-1},$$ or, the number of electrostatic units of quantity in one electromagnetic unit is the velocity $$v.$$

In Weber and Kohlrausch's method the charge of a Leyden jar was measured in electrostatic units by a determination of its capacity and the difference of potential between its coatings. The current produced by its discharge through a galvanometer was used to measure the same quantity in electromagnetic measure.

Thomson determined $$v$$ by a comparison of an electromotive force measured in the two systems. He sent a current through a coil of very high known resistance, and measured it by an electro-dynamometer. The electromagnetic difference of potential between the two ends of the resistance coil was then equal to the product of the current by the resistance. The electrostatic difference of potential between the same two points was measured by an absolute electrometer. From the dimensional formulas we have $$\left[ \frac{E}{e} \right] = \frac{M^{\frac{1}{2}}L^{\frac{1}{2}}T^{-1}}{M^{\frac{1}{2}}L^{\frac{3}{2}}T^{-2}} = L^{-1}T.$$ The number of electromagnetic units of electromotive force in one electrostatic unit is $$v.$$ The ratio of the numbers expressing the electromagnetic and the electrostatic measures of the electromotive force in Thomson's experiment is therefore the quantity $$v.$$ This experiment was carried out by Maxwell in a different form, in which the electrostatic repulsion of two similarly charged disks was balanced by an electromagnetic attraction between currents passing through fiat coils on the back of the two disks.

Other methods, depending on comparisons of currents, of resistances, and other electrical quantities, have been employed. The methods described are historically interesting as being the first ones used. The values of $$v$$ obtained by them differed rather widely from one another. Recent determinations, however, give