VI. A determination of “v,” the ratio of the electromagnetic unit of electricity to the electrostatic unit

Abstract

The experiments made by one of us in 1883 having given a value of " v " considerably smaller than the one found by several recent researches, it was thought desirable to repeat those experiments. The method used in 1883 was to find the electrostatic and electromagnetic measures of the capacity of a condenser; the electrostatic measure being calculated from the dimensions of the condenser, the electromagnetic measure determined by finding the resistance which would produce the same effect as that produced by the repeated charging of the condenser placed in one arm of a Wheat-stone’s Bridge. In the experiments of 1883 the condenser used in determining the electromagnetic measure of the capacity was not the same as the one for which the electrostatic measure had been calculated, but an auxiliary one, without a guard ring, the equality of the capacity of this condenser and that of the guard ring condenser being tested by the method given in Maxwell’s ‘Electricity and Magnetism,’ vol. 1, p. 324. In repeating the experiment we adopted at first the method used before, using, however, a key of different design for testing the equality of the capacity of the two condensers by Maxwell’s method. We got very consistent results, practically identical with the previous ones. We may mention here, since it has been suggested that the capacity of the leads might account for the small values of " v " obtained, that this capacity is allowed for by the way the comparison between the capacities of the auxiliary and guard ring condensers is made, for the same leads are used both in this comparison and in the determination of the electromagnetic measure of the capacity of the auxiliary condenser; the capacity of the auxiliary condenser, plus that of its leads, is made equal to the capacity of the guard ring condenser, and it is the capacity of the auxiliary condenser, plus its leads, which is determined in electromagnetic measure. As the introduction of the auxiliary condenser introduced increased possi­bilities of error, we endeavoured to determine directly the electromagnetic measure of the capacity of the guard ring condenser, by using a complicated commutator which worked both the guard ring and the condenser. At first we tried one where the contacts were made by platinum styles attached to a tuning fork, but as the results were not so regular as we desired, we replaced the tuning fork commutator by a rotating one driven by a water motor. A stroboscopic arrangement was fixed to this commu­tator so that its speed might be kept regular and measured. With this arrangement, which worked perfectly, we got values for the electromagnetic measure of the capacity of the condenser distinctly less than those obtained by the old method. We then endeavoured to find out the cause of this difference, and after a good deal of trouble discovered that in the experiments by which the equality of the capacities of the guard ring and auxiliary condensers was tested by Maxwell’s method, the guard ring did not produce its full effect. When the guard ring of the standard condenser was taken off, and its capacity made equal by Maxwell’s method to the capacity of the auxiliary condenser, the two methods gave identical results; but the effect of adding the guard ring was less in the old method than in the new. We found also, by calculation, that the effect produced by the guard ring in the old method was distinctly too small, while that determined by the new method agreed well with its calculated value. As the new method was working perfectly satisfactorily, and as it possesses great advantages over the old one, inasmuch as we get rid entirely of the auxiliary condenser, and can also alter the speed of the rotating commutator with very much greater ease and considerably greater accuracy than in any arrangement where the speed is governed by a tuning fork, we discarded the old method and adopted the new one which we now proceed to describe, beginning by considering the errors to which this method is liable.