Professor Thomson suggested to the committee the celebrated method of determining the resistance of a circuit by revolving a coil, which formed the main part of the circuit about a vertical axis in the earth's magnetic field. An account of the experiments made with this method is contained in the Report of 1863. They were carried out at King's College, London, where Maxwell was then Professor of Experimental Physics, by Maxwell, Balfour Stewart, and Fleeming Jenkin. The theoretical discussion and the description of the experiments was written by Maxwell, the details of the apparatus were described by Jenkin.
The principle of the method is essentially the same as that of the simple magneto-electric machine, to which reference has just been made. Two parallel coils of wire were wound in channels cut round rings of brass, which, however, were cut across by slots filled with vulcanite, to prevent induced currents from circulating in the brass. These coils were mounted in a vertical position and could be driven as a rigid system, at a constant measured speed, about a vertical axis passing through the centre of the system. Between the coils at this centre was hung, from a steady support, a small magnetic needle by a single fibre of silk; and a surrounding screen prevented the needle and suspension from being affected by currents of air.
The ends of the coil were connected together so that the whole revolved as a closed circuit about the vertical axis. When the coil system was at right angles to the magnetic meridian there was a magnetic induction through it of amount AH, where A denotes the effective area of the coils, and H the horizontal component of the earth's magnetic field. By one half-turn the coil was reversed with reference to this magnetic induction, and as the coil turned an induced current was generated, which depended at any instant on the rate at which the magnetic induction was varying at the instant, on the inductive electromotive force due to the varying of the current in the coil itself, and on the resistance of the circuit. A periodic current thus flowed in one direction relatively to the coil in one half-turn from a position perpendicular to the magnetic meridian, and in the opposite direction in the next half-turn. But as the position of the coil was reversed in every half-turn as well as the current in it, the current flowed on the whole in the same average direction relatively to the needle, and but for self-induction would have had its maximum value always when the plane of the coil was in the magnetic meridian.
The needle was deflected as it would have been by a certain average current, and the deflection was opposed by the action of the earth's horizontal magnetic field H. But this was the field cut by the coil as it turned, and therefore (except for a small term depending on the turning of the coil in the field of the needle) the value of H did not appear in the result, and did not require to be known.
Full details of the theory of this method and of the experiments carried out to test it will be found in various memoirs and treatises[23]; but it must suffice here to state that the resistance of the coil was determined in this way, by a large series of experiments, before and after every one of which the resistance was compared with that of a German-silver standard. The resistance of this standard therefore became known in absolute units, and copies of it, or multiples or sub-multiples of it, could be made.
A unit called the B.A. unit, which was intended to contain 109 C.G.S. electromagnetic units of resistance, was constructed from these experiments, and copies of it were soon after to be found in nearly all the physical laboratories of the world. Resistance boxes were constructed by various makers, in which the coils were various multiples of the B.A. unit, so that any resistance within a certain range could be obtained by connecting these coils in series (which was easily done by removing short circuiting plugs), and thus the absolute units of current electromotive force and resistance came into general use.
In 1881 Lord Rayleigh and Professor Schuster carried out a very careful repetition of the British Association experiments with the same apparatus at the Cavendish Laboratory, and obtained a somewhat different result. They found that the former result was about 1.17 per cent. too small. Lord Rayleigh next carried out an independent set of experiments by the same method with improved apparatus, and found that this percentage error must be increased to about 1.35.
It may be noticed here that the simple disk machine, of Thomson's illustration of the absolute unit of electromotive force, has been used by Lorenz to give a method of determining resistance which is now recognised as the best of all. It is sketched here that the reader may obtain some idea of later work on this very important subject; work which is a continuation of that of the original British Association Committee by their successors. A circuit is made up of a standard coil of wire, the ends of which are made to touch at the circumference and near the centre of the disk, which is placed symmetrically with respect to a cylindrical coil, and within it. A current is sent round this coil from a battery, and produces a magnetic field within the coil, the lines of magnetic force of which pass across the plane of the disk. This current, or a measured fraction of it, is also made to flow through the standard coil. The disk is now turned at a measured speed about its axis, so that the electromotive force due to the cutting of the field tends to produce a current in the standard coil of wire. The electromotive force of the disk is made to oppose the potential difference between the ends of this coil due to the current, so that no current flows along the disk or the wires connecting it with the standard coil. The magnetic field within the coil can be calculated from the form and dimensions of the coil and the current in it (supposed for the moment to be known), and the electromotive force of the disk is obtained in terms of its dimensions and its speed and the field intensity. But this electromotive force, which is proportional to the current in the coil, is equal to the product of the resistance of the wire and the same current, or a known fraction of it. Thus the current appears on both sides of the equation and goes out, and the value of the resistance is found in absolute units.
Lord Rayleigh obtained, by this method, a result which showed that the B.A. unit was 1.323 per cent. too small; and exact experiments have been made by others with concordant results. Values of the units have been agreed on by International Congresses as exact enough for general work, and with these units all electrical researches, wherever made, are available for use by other experimenters.
A vast amount of work has been done on this subject during the last forty years, and though the value of the practical unit of resistance—109 C.G.S. units, now called the "ohm"—is taken as settled, and copies can now be had in resistance boxes, or separately, adjusted with all needful accuracy, at the National Physical Laboratory and at the Bureau of Standards at Washington, and elsewhere, experiments are being made on the exact measurement of currents; while a careful watch is kept on the standards laid up at these places to see whether any perceptible variation of their resistance takes place with lapse of time.