CHAPTER XIII
BRITISH ASSOCIATION COMMITTEE ON ELECTRICAL STANDARDS
When Professor Thomson began his work as a teacher in the University of Glasgow, there was, as has already been noticed, great vagueness of specification of physical quantities. Few of the formal definitions of units of measurement, now to be found in the pages of every elementary text book, had been framed, and there was much confusion of quantities essentially distinct, a confusion which is now, to some extent at least, guarded against by the adoption of a definite unit, with a distinctive name for each magnitude to be measured. Thus rate of working, or activity, was confused with work done; the condition for maximum activity in the circuit of a battery or dynamo was often quoted as the condition of greatest efficiency, that is of greatest economy of energy, although it was exactly that in which half the available energy was wasted.
Partly as a consequence of this vagueness of specification, there was a great want of knowledge of the values of physical constants; for without exact definitions of quantities to be determined, such definitions as would indicate units for their measurement, related to ordinary dynamical units according to a consistent scheme, it was impossible to devise satisfactory experimental methods to do for electricity and magnetism what had been done by Regnault and others for heat.
The first steps towards the construction of a complete system of units for the quantitative measurement of magnetic and electric quantities were taken by Gauss, in his celebrated paper entitled Intensitas vis magneticæ terrestris ad mensuram absolutam revocata, published in 1832. In this he showed how magnetic forces could be expressed in absolute units, and thus be connected with the absolute dynamical units which Gauss, in the same paper, based on chosen fundamental units of length, mass, and time. Thus the modern system of absolute units of dynamical quantities, and its extension to magnetism, are due to the practical insight of a great mathematician, not to the experimentalists or "practicians" of the time.
Methods of measuring electric quantities in absolute units were described by W. Weber, in Parts II and III of his Elecktrodynamische Maassbestimmungen, published in 1852. These were great steps in advance, and rendered further progress in the science of absolute measurement comparatively easy. But they remained the only steps taken until the British Association Committee began their work. We have already (pp. [74-76]) referred to the great importance of that work, not only for practical applications but also for the advancement of science. But it was not a task which struck the imagination or excited the wonder of the multitude. For the realisation of standards of resistance, for example, involved long and tedious investigations of the effects of impurities on the resistance of metals, and the variation of resistance caused by change of temperature and lapse of time. Then alloys had to be sought which would have a temperature effect of small amount, and which were stable and durable in all their properties.
The discoveries of the experimentalist who finds a new element of hitherto undreamed-of properties attract world-wide attention, and the glory of the achievement is deservedly great. But the patient, plodding work which gives a universal system of units and related standards, and which enables a great physical subject like electricity and magnetism to rise from a mere enumeration of qualitative results to a science of the most delicate and exact measurement, and to find its practical applications in all the affairs of daily life and commerce, is equally deserving of the admiration and gratitude of mankind. Yet it receives little or no recognition.
The construction of a standard of resistance was the first task undertaken by the committee; but other units, for example of quantity of electricity, intensity of electric field and difference of potential, had also to be defined, and methods of employing them in experimental work devised. It would be out of place to endeavour to discuss these units here, but some idea of the manner in which their definitions are founded on dynamical conceptions may be obtained from one or two examples. Therefore we shall describe two simple experiments, which will illustrate this dynamical foundation. An account has been given in Chapter XI of the series of electrometers which Thomson invented for the measurement of differences of electric potential. These all act by the evaluation in terms of ordinary dynamical units of the force urging an electrified body from a place of higher towards a place of lower potential.
Some indication of the meaning of electrical quantities has been given in Chapter IV. Difference of electric potential between two points in an electric field was there defined as the dynamical work done in carrying a unit of positive electricity against the forces of the field from the point of lower to the point of higher potential. Now by the definition of unit quantity of electricity given in electrical theory—that quantity which, concentrated at a point at unit distance from an equal quantity also concentrated at a point, is repelled with unit force—we can find, by the simple experiment of hanging two pith balls (or, better, two hollow, gilded beads of equal size) by two fine fibres of quartz, a metre long, say, electrifying the two balls as they hang in contact, and observing the distance at which they then hang, the numerical magnitude in absolute units of a charge of electricity, and apply that to finding the charge on a large spherical conductor and the potential at points in its field also in absolute units. If m be the mass of a ball, g gravity in cm. sec. units, d the distance in cms. of the centres of the balls apart, and l the length in cms. of a thread, the charge q, say, on each ball is easily found to be
Thus the charge is got in absolute centimetre-gramme-second units in terms of the mass m obtained by ordinary weighing, and l and d obtained by easy and exact measurements.
If one of the balls be now taken away without discharging the other, and the latter be placed in the field of a large electrified spherical conductor, the fibre will be deflected from the vertical by the force on the ball. Let the two centres be now on the same level. That force is got at once from the angle of deflection (which is easily observed), the charge on the ball, and the value of m. The electric field-intensity is obtained by dividing the value of the force by q. The field intensity multiplied by D, the distance apart in cms. of the centres of the ball and the conductor, gives the potential at the centre of the ball in C.G.S. units. Multiplication again by D gives the charge on the conductor.
When it made its first Report in 1862 (to the meeting at Cambridge) the committee consisted of Professors A. Williamson, C. Wheatstone, W. Thomson, W. H. Miller, Dr. A. Matthiessen, and Mr. F. Jenkin. At the next meeting, at Newcastle, it had been augmented by the addition of Messrs. Balfour Stewart, C. W. Siemens, Professor Clerk Maxwell, Dr. Joule, Dr. Esselbach, and Sir Charles Bright. The duty with which the committee had been charged was that of constructing a suitable standard of resistance. A reference to the account given in Chapter X above, of the derivation of what came to be called the electromagnetic unit of difference of potential, or electromotive force, by means of a simple magneto-electric machine—a disk turning on a uniform magnetic field, or the simple rails and slider and magnetic field arrangement there described—will show how from this unit and the electromagnetic unit of current (there also defined) the unit of resistance is defined. It is the resistance of the circuit of slider, rails, and connecting wire, when with this electromagnetic unit of electromotive force the unit of current is made to flow.
This was one clear and definite way of defining the unit of current, and of attaining the important object of connecting the units in such a way that the rate of working in a circuit, or the energy expended in any time, should be expressed at once in ordinary dynamical units of activity or energy. A considerable number of proposals were discussed by the committee; but it was finally determined to take the basis here indicated, and to realise a standard of resistance in material of constant and durable properties, which should have some simple multiple of the unit of resistance, in the system of dynamical units based on the centimetre as unit of length, the gramme as unit of mass, and the second as unit of time—the so-called C.G.S. system. The comparison of the different metals and alloys available was a most important but exceedingly laborious series of investigations, carried out mainly by Dr. Matthiessen and Professor Williamson.
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.
The British Association Committee also worked out a complete system of units for all electrical and magnetic quantities, and gave the first systematic statement of their relations, that is, of the so-called dimensional equations of the quantities. This will be found in the works to which reference has already been made (p. [251]).