Lord Kelvin: An account of his scientific life and work

by Andrew Gray

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.