Electrolysis and Electrical Units
In December 1851 Thomson communicated an important paper to the Philosophical Magazine on "The Mechanical Theory of Electrolysis," and "Applications of Mechanical Effect to the Measurement of Electromotive Forces, and of Galvanic Resistances, in Absolute Units."
In the first of these he supposed a machine of the kind imagined by Faraday, consisting of a metal disk, rotating uniformly with its plane at right angles to the lines of force of a uniform magnetic field, and touched at its centre and its circumference by fixed wires, to send a current through an electrochemical apparatus, to which the wires are connected. A certain amount of work W was supposed to be spent in a given time, during which a quantity of heat H was evolved in the circuit, and a certain amount of work M spent in the chemical apparatus in effecting chemical change. If H be taken in dynamical units, W = H + M.
The work done in driving the disk, if the intensity of the field is I, the current produced c, the radius of the disc r, and the angular velocity of turning w, is ½Ir2cw.
Thomson assumed that the work done in the electrochemical apparatus was equal to the heat of chemical combination of the substance or substances which underwent the chemical action, taken with the proper sign according to the change, if more compound substances than one were acted on. Hence M represented this resultant heat of combination.
The electrochemical apparatus was a voltameter containing a definite compound to be electrolysed, or a voltaic cell or battery. And by Faraday's experiments on electrolysis it was known that the amount of chemical action was proportional to the whole quantity of electricity passed through the cell in a given time, so that the rate at which energy was being spent in the cell was at any instant proportional to the current at that instant.
The chemical change could be measured by considering only one of the elements set free, or made to combine, by the passage of the current, and considering the quantity of heat θ, say, for the whole chemical change in the cell corresponding to the action on unit mass of that element. Thus if E denote the whole quantity of that element operated on the heat of combination in the vessel was θE. If E be taken for unit of time, and ε denote the quantity set free by the passage of unit quantity of electricity, then E = εc, since a current conveys c units of electricity in one second. The number ε is a definite quantity of the element, and is called its electrochemical equivalent. Again, from Joule's experiments, H = Rc2, if R denote the resistance of the current, and so
and
The quantity ½Ir2w is the electromotive force due to the disk.
Thus c was positive or negative according as ½Ir2w was greater or less than θε, and was zero when ½Ir2w = θε. Thus the electromotive force of the disk was opposed by a back electromotive force θε due to the chemical action in the voltameter or battery, to which the wires from the disk were connected.
The conclusion arrived at therefore was that the electromotive force (or, as it was then termed, the intensity) of the electrochemical action was equal to the dynamical value of the whole chemical change effected by a current of unit strength in unit of time.
From this result Thomson proceeded to calculate the electromotive forces required to effect chemical changes of different kinds, and those of various types of voltaic cell. Supposing a unit of electricity to be carried by the current through the cell, he considered the chemical changes which accompanied its passage, and from the known values of heats of combination calculated their energy values. In some parts the change was one of chemical combination, in others one of decomposition of the materials, and regard had to be paid to the sign of the heat-equivalent. By properly summing up the whole heat-equivalents a net total was obtained which, according to Thomson, was the energy consumed in the passage of unit current, and was therefore the electromotive force. The theory was incomplete, and required to be supplemented by thermodynamic theory, which shows that besides the electromotive force there must be included in the quantity set against the sum of heats a term represented by the product of the absolute temperature multiplied by the rate of variation of electromotive force with alteration of temperature. Thus the theory is only applicable when the electromotive force is not affected by variation of temperature. The necessary addition here indicated was made by Helmholtz.
In the next paper, which appeared in the same number (December 1851) of the Philosophical Magazine, the principle of work is applied to the measurement of electromotive forces and resistances in absolute units. The advantages of such units are obvious. Nearly the whole of the quantitative work of the older experimenters was useless except for those who had actually made the observations: it was hardly possible for one man to advance his researches by employing data obtained by others. For the results were expressed by reference to apparatus and materials in the possession of the observers, and to these others could obtain access only with great difficulty and at great expense—to say nothing of the uncertainty of comparisons made to enable the results of one man to be linked on to those made elsewhere, and with other apparatus, by another. It was imperative, therefore, to obtain absolute units—units independent of accidents of place and apparatus—for the expression of currents, electromotive forces, and resistances, so as to enable the results of the work of experiments all over the world to be made available to every one who read the published record. (See Chap. [XIII].)
The magneto-electric machine imagined in the former paper gave a means of estimating the electromotive force of a cell or battery in absolute units. The same kind of machine is used here, in the simpler form of a sliding conductor connecting a pair of insulated rails laid with their plane perpendicular to the lines of force of a uniform magnetic field. If the rails be connected by a wire, and the slider be moved so as to cut across the lines of force, a current will be produced in the circuit. The current can be measured in terms of the already known unit of current, that current which flowing in a circle of radius unity produces a magnetic field at the centre of 2π units. This current, c, say, in strength, flowing in the circuit, renders a dynamical force cIl necessary to move the slider of length l across the lines of force of the field of intensity I, and if the speed of the slider required for the current c be v, the rate at which work is done in moving the slider is cIlv. This must be the rate at which work is done in the circuit by the current, and if the only work done be in the heating of the conductor, we have cIlv = Rc2, or Ilv = Rc, so that Ilv is the electromotive force. Any electromotive force otherwise produced, which gave rise to the same current, must obviously be equal to Ilv, so that the unit of electromotive force can thus be properly defined.
Thomson used a foot-grain-second system of units; but from this arrangement are now obtained the C.G.S. units of electromotive force and resistance. If I is one C.G.S. unit, l one centimetre, and v one centimetre per second, we have unit electromotive force in the C.G.S. system. Also in one C.G.S. unit of resistance if c be unity as well as Ilv.
The idea of the determination of a resistance in absolute units on correct principles was due to W. Weber, who also gave methods of carrying out the measurement; and the first determination was made by Kirchhoff in 1849. Thomson appears, however, to have been the first to discuss the subject of units from the point of view of energy. This mode of regarding the matter is important, as the absolute units are so chosen as to enable work done by electric and magnetic forces to be reckoned in the ordinary dynamical units. A vast amount of experimental resource and skill has been spent since that time on the determination of resistance, though not more than the importance of the subject warranted. We shall have to return to the subject in dealing with the work of the British Association on Electrical Standards, of which Thomson was for long an active member.