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.)