The experiments here asked for had already, as was soon after perceived by Thomson, been made by Joule, not merely in his determinations of the dynamical equivalent of heat, but in his exceedingly important investigation of the energy changes in the circuit of a voltaic cell, or of a magneto-electric machine. Moreover, the answer to this "very perplexing question" was afterwards to be given by Thomson himself in his paper, "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy," published in the Edinburgh Proceedings in 1852.
Again, we find, a page or two earlier in the "Account of Carnot's Theory," the question asked with respect to the heat evolved in the circuit of a magneto-electric machine, "Is the heat which is evolved in one part of the closed conductor merely transferred from those parts which are subject to the inducing influence?" and the statement made that Joule had examined this question, and decided that it must be answered in the negative. But Thomson goes on to say, "Before we can finally conclude that heat is absolutely generated in such operations, it would be necessary to prove that the inducing magnet does not become lower in temperature and thus compensate for the heat evolved in the conductor."
Here, apparently, the idea of work done in moving the magnet, or the conductor in the magnetic field, is not present to Thomson's mind; for if it had been, the idea that the work thus spent might have its equivalent, in part, at least, in heat generated in the circuit, would no doubt have occurred to him and been stated. This idea had been used just a year before by Helmholtz, in his essay "Die Erhaltung der Kraft," to account for the heat produced in the circuit by the induced current, that is, to answer the first question put above in the sense in which Joule answered it. The subject, however, was fully worked out by Thomson in a paper published in the Philosophical Magazine for December 1851, to which we shall refer later.
Tables of the work performed by various steam engines working between different stated temperatures were given at the close of the "Account," and compared with the theoretical "duty" as calculated for Carnot's ideal perfect engine. Of course the theoretical duty was calculated from the temperatures of the boiler and condenser; the much greater fall of temperature from the furnace to the boiler was neglected as inevitable, so that the loss involved in that fall is not taken account of. Carnot's theory gave for the theoretical duty of one heat unit (equivalent to 1390 foot-pounds of work) 440 foot-pounds for boiler at 140° C. and condenser at 30° C.; and the best performance recorded was 253 foot-pounds, giving a percentage of 57.5 per cent. The worst was that of common engines consuming 12 lb. of coal per horse-power per hour, and gave 38.1 foot-pounds, or a percentage of 8.6 per cent. These percentages become on the dynamical theory 68 and 10.3, since the true theoretical duty for the heat unit is only 371 foot-pounds.
It is worthy of notice that the indicator-diagram method of graphically representing the changes in a cycle of operations is adopted in Thomson's "Account," but does not occur in Carnot's essay. The cycles consist of two isothermal changes and two adiabatic changes; that is, two changes at the temperatures of the source and refrigerator respectively, and two changes—from the higher to the lower temperature, and from the lower to the higher. These changes are made subject to the condition in each case that the substance neither gains nor loses energy in the form of heat, but is cooled in the one case by expansion and heated in the other by compression. The indicator diagram was due not to Thomson but to Clapeyron (see p. [99] above), who used it to illustrate an account of Carnot's theory.
There appeared in the issue of the Edinburgh Philosophical Transactions for January 2, 1849, along with the "Account of Carnot's Theory," a paper by James Thomson, entitled, "Theoretical Considerations on the Effect of Pressure in Lowering the Freezing Point of Water." The author predicted that, unless the principle of conservation of energy was at fault, the effect of increase of pressure on water in the act of freezing would be to lower the freezing point; and he calculated from Carnot's theory the amount of lowering which would be produced by a given increment of pressure. The prediction thus made was tested by experiments carried out in the Physical Laboratory by Thomson, and the results obtained completely confirmed the conclusions arrived at by theory. This prediction and its verification have been justly regarded as of great importance in the history of the dynamical theory of heat; and they afford an excellent example of the predictive character of a true scientific theory. The theory of the matter will be referred to in the next chapter.