Carnot showed that the work done by an ideal engine, in transferring heat from one temperature to another, was to be found by means of a certain function of the temperature, hence called "Carnot's function." The corresponding function in the true dynamical theory is always called Carnot's. A certain assignment of value to it gave, as we shall see, Thomson's famous absolute thermodynamic scale of temperature. In the light of the facts and theories which now exist, and are almost the commonplaces of physical text books, it is very interesting to review the ideas and difficulties which occurred to the founders of the science of heat sixty years ago. For example, Thomson asks, in his "Account of Carnot's Theory," what becomes of the mechanical effect which might be produced by heat which is transferred from one body to another by conduction. The heat leaves one body and enters another and no mechanical effect results: if it passed from one to the other through a heat engine, mechanical effect would be produced: what is produced in place of the mechanical effect which is lost? This he calls a very "perplexing question," and hopes that it will, before long, be cleared up. He states, further, that the difficulty would be entirely avoided by abandoning Carnot's principle that mechanical effect is obtained by "the transference of heat from one body to another at a lower temperate." Joule urges precisely this solution of the difficulty in his paper, "On the Changes of Temperature produced by the Rarefaction and Condensation of Air" (_Phil. Mag._, May 1845). Thomson notes this, but adds, "If we do so, however, we meet with innumerable other difficulties--insuperable without further experimental investigation, and an entire reconstruction of the theory of heat from its foundation. It is in reality to experiment that we must look, either for a verification of Carnot's axiom, and an explanation of the difficulty we have been considering, or for an entirely new basis of the Theory of Heat." 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.