and so the scale of temperature thus defined may be termed absolute. Moreover, such a scale leads at once to the idea of an absolute zero, for no engine could be supposed to convert more heat-energy into work than it received; and, choosing the temperature of the refrigerator (calling it T), so that no heat-energy is rejected by the engine, but all the heat-energy taken from the source is turned into work, it is impossible for T to be negative, else the engine would have an efficiency greater than 100 per cent. Therefore zero is the smallest algebraic value the temperature of the refrigerator can have, and temperatures reckoned from this zero are called absolute. The size of the degrees on this scale is arbitrary, and has been conveniently chosen so that there are one hundred degrees between the temperatures of boiling and freezing water. If now a reversible engine be worked between these temperatures and the quantities of heat-energy received and rejected be measured, the temperature of boiling water on the absolute scale may be found. It is not necessary actually to try the experiment, for the work done by the expansion of a substance which obeys the ordinary laws of gases may be calculated by the methods of the infinitesimal calculus. In this way Kelvin's thermodynamic scale has been shown to be practically identical with that of a perfect gas thermometer, which shows the absolute zero of the thermodynamic scale to lie about 273 degrees below the zero of the Centigrade scale.
Professor Tait has said:"Without this work of Carnot, the modern theory of energy, and especially that branch of it which is at present by far the most important in practice, the dynamical theory of heat, could never have attained in so few years its now enormous development. Carnot 's claims to recognition are of an exceedingly high order, because they depend not merely upon his method, which is one of startling novelty and originality and is not confined to the subject of heat; but upon the fundamental principle upon which he based his mode of comparing the heat employed with the work procured from it. Every reasoner who has applied himself to the subject of heat since Carnot has gone right so far as he attended to Carnot 's principle; but has inevitably gone wrong when he forgot or did not attend to it."
The two things which Carnot introduced, which were entirely original with him and which left his hands in an almost perfect form, were the idea of a 'Cycle of Operations' and the further idea of a 'Reversible Cycle,' giving also the notion of a 'Reversible and Perfect Engine,' showing that the efficiency of such depends only on temperature.
The peculiar merit of Carnot's reasoning consists in the idea of bringing the body back to its initial state as to temperature, density and molecular condition, after a cycle of operations, before making any assertion as to the amount of heat-energy gained or lost. This he
