To those who can accept Thomson’s axiom with the explanation appended to it, Carnot’s proposition that a reversible engine is perfect (in the sense of being the best possible) is demonstrated at once, as follows, _ex absurdo_. Suppose there could be an engine, M, more perfect than a reversible engine, N. Set the two to work together as a compound engine, M letting down heat from boiler to condenser, and doing work; N spending work in pumping back again the heat to the boiler. If N be made to restore to the boiler at every stroke exactly what M takes from it, the compound engine will do external work, for, by hypothesis, M is more perfect than N. Whence does the work come? Not from the boiler, for it remains as it was. Hence N must take more heat from the condenser than M gives it; _i.e._ you get work by cooling the condenser. Carry the reasoning a little further, and we see that if the excess of work given by M were spent upon N, and thus no work on the whole either spent or given out, the condenser would be still further cooled, and the boiler heated! This, to most people, would seem to imply an ample _reductio ad absurdum_. But Clerk-Maxwell has shown it to be physically possible, and has thus thoroughly justified Thomson’s caution about his axiom. As this is a point of very great importance, we offer no excuse for treating it pretty fully. * 111. Clerk-Maxwell’s reasoning is given as depending upon the molecular theory of gases, but the only necessity for so restricting it appears to be that we thereby connect the reasoning more directly with _Heat_, which, on this theory, is supposed to be the energy of motion of the molecules of the gas. The illustration, however, is more general, and at the same time more simple, if we do not at first refer either to heat or to the molecular hypothesis of the constitution of gases, but treat the question simply as one concerning the possible motions of a number of little material particles.