The principle of Carnot, of a nature analogous to the principle of the conservation of energy, has also a similar origin.  It was first enunciated, like the last named, although prior to it in time, in consequence of considerations which deal only with heat and mechanical work.  Like it, too, it has evolved, grown, and invaded the entire domain of physics.  It may be interesting to examine rapidly the various phases of this evolution.  The origin of the principle of Carnot is clearly determined, and it is very rare to be able to go back thus certainly to the source of a discovery.  Sadi Carnot had, truth to say, no precursor.  In his time heat engines were not yet very common, and no one had reflected much on their theory.  He was doubtless the first to propound to himself certain questions, and certainly the first to solve them.

It is known how, in 1824, in his Reflexions sur la puissance motrice du feu, he endeavoured to prove that “the motive power of heat is independent of the agents brought into play for its realization,” and that “its quantity is fixed solely by the temperature of the bodies between which, in the last resort, the transport of caloric is effected”—­at least in all engines in which “the method of developing the motive power attains the perfection of which it is capable”; and this is, almost textually, one of the enunciations of the principle at the present day.  Carnot perceived very clearly the great fact that, to produce work by heat, it is necessary to have at one’s disposal a fall of temperature.  On this point he expresses himself with perfect clearness:  “The motive power of a fall of water depends on its height and on the quantity of liquid; the motive power of heat depends also on the quantity of caloric employed, and on what might be called—­in fact, what we shall call—­the height of fall, that is to say, the difference in temperature of the bodies between which the exchange of caloric takes place.”

Starting with this idea, he endeavours to demonstrate, by associating two engines capable of working in a reversible cycle, that the principle is founded on the impossibility of perpetual motion.

His memoir, now celebrated, did not produce any great sensation, and it had almost fallen into deep oblivion, which, in consequence of the discovery of the principle of equivalence, might have seemed perfectly justified.  Written, in fact, on the hypothesis of the indestructibility of caloric, it was to be expected that this memoir should be condemned in the name of the new doctrine, that is, of the principle recently brought to light.

It was really making a new discovery to establish that Carnot’s fundamental idea survived the destruction of the hypothesis on the nature of heat, on which he seemed to rely.  As he no doubt himself perceived, his idea was quite independent of this hypothesis, since, as we have seen, he was led to surmise that heat could disappear; but his demonstrations needed to be recast and, in some points, modified.