the first statement of the second law of thermodynamics, that as water flows towards the sea-level, but never backwards to its source, so heat can not flow from a colder to a warmer body. But Carnot, like every one else in his day, still thought that heat (calorique), like the water in the waterfall, was an indestructible, material substance and that the quantity of heat given out by the exhaust chamber of the engine is exactly the same as that taken in at the boiler. Although his posthumous papers indicate that he corrected this view before his death, he assumed that if we could find some way to consume the heat of a given body without the necessity of conveying it to a colder body, we might create motor power without fuel or obtain work from nothing, which would be perpetual motion. As late as 1865 an authority like Rankine[1] still believed that heat is of material essence, and when in 1842-7 the labors of Robert Mayer and of Joule established the mechanical equivalent of heat and Helmholtz[2] in 1847 showed that the first law of thermodynamics, the principle of conservation of energy, is applicable to all physical phenomena, it was found difficult to reconcile this principle with Carnot's tacit assumption that heat is unchangeable and indestructible. Even a physicist like William Thomson[3] (the late Lord Kelvin) confessed himself baffled by the problem in 1849 and turned aside to establish his "absolute scale of temperature," without which further progress in the science would have been impossible; but his brother James Thomson, one of the earlier pioneers of physical chemistry, was able, by an implicit denial of Carnot's assumption, to predict and prove that the freezing point of water would be lowered by pressure (1849).[4] The difficulty was, at length, settled in 1850 by Clausius, whose memoir "On the motor power of heat," "marks," says Gibbs, "an epoch in the history of physics," for before its publication, "truth and error were in a confusing state of mixture,"[5] and "wrong answers were confidently urged by the highest authorities."
To Clausius we owe the doctrine, foreshadowed by Bacon, that the heat of a body is the rapid movement, or vis viva, of its molecules; the kinetic theory of gases and the molecular theory of electrolysis, since extended by Arrhenius into the doctrine of electrolytic or ionic dissociation. Clausius showed that part of the heat in a Carnot cycle is converted into available mechanical energy and consumed as work, while the rest of the heat can not be so utilized, because it exists in a completely diffused state. The perpetual motion which might be obtained from utilizing the heat of surrounding objects is impossible because such heat being completely diffused is, in Lord Kelvin's phrase, un-
