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The idea, then little noticed, had been revived about a century later by William Herapath, and again with some success by J. J. Waterston, of Bombay, about 1846; but it gained no distinct footing until taken in hand by Clausius in 1857 and by Clerk-Maxwell in 1859.

The efforts of Helmholtz, Clausius, and Lord Kelvin to introduce the principle of the conservation of energy into mechanics, were far from useless. These illustrious physicists succeeded in giving a more precise form to its numerous applications; and their attempts thus contributed, by reaction, to give a fresh impulse to mechanics, and allowed it to be linked to a more general order of facts.

The entire energy of a molecule of gas, for example, is not measured by its momentum, but by this plus its energy of vibration and rotation, due to the collisions already referred to. Clausius has even estimated the relative importance of these two quantities, showing that the translational motion of a molecule of gas accounts for only three-fifths of its kinetic energy.

Now, however, guided by the views which Clausius and Williamson have given us of the continuous interchange of partners between the compound molecules constituting chemical compounds in the gaseous state, we see in Deville's theory of dissociation a point of contact of the most transcendent interest between the chemical and physical lines of scientific progress.

No doubt the first idea of it arose, in the thought of Carnot, out of certain quantitative considerations on the yield of thermic machines. Unquestionably, too, the terms in which Clausius generalized it were mathematical, and a calculable magnitude, "entropy," was, in fact, the final conception to which he was led. Such precision is necessary for practical applications.

But what a splendid and useful building has been placed on this foundation by Clausius and Maxwell, and what a beautiful ornament we see on the top of it in the radiometer of Crookes, securely attached to it by the happy discovery of Tait and Dewar, that the length of the free path of the residual molecules of air in a good modern vacuum may amount to several inches!

The formula obtained, which is based on these hypotheses, agrees completely with the classic results of Clausius and of Lord Kelvin.

This is, in fact, all we have of the kinetic theory of gases up to the present time, and this has done for us, in the hands of Clausius and Maxwell, the great things which constitute our first step toward a molecular theory of matter.

In the case of gases, a molecular theory has been developed by Clausius and others, capable of mathematical treatment, and subjected to experimental investigation; and by this theory nearly every known mechanical property of gases has been explained on dynamical principles; so that the properties of individual gaseous molecules are in a fair way to become objects of scientific research.

Rankine's literary career commenced while he was in Edinburgh with the publication of a series of papers on the mechanical action of heat. His theory of the development of heat as one of the forces of thermo-dynamics was propounded simultaneously with that of Professor Clausius of Berlin, in 1849, and supplied the only link that was wanted to make the theory of the steam engine a perfect science.