conclusions concerning the universe, was developed and extended in his address before the Congress of German Physicians and Naturalists at Frankfort in 1867, eliciting the principle that the entropy of the universe tends toward a maximum.
The principal works of Clausius, on which his chief title to fame must rest, are those on "The Potential Function and the Potential" (1857), and on "The Mechanical Theory of Heat," the first volume of which was published in 1864. The properties of the potential function, while they had been neglected for a considerable time in France, had been put to their best use by all the philosophers of Germany and England who had treated of the natural forces of attraction and repulsion—particularly by such students as Gauss, Kirchhoff, and Thomson. In the preface to the second edition of his work on this subject. Prof. Clausius made the modest declaration that it was not his aim to institute new researches on the fundamental properties of the function, but simply to expound an existing theory. But it is evident through the treatise, as M. P. Langlois has shown, that while he takes up the ideas of Green and Gauss, he makes them his own by the simplifications which he has brought to them on one side and the extension which he has on the other hand given to some parts of the research. The work is distinguished beyond all other things, M. Langlois adds, by the strength of the analytic faculty displayed in it, which is carried to its ultimate limit. "Not contented with having established a formula, Clausius knew how to make it of remarkable utility. Two fundamental and particular ideas are developed in the treatise. First, the author fixes with precision the difference between the potential function and the potential, and shows the exact significance that should be given to the two, which are so much used in mathematical physics, and especially now in questions of electric dynamics; and he elucidates alike the idea of the potential of a mass upon itself and restores to the potential its true value, which had been erroneously doubled. . . . But it is not to this work that Clausius is indebted for his legitimate fame. His name is pre-eminently attached to the great problem of thermodynamics; and it is in his studies in this branch that his influence has made itself predominantly felt."
Thermodynamics may be said to date from 1824, when Sadi Carnot published his "Reflections on the Motor Power of Fire and on Machines suitable for developing it." The question of the nature of heat had already occupied Rumford and Davy, to say nothing of Bacon and Stahl; and being a dominating one in the problems into which it entered, arrested all physicists, who had only one step more to make to create thermodynamics. Carnot introduced the idea of mechanical work into the study, and sought to fix the relation that exists between the work of a thermic machine and