SKETCH OF RUDOLF CLAUSIUS. 119 



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 puhlished in 1864. The properties of 

 the potential function, while they had been neglected for a con- 

 siderable 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 sim- 

 plifications 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 de- 

 veloped 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 legiti- 

 mate fame. His name is pre-eminently attached to the great prob- 

 lem 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 Car- 

 not 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 



