# Popular Science Monthly/Volume 35/May 1889/Sketch of Rudolf Clausius

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RUDOLF J. E. CLAUSIUS.
* SKETCH OF RUDOLF CLAUSIUS.
THE name of Prof. Clausius—"one of the most brilliant lights of the nineteenth century," as he is called by one of the Vice-Presidents of the British Association—is conspicuously associated, along with those of Rankine and Prof. William Thomson, in the development of the science of thermodynamics, or the demonstration of the mechanical theory of heat; and to him is credited the first placing of the kinetic theory of gases on a secure scientific basis. England and France mourned almost equally with Germany in his death—England, because of his association with the great British ​students of the nature of heat; and France, because he completed a work begun by her own Sadi Carnot, and because of a sentimental affection to which she had already given a unique expression.
Rudolf Julius Emanuel Clausius was born in Cöslin, Pomerania, January 12, 1823, and died in Bonn, August 24, 1888. He began his course of studies at the gymnasium in Stettin, where he made such marked progress as to attract the attention of his teachers and secure for him an early transfer to the University of Berlin. Here he evinced a predominant taste for the mathematical branches. He afterward went to the University of Halle, and received its doctor's degree in 1848. He then won the position of a Privat Docent at the University of Berlin, and a few months afterward was appointed Instructor of Natural Philosophy in the School of Artillery. At about this time he began his contributions of scientific papers to Poggendorff's "Annalen," some of the earliest of which were selected for translation in the first volume of Taylor's "Scientific Memoirs." In 1857 he was appointed by the Swiss Federal Government Professor of Natural Philosophy in the Polytechnic School at Zurich. His career at this place was distinguished by continued activity in his favorite fields of research, besides which "he published some short papers on some purely mathematical questions, suggested, however, by physical problems, and some papers dealing with what is generally known as physical chemistry." He gave up his chair in Zurich in 1867 to go to a similar position in Wurzburg, whence two years afterward he removed to become Professor of Natural Philosophy in the University of Bonn. He became dean of this institution in 1874, and continued there till his death.
The memoirs published by Clausius are estimated to number more than a hundred. Seventy-seven are recorded on the lists of the Royal Society up to 1873. Among his earlier papers the most famous are those "On the Nature of those Constituents of the Atmosphere by which the Reflection of the Light within it is effected," and "On the Blue Color of the Sky, and on the Morning and the Evening Red," which were published while he was in his tutorship at Berlin. While at Zurich he published "The Influence of Pressure on the Freezing-Point"; "The Mechanical Equivalent of an Electric Discharge, and the Heating of the Conducting Wire which accompanies it"; "Electrical Conduction in Electrolytes"; and "The Effect of Temperature on Electric Conductivity." In 1866 he published an important paper "On the Determination of the Energy and Entropy of a Body," in which a very valuable and suggestive conception was set forth. The idea of entropy, by which term is designated the available energy of a system, or that which can be converted into mechanical work, which he first conceived in 1854, and which led him to some extremely general and bold ​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 ​the heat which, it employs. Waiving the too subtile question of the nature of heat, he devoted himself principally to fixing the conditions under which a maximum of work is yielded with a given quantity of heat. Guided by the purely philosophical idea of the equivalence of the work expended and the work produced, in perfect mechanics, he affirmed the analogous principle that the possible work is proportional to the quantity of heat employed and to certain functions of the temperatures of the vapor on coming in and going out. Carnot's annunciation of his theory was defective in that it took no notice of the fact that the hot body gives out more heat than the cold one receives from it, and that it regarded as equal the amount of heat received upon one isothermal side of a cycle and that emitted from the other side; a principle that may hold good for infinitely small cycles, but not for larger ones, in which a difference exists between the thermic quantities proportioned to the size of the cycle. This error and the true condition as pointed out by Clausius are defined by Prof. Rankine, who says, in his paper "On the Economy of Heat in Expansive Machines": "Carnot was the first to assert the law that the ratio of the maximum mechanical effect to the whole heat expended in an expansive machine is a function solely of the two temperatures at which the heat is respectively received and emitted, and is independent of the nature of the working substance. But his investigations, not being based on the principle of the dynamic convertibility of heat, involve the fallacy that power can be produced out of nothing. The merit of combining Carnot's law, as it is termed, with that of the convertibility of heat and power, belongs to Mr. Clausius and Prof. William Thomson; and, in the shape in which they have brought it, it may be stated thus: The maximum proportion of heat converted into expansive power by any machine is a function solely of the temperatures at which heat is received and emitted by the working substance, which function for each pair of temperatures is the same for all substances in nature." The law as thus modified and newly expressed might, as M. Langlois remarks, be designated as the equation of Clausius. But Clausius himself, acknowledging the influence which the Frenchman's ideas had exercised upon him, called it the theorem of Carnot. The second volume of the "Mechanical Theory of Heat" is almost wholly devoted to applications to electrical phenomena.
The reviewer in "Nature" of the English translation of this work says that the method of treatment pursued in it left hardly anything to be desired, "even from the point of view of a student previously ignorant of the subject. The reader is nowhere perplexed by uncouth symbols or analytical operations beyond those which are familiar to all acquainted with the principles of the differential and integral calculus. At the same time, . . . the reader is ​never allowed to lose sight of the essential meaning of the symbols employed. . . . Any one wishing to gain a general acquaintance, thorough as far as it goes, with the subject, can scarcely do so with the expenditure of less time and labor than are required for the perusal of this book. As a mathematical study the book may replace some of the luxuriant growths of modern geometry and analysis with great advantage to the brains of the student."
In his later years Clausius was interested principally in the study of the questions raised by dynamo-electric machines. He published a theory of dynamo-motors in "La Lumière électrique," in 1884, in which he sought to fix more general equations, resting on more solid theories than those in use; but, notwithstanding his memoir is marked by his peculiar qualities, the theories have not been accepted, and have only been partly, if at all, confirmed by late researches. Yet it is to him that we owe a brilliant and clear exposition, and one of the first that was made, of certain phenomena of self-induction.
The Franco-German War occurred while Prof. Clausius was at Bonn. Although he was not liable to draft in the general mobilization, he was engaged in the ambulance service, and diligently interested himself in the care of the wounded. After the war was over, the German Government decorated him with the order of the Iron Cross, and the French with that of the Legion of Honor. The reason of the French awarding such a distinction upon an eminent German at such a time, when resentments still lively enough were at their height, is most probably to be found in the fact that he did not observe distinctions of nationality in his attentions. The incident affords a striking illustration of the effect of scientific studies in widening the range of thought and sympathy.
Prof. Clausius is described by M. Langlois as having been a teacher of remarkable clearness and simplicity in his explanations. His instruction was marked by a particular care to keep always within the limits of true physical principles. While he was remarkably versed in mathematical methods, he always kept the physical notations in the minds of his readers, and never allowed himself to be carried by his analyses into the regions of too vague conceptions. Mr. G. W. de Tunzelmann agrees with this conclusion in his obituary sketch in "Nature," saying that Clausius formed a center of attraction at Bonn, "not only as a great investigator, but as a teacher of almost unrivaled ability. The secret of his powers as a teacher may easily be guessed from the study of his published papers and treatises." The greater part of his work, the writer adds, had the additional advantage of being effected by the aid of comparatively simple analysis.
Prof. Clausius was elected a foreign member of the Royal Society in 1868, and received its Copley medal in 1879.