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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.