by any of those brilliant discoveries in analysis, I had almost said of those sublime inspirations, which were so familiar to him.  Fortunately Euler appended to his memoir a supplement truly worthy of his genius.  Father Lozeran de Fiesc and the Count of Crequi were rewarded with the high honour of seeing their names inscribed beside that of the illustrious geometer, although it would be impossible in the present day to discern in their memoirs any kind of merit, not even that of politeness, for the courtier said rudely to the Academy:  “the question, which you have raised, interests only the curiosity of mankind.”

Among the competitors less favourably treated, we perceive one of the greatest writers whom France has produced; the author of the Henriade.  The memoir of Voltaire was, no doubt, far from solving the problem proposed; but it was at least distinguished by elegance, clearness, and precision of language; I shall add, by a severe style of argument; for if the author occasionally arrives at questionable results, it is only when he borrows false data from the chemistry and physics of the epoch,—­sciences which had just sprung into existence.  Moreover, the anti-Cartesian colour of some of the parts of the memoir of Voltaire was calculated to find little favour in a society, where Cartesianism, with its incomprehensible vortices, was everywhere held in high estimation.

We should have more difficulty in discovering the causes of the failure of a fourth competitor, Madame the Marchioness du Chatelet, for she also entered into the contest instituted by the Academy.  The work of Emilia was not only an elegant portrait of all the properties of heat, known then to physical inquirers, there were remarked moreover in it, different projects of experiments, among the rest one which Herschel has since developed, and from which he has derived one of the principal flowers of his brilliant scientific crown.

While such great names were occupied in discussing this question, physical inquirers of a less ambitious stamp laid experimentally the solid basis of a future mathematical theory of heat.  Some established, that the same quantity of caloric does not elevate by the same number of degrees equal weights of different substances, and thereby introduced into the science the important notion of capacity.  Others, by the aid of observations no less certain, proved that heat, applied at the extremity of a bar, is transmitted to the extreme parts with greater or less velocity or intensity, according to the nature of the substance of which the bar is composed; thus they suggested the original idea of conductibility.  The same epoch, if I were not precluded from entering into too minute details, would present to us interesting experiments.  We should find that it is not true that, at all degrees of the thermometer, the loss of heat of a body is proportional to the excess of its temperature above that of the medium in which it is plunged; but I have been desirous of showing you geometry penetrating, timidly at first, into questions of the propagation of heat, and depositing there the first germs of its fertile methods.