Judged by a modern code the gravest defect of Laplace’s great work is rather of a moral than of a mathematical nature.  Lagrange and he advanced together in their study of the mechanics of the heavens, at one time perhaps along parallel lines, while at other times they pursued the same problem by almost identical methods.  Sometimes the important result was first reached by Lagrange, sometimes it was Laplace who had the good fortune to make the discovery.  It would doubtless be a difficult matter to draw the line which should exactly separate the contributions to astronomy made by one of these illustrious mathematicians, and the contributions made by the other.  But in his great work Laplace in the loftiest manner disdained to accord more than the very barest recognition to Lagrange, or to any of the other mathematicians, Newton alone excepted, who had advanced our knowledge of the mechanism of the heavens.  It would be quite impossible for a student who confined his reading to the “Mecanique Celeste” to gather from any indications that it contains whether the discoveries about which he was reading had been really made by Laplace himself or whether they had not been made by Lagrange, or by Euler, or by Clairaut.  With our present standard of morality in such matters, any scientific man who now brought forth a work in which he presumed to ignore in this wholesale fashion the contributions of others to the subject on which he was writing, would be justly censured and bitter controversies would undoubtedly arise.  Perhaps we ought not to judge Laplace by the standard of our own time, and in any case I do not doubt that Laplace might have made a plausible defence.  It is well known that when two investigators are working at the same subjects, and constantly publishing their results, it sometimes becomes difficult for each investigator himself to distinguish exactly between what he has accomplished and that which must be credited to his rival.  Laplace may probably have said to himself that he was going to devote his energies to a great work on the interpretation of Nature, that it would take all his time and all his faculties, and all the resources of knowledge that he could command, to deal justly with the mighty problems before him.  He would not allow himself to be distracted by any side issue.  He could not tolerate that pages should be wasted in merely discussing to whom we owe each formula, and to whom each deduction from such formula is due.  He would rather endeavour to produce as complete a picture as he possibly could of the celestial mechanics, and whether it were by means of his mathematics alone, or whether the discoveries of others may have contributed in any degree to the result, is a matter so infinitesimally insignificant in comparison with the grandeur of his subject that he would altogether neglect it.  “If Lagrange should think,” Laplace might say, “that his discoveries had been unduly appropriated, the proper course would be for him to do exactly what I