Laplace’s most famous work is, of course, the “Mecanique Celeste,” in which he essayed a comprehensive attempt to carry out the principles which Newton had laid down, into much greater detail than Newton had found practicable.  The fact was that Newton had not only to construct the theory of gravitation, but he had to invent the mathematical tools, so to speak, by which his theory could be applied to the explanation of the movements of the heavenly bodies.  In the course of the century which had elapsed between the time of Newton and the time of Laplace, mathematics had been extensively developed.  In particular, that potent instrument called the infinitesimal calculus, which Newton had invented for the investigation of nature, had become so far perfected that Laplace, when he attempted to unravel the movements of the heavenly bodies, found himself provided with a calculus far more efficient than that which had been available to Newton.  The purely geometrical methods which Newton employed, though they are admirably adapted for demonstrating in a general way the tendencies of forces and for explaining the more obvious phenomena by which the movements of the heavenly bodies are disturbed, are yet quite inadequate for dealing with the more subtle effects of the Law of Gravitation.  The disturbances which one planet exercises upon the rest can only be fully ascertained by the aid of long calculation, and for these calculations analytical methods are required.

With an armament of mathematical methods which had been perfected since the days of Newton by the labours of two or three generations of consummate mathematical inventors, Laplace essayed in the “Mecanique Celeste” to unravel the mysteries of the heavens.  It will hardly be disputed that the book which he has produced is one of the most difficult books to understand that has ever been written.  In great part, of course, this difficulty arises from the very nature of the subject, and is so far unavoidable.  No one need attempt to read the “Mecanique Celeste” who has not been naturally endowed with considerable mathematical aptitude which he has cultivated by years of assiduous study.  The critic will also note that there are grave defects in Laplace’s method of treatment.  The style is often extremely obscure, and the author frequently leaves great gaps in his argument, to the sad discomfiture of his reader.  Nor does it mend matters to say, as Laplace often does say, that it is “easy to see” how one step follows from another.  Such inferences often present great difficulties even to excellent mathematicians.  Tradition indeed tells us that when Laplace had occasion to refer to his own book, it sometimes happened that an argument which he had dismissed with his usual formula, “Il est facile a voir,” cost the illustrious author himself an hour or two of hard thinking before he could recover the train of reasoning which had been omitted.  But there are certain parts of this great work which have always received the enthusiastic admiration of mathematicians.  Laplace has, in fact, created whole tracts of science, some of which have been subsequently developed with much advantage in the prosecution of the study of Nature.