been able to add comparatively little. The general part of the work was translated into German by Joh. Karl Burkhardt,
and appeared in Berlin, 1800–1802. Nathaniel Bowditch
brought out an edition in English, with an extensive commentary, in Boston, 1829–1839. The Mécanique Céleste is not easy reading. The difficulties lie, as a rule, not so much in the subject itself as in the want of verbal explanation. A complicated chain of reasoning receives often no explanation whatever. Biot, who assisted Laplace in revising the work for
the press, tells that he once asked Laplace some explanation of a passage in the book which had been written not long before, and that Laplace spent an hour endeavouring to recover the reasoning which had been carelessly suppressed with the remark, "Il est facile de voir." Notwithstanding the important researches in the work, which are due to Laplace himself, it naturally contains a great deal that is drawn from his predecessors. It is, in fact, the organised result of a century of patient toil. But Laplace frequently neglects to properly acknowledge the source from which he draws, and lets the reader infer that theorems and formulæ due to a predecessor are really his own.
We are told that when Laplace presented Napoleon with a copy of the Mécanique Céleste, the latter made the remark, "M. Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned its Creator." Laplace is said to have replied bluntly, "Je n'avais pas besoin de cette hypothèse-la." This assertion, taken literally, is impious, but may it not have been intended to convey a meaning somewhat different from its literal one? Newton was not able to explain by his law of gravitation all
questions arising in the mechanics of the heavens. Thus, being unable to show that the solar system was stable, and suspecting in fact that it was unstable, Newton expressed the
opinion that the special intervention, from time to time, of a powerful hand was necessary to preserve order. Now Laplace was able to prove by the law of gravitation that the solar system is stable, and in that sense may be said to have felt no necessity for reference to the Almighty.
We now proceed to researches which belong more properly to pure mathematics. Of these the most conspicuous are on the theory of probability. Laplace has done more towards
advancing this subject than any one other investigator. He published a series of papers, the main results of which were collected in his Théorie analytique des probabilités, 1812. The third edition (1820) consists of an introduction and two books. The introduction was published separately under the title, Essai philosophique sur les probabilités, and is an admirable and masterly exposition without the aid of analytical formulæ of the principles and applications of the science. The first book contains the theory of generating functions, which are applied, in the second book, to the theory of probability. Laplace gives in his work on probability his method of approximation to the values of definite integrals. The solution of linear differential equations was reduced by him to definite integrals. One of the most important parts of the work is the application of probability to the method of least squares, which is shown to give the most probable as well as the most convenient results.
The first printed statement of the principle of least squares
was made in 1806 by Legendre, without demonstration. Gauss