Methods of Computing the Orbit of a Comet or Planet: Appendix to the Third Volume of the Translation of the Mécanique Céleste.

[4], [761]-910, [107] pp. Cloth-backed marbled boards, 4to (28.4x22 cm/11¼x8¾ in.), paper spine label. Corners of boards slightly worn, date '1834' written on title page. Else Very Good. Bowditch's celebrated translation of Vols. I-IV of Laplace's Mécanique céleste (1st French ed., 5 Vols., 1799-1825) was published in four volumes (1829-1832-1834-1839). 'There are two early English translations of Book I and Books I and II respectively . . . Both were entirely superseded by the splendid work of Nathaniel Bowditch, Mécanique céleste by the Marquis de La Place. Translated, with a Commentary, 4 vols. (Boston, 1829-1839). Bowditch's commentary in the footnotes is an indispensable vade mecum for the study of Laplace, explaining and filling out the demonstrations, and containing a great body of historical as well as mathematical and astronomical elucidation. Bowditch did not translate Volume V of Mécanique celeste' (D.S.B. XV: 388). 'By 1818 Bowditch had completed his translation of the first four volumes of the Mécanique celeste. His purpose was threefold: to supply steps omitted from the original text; to incorporate later results into the translation; and to give credits omitted by Laplace. There is no evidence that Laplace ever responded to any communication from Bowditch, a fact sometimes ascribed to the third purpose. The four volumes appeared in 1829, 1832, 1834, and 1839, the last posthumously [Bowditch died March 16, 1838]. The delay in publication was undoubtedly due in part to financial problems. Bowditch, who would not have people subsidize, out of regard for him or other irrelevant reasons, a book they could not read, printed the work at his own expense. It is also most likely that he continued to work over the volumes between 1818 and their appearance, particularly to bring the subject matter up to date . . . Probably the only person who aided Bowditch was Benjamin Peirce, who read over part of the text for errors. Printed in a small edition, the work was perhaps more widely admired than read, simply serving to confirm the translator's already high reputation. Nevertheless, outside of France, particularly in English-speaking countries, Bowditch's edition, rather than the original, was often the means of learning about the mechanics of the heavens' (D.S.B. II: 368). 'Bowditch made the translation between 1815 and 1817. He held off publishing it in the expectation that Laplace intended to issue a revised edition of Vol. 1 in order to incorporate the material from the supplement to vol. 3 [offered here], which developed an improvement Poisson had made in the proof of the invariability of planetary mean motions by taking account of the square of the perturbing masses. Bowditch expected that Laplace would also revise Book III, vol. 2, in order to remedy certain defects in the calculation of the action of spheroids pointed out by James Ivory' (Gillispie, Pierre-Simon Laplace, p. 283). Houzeau & Lancaster 11976. Bowditch wanted to 'point out some of the important improvements made by Gauss, Olbers, and others, in the calculation of the orbit of a planet or comet, moving in ellipses, parabola or hyperbola' (Introduction).…