Laplace’s personality seems to have been less attractive than that of Lagrange. He was vain of his reputation as a mathematician and not always generous to rival discoverers. To Lagrange, however, he was always friendly, and he was also kind in helping young mathematicians of promise. While he was perfectly honest and courageous in upholding his scientific and philosophical opinions, his politics bore an undoubted resemblance to those of the Vicar of Bray, and were professed by him with great success. He was appointed a member of the Commission for Weights and Measures, and afterwards of the Bureau des Longitudes, and was made professor at the École Normale when it was founded. When Napoleon became First Consul, Laplace asked for and obtained the post of Home Secretary, but—fortunately for science—was considered quite incompetent, and had to retire after six weeks (1799)[145]; as a compensation he was made a member of the newly created Senate. The third volume of the Mécanique Céleste, published in 1802, contained a dedication to the “Heroic Pacificator of Europe,” at whose hand he subsequently received various other distinctions, and by whom he was created a Count when the Empire was formed. On the restoration of the Bourbons in 1814 he tendered his services to them, and was subsequently made a Marquis. In 1816 he also received a very unusual honour for a mathematician (shared, however, by D’Alembert) by being elected one of the Forty “Immortals” of the Académie Française; this distinction he seems to have owed in great part to the literary excellence of the Système du Monde.
Notwithstanding these distractions he worked steadily at mathematics and astronomy, and even after the completion of the Mécanique Céleste wrote a supplement to it which was published after his death (1827).
His last words, “Ce que nous connaissons est peu de chose, ce que nous ignorons est immense,” coming as they did from one who had added so much to knowledge, shew his character in a pleasanter aspect than it sometimes presented during his career.
239. With the exception of Lagrange’s paper on libration, nearly all his and Laplace’s important contributions to astronomy were made when Clairaut’s and D’Alembert’s work was nearly finished, though Euler’s activity continued for nearly 20 years more. Lagrange, however, survived him by 30 years and Laplace by more than 40; and together they carried astronomical science to a far higher stage of development than their three predecessors.
240. To the lunar theory Lagrange contributed comparatively little except general methods, applicable to this as to other problems of astronomy; but Laplace devoted great attention to it. Of his special discoveries in the subject the most notable was his explanation of the secular acceleration of the moon’s mean motion (chapter X., [§ 201]), which had puzzled so many astronomers. Lagrange had attempted to explain it (1774), and had failed so completely that he was inclined to discredit the early observations on which the existence of the phenomenon was based. Laplace, after trying ordinary methods without success, attempted to explain it by supposing that gravitation was an effect not transmitted instantaneously, but that, like light, it took time to travel from the attracting body to the attracted one; but this also failed. Finally he traced it (1787) to an indirect planetary effect. For, as it happens, certain perturbations which the moon experiences owing to the action of the sun depend among other things on the eccentricity of the earth’s orbit; this is one of the elements ([§ 236]) which is being altered by the action of the planets, and has for many centuries been very slowly decreasing; the perturbation in question is therefore being very slightly altered, and the moon’s average rate of motion is in consequence very slowly increasing, or the length of the month decreasing. The whole effect is excessively minute, and only becomes perceptible in the course of a long time. Laplace’s calculation shewed that the moon would, in the course of a century, or in about 1,300 complete revolutions, gain about 10″ (more exactly 10″·2) owing to this cause, so that her place in the sky would differ by that amount from what it would be if this disturbing cause did not exist; in two centuries the angle gained would be 40″, in three centuries 90″, and so on. This may be otherwise expressed by saying that the length of the month diminishes by about one-thirtieth of a second in the course of a century. Moreover, as Laplace shewed ([§ 245]), the eccentricity of the earth’s orbit will not go on diminishing indefinitely, but after an immense period to be reckoned in thousands of years will begin to increase, and the moon’s motion will again become slower in consequence.
Laplace’s result agreed almost exactly with that indicated by observation; and thus the last known discrepancy of importance in the solar system between theory and observation appeared to be explained away; and by a curious coincidence this was effected just a hundred years after the publication of the Principia.
Many years afterwards, however, Laplace’s explanation was shewn to be far less complete than it appeared at the time (chapter XIII., [§ 287]).
The same investigation revealed to Laplace the existence of alterations of a similar character, and due to the same cause, of other elements in the moon’s orbit, which, though not previously noticed, were found to be indicated by ancient eclipse observations.
241. The third volume of the Mécanique Céleste contains a general treatment of the lunar theory, based on a method entirely different from any that had been employed before, and worked out in great detail. “My object,” says Laplace, “in this book is to exhibit in the one law of universal gravitation the source of all the inequalities of the motion of the moon, and then to employ this law as a means of discovery, to perfect the theory of this motion and to deduce from it several important elements in the system of the moon.” Laplace himself calculated no lunar tables, but the Viennese astronomer John Tobias Bürg (1766-1834) made considerable use of his formulae, together with an immense number of Greenwich observations, for the construction of lunar tables, which were sent to the Institute of France in 1801 (before the publication of Laplace’s complete lunar theory), and published in a slightly amended form in 1806. A few years later (1812) John Charles Burckhardt (1773-1825), a German who had settled in Paris and worked under Laplace and Lalande, produced a new set of tables based directly on the formulae of the Mécanique Céleste. These were generally accepted in lieu of Bürg’s, which had been in their turn an improvement on Mason’s and Mayer’s.
Later work on lunar theory may conveniently be regarded as belonging to a new period of astronomy (chapter XIII., [§ 286]).