# Catalogue Entry: OTHE00129

## Chapter XIII

^{[1]} *Systéme du Monde*, p. 336.

^{[2]} *Ibid.,* p. 340.

^{[3]} Professor Playfair adds, that this was "the more remarkable, as the interests of navigation were deeply involved in the question of the lunar theory, so that no motive which a regard to reputation or to interest could create was wanting to engage the mathematicians of England in the inquiry." — *Edinburgh Review*, vol. xi., p. 280. Jan. 1808.

^{[4]} *History of Physical Astronomy*, &c., p. 108. London, 1852. Mr. Grant also remarks, "that with the exception of Maclaurin and Thomas Simpson, hardly any individual of these islands deserves even to be mentioned in connexion with the history of physical astronomy during that period ;" and that, at the beginning of the present century, "there was hardly an individual in this country who possessed an intimate acquaintance with the methods of investigation which had conducted the foreign mathematicians to so many sublime results."

^{[5]}

Referring our readers to the statement at the end of Chapter IV., as showing the probable cause of the success of the French mathematicians, and of the inglorious failure of our own, we beg their attention to the following confirmation of our views by one of the wisest and most eminent of our Scottish mathematicians. In a review of Laplace's *Systéme du Monde*, Professor Playfair makes the following observations.

"The literary institution which has most completely produced its effect of any in modern times, and that has been most successful in promoting the interests of science, is that of the Royal Academy of Sciences of Paris, where *small pensions and great honours,* bestowed on a few men for devoting themselves exclusively to works of invention and discovery, have been the means of advancing the mathematical sciences in France to a state of unexampled prosperity.

"In England, *where such an institution as that just mentioned was wanting,* and where the public is perpetually prepared, with the question *cui bono,* to repress what seems the luxury of science, the same progress has not been made ; and our mercantile prejudices have so far defeated our own purpose, that if the matter had been left to us, the theory of the moon's motion would still have been extremely imperfect, and the great nautical problem of finding the longitude could have received nothing like an accurate solution." — *Edinburgh Review*, vol. xv. p. 39. Jan. 1810.

^{[6]} See the Article Mathematics in the *Edinburgh Encyclopædia*, vol. xiii. p. 380, where Sir John Herschel pronounces a beautiful eulogium on the conduct of Euler.

^{[7]} M. Leverrier has recently shewn that the earth's eccentricity will diminish during the period of *twenty-four thousand years!*

^{[8]} *History of Physical Astronomy*, pp. 63, 64.

^{[9]} *Edinburgh Review,* vol. xi. p. 261.

^{[10]} The Academy of Sciences proposed the moon's acceleration as the subject of their prize for 1770. Euler gained it, but came to the conclusion that it was not produced by the force of gravity. The same subject was again proposed in 1772, and the prize was divided between Euler and Lagrange. Euler ascribed the acceleration to a resisting medium, and Lagrange evaded the difficulty. The prize was again offered in 1774, and was gained by Lagrange, and he now doubted the existence of the inequality. It was under these circumstances that Laplace took up the ect, and obtained the results which we have mentioned.

^{[11]} *Mécanique Céleste*, tom. ii., liv. iii., chap. v.; and *Système du Monde*, liv. iv., chap. vii.

^{[12]} *Mécanique Céleste*, part i., liv. iv., chap. i., tom. ii., p. 171; and *Système du Monde*, liv. iv., chap. x., p. 248.

^{[13]} See *Mécanique Céleste*, part i., liv. iv., chap. ii., tom. ii., p. 204; and *Système du Monde,* liv. iv., chap. xi., p. 265.

^{[14]} *Système du Monde*, liv. iv., chap. xiii., pp. 276, 277. See also *Mécanique Céleste*, part i., liv. v., chap. i., tom. ii., p. 347.

^{[15]} *Mécanique Céleste*, tom. ii., pp. 354, 355.

^{[16]} Laplace has shewn that the stability of the equilibrium of the rings requires that they be irregular solids, unequally wide in different parts of their circumference, so that their centres of gravity do not coincide with their centres of figure. — See *Mécanique Céleste,* part i., liv. iii., chap. vi., tom. ii., p. 155; *Système du Monde*, liv. iv., chap. viii., p. 242.

^{[17]} *Considérations sur l'ensemble du Système des petites Planètes situées entre Mars et Jupiter par* M. U. J. Leverrier. Lu 28 Nov. 1853. *Comptes Rendus*, &c., tom. xxxvii. pp. 793-798.

^{[18]} M. Leverrier takes occasion to remark, "that we might perhaps find some systematic difference between the mean direction of the ascending nodes of the planets near the Sun, and that of the ascending nodes of the more distant planets, and that we may thus conjecture that these planets belong in reality to three distinct groups." — *Comptes Rendus*, &c., tom. xxxvii. p. 795.

^{[19]} Sir John Herschel has ventured to say, "that the orbit of Biela's comet so nearly intersects that of the Earth, that an actual collision is not impossible, and indeed (supposing neither orbit variable) must, *in all likelihood,* happen in the lapse of some millions of years." — *Outlines of Astronomy,* § 585.

^{[20]} This comet ought to have appeared *thirteen* times since 1770, and, as it has not been since seen, it must be lost. Burckhardt supposed that it might have become a satellite to Jupiter, from its aphelion being near that planet!

^{[21]} A table of the elements of their orbits is given by Sir John Herschel in his *Outlines of Astronomy*, § 843.

^{[22]} M. Madler has adduced an instance, (p Ophiuchi,) where he regards the deviations from an elliptic orbit too considerable to be accounted for by an error of observation ; but we cannot view a single fact of this kind as affecting the generality of the law of gravity.

^{[23]} M. Prévost, who used Mayer's proper motions, made the right ascension only 230°.

^{[24]} *Etudes d'Astronomie Stellaire,* of which we have given a copious abstract in the *North British Review*, vol. viii. pp. 523-534.