In 1750 Clalrsut gained the prize of the Petersburg Academy for his paper on the "lheory of the Moon.' It is more essential for us here to state the position which be occupies among the successors of Newton, than to enter into details which are better suited to other articles. Newton had left one prominent point of the lunar theory altogether unesplalued by his theory of gravitation, namely, the motion of the lunar apogee, of which, though able to assign a sufficient reason for the phenomenon of progression, ho was not able to deduce more than half the quantity of the phenomenon. Clairaut at first concluded that the law of gravitation N'1111 Incompletely expressed; but further consideration, and mote extensive application of analysis, showed that the whole motion was a necessary consequence of the Newtonian supposition of mutual attraction. In two points of view, therefore, as the first who applied what is now called the modern analysis to the problem of the lunar motion, and as the first who added an unexplained phenomenon to the theory which Newton had left, Clairaut stands io a conspicuous position.
Clairaut was the first who applied the Newtonian theory to the motion of comets, in reference to the perturbatiou of their motions by the attraction of the Okuda. In 1757 astronomers began to expect the fultihneut of Halley's prediction relative to the comet (whose appearance in 1S35 again excited much public curiosity). Lalonde proposed to Claireut to undertake the actual computation of the quantity of Jupiter's action on the comet during a revolution, and offered hie assistance In the drudgery of the work. For the manner in which this enormous labour was executed the reader may consult the article ' Halley 's% Comet,' in the ' Compauiou to the Almanac for 1835.' The result was that Clairaut's prediction came very near the truth; the return of the comet was at first placed iu November 175S; in that month Clairaut predicted that it would arrive at its nearest point to the sun about April 13, 1759, stating that lie might possibly be wrong by a month. The observed perihelion of the comet was on the 13th of March. The error would have been considerably less if the existence of Uranus, and a more correct value of the mass of Saturn, had been known.
The figure of the earth, the theory of the moon, and lialley's comet, are the three prominent points on which the fame of Clairaut rests. We might mention his work on ' Geometry,' drawn up, it is said, for the use of Madame du Chastellet ; his' Elements of Algebra,' remark able at the time for the abandonment of the dogmatical form in which it was customary to write elementary works; and many papers in the ' Memoirs of the Academy,' contaiuing several remarkable discoveries in pure mathematics. But we shall palm on to some uotico of his career in connection with that of D'Alembert. These two great men were rivals in their scientific labours, and though their disputes never passed the bounds of courtesy, the life of each, with respect to the other, was either armed truce or open war. The characters of the two were essentially opposite : Clairaut was a man of the world, of high polish, and who took great care never to offend the self-love of any one; D'Alembert was blunt and rude, though essentially well meaning and kind; if we may use such a colloquial phrase, he stood no nonsense ;"j'asuie mieux titre incivil qu'ennuy6' was his avowed maxim. Clairaut was always in the world, desirous to shine, and to
unite the man of fashion with the philosopher, of all which D'Alembert was the reverse. The attacks usually came from the latter, confined entirely to the writings of his opponent; and he was frequently right, being a thinker of a more safe and cautious order than Clairaut, who was more than once too hasty. For instance, when Clairaut took the whole revolution of Haller° comet, or more than fifty years, as the unit of which the error committed by him should be considered as a fraction, D'Alembert asserted that the magnitude of the latter should be compared, in the estimation of precision, with the difference between two successive revolutions, or about a year and a balf. Later analysts, and Laplace in particular, have considered that D'Alembert was right. The preceding comparison is drawn from Bossut (' Hist. des Math.'), who was the personal friend and the decided eulogist of both. Ile adds that the polished character of Clairaut procured him an existence and a consideration in the great world which talent alone would not have sufficed to gain ; and more than insinuates that dissipation destroyed his constitution. However this may be, Clairaut died at Paris, May 17, 1765, at the age of 52. lIe was never married : his father (who aurvived him a short time) had a very numerous family, of whom only one daughter survived.
(See the Liege in the Memoirs of the Academy ; the Life by Lacroix In the Biog. Univ.; and the work of Boasut above cited.) The works of Clairaut, independently of Memoirs preaented to the Academy, are :-1. 'Recherchea sur los Courbee It double Courbure,' Paris, 1731. 2. 'Ehlusens do Geom6trie,' ;Paris, 1741; and various editions up to 1765. 3. La Figure de la Terre d6tormin6e,' &c. (' Account of the Lapland Measure, by Maupertuis, Clairaut; &c.); Paris, 1738; in Latin, by Zeller ; Leipzig, 1742. 4, La Th6orio do Is Figure de la Terre,' Paris, 1743; again in 1808. 5. Elements d'Algare,' Paris, 1740; again iu 1760 (' tres catim6e,' Lacroix); again in 1797 and 1801 (marked sixth edition), by Clumsier, with a Preliminary Treatise on Arithmetic. 6. Th6urie do In Luoo,' St. Petersburg, 1752 ; (prize essay) second edition, 1765. 7. Tables de la Lune, Paris, 1754; republished with (6) in 1705. 8. Theorio du Motive:neut. des Cometes; Park, 1760; the account of the great process relative to Ilalley's comet. D'Alembert wrote against this iu the 'Journ. Eticycl.; February 1761 ; Clairaut replied in the Joum. des Say.; June 1761. 9. Recherches cur la Comets; &c., St. Petersburg, 1762 (Supplement to 8). 10.
Explication des I'rincipaux PlAnoinimes, &c., compiled by Madame du Chastellet from Clairaut's Instructions, and printed at the end of her translation of Newton, Paris, 1759. (Cuaszetsicr, MADAME DU.]