CLAIRAUT. 



669 



riraut. In the year I 1 /*?, Clairaut shared the honour, along 

 -r""' with Euler and d' Alembert, of having solved the problem 

 of three bodies. In the three solutions of this great 

 problem which had been separately obtained, without 

 any communication, by these illustrious mathematicians, 

 it turned out, to the astonishment of them all, that the 

 calculus gave only half the observed motion of the moon's 

 apogee. Clairaut proposed to make a slight alteration 

 upon the law of gravity, in order to produce a corre- 

 spondence between the theory and the observations; but 

 thi; idea was warmly attacked by Buffon, and Clairaut 

 at last discovered that he and his learned associates had 

 neglected some small quantities in the series, and that the 

 result thus corrected was perfectly consonant to the 

 theory of gravitation. He gained the prize for this sub- 

 ject, which was given in 1751 by the Academy of St 

 Petersburgh, and in 1754 he published his Lunar Tables, 

 which were founded upon his own solution of the pro- 

 blem of three bodies, and which greatly exceeded in ac- 

 curacy those that had been formerly in use. A new and 

 correct edition of this work was published in 1765. 



The application of the problem of three bodies to the 

 theory of the comet of 1759, formed the most important 

 epoch in the life of Clairaut ; but as we have already dis- 

 cussed this subject at sufficient length both in the article 

 ASTRONOMY and in the life of D'ALEMBERT, we can- 

 not resume it in this place. 



Next to the lunar theory, the most important subject 

 which then exercised the genius of mathematicians, was 

 the improvement of the achromatic telescope. This sub- 

 ject occupied much of Clairaut's attention, and he pub- 

 lished the result of 'his researches in three memoirs, which 

 appeared in 1756, 1757, and 1762, and which contain a 

 mult complete investigation of the various forms in which 

 chromatic object glasses may be constructed. 'In the 

 course of this enquiry, Clairaut discovered that the co- 

 loured space* in equal spectra produced by substances of 

 different dispersive powers, were not proportional, and 

 therefore that a coinfi/fte correction of colour could not 

 be effected by two kii Js of glass. This beautiful dis- 

 covery of a secondary spectrum was made about the same 

 time by Boscovich, without any knowledge of what 

 Clairaut had done; and this able mathematician has shewn 

 how a more complete correction of colour may be ob- 

 tained by employing three different substances in the 

 construction of the object-glass. This curious subject, 

 o intimately connected with the perfection of the achro- 

 matic ttlcscope, has been recently investigated by 

 Dr Brewster, who has determined the relative propor- 

 tions of the coloured spaces for a great variety of trans- 

 parent bodies. He has found that the uncorrected co- 

 lour generally increases with the difference between the 

 dispersive powers of the two substances by which the 

 opposite dispersions are produced ; that sulphuric acid 

 exceeds all transparent substances in its action on the 

 green rays, while oil of cassia exerts the least action upon 

 them of any known substance, and that there is a ter- 

 tiary spectrum which may be formed even when the 

 opposite dispersions are produced by two prisms or lenses 

 of the same substances. The application of these results 

 to the improvement of the achromatic telescope, will be 

 pointed out in the article OI-TICS.* 



In order to render his investigations of real utility to 

 the practical optician, Clairaut began to reduce all his 

 results into tables, and to compute the thickness and 

 radii of the different lenses which were requisite to form 

 an achromatic object-glass; but he unfortunately did not 



Clairaiit. 



live to finish this work. Although he had laid down a 



rule never to sup in Paris, yet he was on one particular ""Y" 



occasion induced by some of his friends to transgress it. 



So fatal was this rash indulgence, that he scarcely lived 



to repent it. He was attacked with indigestion and 



rheumatism, which baffled the skill of his physicians, and 



carried him off on the 17th of May 1765, in the 52J year 



of his age. 



The following is a list of the works which he publish- List of 

 ed separately. oairaut's 



Recherches sur les courbes a double courbure. Paris, st l'" a t 

 1730, in 4to. 



Elemens de Geometric. Paris, 1741, in 8vo. 



Elem6ns d'Algebre. Paris, 1746, in 8vo. 



Theorie de la Figure de la Terre. Paris, 1743, in 8vo. 



Tables de la Lune. Paris, 1745, in 8vo. 



The Memoirs which he published in the Memoires de LUt of hi 

 I' Academic are the following : Memoirs. 



Observations sur un instrument par le moyen duquel 

 on peut prendre les Angles, et faire les calculs arithme- 

 tiques, 172T. Hist. 142. 



Nouvelle manierede trouver les formules des centres de 

 gravite, 1731, 159. 



Obs. sur les courbes que 1'on forme en coupant une 

 surface courbe quelconque par un plan donne de position, 

 1731, p. 483. 



Des epicyclo'ides sphcriques, 1732, p. 289. 



Maniere de trouver des courbes Algebriques et recti- 

 fiables sur la surface d'un cone, 1732, p. 385. 



Solution d'un probleme de Geometric, 1732, p. 435. 



Obs. sur quelques questions de maximis et minimi's, 

 1733, p. 186. 



Determination Geometrique de la perpendiculaire, a 

 la meridienne, tracee par M. Cassini, avec plusieurs mc- 

 thodes d'en tirer la grandeur et la figure de la Terre, 

 1733, p . 406, H. 59. 



Solution de plusieurs problcmes, ou il s'agit detrouver 

 des courbes dont la propriete consiste dans une certaine 

 relation entre leurs branches, exprimee par une'equation 

 donnee, 1734, p. 196. 



Remarques sur la methode de M. Fontaine, pour r&- 

 soudre le probleme ou il s'agit de trouver une courbe qui 

 touche les cotes d'un angie constant dont le sommet 

 glisse dans une courbe donntv, 1734, p. 531. 



Obs. sur le nouvelle methode de M. Cassini pour 

 connoitre la figure de la Terre, 1735, p. 117. H. 51. 



Examen des differentes oscillations qu'un corps sus- 

 pendu par un fil, peut faire lorsqu'on lui donne une im- 

 pulsion quelconque, 1735, p. 281, H. 92. 



Examen de la response de M. Fontaine a mes objec- 

 tions, sur la methode pour trouver une courbe qui 

 touche continuellement les c6tcs d'un angle constant , 

 dont le sommet glisse dans une courbe donnee, 1735, p. 

 577. 



Solution de quelques problcmes de dynamiqueSi 1736, 

 p. 1. H. 105. 



Obs. sur la mesure de la Terre par plusieurs arcs de 

 meridien pris a differentes latitudes, 1736, p. 111. 



De 1'aberration apparente des etoiles causee par le 

 mouvement progressif de la lumiere, 1737. p. 205. H. 

 76. 



Des centres d'oscillations dans des milieux resistsns, 

 1738, p. 159. 



Suite d'un memoire donnee en 1733 qui a pour titre : 

 Determination GcoiHetrique de la pcrpenditulairc a la 

 Meridienne, 1739, p. 83. 



1 See Brewitcr' Tnatue on fftv PUlotopkical Initrumentr, *ith Experiments an Light and Colour, p. 353 4CO. Edin. 1813. 



