668 



C L A I R A U T. 



the age of nine years, hit attention was directed 

 to M. Guisoee's Treatise on the Application of Algebra 

 to Geometry. With the help which he received from 

 kit father, he speedily read this work, and, after study- 

 ing it a second and a third time by himself, he resolved 

 the greater number of the problem* hi a more-simple and 

 ingenious manner than the author hinrelf. Clairant now 

 began to experience the delight which spring* from the 

 successful exercise of genius, and he continued his studies 

 with an intensity of application, which, if not seasonably 

 checked, would have endangered his hraltb. At the age 

 of ten, he read the Marqui* de L'Hopital's Cnnic Sec- 

 tions, but he experienced considerable difficulty in ma- 

 king himself master of the subject. M. de Lisle, who 

 wa* visiting his father, happened to see ywung Clairaut 

 with this volume in his hands, and remarked, with a kind 

 of sarcastic severity, that he could understand this book 

 only by its title and its cover. The young geometer was 

 affronted with the remark, though he felt it to a cer- 

 tain degree true, and he gave himself no rest till he was 

 completely master of the subject. He next studied the 

 analysis of infinites of the tame author, and initiated him- 

 self into the differential and integral calculus. 



The reputation of Clairaut, which was hitherto confi- 

 ned to his own friends, now began to extend with rapidi- 

 ty. The celebrated M. Nericaut Destouches having just 

 arrived from England with his lady, who was about to be 

 confined, took lodgings immediately below the house of 

 Clairaut, and sent up a request to the family to make as 

 little noise as possible, both on account of his wife's in- 

 disposition, and as he was himself employed in writing 

 his fine tragedy of the Philotophe Marie'. This request 

 was so scrupulously attended to, that M. Destouches 

 went in person to thank M. Clairaut for his kindness. 

 He was surprised to find, that he had been living below 

 a family of 1 1 children ; and he was so much pleased with 

 the young mathematician, that he introduced him to the 

 Abbe Bignon, and to other celebrated members of the 

 Academy. 



About this time, M. Clairaut removed to another 

 boose, in which there was a small room, which was al- 

 lotted to the use of our author and his younger brother, 

 of whom we have already spoken. This room was so 

 situated, that they could go in and come out without 

 being perceived, and the two brothers did not fail to 

 abuse this advantage. They procured a flint, by means 

 of which they might light their candle, and when the fa- 

 mily imagined them to be buried in sleep, they were 

 eagerly engaged in the study of geometry. Alexis was 

 now secretly occupied with a mtmoir on four curves of 

 the third order, which he had newly discovered, and by 

 means of which he could find any number of mean pro- 

 portionals between two given lines, and he wished to sur- 

 prise his father with this memoir when completed. Be- 

 fore it was finished, kowcver, the geometrical plot was 

 detected, and the young culprits received a severe repri- 

 mand. Delighted with the discovery of the new curves, 

 M. Chiraut presented his son to the Academy of Sci- 

 ences, for the purpose of reading his memoir to that 

 learned body ; but his size bore so slender a proportion 

 to the abilities which were displayed, that it was only 

 after a rigid examination of the young man, that the 

 academicians believed him to be the author of the disco- 

 very. Father Reyneau, whose Analyse Demonlree had 

 first roused the genius of D'Alcmbert, and who was 

 present at this meeting of the Academy, burst into tears 

 f joy at the exhibition of such wonderful and premature 



talents. The memoir of our author was published in the CUiraut. 

 Htmra Berolincnsia for 17-1-, with an honourable v *""~.~**' 

 certificate from the Academy. 



About this time, Clairaut laid the foundation of his 

 excellent work >Sur let courbts a double courbiirc, which 

 he finished at the age of 13, with an assiduity which 

 threw him into a violent fever. He continued his investi- 

 gations on this subject, and in 1730 they were published, 

 with a certificate from the Academy, which expressly 

 stated, that the author had accomplished, at the age of 

 Hi, what would have done honuur to the most celebrated 

 geometers. 



The academicians were now desirous to rank Clairaut 

 among their number ; but, by the rules of the Acade- 

 my, this could not be accomplished till he had reached 

 his 20di year. Application was, however, made to the 

 king, and a special dispensation was granted in favour of 

 the young candidate, who, on the 14th July 1731, was 

 admitted adjunct mechanician at the early age ot IK. 



The joy with which this event naturally inspired M. 

 Clairaut and hi* family, was painfully alloyed by the death 

 of the younger brother, whom we have already mentioned, 

 and who was carried off in two days by the small-pox. 



After Clairaut had recovered from this dreadful shuck, 

 which for a while threatened his own life, he chearfully 

 accepted an offer from M. Maupertuis, to accompany 

 him to Basle on a visit to John Bernoulli. On his re- 

 turn from this excursion, with which he was peculiarly 

 delighted, he found his associates in the Academy occu- 

 pied with the question of the figure of the earth, and he 

 resolved to devote his attention to this important sub- 

 ject. With this view, he and M. Maupertuis retired to 

 Mount Valerien, where they formed the project of a voy- 

 age to Lapland, in the execution of winch our author 

 was of the most essential service. The Marchioness of 

 Chatelet having taken a fancy for the study of geometry, 

 went frequently on horseback to visit Clairaut at Mont 

 Valerien ; and it was for this lady that he composed his 

 Elemens de Geometric, which appeared in 1741. 



After his return from measuring a degree of the me- 

 ridian in Lapland, the king granted him a pension of a 

 thousand livres, which in less than a year was followed 

 by another that had been vacated by M. Chevalier. 



In the year 1758, on the death of Bouguer, his pen- 

 sion of 3000 livres was divided between Clairaut and Le 

 Monnier ; and in consequence of this encouragement, he 

 laid before the Academy an excellent Memoir on Naval 

 Tactics. 



It would lead us much beyond the limits of a biogra- 

 phical article, were we to follow Clairaut through the 

 numerous memoirs which he communicated to the Aca- 

 demy of Sciences. The progress of his researches, and 

 the various subjects which attracted his attention, will 

 be more readily seen from the list of his Memoirs which 

 is given at the end of the present article. We shall there- 

 fore only notice at present such of his works as have 

 been most conducive to the advancement of science. 



In his Theorie de la Figure de la Terre suivant let 

 princ'ifies de l'Hi/Jroslatu]iie, which appeared in 1743, 

 he has treated this interesting subject with unusual abi- 

 lity. He has determined, upon the Newtonian theory, 

 what would be the figure of the earth if it were wholly 

 fluid i and either uniformly dense, or consisting of con- 

 centric strata of variable density : He has examined what 

 would take place if a part of it were rendered solid ; and 

 by an application of the same principles, he has given 

 the first philosophical theory of capillary attraction.* 



See Cru.iAt Attraction, vol. v. p. 411. where we have given an account of Clairaul's Theory. 



5 



