CLAIRAUT. ALEXIS CLAUDE. 



CLAIRON, CLAIRE JOSEPH E. 



1M 



Oviedo soflered with the rest, and in revenge have defamed 



White Charles remained in Flanders, every pretender to favour 

 resorted thither, but nothing could be obtained without pecuniary 

 application to his favourite Chievres. Great sums were drawn out of 

 Spain, and everything was disposed of to the highest bidder. The 

 inferior oAoers followed the Tinm)- 1 " of their head, and this infamous 

 traffic became general. On the other hand, seeing Flanders on the 

 eve of becoming a distant province of a vast monarchy, the Flemish 



detained the king as long as they could, spreading all the 

 time delusive reports of bis instant departure, and cheating the cardi- 

 nal under the pretext of defraying the expense of the king's voyage. 

 When after twenty months of entreaties Cisneros prevailed on Charles 

 to embark for Spain, and was himself proceeding towards the coast to 

 meet him, he was seized with a violent disorder, at the convent of 

 Hins,iinis. near Aranda de Duero, which was attributed to poison. 

 The Spanish grandees and FlsuiUh courtiers now regulated the 

 advance of the court by the probable extent of tho cardinal's life. 

 Weakened by disease, fatigue, and austerities, he still directed, to tho 

 great vexation of the courtiers, the helm of state, and seemed to sur- 

 vive only to evince bis greatness of spirit unimpaired by bodily 

 nflering. Under pretext of giving time to the towns for preparing 

 tips honour* doe to the kins;, they succeeded in deferring his entry 

 into Castile till tho cardinal's death, which happened on tho 8th of 

 November 1517, but not before Charles, whose pride was worked upon 

 by hi* flatterers, had written, with signal ingratitude, a letter to Cis- 

 neros signifying to him hi* dismissal. The rare union of calmness, 

 nnnnees, and decision in Cisneros, is well shown in Gotnetius (Gomez 

 de Castro), 'De Rebus gestu a Francisco Ximenio;' in Marsollier, 

 Flechier, Morrri, and Robertson. 



CLAIRAUT, ALEXIS CLAUDE, sometimes spelt CLAIRAULT 

 (we have taken the spelling from the title of his own works), waa 

 born at Paris, May 7, 1713. His father, John Baptist Clairaut, was a 

 teacher of mathematics. The early proficiency of the son in mathe- 

 matics is better attested than in any other similar case, by the actual 

 appearance of his celebrated treatise on ' Curves of Double Curvature,' 

 in 1731, when he was eighteen years of age, accompanied by the 

 u.ual official recommendations, which prove that it was ready for 

 the press two years before ; it is said to have been begun when he 

 was only thirteen years old. He read the 'Conic Sections' of De 

 L'HopiteL, and also the ' Infiniinenta Petite' of the same author, 

 when he was only ten yean old ; a fact which we should have forborne 

 to state, had it not been for the evidence contained in the treatise 

 just cited, and in this fact, of public notoriety, that at the age of 

 twelve yean he presented a memoir on some remarkable curves to the 

 Academy of Sciences, and removed all doubts as to its authorship by 

 his personal explanations. 



In 1731, being then under the legal age, Clairaut was admitted into 

 the Academy of Science*. He formed an intimate acquaintance with 

 Maupertuis, and commenced at this period his researches on the figure 

 of the earth. In 1735 ho accompanied Maupertuis, Camus, Lemon- 

 nter, Ac. in their ex|>editiou to Lapland, for the purpose of measuring 

 a degree of the meridian. This measure has frequently been con- 

 sidered as of little value : it must however be remarked, that such an 

 opinion lias been formed on the strength of discrepancies which were 

 sufficiently apparent to the measurers themselves, and which caused 

 them to review all their operations; as alo, that circumstances con- 

 nected with local attractions are fully sufficient to explain the whole 

 difficulty. The work of Clairaut on the 'Figure of the Earth' 

 appeared in 1743, and was reprinted in 1808. It contains the remark- 

 able discovery which i* usually called Clairaufs Theorem. Considering 

 the earth as an elliptic spheroid, it should seem that the variation of 

 gravity on the surface would depend upon the law of density of the 

 interior strata. Hut CUiraut showed that this variation is altogether 

 independent of the Uw of density, and may be deduced from a know- 

 ledge of the form of the exterior surface. In this theorem, the 

 second and higher powers of the eccentricity are rejected. Mr. Airy 

 (in an early volume of the ' Cambridge Transactions ') has shown that 

 it remains true when the higher powcn are taken into account. 



In 1750 Clairaut gained the prise of the Petersburg Academy for 

 his paper on the Theory of the Moon.' It is more essential for us 

 here to state the position which be occupies among the successors of 

 Newton, than to rater into details which are better suited to other 

 articles. Newton had left one prominent point of the lunar theory 

 altogether unexplained 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, he was not able to deduce 

 than half the quantity of the phenomenon. Clairaut at first 



"K"f U*j "> of gravitation Vat incompletely expressed; 

 Mt further consideration, and more extensive application of analysis, 

 sbowrd that the whole motion was a nummary 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 

 analysts to the problem of the lunar motion, and as the first who 

 added an unexplained phenomenon to the theory which Newton had 

 left, CUiraut staud* in a conspicuous position. ' 



Clairairt was the first who applied the Newtonian theory to the 

 motion of oooMte, in reference to the perturbation of their motions 



by the attraction of the planets. In 1757 astronomer* began to expect 

 the fulfilment of Halley's prediction relative to the comet (whow 

 appearauoa in 1835 again excited much public curiosity). Lalande 

 proposed to Clairaut to undertake the actual computation of the 

 quantity of Jupiter's action on the comet during a revolution, and 

 offered his assistance in the drudgery of the work. For the manner 

 in which this enormous labour was executed the reader may consult 

 the article ' Halley'a Comet,' in the ' Companion to the Almanac for 

 1835.' The result was that Clairaufs prediction came very near the 

 truth ; the return of the comet was at first placed in November 1758 ; 

 in that month Clairaut predicted that it would arrive at its nearest 

 point to the son about April 13, 1759, stating that he 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 loss 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 Halley'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 waa customary to write elementary works ; and many papers iu the 

 ' Memoirs of the Academy,' containing several remarkable discoveries 

 iu pure mathematics. Hut we shall pass on to some notice of his 

 career iu connection with that of D'Aleinbert These two groat men 

 were rivals in their scientific labours, and though their disputes never 

 passed the bounds of courtesy, tho life of each, with respect to the 

 other, was either armed truce or open war. The characters of tho 

 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'Aleinbert was blunt and rude, though essentially well- 

 meaning and kind ; if we may use such a colloquial phrase, he ' stood 

 no nonsense;' 'j'amie mieux utre incivil qu'eunuyc' ' was his avowed 

 maxim. Clairaut was always iu 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 tho 

 whole revolution of Halley's comet, or more than fifty years, as the 

 unit of which the error committed by him should be considered as a 

 fraction, D'Alembert assorted that the magnitude of the latter should 

 be compared, in the estimation of precision, with tho difference between 

 two successive revolutions, or about a year and a half. 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, lie 

 adds that tho polished character of Clairaut procured him an e.< 

 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. He waa never married : la; 

 father (who survived him a short time) had a very numerous family, 

 of whom only one daughter survived. 



(See the Eloge iu the Mcmoiri of the Academy ; the Life by Lacroix 

 in the liiog. Univ. ; and the work of Bossut above cited.) 



The works of Clairaut, independently of Memoirs presented to the 

 Academy, ore : 1. ' Kecherches sur le< Couches a double Corn-burn,' 

 Paris, 1731. 2. ' ftldiueus do Geotndtrie,' ; Paris, 1741; ami \ 

 editions up to 1765. 3. ' La Figure de la Terra ddtermino'e,' &c. 

 (' Account of the Lapland Measure, by Maupertuis, Clairaut,' lie.) ; 

 Paris, 173S ; in Latin, by Zeller ; Leipzig, 1742. 4. ' La Thdorie de la 

 Figure de la Terre,' Paris, 1743; again in 1SOS. 5. ' Blemeus d'Algebre,' 

 Paris, 1746 ; again in 1700 (' tr6s oatimue,' Lacroix); again in 17U7 and 

 1801 (marked sixth edition), by Garuier, witli a Preliminary Treatise 

 on Arithmetic. 6. ' The'orie de la Luue,' St. Petersburg, 1752 ; (price 

 essay) second edition, 1765. 7. ' Tables de la Lune,' &o., Paris, 1 7.0 I ; 

 republiahed with (6) in 1 765. 8. ' Thdorie du Mouvement des Comotes,' 

 Paris, 1700; the account of the groat process relative to Halley's comet 

 D'Alembert wrote against this in the 'Jouru. Kncycl.,' February 17'/1 ; 

 Clairaut replied iu tho ' Journ. des Sav.,' June 1761. 9. ' Rechcrchra 

 sur la Coincte,' Ac., St Petersburg, 1762 (Supplement to 8). 10. 

 ' Explication des Priucipaux Phdnorncues,' ke., compiled by Madame 

 du Chastellet from Clairaufs iuatructious, and printed at tho end of 

 her translation of Newton, Paris, 1759. (CHASIEI.LKT, MAD A MI; DU.] 



CLAIRON, CLAIRE JOSEPH!-: l.KY'lMS UK I. A Tim:, a cele- 

 brated French actress, whose name frequently occurs iu the literary 

 mi 'moire and correspondence of her day, was. born near Coml< : , in 

 French Flanders, in 1723. She made her early appearances in tho 

 Flemish theatres and those of the neighbouring provinces of France. 

 In 1782 she was called to the Parisian Opera, and soon afterwards to 

 theComddie Francaiso. Although her name i* now seldom mentioned, 

 no actress of any age or country appears to have been the object of a 

 reputation so wide and an admiration so intense. No one can read 

 the letters of Voltaire and his contemporaries, or the memoirs of 

 Marmoutel and others, without being struck by the frequent recur- 

 rence of her name, associated with enthusiastic eulogies. She was 

 evidently a woman of vicious moral?, yet she was proud and unbending 



