VOL. XL.] PHILOSOPHICAL TRANSACTIONS. Jig 



the Royal Academy of Sciences at Paris. "S" 445, p. 1 9. Translated from 

 the Latin. 



According to Newton's Princip. (cor. 3, prob. 91, lib. 1, and prop. 19, lib. 3) 

 if an elliptic spheroid, consisting of fluid and homogeneous particles, mutually 



father's great attentions, produced very early and extraordinary effects. Having learned the letters 

 of the alphabet from the diagrams in Euclid's Elements, he could read at 4 years of age, and even 

 write tolerably well. In a similar degree of advance he passed through the mathematical sciences of 

 arithmetic, algebra, geometry, &c. so as to master Guisnee's application of algebra to geometry, at 

 9 years of age. At 10 he studied I'Hopital's Conic Sections, and soon after the Analyse des Infini- 

 ments Petits, of the same author. At 12 he astonished the Academy of Sciences, by reading to them 

 his discovery of four curves of the third order, by means of which may be found any number of 

 mean proportionals between two given lines. And at 13 he laid the foundation of his excellent work 

 on Cunes of a Double Curvature, printed 3 years after. 



The same year, 1726, our young author formed a juvenile society, by associating together a number 

 of ingenious youths like himself, at once for improving themselves and the mathematical sciences; 

 among whom were several who afterwards became some of the most respectable members of the 

 Royal Academy of Sciences; of which academy young Clairaut himself was admitted a member at 

 18 years of age, being 3 years below the limit prescribed by a regulation of the academy, a regula- 

 tion which tliey dispensed with in this instance on account of his surprising merit. The same year he 

 presented to the academy two ingenious memoirs of his own inventions. Soon after this, he accom- 

 panied M. Maupertuis to Basle on his visit to John Bernoulli ; and on his return, he found the academy 

 much occupied about the question concerning the figure of the earth; in consequence not long after 

 he and Maupertuis, retiring to Mount Valerien, formed the project of the measurements at the 

 polar circle, in which both of them bore so conspicuous a part. In this retreat it was, that the Mar- 

 chioness of Chatelet, having resolved to learn the science of geometr)- from Clairaut, attended him 

 tliere to receive her lessons; which gave occasion to his composing his pleasant little treatise on geo- 

 metry. On the question too of the figure of the earth, about this time, he wrote several interesting 

 memoirs. The delicate observations of Mairan on the lengths of pendulums, gave occasion to Clairaut 

 to present a memoir on their oscillations. And the discovery of Bradley on the aberration of the 

 fixed stars, gave also occasion to Clairaut's presenting a valuable calculation on that subject, in which 

 he made improvements, by extending his views to that of the planets also, dependent on the same 

 cause. 



Several other memoirs, on various subjects, as, the annual parallax of the stars, the nature of the 

 refraction of light, conduct us to his still more important labours, in the application of the geome- 

 trical calculus to the profoundest considerations in physics and astronomy. This produced his work 

 on the theory of the figure of the earth on hydrostatical principles; in which he considered all the 

 circumstances and states of the earth, as to fluidity and rigidity. An-j next his theory of the moon, 

 in which he at length detected a subtile error, which had been committed bv all the best calculators 

 on that delicate subject. After a long continued labour on this object, in 1751 he carried the prize 

 proposed on the subject by the Academy of Petersburg. Also, in 1754 came out the first edition of 

 his Lunar Tables; and in 1765 was given a second edition of the same corrected; to which was added 

 the piece containing the theory which had gained the Petersburg prize. 



During those labours, Clairaut composed his elements of algebra, which appeared in 1746; these 

 elements are in the same easy and familiar stile as those of his geometry, beforementioned. In 175* 



