23i] Euler and Clairaut 293 



mathematics ; problems of abstract dynamics, of optics, of 

 the motion of fluids, and of astronomy were all in turn 

 subjected to his analysis and solved. The extent of his 

 writings is shewn by the fact that, in addition to several 

 books, he wrote about 800 papers on mathematical and 

 physical subjects ; it is estimated that a complete edition 

 of his works would occupy 25 quarto volumes of about 

 600 pages each. 



Euler's first contribution to astronomy was an essay on 

 the tides which obtained a share of the Academy prize for 

 1740 already referred to, Daniel Bernouilli and Maclaurin 

 (chapter x., 196) being the other two Newtonians. The 

 problem of the tides was, however, by no means solved by 

 any of the three writers. 



He gave two distinct solutions of the problem of three 

 bodies in a form suitable for the lunar theory, and made 

 a number of extremely important and suggestive though 

 incomplete contributions to planetary theory. In both 

 subjects his work was so closely connected with that of 

 Clairaut and D'Alembert that it is more convenient to 

 discuss it in connection with theirs. 



231. Alexis Claude Clairaut, born at Paris in 1713, 

 belongs to the class of precocious geniuses. He read the 

 Infinitesimal Calculus and Conic Sections at the age of ten, 

 presented a scientific memoir to the Academy of Sciences 

 before he was 13, and published a book containing some 

 important contributions to geometry when he was 18, 

 thereby winning his admission to the Academy. 



Shortly afterwards he took part in Maupertuis' expedition 

 to Lapland (chapter x., 221), and after publishing several 

 papers of minor importance produced in 1743 his classical 

 work on the figure of the earth. In this he discussed in 

 a far more complete form than either Newton or Maclaurin 

 the form which a rotating body like the earth assumes 

 under the influence of the mutual gravitation of its parts, 

 certain hypotheses of a very general nature being made as 

 to the variations of density in the interior ; and deduced 

 formulae for the changes in different latitudes of the accelera- 

 tion due to gravity, which are in satisfactory agreement with 

 the results of pendulum experiments. 



Although the subject has since been more elaborately 



