remained on good terms with the Russian court, and continued to draw his stipend as a member of the St. Petersburg Academy and to contribute to its Transactions. Moreover, after 25 years spent at Berlin, he accepted a pressing invitation from the Empress Catherine II. and returned to Russia (1766). He had lost the use of one eye in 1735, a disaster which called from him the remark that he would henceforward have less to distract him from his mathematics; the second eye went soon after his return to Russia, and with the exception of a short time during which an operation restored the partial use of one eye he remained blind till the end of his life. But this disability made little difference to his astounding scientific activity; and it was only after nearly 17 years of blindness that as a result of a fit of apoplexy “he ceased to live and to calculate” (1783). Euler was probably the most versatile as well as the most prolific of mathematicians of all time. There is scarcely any branch of modern analysis to which he was not a large contributor, and his extraordinary powers of devising and applying methods of calculation were employed by him with great success in each of the existing branches of applied 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.