Shortly after his arrival in St Petersburg, on the 17th July 1766, he lost the sight of his other eye, having been for a considerable time obliged to perform his calcula tions with large characters, traced with chalk upon a slate. His pupils and his children copied his calcula tions, and wrote all his memoirs while Euler dictated to them. To one of his servants, who was quite igno rant of mathematical knowledge, he dictated his Ele ments of algebra, a work of very great merit, which has been translated into the English and many other langua ges. Euler now acquired the rare faculty of carrying on in his mind the most complicated analytical and arith metical calculations ; and M. d'Alembert, when he saw him at Berlin, was astonished at some examples of this kind which occurred in their conversation. With the de sign of instructing his grandchildren in the extraction of roots, lie formed a table of the six first powers of all numbers, from 1 to 100, and he recollected them with the utmost accuracy. Two of his pupils having computed to the 17th term, a complicated converging series, their re sults differed one unit in the fiftieth cypher; and an ap peal being made to Euler, he went over the calculation in his mind, and his decision was found correct.
His principal amusement, after he lost his sight, was to make artificial loadstones, and to give lessons on ma thematics to one of his grand-children, who seemed to evince a taste for the science.
In 1771, a dreadful fire broke out in St Petersburg, and reached the house of Euler. M. Grimm, a native of Basle, having learned the danger in which his illustri ous countryman was placed, threw himself among the flames, and, reaching Euler's apartment, brought him off on his shoulders, at the risk of his life. His library, how ever, and his furniture, were consumed, but by the acti vity of Count Orloff, his MSS. were saved.
Having revised the lunar theory with the aid of his son, and of Krafft and Lexell, he constructed a set of new lunar tables, which appeared in 1772. These tables were, at the suggestion of Turgot, rewarded by the Board of Longitude in France; and when the more per feet tables of Mayer obtained the great premium of three thousand pounds offered by the British Parliament, the aunt of three hundred pounds was given to Euler for ha ving furnished the theorems made use of by Mayer in his theory.
In the year 1773, Euler published, at St Petersburg, his great work on the construction and management of vessels. A new edition soon afterwards appeared at Paris, and at the desire of the French king, it was intro duced into the schools of Marine, and a reward of 1000 rubles transmitted to the author, accompanied by a hand .some letter from the celebrated Turgot. About the same time an Italian, an English, and a Russian translation of it appeared, and the Russian government presented Eu
. ler with a gift of 2000 rubles.
Three of Euler's memoirs on the Inequalities in the motions of the Planets, were crowned by the French _Academy of sciences, and he also gained the prizes of 1770 and 1772, by his pet feetion of the lunar theory.
Having lost his first wife, by whom he had thirteen children, eight of whom died in early life, he was mar iied a second time in 1776, to Mademoiselle Gscll, the aunt of his first wife.
Euler underwent the operation of couching, which was attended with the happy result of restoring his sight ; but whether from the negligence of his surgeon, of from his being too eager to avail himself of his new organs, he again lost his sight, and suffered much severe pain from the relapse. His love for science, however, continued unabated, and in the course of seven years, he transmitted 70 memoirs to the Academy of St Peters burg. On the 7th of September 1783, alter having amu sed himself w ith calculating upon a slate the laws of the ascensional motion of balloons, which, at that time, oc cupied the attention of philosophers, he dined with his relation M. I, Nell, and spoke of the planet Herschel, and or the calculations by which its orbit was determin ed. A short time afterwards, he was amusing himself with one of his on, when, on a sudden, his pipe fell from his hand, and. he expired of an apoplec tic stroke, in the 76th year of his age.
Euler left behind him three sons, having lost his two daughters in the lam' years of his life. Twenty-six out of thirty of his grand-children were alive at the time of his death.
After a long life, so successfully devoted to the scien ces, Euler's reputation was very widely extended. Be sides being a foreign member of the Academy of Scien ces at Paris, he was a Fellow of the Royal Society of London, and he had received front most of the Princes of the North, with whom he was well acquainted, the most flattering marks of their esteem. When the Prince Royal of Prussia visited St Petersburg, he anticipated the visit of Euler, and passed several hours at the bed side of this great man, holding him all the time by the hand, and having, at the same time, upon his knee, one of Euler's grand-children, who had displayed a prema ture attachment to geometry. The death of Euler was considered as a public loss even in the country where he lived ; and the Academy of St Petersburg decreed to him, at their own expellee, a marble bust, which was placed in their public hall. In an allegorical picture which the Academy had put up during his life, Geome•. try was represented as placed upon a basement covered with calculations. These calculations were the formul= of Euler's Theory of the Lunar Motions.