ACIIBOM tTIC TELESCOPES, ALGEBRA, ARITHMETIC of Sines, ASTRONOMY, FLU MONS, MECHANICS, and, in short, to almost every article in mathematics and physics which occurs in our work. A full account of Euler's discove ries and investigations will be found in these articles, and it would only be a waste of time to resume these sub jects under the present head. In many of his physical memoirs, Euler has been justly reproached for having applied the calculus to the most unfounded physical hy potheses. or to metaphysical principles, which had not been sufficiently examined ; and on this account many of his memoirs have no value whatever, except in so far as they exhibit fine specimens of the resources of analy sis. His Dissertations on Wind Mills, on Achromatic Telescopes, on Naval Architecture, and on Gunnery, are among the number of those which are liable to this cri ticism.
When Euler was at Berlin, the Princess of Anhalt Dessau, the niece of the King of Prussia, was desirous to receive from him some instruction in the different branches of natural philosophy ; and for her use he drew up a work, entitled, Lettres a une Prineesse d'allemagne, which was translated into English by the late Dr Henry hunter, and which, with the exception of the metaphy sical part, has always been much esteemed, particularly for the singular perspicuity with which its author has explained some of the most profound truths in physics. The King of Prussia often employed Euler in calcula tions relative to the mint, and other objects of finance, in the conducting of the waters of San Souci, and in the examination of canals, and other public works.
In 1744, Euler was appointed director of the mathe matical class of the academy, and in the same year he obtained the prize offered by the Academy of Sciences of Pari for the best work on the theory of magnetism.
About this time Robin's 'Treatise on Gunnery had ap peared in England, and though our countryman had treated Euler with great severity, this act of injustice did not prevent him from recommending it to the king of Prussia, as the best book on the subject. He even translated it, and in the additions which he made, he gave a complete theory of the motion of projectiles. M. Turgca ordered this work to be translated into French, and introduced into the schools of artillery ; and about the same time there appeared a splendid edition of it in England.
In 1746, he published his new Theory of Light and Colours, and in 1759, his memoir Sur les effets du Ron lis du Tangage, gained the prize offered by the French Academy of Sciences.
In 1750, Euler went to Frankfort to receive his mo ther, who was then a widow, and to conduct her to Ber lin, where she remained till the time of her death in 1661 ; having enjoyed for 11 years the assiduous atten tions of a favourite son, and the high pleasure of seeing him universally esteemed and admired.
When Euler remained at Berlin, he formed an intimate acquaintance with M. De Maupertuis, the learned Pre sident of the Prussian Academy of Sciences, and he de fended Matpertuis's celebrated and favourite principle of the least action, by resolving by means of it some of the most difficult problems in mechanics. In the dis pute into which he was thus led with Koenig, who had attacked Maupertuis in 1751, he lost for a while his usual serenity, and became one of the enemies of that unfortunate individual.
Although the number of foreign associates in the French Academy of sciences was limited to eight; yet Euler was appointed to the ninth place in 1755, on the condition that no appointment should take place at the first vancancy.
In the year 1760, the Russian army under General Tottleben penetrated into the Marche of Brandenburg, and pillaged a farm which Euler possessed near Char lottenberg. As soon as the Russian general was inform ed of the event, he immediately repaired the loss by a very large sum ; and upon giving notice of the circum stance to the Empress Elizabeth, she added to this in demnity a present of four thousand florins. This act of generosity, no doubt, had a powerful effect in attaching Euler to the Russian government, which, in spite of his absence, had always paid him the pension which it grant ed him in 1742. Having received an invitation from the Empress Catherine, he obtained permission from the King of Prussia to return to St Petersburg to spend the remainder of his days ; but his eldest son was not allow ed to accompany him. When Euler was on the eve of his departure, Prince Czartorisky invited him, in the name of the King of Poland, to take the road of War saw, where, loaded with kindness, he spent 10 days with Stanislaus, who afterwards honoured him with his cor respondence.