did in 1735 is almost incredible. An important calculation was to be made, without lofs of time; the other academicians had demanded some months to do it. Euler afked three days→→ in three days he did it; but the fatigue threw him into a fever, and the fever left him not without the lofs of an eye, an admonition which would have made an ordinary man more sparing of the other. The great revolution, produced by the difcovery of fluxions, had entirely changed the face of mechanics; ftill, however, there was no complete work on the fcience of motion, two or three only excepted, of which Euler felt the infufficiency. He faw, with pain, that the best works on the fubject, viz. "Newton's Principia," and "Herman's Phoronomia," concealed the method by which these great men had come at fo many wonderful difcoveries, under a fynthetic veil. In order to lift this up, Euler employed all the refources of that analysis which had ferved him fo well on fo many other occafions; and thus uniting his own discoveries to those of other geometers, had them published by the academy in 1736. To fay that clearness, precifion, and order, are the characters of this work, would be barely to fay, that it is, what without these qualities no work can be, claffical of its kind. It placed Euler in the rank of the first geometricians then exifting, and this at a time when John Bernouilli was ftill living. Such labours demanded some relaxation; the only one which Euler admitted was mufic, but even to this he could not go without the spirit of geometry with him. They produced together the effay on a new theory of mufic, which was published in 1739, but not very well received, probably, because it contains too much geometry for a musician, and too much music for a geometrician. Independently, however, of the theory, which is built on Pythagorean principles, there are many things in it which may be of fervice, both to compofers, and to makers of inftruments. The doctrine, likewife, of the genera and the modes of mufic is here cleared up with all the clearness and precifion which mark the works of Euler. In 1740, his genius was again called forth by the academy of Paris (who, in 1738, had adjudged the prize to his paper on the nature and properties of fire) to difcufs the nature of the tides, an important question, which demanded a prodigious extent of calculations, and an entire new fyftem of the world. This prize Euler did not gain alone; but he divided it with Maclaurin and D. Bernouilli, forming with them a triumvirate of candidates, which the realms of science had not often beheld. The agree ment of the several memoirs of Euler and Bernouilli, on this occafion, is very remarkable. Though the one philofopher had fet out on the principle of admitting vortices, which the other rejected, they not only arrived at the fame end of the jour

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ney, but met feveral times on the road; for instance, in the determination of the tides under the frozen zone. Philofophy, indeed, led these two great men by different paths; Bernouilli, who had more patience than his friend, fanétioned every phyfical hypothefis he was obliged to make, by painful and laborious experiment. Thefe Euler's impetuous genius fcorned; and, though his natural fagacity did not always fupply the lofs, he made amends by his fuperiority in analysis, as often as there was any occafion to fimplify expreffions, to adapt them to practice, and to recognize, by final formulæ, the nature of the refult. In 1741, Euler received fome very advantageous propofitions from Frederic the fecond (who had just afcended the 'Pruffian throne), to go and affift him in forming an academy of sciences, out of the wrecks of the Royal Society founded by Leibnitz. With thefe offers the tottering state of the St. Peterfburgh academy, under the regency, made it neceffary for the philofopher to comply. He accordingly illumined the laft volume of the "Melanges de Berlin," with five effays, which <are, perhaps, the best things in it, and contributed largely to the academical volumes, the first of which was published in 1744. No part of his multifarious labours is, perhaps, a more I wonderful proof of the extensiveness and facility of his genius, than what he executed at Berlin, at a time when he contrived alfo that the Petersburg acts should not fuffer from the lofs of him. In 1744, Euler published a complete treatise of ifoperimetrical curves. The fame year beheld the theory of the motions of the planets and comets; the well-known theory of magnetism, which gained the Paris prize; and the much-amended tranflation of Robins's Treatife on Gunnery." In 1746, his 24 Theory of Light and Colours" overturned Newton's ༣་པ་ Syftem of Emanations;" as did another work, the, at that time triumphant," Monads of Wolfe and Leibnitz." Navigation was now the only branch of ufeful knowledge, for which the labours of analyfis and geometry had done nothing. The hydrographical part alone, and that which relates to the direction of the courfe of fhips, had een treated by geometricians conjointly with nautical aftronomy. Euler was the first who conceived and executed the project of making this a complete fcience. A memoir on the motion of floating bodies, communicated to the academy of St. Petersburg in 1735, by M. le Croix, firft gave him this idea. His refearches on the equilibrium of fhips furnished him with the means of bringing the stability to a determined measure. His fuccefs encouraged him to go on, and produced the great work which the academy published in 1749, in which we find, in fyftematic order, the most sublime notions on the theory of the equilibrium and motion of floating bodies, and on the refiftance

of

of fluids. This was followed by a fecond part, which left nothing to be defired on the fubject, except the turning it into at language eafy of accefs, and divesting it of the calculations which prevented its being of general ufe. Accordingly, in, 1773, from a converfation with admiral Knowles, and other, affiftance, out of the " Scientia Navalis," 2 vols. 4to. was produced, the "Theorie complette de la Conftruction et de la Manœuvre des Vaiffeaux." This work was inftantly tranflated into all languages, and the author received a present of 6000 livres from the French king: he had before had 300l. from the English parliament, for the theorems, by the affistance. of which Meyer made his lunar tables.

And now it was time to collect, into one fyftematical and continued work, all the important difcoveries on the infinitefimal analyfis, which Euler had been making for 30 years, and which lay difperfed in the memoirs of the different academies. This, accordingly, the Profeffor undertook; but he prepared the way by an elementary work, containing all the previous requifites for this ftudy. This is called "An Introduction to the analysis of infinitefimals," and is a work in which the author has exhausted all the doctrine of fractions, whether algebraical or tranfcendental, by fhewing their transformation, their refolution, and their development. This introduction was foon followed by the author's feveral leffons on the "calculus integralis" and "differentialis." Having engaged himself to count Orlow, to furnish the academy with papers fufficient to fill their volumes for twenty years after his death, the philofopher is likely to keep his word, having prefented seventy papers, through Mr. Golofkin, in the courfe of his life, and left two hundred and fifty more behind him; nor is there one of these that does not contain a difcovery, or something that may lead to one. The most ancient of these memoirs form the collection then published, under the title of "Opufcula Analytica." Such were Euler's labours, and thefe his titles to immortality! His memory fhall endure till Science herself is no more! Fe men of letters have written fo much as Euler ; no geometrician has ever embraced fo many objects at one time, or has equalled him, either in the variety or magnitude of his discoveries. When we reflect on the good fuch men do their fellow-creatures, we cannot help indulging a wish (vain, alas! as it is) for their illuftrious courfe to be prolonged beyond the term allotted to mankind. Euler's, though it has had an end, was very long and very honourable; and it affords us fome confolation for his lofs, to think that he enjoyed it exempt from the ordinary confequences of extraordinary application, and that his laft labours abounded in proofs of that vigour of understanding, which marked his early days, and which he pre

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ferved to his end. Some fwimmings in the head, which feized him on the first days of September 1783, did not prevent his laying hold of a few facts, which reached him through the channel of the public papers, to calculate the motions of the aeroftatical globes; and he even compaffed a very difficult integration, in which the calculation had engaged him [c]. But the decree was gone forth on the 7th of September he talked with Mr. Lexell, who had come to dine with him, of the new planet, and difcourfed with him upon other fubjects, with his ufual penetration. He was playing with one of his grandchildren at tea-time, when he was feized with an apoplectic fit." I am dying," said he before he loft his fenfes, and he ended his glorious life a few hours after, aged feventy-fix years, five months, and three days. His latter days were tranquil and ferene. A few infirmities excepted, which are the inevitable lot of an advanced age, he enjoyed a fhare of health, which allowed him to give little time to repofe. Euler poffeffed, to a great degree, what is commonly called erudition he had read all the Latin claffics; was perfect mafter of ancient mathematical literature, and had the hiftory of all ages, and all nations, even to the minutest facts, ever present to his mind. Befides this, he knew much more of phyfic, botany, and chemistry, than could be expected, from any man who had not made these sciences his peculiar occupation." I have feen," fays Mr. Fufs, " ftrangers go from him with a kind of furprife mixed with admiration; they could not conceive how a man, who, for half a century, had feemed taken up in making and publishing difcoveries in natural philosophy and mathematics, could have found means to preferve so much knowledge, that seemed useless to himself, and foreign to the ftudies in which he was engaged. This was the effect of a happy memory, that loft nothing of what had ever been entrusted to it; nor was it a wonder that the man who was able to repeat the whole Æneis, and to point out to his hearers the first and laft verses of every page of his own edition of it, fhould not have loft what he had learned, at an age when the impreffions made upon us are the strongest [D]. Nothing can equal the ease

[c] This reminds us of the illuftrious Boerhaave, who kept feeling his pulfe the morning of his death, to fee whether it would beat till a book he was eager to fee was published, read the book, and faid, "Now the business of life is over." -Such men feem not to die, but to be tranflated to the place where they refame their occupations.

[D]"Another proof of the ftrength of his memory and imagination deferves to be related. Being engaged in teach

ing his grandchildren geometry and algebra, and obliged, in confequence, to initiate them in the extraction of roots; he was obliged to give them numbers, which fhould be the powers of other numbers; thefe he used to make in his head'; and one night, not being able to fleep, he calculated the fix firft powers of all the numbers above twenty, and, to our great aftonishment, repeated them to us feveral days after."

with which, without expreffing the leaft degree of ill-humour, he could quit his abftrufe meditations, and give himself up to the general amusements of fociety. The art of not appearing wife above one's fellows, of defcending to the level of those with whom one lives, is too rare in thefe days not to make it a merit in Euler to have poffeffed it. A temper ever equal, a natural and easy chearfulness, a species of fatirical wit, tempered with urbane humanity, the art of telling a story archly, and with fimplicity, made his converfation generally fought. The great fund of vivacity, which he had at all times poffeffed, and without which, indeed, the activity we have just been admiring could not have exifted, carried him fometimes away, and he was apt to grow warm; but his anger left him as quickly as it came on, and there never has existed a man to whom he bore malice. He poffeffed a precious fund of rectitude and probity. The fworn enemy of injustice, whenever or by whomfoever committed, he used to cenfure and attack it, without the least attention to the rank or riches of the offender.-Recent examples of this are in the recollection of all who hear me. As he was filled with refpect for religion, his piety was fincere, and his devotion full of fervour.-He went through all his christian duties with the greatest attention. Euler loved all mankind, and if he ever felt a motion of indignation, it was against the enemy of religion, particularly against the declared apoftles of infidelity. He defended revelation against the objections of these men, in a work published at Berlin, in 1747. He was a good husband, a good father, a good friend, a good citizen, a good member of private fociety!

"Euler was twice married, and had thirteen children, four of whom only have furvived him. The eldest fon is well known as his father's affiftant and fucceffor; the fecond is phyfician to the emprefs; and the third is a lieutenant-colonel of artillery, and director of the armory at Sefterbeck. The daughter married major Bell. From thefe children he had 38 grandchildren, 26 of whom are still alive. Never have I been prefent at a more touching fight than that exhibited by this venerable old man, furrounded, like a patriarch, by his numerous offspring, all attentive to make his old age agreeable, and enliven the remainder of his days, by every fpecies of kind folicitude and care. It would be vain for me to attempt to describe to you thefe touching scenes of domeftic felicity; feveral of you have yourselves been eye-witneffes of them; you, efpecially, gentlemen, who make it your boaft to have had him for your mafter. Here we ftand, five of us in number! has there ever exifted a man of letters, who could glory himself in having feen fo many of his scholars the members of fo learned a fociety?

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