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In 1783–The streets are infested, built, the open ballusters have been as formerly, by idle ballad-fingers. complained of; and, in 1783, paffenThe only difference is, that their bal- gers continue to be blown from the lads are infinitely more blackguard than pavement into the mud in the middle they were, and that servants and citi- of the bridge. An experiment was zens children make excuses to be ab: made last year, by putting up part of sent, to listen to these abominable pro- these ballusters, on the south-eni, and moters of vice and low manners. having been found effectual in defen“

In 1783–The streets are as much ing patiengers from the violent gusts infested with beggars as in any former of wind, and screening their eyes from period of the history of the city, and blood and flaughter, nothing more has probably will continue to be fo till a been done. Bridewell is provided.

Many of the facts I have now furIn 1783- The College is in the same nished you with are curious. They ruinous condition that it was in 1763, point out the gradual progress of luxand the most celebrated university at ury, and by what imperceptible depresent in Europe is the worst accom- grees society may advance from refinemodated. Some of the professors are ment to corruption, and yet matters even obliged to have lecturing rooms of real utility be neglected. without the College for their numerous I am, Sir, &c. ftudents.

THEOPHRASTUS. Although the bridge was not built Edin. Jan. 12, 1784. in 1763, yet, ever lince it has been

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Α Ν Ε C D Ο Τ Ε.
THEN the late Dr. Henry God- door, appeared a tall meagre figure, in

dard, a learned and able phy- a black gown, a night cap, over which sician, who practised at York, was an was a broad brimmed hat, on his head, under graduate at St. John's College, in and a twinkling taper in his hand. Cambridge, his room was immediately Without giving the apparition time to above that of Mr. Baker, the famous speak, Browne started up, and reantiquary, who being ancient and in- peated from Shakspeare, firm, was easily disturbed and affected Angels and ministers of grace defend us!

any unusual noise in the neigh- Be thou a spirit of health, or goblin dunn bouring apartments. On this account Bring with thee airs from heaven, or blasts from Goddard, who was a very sober, re

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Be thy intents wicked or charitable, gular person, had his room matted, Thou com’t in such a quettionab.e ihape that he might not incommode the wor- That I will speak to thce thy old gentleman. One night, how- This, which, in other circumítances, ever, having invited some of his friends, would have appeared a cruel infult, among whom was Mr. Browne*, to was really no more than an enthufiaitic {pend the evening with him, the chear- impulse, neither the effect of intoxifulness of their conversation, notwith- cation, nor of a spirit of malignity; standing Mr. Goddard's frequent re- accordingly, it was readily excuted by monftrances, put them off their guard, the good old man, after a genteel apoand in the end brought up Mr. Baker, logy from Mr. Browne in person was to fue for peace. Upon opening the made the next morning.

REFLECTION. IN N all the various arts which shew that delight the senses; while the sub

the invention of mankind, the beau- lime owes its original to hate, anger, tiful arises from the expressions of love, fear; and the terrible paflions, as well pity, defire, and the tender pallions, as to the objects which are unpleasing as well as by the description of objects to the senses.

BIOGRAPHY.

2 • The calabretell i Heli Braun

BIOGRAPHY.
THE MEMOIRS OF LEONARD EULER,

THE CELEBRATED MATHEMATICIAN.

Pafil, on

on the 14th of April, 1707; class, in which, from the circumstances he was the son of Paul Euler, and of of the times, as Newton, Leibnitz, Margaret Brucker (of an illustrious and so many other great men were family in letters) and spent the firit juft dead, no easy laurels were to be years of his life at the village of Richen, gathered. Nature, however, who had of which place his father was minister.

organized so many mathematicians it As he was intended for the church, one time, was not yet tired of her mihis father, who had himself studied un- racles, and she added Euler to the der James Bernouilli, taught him ma- number. thematics, with a view to their proving He was, indeed, much wanted; the the ground work of his other itudies, science of the calentus integralis, hardly and in hopes that they would turn out come out of the hands of its creators, a noble and useful secondary occupa- was still too near the stage of its intion; but they were destined to become fancy to be perfect. Mechanics, dya principal one, and Euler, affifted namics, and especially hydrodynamics, and, perhaps, secretly encouraged by and the science of the motion of the John Bernouilli, who foon discovered heavenly bodies, felt the imperfection. that he was to be among the greatest The application of the diferential calscholars whose education would be culus to them had been fufficiently trusted to his care, foon declared his successful, but there were difficulties, intention of devoting his life to the whenever it was necessary to go from pursuit; an intention which the wise the fuxional quantity io the fluent. father did not thwart, and which the With regard to the nature and propersensible fon did not follow so close, as ties of numbers, the writings of fernot to connect with it a more than mat (who had been so successful in common improvement in every other them) and together with these all his species of useful learning, insomuch, profound researches, were lost. "Enthat in his latter days men were afto- gineering and navigation were reduced nished that with such a superiority in to vague principles, and were founded one branch, he liould be so near emi- on obfervations often contradictory, nence in all the rett.

more than on a regular theory. The Upon the foundation of the Aca- irregularities in the motions of the demy of Sciences at Petersburgh, in celcitial bodies, and especially the 1723, by Catharine the First, the two complication of forces which influence younger Bernouilli had gone thither, that of the moon, was still the disgrace promising, when they set out, to en- of geometers. Practical astronomy had deavour to procure Euler a place in it; ftill to wrestle with the imperfection they accordingly wrote to him foon of telescopes, insomuch, that it could after, to apply his mathematics to phy- hardly be faid that any rule for making fiology; he did fo, and studied physic them exifted. Euler turned his eyes under the best physicians at Basil, but to all these objects; he perfected the in 1727 publithed a differtation on calculus integralis; he was the inventor the nature and propagation of sound; of a new kind of calculus, that of and an answer to the question on the Sines; he simplified analytical operamafting of ships, which the Academy. tions; and, aided by these powerful of Sciences at Paris judged worthy of helpmates, and the astonishing facility the accdit.

with which he knew how to subdue Soon after this he was called to Pe- expressions the most intractable, he threw tersburgh, and declared adjutant to the a new light on all the branches of the

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mathematics. But at Catharine's Such labours demanded some relaxadeath the academy was threatened with tion; the only one which Euler admitextinction, by men who knew not the ted was music, but even to this he connection which arts and sciences have could not apply without being accom with the happiness of a people. Euler panied by the spirit of geometry. was offered and accepted of a lieute- They produced together an effay on a nancy on board one of the Empress's new theory of mutic, which was pubtrips, with the promise of speedy ad- lished in 1739, but not very well revancement. Luckily things changed, ceired, probably, because it contains and our doctor-captain again found his too much geometry for a musician, own element, and was named Professor and too much music for a geometrician. of Natural Philosophy in 1733, in the Independently, however, of the theory, room of his friend John Bernouilli. which is built on Pythagorean princi

The number of memoirs which Eu- ples, there are many things in it which ler produced prior to this period is may be of service, both to the comaftonithing*, but what he did in 1735 poser and maker of inftruments. The is almost incredible. An important doctrine, likewise, of the genera and calculation was to be made, without the modes of music is here marked out loss of time; the other academicians with all the clearness and precision had demanded some months to do it; which distinguish the works of Euler. Euler asked three days—in three days As to the theory, the physical part of he did it; but the fatigue threw him which is beyond dispute, Mr. Euler into a fever, and the fever left him not contends that all the pleasure of harbut with the loss of an eye, an ad- mony arifes from the love of order in monition which would have made or- man, in consequence of which, all the dinary men more sparing of the other. agreeable sensations excited by hear

The great revolution produced by ing fine music come from the percepthe discovery of fluxions had entirely tion of the relations which the different changed the face of mechanics ; ftill, sounds have to each other, as well with however, there was no complete work regard to the duration of their fucon the science of motion, two or three cession, as to the frequency of the vionly excepted, of which Euler felt the brations of the air which produces infúficiency. He saw, with pain, them. Mr. Euler's system refts upon that the best works on the subject, viz. this metaphysical principle, which he Newton's Principia, and Herman's has modined and applied to all the Phoronomia, concealed the method by parts of music. The principle may be which these great men had come at so insufficient, but it is imposible to reamany wonderful discoveries, under a fon with more fubtlety and penetration synthetic veil. In order to lift this upon it than Euler has done. up, Euler employed all the resources In 1740, his genius was again called of that analysis which had served him forth by the academy of Paris, who, on fo many occasions; and uniting his in 1738, had adjudged the prize to his own discoveries to those of other geo- paper on the nature and properties of meters, he had them published by the fire, to discuss the question of the Academy in 1736. To say that clear- tides, an important que ion, but which nefs, precision, and order are the cha- demanded an almost infinite number of racters of this work, would be barely calculations, and an entire new system to say, that it is, what without these of the world. This prize Euler did qualities no work can be, classical of not gain alone, but he divided it with its kind. It placed Euler in the rank Maclaurin and D. Bernouilli, forming of the first geometricians then existing, with them such a triumvirate of can. and this at a time when John Bernou- didates, as the altars of science had not illi was still living.

often beheld. Euler's memoir is re.

markable * On the theory of the more remarkable curves—the nature of oumbers and series—the calculus integralis--the movement of the celestial bodies-ihe attraction of spheroidico-elliptical bodies the famous folution of the isoperimetrical problem--and an infinity of other objects, the hundredth part of which would have made an ordinary man illustrious.

markable for the clearness with which he executed at Berlin, at a time when he explains the effects which the action he contrived that the Petersburgh acts of the sun and moon, exclufively of fould not suffer from the loss of him. other forces, exercise on the sea; for Posterity will with difficulty believe his noble determination of the earth's that the life of one man could be suffifigure, in as much as it is changed by cient for so many works, and on such the action of the forces; for the pene- abitruse subjects. tration with which, in considering the In 1744, Euler published a complete motions of the sea as oscillatory, he treatise of isoperimetrical curves, in fupplies the effects of the ris merria which he lowed the seeds of the calculus of the waters, which he had been of variations, by conlidering the curves, obliged to fuppofe null in the begin- which differ infinitely little from a ning; for the happy integrations, which proposed curve. The same year beheld the consideration of this reciprocal mo- the theory of the motions of the plation required; and, tinally, for the fa- nets and comets; the theory of maggacity thewn in the explanation of the netism, which gained the famous Paris several phenomena of the tides, accord- prize; and the much-improved traning to the theory laid down. The Ilation of Robins's Treatise on Gunagreement of the several memoirs of

nery. Euler and Bernouilli, on this occafion, In the year 1746, his theory of light is very remarkable. Though the one and colours overturned Newton's lyfpliilosopher had set out on the princi- tem of emanations, as did another work ple of admitung vortices, which the the once triumphant Monads of Wolfe ether rejected, they not only arrived at and I.eibnitz. the same end of the journey, but met · Navigation now seemed the only feveral times on the road; particularly branch of useful knowledge in which in the determination of the tides under the labours of analysis and geometry the frozen zone.

had not been employed. The hydroThilosophy, indeed, led these two graphical part alone, and that which great men by two different paths; Ber- relates to the direction of the course of . Rouilli, who had more patience than fhips, had been treated by geometrihis friend, fanctioned every phyfical cins conjointly with nautical astrohypothesis he was obliged to make by nomy. Euler was the first who conpainful and laborious experiment. ceived and executed the project of These Euler's impetuous genius dif- iraking this science complete. A medained, and, though his natural faga- moir on the motion of floating bodies, city did not always supply the loss, he comniunicated to the academy of Pe. made amends by his fuperiority in ana- te burghin 1735, by M. le Croix, gave lyfis, as often as there was any occafion him the first idea. His great work on to fimplify exprefrons, to adapt them the subject was published by the Acato practice, and to recognize, by final demy in 1759, in which we find, in formulæ, the nature of the result. systematic order, the most sublime

In 1741, Euler received fome very things in the theory of the equilibrio advantageous propofitions from Frede- and motion of floating bodies, and ric the Second, who had just ascended on the existence of fluids; this was the Pruílian throne. · He was in ited to followed by a second part, which left aslift him in forming an academy of nothing to be desired on the subject, fciences out of the wrecks of the except the turning it into a language Royal Society founded by Leibnitz. caly of access, and divesting it of the The tottering state of the Petersburgh calculations which prevented its being Academy, under the regency, made it of general utily. Accordingly, in 1773, necessary for oar philosopher to com- from a conversation with Admiral ply with these offers. No part of his Knowles, and other aslistance, out of multifarious labours is, perhaps, a more the Scientia Navalis, 2 vols. 4to. was wonderful proof of the extenfiveness produced the Theorie completre de la and facility of his genius, than what Construtiion et de la Manæuvres des Vail4.

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seaux. This work was instantly tran- that he engaged to furnish the academy flated into all languages, and the au- with papers sufficient to fill their vo thor received a present of fix thousand lumes for twenty years after his death, livres from the French King; he had and he did not break his promise. For before had three hundred pounds from he presented seventy papers, through the English parliament, for the theo- Mr. Golofkin, in the course of his rems, by the assistance of which Mayer life, and left two hundred and fifty made his lunar tables.

more behind him; of which every one And now it was time to collect into contains something important. 'They one systematical and continued work abound in the happiest integrations; in all the important discoveries on the a multiplicity of refined artifices of the infiniteffimal analysis, which Euler had highest analysis; in the most profound been making for thirty years, and researches into the nature and properwhich lay dispersed in the memoirs of ties of numbers ; in the ingenious dethe different academies. This, accord- monitration of several theorems ef Feringly, now employed our profetior, mat's; in the folution of a quantity of but he prepared the way by an elemen- very difficult problems, on the equilitary work, containing all the previous brio and motion of folid, flexible, and requisites for this study. This is called elastic bodies; and in the unweaving An Introduction to the Analysis of Infini- of several apparent paradoxes. Whattellinals.

ever is moit thorny, and moft difficult This introduction was soon followed in the theory of the motion of the by the author's several lessons on the heavenly bodies, is here made as clear calculus integralis and differentialis. The as it could be made by the calculations merit of the first of these works consists of the greatest of geometricians. The in the point of view in which Euler most ancient of these memoirs form has shewn its first principles; in the the collection this year published, under fyftematical arrangement which he has the title of Opuscula Analytica. given to this matter; in the method Such were Mr. Euler's labours, and which obtains throughout the whole they entitle him to immortality! His of the work; in the clearness with memory shall endure till fcience herself which he has demonstrated the use of is no more! this calculus, with regard to the doc- Few men of letters have written as trine of series, and the theory of greater much as Mr. Euler; no geometrician and lefs.

has ever embraced so many objects at The third volume of his calculus in- one time, or has equalled him, either tegralis contains the new kind of calcu- in the variety or magnitude of his dislus with which Euler has enriched the coreries. analysis of infiniteffimals; i. p. the cal- When we reflect on the advantages culus of variations. It has been already which mankind derive from such men, obferved, that what give rise to it was we cannot help indulging a with (vain, the isoperimetrical problem. This alas! as it is) that their illustrious was eagerly feised by M. de la Grange, course were prolonged beyond the term who disengaged it from all geometri- allotted to humanity. Euler's, though cal considerations, made an analytical it has terminated, was a very long, and problem of it, and folved it by the a very honourable one; and it affords new calculus, which Mr. Euler has so us fone consolation for his loss, to much perfected since that time, and think that he ran it exempt from the which he has called the calculus of va- ordinary consequences of extraordinary riations, because the relation betwixt application, and that his lait labours the variable quantities is itself confi- abound in proofs of that vigour of undered as variable.

derlanding which marked his carlier To enumerate the various works of days, and which he preserved to the this great man would far exceed our end of his existence. limits. We must now hasten to his Some swimmings in the head, which moral character. Yet we must add, seised him on the first days of last Sep

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