In 1783-The ftreets are infefted, formerly, by idle ballad-fingers. e only difference is, that their balare infinitely more black guard than y were, and that fervants and citichildren make excufes to be ab t, to liften to thefe abominable pro ters of vice and low manners. 1783-The ftreets are as much fed with beggars as in any former od of the history of the city, and ably will continue to be fo till a well is provided. a1783-The College is in the fame ous condition that it was in 1763, the most celebrated univerfity at fat in Europe is the worst accomdated. Some of the profeffors are en obliged to have lecturing rooms the College for their numerous adents. built, the open ballufters have been complained of; and, in 1783, paffengers continue to be blown from the pavement into the mud in the middle of the bridge. An experiment was made laft year, by fhutting up part of thefe ballufters, on the fouth-end, and having been found effectual in defending paffengers from the violent gufts of wind, and fcreening their eyes from blood and flaughter, nothing more has been done. Many of the facts I have now furnifhed you with are curious. They point out the gradual progrefs of luxury, and by what imperceptible degrees fociety may advance from refinement to corruption, and yet matters of real utility be neglected. I am, Sir, &c. THEOPHRASTUS. Although the bridge was not built Edin. Jan. 12, 1784. 1753, yet, ever fince it has been ANECDOTE. VHEN HEN the late Dr. Henry Goddard, a learned and able phyin, who practifed at York, was an dergraduate at St. John's College, in mbridge, his room was immediately e that of Mr. Baker, the famous Squary, who being ancient and in, was eafily disturbed and affected y unufual noife in the neighag apartments. On this account ard, who was a very fober, reperfon, had his room matted, he might not incommode the worold gentleman. One night, hower, having invited fome of his friends, oh whom was Mr. Browne*, to nd the evening with him, the chearlinefs of their converfation, notwithing Mr. Goddard's frequent retrances, put them off their guard, ad in the end brought up Mr. Baker, fue for peace. Upon opening the REFLECTIO N. all the various arts which fhew the invention of mankind, the beautiful arifes from the expreffions of love, pity, defire, and the tender paffions, as well as by the defcription of objects that delight the fenfes; while the fublime owes its original to hate, anger, fear, and the terrible paffions, as well as to the objects which are unpleafing to the fenfes. 3 P 2 BIOGRAPH BIOGRAPHY. THE MEMOIRS OF LEONARD EULER, LEONARD EULER was born at Eafil, on the 14th of April, 1707; he was the fon of Paul Euler, and of Margaret Brucker (of an illuftrious family in letters) and fpent the firft years of his life at the village of Richen, of which place his father was minifter. As he was intended for the church, his father, who had himself studied under James Bernouilli, taught him mathematics, with a view to their proving the ground work of his other ftudies, and in hopes that they would turn out a noble and ufeful fecondary occupation; but they were deftined to become a principal one, and Euler, affifted and, perhaps, fecretly encouraged by John Bernouilli, who foon difcovered that he was to be among the greatest fcholars whofe education would be trufted to his care, foon declared his intention of devoting his life to the purfuit; an intention which the wife father did not thwart, and which the fenfible fon did not follow fo clofe, as not to connect with it a more than common improvement in every other fpecies of ufeful learning, infomuch, that in his latter days men were aftonished that with fuch a fuperiority in one branch, he fhould be fo near eminence in all the reft. Upon the foundation of the Academy of Sciences at Petersburgh, in 1723, by Catharine the First, the two younger Bernouilli had gone thither, promifing, when they fet out, to endeavour to procure Euler a place in it; they accordingly wrote to him foon after, to apply his mathematics to phyfiology; he did fo, and ftudied phyfic under the best phyficians at Bafil, but in 1727 published a differtation on the nature and propagation of found; and an anfwer to the queftion on the mafting of fhips, which the Academy of Sciences at Paris judged worthy of the acceffit. Soon after this he was called to Petersburgh, and declared adjutant to the mathematical clafs in the academy, clafs, in which, from the circumftance of the times, as Newton, Leibni and fo many other great men w juft dead, no eafy laurels were to gathered. Nature, however, who organized fo many mathematicians one time, was not yet tired of her racles, and fhe added Euler to number. He was, indeed, much wanted; fcience of the calculus_integralis, bas come out of the hands of its create was ftill too near the ftage of its fancy to be perfect. Mechanics, namics, and efpecially hydrodyna and the fcience of the motion of heavenly bodies, felt the imperfectio The application of the differential culus to them had been fufficien fuccefsful, but there were difficul whenever it was neceffary to go fre the fluxional quantity to the fuc With regard to the nature and prope ties of numbers, the writings of mat (who had been fo fuccefsful them) and together with thefe all profound refearches, were lot. gineering and navigation were reduc to vague principles, and were found on obfervations often contradictor more than on a regular theory. T irregularities in the motions of th celestial bodies, and especially th complication of forces which influenc that of the moon, was ftill the difgra of geometers. Practical aftronomy ftill to wrestle with the imperfecu of telescopes, infomuch, that it co hardly be faid that any rule for makin them exifted. Euler turned his e to all thefe objects; he perfected tie calculus integralis; he was the invente: of a new kind of calculus, that e Sines; be fimplified analytical oper tions; and, aided by these powertil helpmates, and the aftonishing facility with which he knew how to fubdue expreffions the most intractable, he threw a new light on all the branches of the mathema matics. But at Catharine's Such labours demanded fome relaxation; the only one which Euler admitted was mufic, but even to this he could not apply without being accom panied by the fpirit of geometry. They produced together an 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 mufic 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 the compofer and maker of inftruments. The doctrine, likewife, of the genera and the modes of mufic is here marked out with all the clearnefs and precifion which diftinguifh the works of Euler. As to the theory, the physical part of which is beyond difpute, Mr. Euler contends that all the pleasure of harmony arifes from the love of order in man, in confequence of which, all the agreeable fenfations excited by hearing fine mufic come from the perception of the relations which the different founds have to each other, as well with regard to the duration of their fucceffion, as to the frequency of the vibrations of the air which produces them. Mr. Euler's fyftem refts upon this metaphyfical principle, which he has modified and applied to all the parts of mufic. The principle may be infufficient, but it is impofiible to reafon with more fubtlety and penetration upon it than Euler has done. the academy was threatened with as ftill living. 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 queftion of the tides, an important question, but which demanded an almoft infinite number 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 fuch a triumvirate of candidates, as the altars of fcience had not often beheld. Euler's memoir is remarkable On the theory of the more remarkable curves-the nature of numbers and feries-the calculus s--the movement of the celestial bodies--the attraction of fpheroidico-elliptical bodies-the lolution of the ifoperimetrical problem-and an infinity of other objects, the hundredth part ch would have made an ordinary man illustrious. markable for the clearness with which he explains the effects which the action of the fun and moon, exclufively of other forces, exercife on the fea; for his noble determination of the earth's figure, in as much as it is changed by the action of the forces; for the penetration with which, in confidering the motions of the fea as ofcillatory, he fupplies the effects of the vis inertia of the waters, which he had been obliged to fuppofe null in the begin ning, for the happy integrations, which the confideration of this reciprocal motion required; and, finally, for the fagacity fhewn in the explanation of the feveral phenomena of the tides, according to the theory laid down. The agreement of the feveral 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 ether rejected, they not only arrived at the fanie end of the journey, but met feveral times on the road; particularly in the determination of the tides under the frozen zone. Thilofophy, indeed, led thefe two great men by two different paths; BerRouilli, who had more patience than his friend, fanctioned every phyfical hypothefis he was obliged to make by painful and laborious experiment. Thefe Euler's impetuous genius difdained, and, though his natural fagacity did not always fupply the lofs, he made amends by his fuperiority in analyfis, 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 Second, who had juft afcended the Pruflian throne. He was invited to affift him in forming an academy of fciences out of the wrecks of the Royal Society founded by Leibnitz. The tottering ftate of the Peterburgh Academy, under the regency, made it neceffary for our philofopher to comply with thefe offers. No part of his multifarious labours is, perhaps, a more wonderful proof of the extenfivenefs and facility of his genius, than what he executed at Berlin, at a time wh he contrived that the Petersburgh a fhould not fuffer from the lofs of t Pofterity will with difficulty beley that the life of one man could be fu cient for fo many works, and on fis abftrufe fubjects. In 1744, Euler published a comp treatife of ifoperimetrical curves which he fowed the feeds of the cale of variations, by confidering the cur which differ infinitely little from propofed curve. The fame year beh the theory of the motions of the nets and comets; the theory of netifm, which gained the famous prize; and the much-improved flation of Robins's Treatife on nery. In the year 1746, his theory of and colours overturned Newton tem of emanations, as did another the once triumphant Monads of W and Leibnitz. Navigation now feemed the branch of ufeful knowledge in the labours of analysis and geo had not been employed. The graphical part alone, and that relates to the direction of the cou fhips, had been treated by geom cians conjointly with nautical nomy. Euler was the first who ceived and executed the proje making this feience complete. A moir on the motion of floating communicated to the academ tertburgh in 1735, by M. le Crois. him the first idea. His great the fubject was published by the. demy in 1759, in which we fird fyftematic order, the most f things in the theory of the equal and motion of floating bodie on the existence of fluids; this followed by a fecond part, whi nothing to be defired on the i except the turning it into a lar cafy of accefs, and divefting it t calculations which prevented is t of general utily. Accordingly, in from a converfation with Ai Knowles, and other affiftance, or the Scientia Navalis, 2 vols. 4to. produced the Theorie complet Conftruction et de la Manawores da • This work was inftantly traninto all languages, and the aureceived a prefent of fix thoufand from the French King; he had e had three hundred pounds from English parliament, for the theoby the afliftance of which Mayer lanar tables. i now it was time to collect into tematical and continued work he important difcoveries on the mal analyfis, which Euler had making for thirty years, and lay difperfed in the memoirs of rent academies. This, accordnow employed our profeffor, e prepared the way by an elemen, containing all the previous tes for this ftudy. This is called in to the Analyfis of Infini kas introduction was foon followed e author's feveral leffons on the integralis and differentialis. The of the first of thefe works confifts e point of view in which Euler hewn its first principles; in the atical arrangement which he has to this matter; in the method obtains throughout the whole * work; in the clearness with he has demonftrated the ufe of ellas, with regard to the docof jeries, and the theory of greater 4. third volume of his calculus incontains the new kind of calcuth which Euler has enriched the s of infiniteffimals; i. e. the calof variations. It has been already ped, that what give rife to it was ilperimetrical problem. This ely feifed by M. de la Grange, fengaged it from all geometritenderations, made an analytical em of it, and folved it by the alculus, which Mr. Euler has fo perfected fince that time, and th he has called the calculus of va, because the relation betwixt ariable quantities is itfelf confidas variable. To enumerate the various works of great man would far exceed our We muft now haften to his character. Yet we muft add, a that he engaged to furnish the academy with papers fufficient to fill their volumes for twenty years after his death, and he did not break his promife. For he prefented feventy papers, through Mr. Golofkin, in the courfe of his life, and left two hundred and fifty more behind him; of which every one contains fomething important. They abound in the happiest integrations; in multiplicity of refined artifices of the higheft analyfis; in the moit profound refearches into the nature and properties of numbers; in the ingenious demonftration of feveral theorems of Fermat's; in the folution of a quantity of very difficult problems, on the equilibrio and motion of folid, flexible, and elastic bodies; and in the unweaving of feveral apparent paradoxes. Whatever is most thorny, and moft difficult in the theory of the motion of the heavenly bodies, is here made as clear as it could be made by the calculations of the greatest of geometricians. The moft ancient of thefe memoirs form the collection this year published, under the title of Opufcula Analytica. Such were Mr. Euler's labours, and they entitle him to immortality! His memory fhall endure till science herself is no more! Few men of letters have written as much as Mr. Euler; no geometrician. has ever embraced fo many objects at one time, or has equalled him, either in the variety or magnitude of his difcoveries. When we reflect on the advantages which mankind derive from fuch men, we cannot help indulging a with (vain, alas! as it is) that their illuftrious courfe were prolonged beyond the term allotted to humanity. Euler's, though it has terminated, was a very long, and a very honourable one; and it affords us fome confolation for his lofs, to think that he ran it exempt from the ordinary confequences of extraordinary application, and that his lait labours abound in proofs of that vigour of underftanding which marked his earlier days, and which he preferved to the end of his exiftence. Some fwimmings in the head, which feifed him on the firft days of last Sep tember, |