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feem to call for affiftance from the Gods, though defpair at the fame inftant overwhelms him at the fight of his own fate, and that of his unfortunate fons, half smothered and devoured by the monsters, who crush them all three. The expreflion of that group is admirable: but the fculptors have diftinguished a principal object in it: for, although the fons are equally well executed, and the one to the left in particular claims our fympathy, by the horrid ftate of pain in which he is reprefented, (one of the ferpents beginning to tear open his fide) yet the father attracts the chief notice. He is that principal part of the whole, to which all others are referred; and it is by that judicious fubordination and reference, that the artifts have found means to imprefs the fpectator with all the fentiments they meant to convey, and which, without labour to the mind, give it all the pleasure fuch a reprefentation is able to produce.

The pleafure we receive from a good painting, is alfo chiefly owing to this fubordination of parts, and reference of them to the principal object. Painters call it compoJition; and those masters have obtained the first rank among them, who have been most attentive to it. It was Raphael's and Rubens' forte; and being the happy refult of great genius, combined with a well cultivated tafte, is always fure of caufing the most agreeable fenfations to the mind that contemplates the effects of it.

In poetry, but particularly in epic and dramatic performances, the obfervation or neglect of this rul: becomes, likewife, the teft of the pleasure they afford to a perfon of tafte. The different actors that appear in the narration, or on the scene, muft all concur in their different itations to fet off the main object, and keep the attention fixed upon it; or else, the mind, diftracted with a multiplicity of objects, that feem to lay an equal claim to its notice, and perhaps to its feelings, grows weary, difgufted, and indifferent to them all. Unity of action, in painting and in poetry, is another confequence of the attention of artifts to the principle I meant to illuftrate. For nothing can be more fatisfactory to the mind, than to take in, as it were, with a glance, a multitude of facts connected together, by their mutual relation to fome great and important action. One may intro duce, indeed, in a poem, several fables or plots, and collect in it, as it were in a gallery of pictures, a feries of portraits. It is what Ovid, Statius, A iofto, Shakespeare in his hiftorical plays, and teveral others, have done. But, many centuries before the oldeft of them, the great genius of Homer had conceived, that it would be prefenting a fpectacle far

more agreeable to the mind, if a multitudė of perfons were collected together in the fame picture, and were made to contribute to one and the same action; and upon that idea he formed the plan of the epic poem.

Many years after him, Efthylus, the first who gave fome order and fome propriety to the drama, took from the epic poem. the plan of tragedy, which he made to be, the reprefentation of an event unfolded in all its circumftances. That great Poet likewife understood that this representation would far more please the mind, if all the tcenes of it were connected by fome principal action, which would help the memory to retain them easily.

He carried, moreover, this idea still farther, and to the unity of action joined thofe of time and place. Sophocles and Euripides, but especially the former, followed him pretty thretly, and Ariftotle drew his rules from their practice. Swayed by the autho rity of great names, and, perhaps, led away too far by this principle, that there is a pleafure inherent in whatever enables the mind to get a clear and diftinct perception of the object prefented to it, the French critics defended, and the French dramatic poets wrote after, thefe rules. In England, the amazing genius of Shakespeare, probably unacquainted with Ariftotle and his precepts, having early, and in general happily, foared above all reftraints, gave, perhaps, a bias to the tafte of the nation; or a fanétion, at least, to future dramatic authors, for not attending fcrupulously to the ftrict unities. Thefe, however, were alto defended by the English critics, and, in theory, admitted by the beft poets: but the practice did not correfpond; and there is not a theatre at prefent in Europe, in which thefe rules are lefs obferved.

I do not mean this as an abfolute re. proach. Convinced, as I am, that the pleafares of the heart are much fuperior to thofe of the mind, I think, that rules invented to give eate and pleature to the latter, may often be facrificed to a multitude of interenting events and fituations, that raife ftrong emotions in the former, and ftrike it forcibly. But, at the fame time, illufion being the charm of theatrical reprefentations, care ought to be taken not to deftroy it, nor diminish the concern and fympathy of the fpectators, by too great a deviation from probability. If, on the itage, an old man were to play the part of a young one; if, the icene being ia a palace, the fceneries were to prefent trees and landscapes to our view; if the dreffes did not correlpond, in fome degree, to the dignity of the persons reprefented; all thefe dif cordances would offend us.

The ame applicable to the deviation

from the three unities. If, in a drama, the principal actions are multiplied, if in the fpace of a few hours many centuries are made to elapfe, if the spectator is tranfport ed in an inftant from one part of the world to another, all thefe abfurdities become fo many warnings against the falfity of the fpec. tacle; and a voice feems to iffue out of them, which bids us not to give fincere tears to feigned misfortunes.

Such are the arguments of the critics who follow the rules of Ariftotle. Lord Kaims, on the other fide, proves, from the different nature of the Grecian and the modern drama, that the unities of time and place are by no means fo neceffary with us, as they were with the ancients.

The interruption of the representation, on our theatre, between the different acts, gives the mind a facility of fuppofing any length of time, or change of place; and it becomes not more difficult for the fpectator at the beginning of an act to imagine a new place, or a different time, than it was at first, to imagine himself at Athens, or in a period of time two thousand years back.

But the fame freedom cannot be taken with the unity of action. The pleasure which the mind, as we obferved above, receives from a chain of facts connected together, and tending to one common end, ren. ders this unity effential, alike in epic and dramatic compofitions. Every thing, however beautiful in itself, that breaks this chain, or interrupts this relation, looks like an excrefcence, and becomes unpleasant. An epic poem with two principal actions, like a play with two main plots, would foon confufe and tire the reader and the spectator; and fo far do the rules of Ariflotle agree with nature. An episode and an under-plot may be allowed for the fake of variety; but they must be

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connected with the principal action, or elle they become great blemishes. Milton, in this respect, as indeed in many others, has the advantage over Homer and Virgil. His epifode of the battle of angels, and the creation of the world, is more intimately connected with his fubject, than the defcription of Achilles' fhield, or even the defcent of Æneas into hell. Far from breaking the unity of action, it rather ftrengthens it, by making us acquainted with the caufe of what we have read, and of what is to follow. It is therefore productive of great mental enjoyment, as there is no relation that pleases the mind more, than that of cause and effect.

This great rule, of the unity of action, is an infuperable objection to tragi-comedy; and inattention to it fhocks perfons of taste in fome of our best plays. In the Provoked Hufband, for instance, all the scenes relating to the family of the Wrong beads, however laughable, and characteristic in themfelves, are certainly to be accounted blemishes, because they ftop the tide of fentiment raised by the interefting fcenes between a fenfible, loving, and justly incensed husband, and a giddy, extravagant, though good-natured wife.

This differtation on the unities will allo be looked upon, I fear, as an excrefcence to this paper, alleady too long; but I indulged myself in it with the thought that it might, probably, give room to fome interefting converfation-the avowed purpofe of the effays prefented to this Society-and in that light, I beg, and I hope for your indulgence.

From what has been read, it will appear, that regularity and contrafi, proportion and congruity, uniformity, variety, and fimplicity, in the objects prefented to the mind, give it an exercife, which is attended with neither trouble nor fatigue, and which is therefore agreeable.

MEMOIRS of the LIFE and WRITINGS of the late celebrated L. EULER. EONARD EULER, Profeffor of Mathematics, Member of the Imperial Academy of Petersburg, ancient Director of the Royal Academy of Berlin, and Fellow of the Royal Society of London, as alfo Correspondtut Member of the Royal Academy of Sciences at Paris, was born at Bafil, April 15th, 1707, of reputable parents. The years of bis infancy were paffed in a rural retreat, where the examples of pious and virtuous parents contributed, no doubt, to form in him that amiable fimplicity of character, and unCommon purity of fentiments and manners, which were manifefted during the whole courfe of his life.

his clerical profeffion, yet he had applied himself, with fuccefs, to the mathematics, under the celebrated James Bernoulli; and, though he defigned his fon for the ministry, he initiated him into this fcience, among the other inftructions of his early education.

Though the ftudies of his father were chiefly directed toward branches of knowledge that had a more immediate relation to ECROP. MAG.

When young EULER was fent to the Univerfity of Bafil, he attended regularly the different Profeffors. As his memory was prodigious, he performed his academical talks with uncommon rapidity, and all the time he gained by this was confecrated to geometry, which foon became his favourite study. The early pro is he made in this fcience, only added new ardour to his application; and thus he obtained a diftingu fhed place in the attention and eftcem of Profefior John Bernoulli, who was, at that time, one of the

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first mathematicians in Europe. EULER became his favourite pupil. He was ftruck with a kind of aftonishment at the afpiring genius and rapid progrefs of the young mathematician and as his own occupations would not admit of his giving the ardent pupil fo much of his time as EULER defired, he appointed one day in the week for removing the difficulties which his difciple had met with in perufing the works of the moft profound mathematicians.

In 1723, M. EULER took his degree as Master of Arts, and delivered on that occafion a Latin difcourfe, in which he drew a comparison between the philofophy of Newton and the Cartehan system, which was received with the greatest applause. He afterwards, at his father's defire, applied himself to the ftudy of theology, and the Oriental languages. Though thefe ftudies were foreign to his predominant propenfity, his fuccefs was confiderable, even in this line: how ever, with his father's confent, he returned to geometry, as his principal object. He continued to avail himself of the counfels and

inftructions of M. Bernoulli; he contracted an intimate friendship with his two fons, Nicholas and Daniel, and it was in confequence of thefe connections, that he became afterwards the principal ornament of the Academy of Petersburg.

The project of erecting this Academy had been formed by Peter the Great; it was executed by Catherine I.: and the two young Bernoullis, being invited to Petersburg in 1725, promited Euler, who was defirous of following them, that they would use their utmoft endeavours to procure for him an advantageous fettlement in that city. In the mean

time, by their advice, he applied himself

with ardour to the ftudy of phifiology, to which he made a happy application of his mathematical knowledge; and he attended the medical lectures of the mott eminent Profeffors of Bafil.

This ftudy, however, did not wholly engrofs his time: it did not even relax the activity of his vaft and comprehentive mind in the cultivation of other branches of natural fcience. For while he was keenly engaged in phifiological refearches, he compofed a Difirtation on the nature and propagation of frund, and an anfwer to a prize queition, con cerning the maling of ships, to which the Academy of Sciences adjudged the acceffit, or fecond rank, in the year 1727. From this latter ducourfe, and other circumstances, it a spears, that EuDER had early embarked in the curious and important thudy of navigation, wn. b he afterwards enriched with fo many Valuable MDW Nes,

M. EULER'S merit would have given him an easy admiffion to honourable preferment, either in the magistracy or university of his native city, if both civil and academical honours had not been there diftributed by lot. The lot being against him in a certain promotion, he left his country, fet out for Petersburgh, and was made joint professor with his countrymen, Meffrs, Hermann and Daniel Bernoulli, in the univerfity of that city.

At his first fetting out in his new career, he enriched the academical collection with many Memoirs, which excited a noble emulation between him and M. D. Bernoulli; and this emulation always continued, without either degenerating into a selfish jealousy, or producing the leaft alteration in their friendship. It was at this time that he carried to new degrees of perfection the integral calculus, invented the calculation of finulles, reduced analytical operations to a greater fimplicity, and thus was enabled to throw new light on all the parts of mathematical science.

In 1730, he was promoted to the Profefforfhip of Natural Philofophy; and in 1733

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he fucceeded his friend D. Bernoulli in the mathematical chair. In 1735, a problem was propofed by the Academy, which required expedition, and for the folution of which feveral eminent mathematicians had demanded the space of fome months. problem was folved by EULER in three days, to the great aftonishment of the Academy; but the violent and laborious efforts it colt him threw him into a fever, which endangered his life, and deprived him of the ufe of his right eye.

The Academy of Sciences at Paris, which, in 1738, had adjudged the prize to his me

moir Concerning the nature and properties of fire, propofed, for the year 1740, the in portant fubject of the fea-tides, a problem whofe folution required the most arducus calculations, and comprehended the theory of the folar fyftem. EULER'S difcourfe un this question was adjudged a mafter-piece of analysis and geometry; and it was more honourable for him to fhare the academical prize with fuch illuftrious competitors as Colin Maclaurin and Daniel Bernoulli, than to have carried it away from rivals of lefs magnitude. Rarely, if ever, did fuch a brilliant competition adorn the annals of the Academy; and no fubject, perhaps, propofed by that learned body was ever treated with fuch accuracy of investigation and force of genius, as that which here difplayed the philofophical powers of these three extraordinary men.

In the year 1741, M. EULER was invited to Berlin, to augment the luftre of the academy, that was there rifing into fame, under

under the anfpicious protection of the prefent King of Pruflia; for whom the Mufes and the Sciences have prepared a wreath, which will bloom unfaded to the latest ages. He enriched the laft volume of the Mifcellanies (Melanges) of Berlin with five memoirs, which make an eminent, perhaps the principal, figure in that collection. These were followed, with an astonishing rapidity, by a great number of important refearches, which are fcattered through the Memoirs of the Pruffian Academy; of which a volume has been regularly published every year, fince its eftablishment in 1744.

The labours of EULER will appear more efpecially aftonishing, when it is confidered, that while he was enriching the Academy of Berlin with a prodigious number of memoirs, on the deepest parts of mathematical science, containing always fome new points of view, often fublime truths, and fometimes difcoveres of great importance; he did not difconLate his philosophical contributions to the Academy of Petersburgh, which granted him a penfion in 1742, and whofe Memoirs difplay the marvellous fecundity of EULER'S genus.

and 1772, were defigned to obtain from the labours of aftronomers a more re perfett Theory of the Moon. M. EULER, affifted by his eldeft fon*, was a competitor for thefe prizes, and obtained them both. In this laft memoir, he referved for farther confideration, several inequalities of the Moon's motion, which he could not determine in his first theory, on account of the complicated calculations in which the method he then employed had engaged him. He had the courage afterward to review his whole theory, with the affiftance of his fon, and Meffrs. Krafft and Lexell, and to purfue his researches, until he had conftructed the new tables, which appeared, together with the great work, in 1772. Inftead of confining himself, as before, to the fruitless integration of three differential équations of the fecond degree, which are furnished by mathematical principles, he reduced them to the three ordinates, which determine the place of the Moon; he divided into claffes all the inequalities of that planet, as far as they depend either on the elongation of the Sun and Moon, or upon the excentricity, or the parallax, or the inclination of the lunar orbit. All thefe means of investigation, employed with fuch art and dexterity as could only be expected from an analytical genius of the first order, were attended with the greatest success; and it is impoffible to observe, without admiration, and a kind of aftonifhment, fuch immenfe calculations on the one hand, and on the other, the ingenious methods employed by this great man to abridge them, and to faci litate their application to the real motion of the Moon.-But this admiration will become aftonishment, when we confider at what period, and in what circumftances all this was effectuated by M. EULER. It was when he was totally blind, and confequently obliged to arrange all his computations by the fole powers of his memory and his genius. It was when he was embarraffed in his domeftic circunftances, by a dreadful fire, that had confumed great part of his fubftance, and forced him to quit a ruined houfe, of which every corner was known to him by habit, which, in fome meafure, fupplied the place of fight. It was in thefe circumitances that About this time M. EULER was honoured EULER compofed a work, which, alone, was by the Academy of Sciences at Paris with the fufficient to render his name immortal.. place of one of the foreign members of that The heroic patience and tranquility of mind learned body; and, after this, the Academi- which he difplayed here needs no description: cal prize was adjudged to three of his me- and he derived them not only from the love moirs, Concerning the Inequalities in the Motions of fcience, but from the power of religion. of the Planets. The two prize queftions His philofophy was too genuine and fublime proped by the fame Academy for 1770 to ftop its analyfis at mechanical caufes; it

It was with much difficulty that this great man obtained, in 1766, permiffion from the King of Prufia to return to Peterburgh, where he defired to pass the rest of his days. Soon after his return, which was graciously rewarded by the munificence of Catherine 11. he was feized with a violent diforder, which term uated in the total lofs of his fight. A cataract, formed in his left eye, which had been effentiaily damaged by a too ardent application to study, deprived him entirely of the use of that organ. It was in this diftreffing fituation, that he dictated to his fervant, a tailor's apprentice, and was abfolutely devoid of mathematical knowledge, his Elemus of Algebra; which by their intrinfical merit, in point of perfpicuity and method, and the unhappy circumftances in which they were compofed, have equally excited applaufe and astonishment. This work, though purely elementary, difcovers the palpable characterifties of an inventive genius; and it is here alue that we meet with a compleat theory the Analyfis of Diophantus. ̧

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M. J. A. EULER, a fon worthy of his illuftrious father, has alfo enriched the academical Mercuirs of Petersburgh with many learned memoirs.

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led him to that divine philofophy of religion, which ennobles human nature, and can alone form a habit of true magnanimity and patience in fuffering.

Some time after this, the famous Wentzell, by couching the cataract, reftored Mr. EuLER's fight; but the fatisfaction and joy that this fuccefsful operation produced, were of fhort duration. Some inftances of negligence, on the part of his furgeons, and his own impatience to ufe an organ, whofe cure was not compleatly finished, deprived him of his fight a fecond time; and this relapfe was accompanied with tormenting pain. He, however, with the affiftance of his fons, and of Mefirs.. Krafft and Lexel, continued his labours; neither the lofs of his fight, nor the inarmities of an advanced age, could damp the ardour of h's genius. He had engaged to furnish the Academy of Peterburgh with as many memoirs as would be fufficient to compleat its As for twenty years after his death. In the fpace of feven years, he tranfmitted to the Academy, by Mr. Golfwin, above feventy memoirs, and above two hundred more, which were revised and completed by the Author of this Paper. Such of thefe memoirs as were of ancient date were feparated from the reft, and form a collection that was published in the year 1783, under the title of Analytical Works. There is not one of thefe pieces, which does not contain fome new difcovery, or fome ingenious view, that may lead to the fuccefsful investigation of truths yet unknown. They contain the happielt integrations, the most refined and fubJime analytical proceffes, deep researches concerning the nature and properties of num⚫ bars, an ingenious demonftration of feveral theorems of Fermat, the folution of many difficult problems relative to the equilibrium and motion of folid, flexible, and claftic bodies, and explications of feveral feeming paradoxes. No part of the theory of the motion of the celeftial bodies, of their mutual action, and their anomalies, however abstract and difficult, was overlooked, or left unimproved, ly M. EULER. There is not one branch of mathematical fcience that h..s not ben ben fited by his labours: No geometrician ever before embraced fo many objects at the fame time: none, perhaps, over equalled him, either in the number of his publications, or in the multitude and variety of his difcoveries. His mare will live as long as the fciences fubütt: It will go down to the latest ages with the immortal names of DESCARTES, GALILEI, NEWTON, LEIBNITZ, and other illustrious men, whofe genius and virtues have ennobled humanity: it will fhine with an uafading luttre, when many names, which have been railed to fame by the fri

volous part of mankind, in our times, fhall be buried in oblivion.

EULER'S knowledge was more univerfal than could be well expected in one, who had purfued with such unremitting ardour, mathematics and aftronomy as his favourite studies. He had made a very confiderable progress in medical, botanical, and chemical fcience. What was still more extraordinary, he was an excellent fcholar, and poffeffed what is generally called erudition, in a very high degree. He had read, with attention and tafte, the most eminent writers of ancient Rome: he was perfectly acquainted with mathematical literature, and the ancient history of that fcience. T'e civil and literary hiftory of all ages and all nations was fam diar to him; and foreigners, who were only acquainted with his works, were astonished to find in the converfation of a man, whose long life feemed folely occupied in mathematical and phyfical refearches and discoveries, fuch an extenfive acquaintance with the most interefting branches of literature. In this refpect, no doubt, he was much indebted to a very uncommon memory, which feemed to retain every idea that was conveyed to it, either from reading or from meditation. He could repeat the Eneid of Virgil, from the beginning to the end, without hesitation, and indicate the first and laft line of every page of the edition he used.

Several attacks of a vertigo, in the begining of September 1783, which did not prevent his calculating the motions of the aeroftatical globes, were, nevertheless, the fore. runners of his mild and happy paffage from this fcene to a better. While he was amufing hinfelf at tea, with one of his grand-children, he was ftruck with at. apoplexy, which terminated his illuftrious career, at the age of 76.

His conftitution was uncommonly strong and vigorous: his health was good, and the evening of his long life was calm and ferene, fweetened by the fame that follows genius, the public esteem and respect that are never with-held from exemplary virtue, and feveral domeftic comforts which he was capable of feeling, and therefore deferved to enjoy. His temper was even, mild, and cheerful; to which were added, a certain roughness, mixed with fimplicity and good humour, and a happy and pleasant knack of telling a story, which rendered his converfation agreeable. The great activity of his mind was neceffarily connected with a proportion of vivacity and quickness, which rendered him susceptible of warmth and irritation. Hs auger, however, was never any thing more than a tranfitory flath; and he knew no fuch thing as permanent ill-will toward any human being.

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