1.  ARCHIMEDES alone would afford sufficient matter for a volume, in giving a detail of the marvellous discoveries of a genius so profound and fertile in invention. We have seen, that some of his discoveries appeared so much above the reach of men, that many of - the learned of our days found it more easy to call them in doubt, than even to imagine the means, whereby be had acquired them. We are again going to produce proofs of the fecundity of genius belonging to this celebrated man. Leibnits did justice to the genius of Archimedes, when he said, that if we were better acquainted with the admirable productions of that great man, we would throw away much less of our applause on the discoveries of eminent moderns.

2.  Wallis calls him a man of admirable sagacity, who laid the foundation of almost all those inventions, which our age glories in having brought to perfection. In reality, what a glorious light hath he diffused over the mathematics, in his attempt to square the circle, and in discovering the square of the parabola, the properties of spiral lines, the proportion of the sphere to the cylinder, and the true principles of statics and hydrostatics! What a proof of his sagacity did he give in discovering the quantity of silver, that was mixed gold in the crown of king Hiero; whilst be reasoned upon that principle, that all bodies immerged in water, lose just so much of their weight, as a quantity of water equal to them in bulk weighs ! Hence he drew this consequence, that gold being more compact -must lose less of its weight, and silver more; and that a mingled mass of both must lose in proportion to the quantities mingled. Weighing there... fore, the crown in water and in air, and two masses, the one of gold,. and the other of silver, equal in weight to the crown; he thence determined what each lost of their weight, and so resolved the problem. He likewise invented a perpetual screw, valuable on account- of its being capable to overcome any resistance; and the screw that still goes by his name, used in elevating of water. He, of himself alone, defended the city of Syracuse, by opposing to the efforts of a Roman general, the resources he found in his own genius. By means -of many various warlike machines, all of his own construction, he tendered Syracuse inaccessible to the enemy. Sometimes he hurled upon their land forces, stones of such an enormous size, as crushed whole bodies of them at once, and put the whole army into confusion. And when they retired from the walls, he still found means to annoy them; for with his balistae, he overwhelmed them with arrows innumerable, and beams of a prodigious weight. If their vessels approached the fort, he seized them by the prows with grapples of iron, which he let down upon them from the walls; and rearing them up in the air, to the great astonishment of every one, shook them with such violence, as either to break them in pieces, or sink them to the bottom.

3.  Superior knowledge he had in sciences, and his confidence in the powers of mechanism, prompted him once to say to king Hero, who was his patron, admirer, and friend, “give me where to stand, and I will move the earth.” And when the king, amazed at what he said, seemed to be in hesitation, he gave him a striking proof of his skill, in launching, singly by himself, a ship of a prodigious weight. He built likewise for the king an immense gallery, of twenty banks of oars, containing spacious apartments, gardens, walks, ponds, and all other conveniencies, suitable to the dignity of a great king. He constructed also a sphere, representing all the motions of the stars, which Cicero esteemed one of the inventions, that did the highest honour to human genius. He perfected the manner of augmenting the mechanic powers, by the multiplication of wheels and pulleys; and, in short, carried mechanics so far, that the works he produced surpass imagination.

4.  Nor was Archimedes the only one, who succeeded in mechanics. The immense machines, and of astonishing force, as were those which the ancients adapted to the purpose of war, are a proof, they came nothing behind us in this respect. It is with difficulty we can conceive, how they reared those bulky towers, a hundred and fifty-two feet in -height, and sixty in compass, ascending by many stories, having at bottom a battering-ram, a machine of strength sufficient to beat down walls; in the middle a drawbridge, to be let down upon the wall of the city attacked, in order to open a passage into the town for the assailants; and at the top a body of men, who, being placed above the besieged, harassed them without running any risk. An ancient historian has transmitted to us an action of an engineer at Alexandria, which deserves to have a place here. In defending that city, when it was attacked by Julius Caesar, he, by means of wheels and other machines, drew from the sea a prodigious quantity of water, which he turned upon the adversary, to their extreme annoyance. Indeed, the art of war gave occasion for a great number of instances of this kind, which cannot but excite in us the highest idea of the enterprising genius of the ancients, and the vigour wherewith they put their designs in execution. The invention of pumps by Ctesibus, and that of water-clocks, cranes, anatomical figures, and wind-machines by Heron, and the other discoveries of the Grecian geometricians, are so very numerous, that it would exceed the limits of a chapter, even to mention them.

5.  Should we pass to other considerations, we should find equally incontestable evidences of greatness of genius among the ancients, in the difficult and indeed astonishing experiments in which they so successfully engaged. Egypt and Palestine still present us with proofs of this, the one in its pyramids, the other in the ruins of Palmyra and Balbec.* Italy is filled with monuments and the ruins of monuments, which aid us in comprehending the former magnificence of that people. And ancient Rome even now attracts much more of our admiration, than the modern.

6.  The greatest cities of Europe give but a faint idea of that grandeur, which all historians unanimously ascribe to the famous city of Babylon; which, being fifteen leagues in circumference, was encompassed with walls two hundred feet in height, and fifty in breadth ;t whose sides were adorned with gardens of a prodigious extent, which arose in terraces one above another, to the very summit of the walls. And for the watering of those gardens, they had contrived machines, which raised the water of the Euphrates to the very highest of these terraces; a height equalling that, to which the water is carried by the machine at Marly. The tower of Belus, arising out of the middle of a temple, was of so vast a height, that some ancient authors not ventured to assign the measure of it: others put it at a thousand paces.

*              It is proper to remark, that the temples and immense palaces of Palmyra, whose magnificence surpasses all other buildings in the world, appear to have been built at the time, when architecture was in its decline.

One celebrated historian states the walls surrounding this famous city, to be 350 feet high, and 87 feet thick, so that eight carriages could pass abreast upon them; their circumference is stated, by the same historian, to be sixty English miles; they formed an exact square, each side being fifteen miles in length.

7.  Ecbatane, the capital of Media, was of immense magnificent being eight leagues in circumference, and surrounded with seven in form of an amphitheatre; the battlements of which were of various colours, white, black, scarlet, blue, and orange; but all of them covered with silver or with gold. Persepolis was also a city, which all historians speak of as one of the most ancient and noble of Asia, There remain the ruins of one of its palaces, which measured six hundred paces in front, and still displays the relics of its ancient grandeur.

8.  The lake Mocris is likewise a striking proof of the vast under takings of the ancients. All historians agree in giving it above a hundred and fifty leagues in circuit: yet was it entirely the work of one Egyptian king, who caused that immense compass of ground to be hollowed, to receive the waters of the Nile, when it overflowed more than ordinary, and to serve as a reservoir for watering Egypt by means of its canals, when the overflowing of the river was not of height sufficient to enrich the country. Out of the midst of this lake arose two pyramids, of about six hundred feet in height.

9.  The other pyramids of Egypt, in their largeness and splidity, so fir surpass whatever we know of edifices, that we should be- ready to doubt of the reality of their having ever existed, did they not still exist to this day. Mr. De Chezele, of the academy of sciences, who travelled into Egypt in the last century, to measure them, assigns to one of the sides of the base of the highest pyramid, a length of six hundred and sixty feet, which reduced to its perpendicular altitude, makes four hundred and sixty-six feet. The free-stones, of which it is composed, are each of them thirty feet long; so that we cannot imagine, how the Egyptians found means to rear such heavy masses to so prodigious a height. The Colossus of Rhodes was another of the marvellous productions of the ancients. To give an idea of its excessive bigness, it need only be observed, that the fingers of it were as large as statues, and very few were able with out-stretched arms to encompass the thumb. Pliny and Diodorus Siculus relate, that Semiramis made the mountain Bagistan, between Babylon and Media, be cut out into a statue of herself, which was seventeen stadia high; that is, near two miles: and around it were a hundred other statues, of proportionable size, though less large. And Plutarch speaks of a very great undertaking, which one Stesicrates proposed to Alexander; viz. to make a statue of him out of mount Athos, which would have been a hundred and fifty miles in circumference, and about ten in height. His design was to make him hold in his left hand a city, large enough to contain ten thousand inhabitants ; and in the other an urn, out of which should flow a -river, poured by him into the sea. See also the same Plutarch, vol. 1. p. 705. But Nitruvius gives to this statuary the name of Dinocrates.

10.  In short, what shall we say of the other structures of the ancients, which still remain to be spoken of- Of their cement, which in hardness equalled even marble itself; of the firmness of their highways, some of which were paved with large blocks of black marble; and of their bridges, some of which still subsist, irrefragable monuments of the greatness of their conceptions The bridge at Gard, three leagues from Nimes, is one of them. It serves at once as a bridge and an aqueduct. It goes across the river Gardon, and joins together the two mountains, between which it is enclosed. It comprehends three stories ; the third is the aqueduct, which conveys the waters of the Eure into a great reservoir, which supplies the amphitheatre and city of Nimes. The bridge of Aleantara, upon the Tagus, is still a work fit to raise in us a great idea of the Roman magnificence: it is six hundred and seventy feet long, and contains six arches, each of which measures above a hundred feet from one pier to the other; and its height from the surface of the water is two hundred feet. The broken remains of Trajan’s bridge over the Danube are still to be seen; which had twenty piers of free stone, some of which are still standing, a hundred and fifty feet high, sixty in circumference, and distant one from another a hundred and seventy. I should never end were I to enumerate all the admirable monuments left us by the ancients: the slight sketch here given of them will more than suffice to answer my purpose. As to the ornaments and conveniencies of their buildings, among many I shall mention but one, that of their using glass in their windows, and in the inside of their apartments, just in the same manner as we do. Seneca and Pliny inform us, that they decorated their rooms with glasses; and do not we the same, in the use of mirrors and pier-glasses But what will now shock the general prejudice is, that they should know how to glaze their windows, so as to enjoy the benefit of light, without being injured by the air; yet this they did very early. Before they discovered this manner of applying glass, which is so delightful and so commodious, the rich made use of transparent stones in their windows, such as the agate, the alabaster, the phengistes, the talcum, &c. whilst the poor were under the necessity of being exposed to all the seventies of wind and weather.

11.  If we admire the ancients in those monuments which remain to us, of the greatness of their undertakings, we shall have no less reason for wonder, in contemplating the dexterity and skill of their artists in works of a quite different kind. Their works in miniature are well deserving of notice. Archytas, who was contemporary with Plato, is famous in antiquity for the artful structure of his wooden pigeon. which imitated the flight and motions of a living one. Cicero, according to Pliny’s report, saw the whole Iliad of Homer written in so fine a character, that it could be contained in a nut-shell. And Elian speaks of one Myrmesides, a Milesian, and of Callicrates, a Lacedemonian; the first of whom made an ivory chariot, so small and so delicately framed, that a fly with its wing could cover it; and a little ivory ship of the same dimensions: the second formed ants and other little animals out of ivory, which were so extremely small, that their component parts were scarcely to be distinguished. He says also in the same place, that one of those artists wrote a distich in golden letters, which be enclosed in the rind of a grain of corn.

12.  It is natural here to inquire, whether in such undertakings as our best artists cannot accomplish, without the assistance of microscopes, the ancients had not any such aid; and the result of this research will be, that they had several ways of helping the sight, of strengthening it. and of magnifying small objects Jamblichus says of Pythagoras, that he applied himself to find out instruments as efficacious to aid the hearing as a rule, or square, or even optic glasses, were to the sight. Plutarch speaks of mathematical instruments, which Archimedes make use of, to manifest to the eye the largeness of the sun; which may be meant of telescopes. Aulus Geflius, having spoken of mirrors, that multiplied objects, makes mention of those which inverted them; and these of course must be concave or convex glasses.-Pliny says that in his time artificers made use of emeralds to assist their sight, in works that required a nice eye; and, to prevent us from thinking that it was on account of its green colour only that they had recourse to it, he adds, that they were made concave, the better to collect the visual rays; and that Nero made use of them in viewing the combats of the gladiators. In short, Seneca is very full and clear upon this head, when he says, that the smallest characters in writing, even such as almost entirely escape the naked eye, may easily be brought to view, by means of a little glass ball filled with water, which had all the effect of a microscope, in rendering them large and clear: and indeed this was the very sort of microscope, that Mr. Gray made use of in his observations. To all this add the burning-glasses made mention -of before, which were in reality magnifying-glasses: nor could this property of them remain unobserved.

13.  It would be a needles task to undertake to show, that the ancients have the preeminence over the moderns in architecture, engraving, sculpture, medicine, poetry, eloquence, and history, The moderns themselves will not contest this with them: on the contrary, the height of their ambition is, to imitate them in those branches of science. And indeed what poets have we to produce, fit to be compared with Homer. Horace, and Virgil; what orators equal to Demosthenes and Cicero; what historians to match Thucidides, Xenophon, Tacitus, and Titus Livius; what physicians, such as Hippocrates and Galen; what sculptors like Phidias, Polycletus, and Praxiteles; what architects to rear edifices similar to those, whose very ruins are still the object of our admiration Till we  have those, whom we can place in competition with the ancients in these respects, it will become our modesty to yield to them the superiority.

14.  ‘Tis worth notice, that the merit of the ancients is generally most controverted by those, who are least acquainted with them. There are very few of those who rail at antiquity qualified to relish the original beauties of the Iliad, Aeneid, and other immortal performances, of the authors just enumerated. There are fewer still, who are capable at one view to take in all that variety of science, which bath been laid before the reader, and which comprehends in it almost the whole circle of our knowledge. Of the remaining admirable monuments, which show to what perfection the ancients carried the arts of sculpture and design, how few have taken any due notice; and of those, how very few have been able to judge of their- real value True it is, that time and the hands of barbarians have destroyed the better part of them; yet still enough is left to prove the excellence of what hath perished, and to justify encomiums bestowed on them by historians. The group of figures in the Niobe of Praxiteles,* and the famous statue of Lacoon, still to be seen at Rome, are, and ever will be models of beauty and true sublime in sculpture; where much more is to be admired, then comes within the comprehension of the eye. The Venus de Medicisa the Hercules stifling Antacus, that other Hercules, who rests upon his club. the dying Gladiator, and that other in the vineyard of Borghese, the Apollo of the Belviderejf the maimed Hercules of the same place, and the Equerry in the action of braking a horse on mount Quirinal, are all

* Some ascribe this piece to Scopas, the cotemporary of Phidia, and who reached the times of Praxiteles. It is still in being, and to be seen at Rome.

The joint labour of Agesander, Folydorus and Athenodorus, of Rhodes: who, according to Maffeus, lived all of them about the eighty-eighth Olympiad; it is in the Belvidere at Rome.

The workmanship of Cleomenes, the Athenian, still to be seen in the Farnesian palace at Florence.

Ascribed to Polycletus, who made the Colossial statues of Juno in gold and ivory, at Argos, which no longer exist.

The work of Glycon, still remaining in the Farnesian palace at Florence

Done by Ctesilas, or Ctesias, in the gallery of the capitol.

By Agathias, of Ephus.

By the same. These two last were at Antiuin, now Nettuno.

Ascribed by some to Phidias, by others to Praxiteles. Those who assign it to the latter imagine it to be that of Alexander breaking Bucephalus. But if it  was done by the former, it must be another subject, that sculptor having flourished. about a century before. It is thought that nothing of this is now remaining His Olympian Jupiter was an object of admiration for many ages, and continued

of them monuments. which loudly proclaim the just pretensions of the ancients to a superiority in those arts. These pretensions are still further supported by their remaining medals, the precious stones of their engraving and their cameos. There is still to be seen medal of Alexander the Great, on the reverse of which there- is sitting on his throne, finished with the finest strokes of art; not a feature, even the smallest, but seems to declare his divinity: stones engraved by Pyrgoteles, who had an exclusive privilege engraving Alexander’s head, as Lysippus had of making his statue, and Apelles of painting him; those of Dioscorides, who engraved the heads on the seals of Augustus; the celebrated Medusa, Diomedes, Cupid, and other performances of Solon; in short, all the other nent pieces of sculpture and engraving, so carefully sought the curious, and with so much reason admired by connoisseurs, under it needless for me to enlarge on the praises of artists sufficiently -renowned, by being the authors of works so lasting and so precious

15.  As to painting, so few and so scanty are the relics, and so more injured by time, than the statues and other remains of sculpture in bronze and marble, that to form a proper judgment of the merit of the ancients in it appears at first very difficult. Yet if due attention be paid to what of that kind has been discovered at Rome, and more lately in the ruins of Herculaneum, we shall be obliged to admit the -justice of that applause, which the painters of antiquity received from their contemporaries; an applause confirmed by all we -have had occasion to observe of their excellency in sculpture. The ancient paintings in freses, still to be seen at Rome, are, a reclining Venus,at full length,* and seven other pieces, taken out of a vault at the foot of mount Palatine; among which are a satyr drinking out of a horn-, and a landscape with figures, both of the utmost beauty. There--are also a sacrificial piece, consisting of three figures and an Oedipus, and a sphinx; which all of them formerly belonged to the tomb of Ovid. These are specimens from which, without temerity, we may form a very advantageous judgment of the ability of the masters who executed them; but those discovered at Herculaneum; disclose beyond all others, a happiness of design and boldness of expression, that could proceed only from the hands of the most accomplished artist. The picture of Theseus vanquishing the Minotaur, that of the birth of

still at Constantinople, in the beginning of the thirteenth century; together with the beautiful Caidan Venus, the happy work of Praxiteles, and the statue of Opportunity, by Lysippus. It is probable, these fine remains were destroyed at the taking of the city by Baldwin.

*              In the Palace of Barbirini.

In the gallery of the college of St. Ignatus.

In the possession of Cardinal Alexander Albani.      

In the Villa Altieri.  

Telephus, that of Chiron and Achilles,* and that of Pan and Olympe, present innumerable beauties to all who have discernment, and strike most the eye of the more intelligent beholder. If indeed we examine the countenance of Achilles in the original picture itself and not in the imperfect impression published of it, we shall perceive in it something inimitably just and line in its air, energy and expression; every thing contributes to display the young hero’s ardour for glory ; and he looks with such eagerness and impatience on his master as if he wanted but an opportunity to acquire it- at all hazards. There were found also, among the ruins of that city, four capital pictures, wherein beauty of design seems to vie with the most skilful management of the pencil. They appear to be -of an earlier date than these we have spoken of, which belong to the first century ; a period when painting, as Pliny informs us, was in its decline. What then are we to think of the paintings of Zeuxis and Apelles, when even this art itself, in its very decline, was capable of exhibiting such productions as these, which however justly exciting our praise, seem to have been but of an inferior kind, when compared to the noble performance of those great masters This accounts for the silence observed by Pliny,- and the other historians, in relation to them.

16.  Another kind of work, of affinity to painting, and which deserves to find a place here, is the mosaic, which the Romans made use of in paving their apartments. One of the most beautiful monuments of that kind, and elegantly described by Pliny, was found some years ago in the ruins of Adrian’s famous country seat at Tivile. It represents a basin of water, with four pigeons around the brim of it, one of which is drinking, and in that attitude its shadow appears in the water. Pliny in the same place says, that on the same pavement, the breaking up of an entertainment was so naturally represented, that you would have thought you really saw the scattered fragments.

17.  Music is as ancient as the world. It seems to have been born with man, to accompany him in his painful career, to sweeten his labours, and charm away his cares. This was its first employment. It was afterward consecrated to divine service, and having thus risen in its dignity, became of principal account among the people, in accompanying the traditional narratives, relative to the characters and’ exploits of their ancestors. Hence it came to be the first science wherein their children were instructed. Music, and poetry its ally, accompanied all their studies. They even deified those, who first distinguished themselves in it: Apollo was of this number. Orpheus, Amphion, and Linus, for their eminent talents in this art, were accounted more than men. Philosophers applied themselves to it; Pythagoras, Socrates, and Plato, recommend it as worthy of being cultivated, not only by their disciples, but by the best regulated states. The Grecians, and particularly the Arcadians, enacted the study of it by law. regarding it as indispensably necessary to the common, welfare. A science so generally cultivated, should have arrived at perfection very early; yet did it continue in a state of imbecility and without principles till the times of Pythagoras. We have seen before in what manner this great man first determined its fundamental rules.

*              These two are, perhaps, the performances of Parrhasius.

Till his time, music was so vague and uncertain that it required as extraordinary effort of genius to reduce it to method and order. He precisely determined the proportions which sounds bear one to other, and regulated harmony upon mathematical principles. let the precision of his mind carry him too far, in subjecting music to the judgment of reason alone, and admitting no pauses or rests, but such as had an arithmetical or geometric proportion in them. texenes, the disciple of Aristotle, thought, on the contrary, that this subject came entirely within the verge of hearing, and that the ear was the only judge of sounds. He therefore regulated the order, the umson and break in tones, solely by the judgment of the earth his system prevailed for some time in Greece. Olympus, a Phrygian. came soon after to Athens, who invented a stringed instrument which, gave the semitones, whereby he introduced so many new graces into music, as gave it entirely another air. He joined Aristoxenes, appealing for the merit of his system to the decision of the ear. At length. the famous Ptolomy appeared, and with superior spirit equally disclaimed the partiality of both sides. He took a middle course, asserting that sense and reason had a joint right to judge of sounds. He accused the Pytbagoreans of fallacy in their speculations, with respect to proportions; as well as of folly in so disregarding the decisions of the ear, as to refuse it that kind of harmony which was agreeable to it, merely because the proportions of it did not correspond with their arbitrary rules. And he charged the partisans of Aristoxenes with absurd neglect of reasoning, in that though they were convinced of the difference of grave and acute tones, and of the proportions subsisting between them; and that those. proportions invariably depended: upon the several lengths of the musical chords; yet they never took the trouble of considering this, so as to enter into the reason of it. Be therefore determined in deciding upon the principles of harmony, to make use not only of reason but also of the ear, as being of aid to one another; and in consequence of this, laid down a sure method for finding out the proportions of sounds. Had the ancients done more with respect to music, than made the discoveries already taken notice of, that science must be infinitely more indebted to them, than it possibly could be to those who succeeded them, for what additions they have afterward made. The’ ancients have the whole. merit of having laid down the first exact principles of music; and the writings of the Pythaoreans, of Aristoxenes, Euclid, Aristides, Nicoma chus, Plutarch, and many others, even such of them as still remain, contain in them every theory of music yet known. They knew, as well as we, the art or noting their tunes, which among them was called the parasemantic, or semeiotic, performed by means of entire letters, either contracted or reversel, placed upon a line parallel to the words and serving for the direction, the one of the voice, and the other of the instrument ; and the scale itself, of which Guy Aretin, is the supposed inventor, is no other than the ancient one of the Greeks a little enlarged, and what Guy may have taken from a Greek manuscript, written above eight hundred years ago. which Kircher says he saw at Mesina in the library of the Jesuits, wherein he found the hymns noted, just as in ‘he manner of Aretin.

18.  As to the effects which music produced, and the manner of performing it, so far were the ancients from filing short of the moderns in these respects, that as to the former, after reducing the accounts we have of it to the most rigid conformity to truth, they still appear therein to have gone far beyond us: and as the latter, though it be alleged, that their instruments were not so complete as ours, and that they knew not, nor put in practice those divisions in harmony which enter into our concerts; yet this seems to be a groundless objection. The lyre, for instance, was certainly a very harmonious instrument, and in Plato’s time was so constructed, and so full of variety, that he regarded it as dangerous, arid too apt to relax the mind. In Anacreon’s time it had already obtained forty strings, Ptolomy and orphyry described instruments resembling the lute and theorby, having a handle with keys belonging to it, and the strings extended from the handle over a concave body of woods There is to be seen at Rome an ancient statue of Orpheus, with a musical bow in his right hand, and a kind of violin in his left. In the commentaries of Philostrastus by Vigenere, is a medal of Nero with a violin upon it. In the passages referred to below, it plainly appears, that the flute was carried to so high a degree of perfection by the ancients, that there were various kinds of them, and so different in sound, as to be wonderfully adapted to express all manner of subjects. And in Tertullian we meet with a very full description of an hydraulic organ, invented by Archimedes, which was so far from being inferior in any respect to ours, that it plainly exceeded them in its mechanism, as being made to play by water. “ Behold,” says Tertullian, “ that astonishing and admirable hydraulic organ of Archimedes, composed of such a number of pieces, consisting each of so many different parts, connected together by such a quantity of joints, and containing such a variety of pipes for the imitation of voices conveyed in such a multitude of sounds, modulated into such a diversity of tones, breathed from so immense a combination of flutes; and yet all taken together constitute but one single instrument.”

19.  Should we for the present confine our views only to harmony or the consenting notes in music, we shall find that the ancients were by no means ignorant of it. Many respectable authors have cursorily treated of it. Macrobius speaks of five notes, among which the bass bears such a symphony with those above it, that however different they’ be among themselves, they come to the ear as if they altogether composed but one sound. Ptolomy, speaking of the monochord, calls it a mighty simple instrument, as having neither unison, accompanyment, variety, nor complication of sounds. Seneca, in one of his letters, says to his friend, “ Don’t you observe how many different voices a band of music is composed of! There you have the bass,” the higher notes, and the intermediate, the soft accents of and the stories of men, intermingled with the sound of flutes, however separately distinct, form altogether but one harmony of sound, in which each hears a share.” Plato sufficiently makes it appear, that he knew what harmony was, when he says, that music is a very proper study for youth, and should employ three years’ of their time ; but that it was improper to put them upon playing alternately in concert, it being enough for them. if they could accompany their voice with the lyre. And the reason he gives for it is, that the accompanyment of various instruments, the bass with those of a higher key, and the variety, and even opposition of symphonies, where music is played in divisions, can only embarrass the minds of youth. True it is, the ancients did not much practice compound music; but that proceeded only from their not liking it. For Aristotle, after asking, why one instrument, accompanied only by a single voice, gave more delight than that very voice would do with a greater number, replies, that the multitude of instruments only obstructed the sound of the song, and hindered it from being heard. Yet the same author in another place expressly says, that music, by the combination of the bass arid higher tones, and of notes long and short, and of a variety, of voices, arises in perfect harmony. And in the following chapter, speaking of the revolutions of the several planets, as perfectly harmonizing with one another, they being all of them conducted by the same principle, he draws a comparison from music to illustrate his sentiments. “Just as in a chorus,” says he, “of men and women, where all the variety of voices, through all the different tones, from the bass to the higher notes, being under the guidance and direction of a musician, perfectly correspond with one another, and form a full harmony.” Aurelius Cassiodorus defines symphony to be the art of so adjusting the bass to the higher notes, and them to it, through all the voices and instruments, whether they be wind or stringed instruments, that thence an agreeable harmony may result And Horace speaks expressly of the bass and higher tones, and the harmony resulting from their concurrence. All these testimonies therefore uniting in favour of the harmony of the ancients, ought not to leave us the least doubt respecting this branch of their knowledge. We have seen the reason why they did not much use harmony in concert. One fine voice alone, accompanied with one instrument, regulated entirely by it, pleased them better than mere music without voices, and made a more lively impression on their feeling minds. And this is what even we ourselves every day experience.

20.  1 come now to consider the effects, which the ancient music produced, and begin with observing, that it is not at all probable they would unanimously consent to impose upon posterity, in matters delivered with such an air of truth. There is scarcely any thing in history better supported. To begin with sacred story. We find there, that the ministers of Saul bid him send for a player upon an instrument, to relieve him of his malady. The consequence of this was, that David came, and administered the expected relief. And to be convinced, that there was nothing supernatural in this, but that music was at that time a known specific in such maladies as Saul complained of, it need only to be remarked, that those, who gave this, advice, were but household servants. Profane history supports us in this reflection, by a great number of instances of the same kind. Aulus Gellius and Athenaeus make mention of many cures performed among the Thebans by music, and cite Theophrastus as to what happened in his time. Galen, a very grave author, and whose authority is of the greatest weight in subjects of this kind, speaks very seriously of this custom. And Aristotle, Appollonius, Dipscolus, Capella. and many others, speak of singing as a nostrum in many maladies. There is a passage in Tzetzes, which gives rise to a conjecture, that may very naturally accompany these facts. He says, that Orpheus recalled Euridice from the gates of death, by the charms of his lyre. Now to take this literally, one might presume from it, that Eurydice had been bit by a tarantula instead of a serpent, as historians give out, and that Orpheus having recovered her by means of music, as is practised in Italy even at this day, in process of time there was founded on this the well known allegory of his descent into hell. But if, in opposition to this, it be alleged, that there are no tarantulas in Thrace, which is what I cannot take upon me to affirm, the objection is easily evaded by admitting with historians, that she was really bit by a serpent, observing withal, that she might still be cured of that bite by means of music. Theophrastus, among other writers, is quoted by Aulus Gellius, as an ocular evidence of the medical effects of music, in the case of persons bit by serpents or vipers, he work indeed referred to is now lost. Another purpose, to which e ancients applied their music was to alleviate the rigour of their punishments; and in this they displayed their humanity. The Americans entertain the same idea of the power of music, having recourse to it to allay the severity of their toils. Plutarch reports of Antigenidas, that he so roused the spirit of Alexander, by playing on the flute, that in a transport of heroism the prince immediately started up from table, and flew to his arms. Every body hath hear of’ the wonderful influence which the music of the famous Timotheus had over the mind of that prince, when touching his lyre. he so inflamed him with rage, that drawing his sabre he suddenly slew one of his guests; which Timotheus no sooner perceived, than, altering the air from the Phrygian to a softer measure, he stripped him of his fury, becalmed his passion, and infused into him the tenderest feelings of grief and compunction for what he had done. Jamblicus relates’ like extraordinary effects of the lyres of Pythagoras and Empedocles The painter Theon dextrously availed himself of this force of music, when going to make a public exhibition of a piece he had finished wherein a soldier was represented as just ready to assail the enemy, he first of all warmed the spirit of the company by a warlike air, and when he found them sufficiently animated, uncovered the picture, which struck the whole assembly with admiration. Plutarch informs us of a sedition quelled at Lacedernon by the lyre of Terpander; and’ Boetius of rioters dispered by the musician Damon.

21.  To conclude this inquiry respecting the merit of the ancients in music, I shall make but two observations. The first is, that their airs in delicacy very much surpassed ours, and that it is in this respect principally, that we may be said to have lost their music. Of these three kinds of music, the diatonic, chromatic, and the enharmonic, there exists now only the first* and second. The difficulty there was to find voices and hands proper to execute the enharmonic kind, brought it first into neglect, and then into oblivion : insomuch that all now remaining of the ancient music is that of coarser sort, which” knows no other refinement, than that of the whole and the deminote, instead of these finer kinds, which carried on the division of a note into threes and fours. Doubtless the prevalency of that system, which referred the determination of sounds to the judgment of the ear, occasioned the rejection of the enharmonic species, which was too fine for the decision of the ear, and sprung entirely from the Pythagoric system. But this by no means ought to hinder us from acknowledging the excellency of that music above the modern, in the extreme delicacy of its tones. The second observation is, that the variety of manner, in which the ancient music was performed, placed it in a rank of dignity, superior to ours. Our modes are but of two kinds, the flat and the sharp: whereas the ancients modified theirs’ into five, the principal of which were the Ionic, the Lydian, the Phrygian, the Doric, the Aeolic each adapted to express and excite different passions ; and by that means, especially, to produce such effects as we have just now taken notice of, not only from the authentic manner in which they have been recorded, but from the very state and condition in which music at that time was.

*Dutens, is mistaken in saying, first, that only the first, viz, the diatonic kind now remains; and secondly, that this divides the tones into semitones; which certainly is done by the chromatic, and not the diatonic scale.

  CONCLUSION

1.  We have seen in how many truths of the greatest importance the ancients preceded the moderns, or at least pointed out, or prepared the way for their discoveries. It appears also, that the latter have not always bad the disinterestedness to own, that the former guided them in attaining their ends. And here it may not be amiss to remark, that those very philosophers, when their opinions were attacked, or when they dreaded they might be so, recurred to the authority of those great men, to put envy and calumny to silence. Descartes, Mallebranche, and some Newtonians, are instances of this.

2.  The first of these, at the conclusion of his principles of philosophy, advertises the reader, that he had advanced nothing but what had been authorised by Aristotle, Democritus, and many other philosophers of antiquity. Mallebranche, observing his system accused not only of being false, but of being impious, immediately bad recourse to the authority of St. Augustin. And some Newtonians, upon seeing that attraction was by many regarded as a mere whim, set about proving, that the ancients owned and taught it; trusting by this to open a reception for it. Some, to conciliate the favour of the public, have had resource to the authority of the ancients ; others, upon being attacked, have tied to them for succour and protection. Others again, distrusting their own ability to support what they advanced, have rather chosen to abdicate the glory of invention, than give up their favourite ideas a prey to their adversaries ; and have therefore, to put them out of reach, placed their origin at a vast distance. Nor are there wanting those, who seeing themselves secure of success, in hazarding certain opinions, have ventured to pass them under their own names, though they belong to others ; and observing, that they were not reclaimed to their real authors by the public, have silently gloried in their borrowed lustre; many conscious that they had no right, and some., though few in number, thinking that they had.

3.  What little we have taken notice of respecting the conduct of Descartes, Locke, and Mallebranche, is sufficient to authorize what we here advance. Descartes bath not specified the authors, from whom in particular he derived his thoughts. He only says in general that the greatest philosophers of antiquity have thought as he has done.  Locke hath passed for an original, though his principles be the same with those of Aristotle, and his distinctions just such as were employed by the stoics. Mallebranche did not at first avow,’ that his opinion was the same with that of the Chaldeans, Permenides, Plato, and St. Augustin ; but when he saw himself warmly attacked by his adversaries, against the philosophical part of them, he held up the buckler of Plato, whilst he fled to St. Augustin for shelter against the divines. The glory of having been the first, who clearly distinguisheth: the properties of the mind from those of the body, and demonstratad, that sensible qualities had their existence in the mind of the percipient, and not in the object perceived, hath been wrongfully ascribed to Descartes ; since we have seen, that he was preceded in all these’ respects by Lencippus, Democritus, Flato, Strato, Aristippus, Plutarch, and Sextus Empiricus.

4.  Leibnits hath not only revived the doctrine of Pythagoras; but employed the very same arguments, which the Pythagoreans made use of to demonstrate the necessity of admitting the existence of simple and uncompounded things, anterior to those that were compounded, and as being the foundation of the existence of body itself. Mr. de Buffon hath sometimes quoted Aristotle and Hippocrates, but never when there was any inquiry about the groundwork of his system, which has always been thought to be new, though it appears to be almost entirely: the same with that of Anaxagoras, Empedocles, and Piotinus. According to the system of Pythagoras, Plato and Epicurus, the production of every thing in nature was ascribed to the concurrent force of simple and active principles, long before Mr. Needham thought of it. The philosophy of Gassendi and the Newtonians, is no other than that of Moschus, Leucippus, Democritus, and Epicurus. The acceleration.. of motion was known to, Aristotle, and the best manner of accounting” for it is that which he makes use of. Lucretius observed long before Galileo, that bodies the most unequal in weight, such as gold and down, must descend with equal velocity in a vacuum. Universal gravity attractive, centripetal, and centrifugal force, were clearly indicated by Anaxagoras, Plato, Airstotle, Plutarch, and Lucretius. We have’ also seen, that, without the aid of telescopes, Democritus and Phavorinus entertained very just ideas of the milky way, and predicated the discovery of the satellites ; that a plurality of worlds, and the doctrine of vortices, were clearly and with precision taught by the ancients; and that Plato had a notion of the theory of colours. We have seen, that two thousand years before Copernicus, Pythagoras had proposed the same system; and that Plato, Aristarchus, and many others, had admitted it; as they did, also, without difficulty. the doctrine of antipodes, which though very reasonable in itself, had so much difficulty is gaining a reception among us. The revolution of the planets about their own axis was known also in the schools of Pythagoras and Plato. There was nothing left to the moderns to say new, respecting the return of comets, their nature, and their orbits. The Chaldeans, Egyptians, Pythagoras, Democritus, Hippocrates of Chios, Artemidorus, and Seneca, had already fully settled the theory of them ; though the moderns, it is true, demonstrated more clearly some parts of it. The mountains, valleys, and inhabitants of the moon, had been suggested and supposed by Orpheus, Pythagoras, Anaxagoras, and Democritus.

5.  Aristotle knew the weight of the air; Seneca its spring anti elasticity. Lucippius, Chrysippus, Aristophanes, and the stoics, had fully accounted for thunder and earthquakes. Pytheas, and Seleucus of Erytherea, preceded Descartes in explaining the cause of the ebbing and flowing of the sea ; and PlinAcibre Sir Isaac Newton had made mention, in that case, of the combined forces of sun and moon.

6.  We have also seen, that Hippocrates and Plato knew the circulation of the blood, and that Rufus described, sixteen hundred years ago, the various parastatae, called by, us the Fallopian tubes. And by the sentiment of an able surgeon of the present age, we have shown, that there were as great advances made in that art a thousand years ago, as there are at present. The art of working metals, of rendering gold potable, glass ductile and malleable ; that of distillation, of painting upon glass, of making gunpowder, and a thousand other chemical preparations, with which we have proved the ancients to have been acquainted, leave not the least doubt of their skill in chemistry. We have seen, that the sentiment of Harvey. Steno, and B.hedi, respecting generation by eggs, was only a renewal of what had been taught by Hippocrates, Empedocles, Aristotle, and Macrobius ; and the system of Hartsoeker, and Leuwenhoeck, with respect to spermatic animalcula, is found in Aristotle, Hippocrates, Plato, Lactantius, and Plutarch. And the sexual system of plants, the merit of discovering which we chiefly assigned to Morland, Grew, Vaillant, and Linnacus, was accurately expounded by Empedocles, Theophrastus, Pliny, and Diodorus Siculus.

7.  Though we did not employ much time in our survey of mathematics and geometry, yet we made it appear, that the noblest discoveries in those sciences were made by the ancients. All the English geometricians agree with Leibnits and Wolf in acknowledging, that, notwithstanding all the attempts made by the ablest geometricians in these last ages, Euclid’s method still remains the most accurate and perfect. We observed, that the most difficult problems in those sciences were solved by Thales, Pythagoras, Plato, Archimedes, and Apollonius. We have seen, that their mechanical contrivances were carried to such a pitch, as to surpass even the conception of the most learned among us. Archimedes’s burning-glasses furnished us with an instance of this. Their application of the equal vibration of the pendulum, their knowledge of the refraction of light, and their attempts to square the circle, their discovery of the fundamental propositions of geometry, and above all that of algebra, and the pre cession of the equinoxes, afford convincing proofs of the depth and acuteness of the genius of the ancients. We have also made it appear, that microscopes were not unknown to them; and that in the arts of pointing, sculpture, and the science of music, they not only equalled, but even surpassed us. In laying before the” eyes. of the reader, a sketch of the admirable works of the ancients in architecture, and in the art of war, we have likewise given proofs, that they were no less able in the arts, than in the sciences; insomuch that there is no part of knowledge in which they have not: either preceded us, directed, or surpassed us.

8.  Now, if it hath been demonstrated, that the writings of those great masters contain the greatest part of what is to be known, that the most celebrated discoveries of the moderns have thence derived their origin; is it not very reasonable, that we should rather go to the fountain head of science, than to confine ourselves entirely to the little streams that issue from it !

But in recommending the study of the ancients, I am far from thinking that the moderns are to be neglected. I apprehend, on the contrary, that it is of great use attentively to consider their labours in order to remark what they have added to the knowledge of the ancients by their experiments; for without doubt there may be daily added something to our knowledge. This makes it necessary attentively to compare the ancients and moderns together; for in these last many things may be found, which have ever been omitted, or but obscurely treated of in the former. Nay, farther, the labours of the moderns may serve to replace, as it were, some of those treatises of the ancients, which have been lost, and of which there now remain only the titles, to give us an idea of the greatness of our loss. Another advantage, which may arise from this comparison, is, to sustain us in our reflections; for where the ancients, and moderns agree, it is natural, that their joint consent should determine our judgment in such or such a point. And even when they differ, the diversity of their reasonings may tend to throw light on the mind.

9.  Free from partiality towards either, we ought to think, that whatever efforts have been made to bring our knowledge to perfection, there will remain something still to be done in that respect, by us and our posterity. There is no man sufficient of himself to establish or perfect any one art or science. Having received from our ancestors the product of all their meditations and researches, we ought daily to add what we can to it, and by that means contribute all in our power to the increase and perfection of knowledge. Let us put on the disposition of Seneca, who expresses himself on ‘this subject with his usual eloquence. "I ‘hold in great veneration says be, “the inventions of the wise, and the inventors themselves. This is an inheritance, which every one may and ought to lay claim to. To me they have been transmitted; for me they have been found out. But let us in this,” continues he, “act like good managers ; let us improve what we have received, and convey this heritage to our descendants, in better condition than it came to us. Much remains for us to do; much will remain for those who come after us. A thousand years hence, there will stilt be occasion, and still opportunity, to add something to the common stock. But had every thing’ been found out by...the ancients, there would still this remain to be done anew, to put their inventions into use, and make their knowledge

When I first read over the preceding treatise, I bad had little though or design of making so large an extract from it. But I afterward considered, 1. That this might be a means of making that valuable work more extensively known, (as men of learning would naturally desire to see and examine the proofs at large ;) and, That it might serve for a kind of recapitulation of the preceding volumes. Such a recapitulation as, on the one hand, could not be unentertaining to the sensible reader; and on the other, might repress the vanity which is apt to arise in our minds, when we imagine we have made new discoveries Alas! how little new has been discovered, even by Gassendi, Mallebranche, Mr. Locke, or Sir Isaac Newton! How plain is it, that is philosophy, as well as the course of human affairs, “ there is nothing new under the sun !"

The more we consider this, the more we shall be convinced of the inconceivable littleness of human knowledge. But although with our utmost efforts, we can know so small a part of the things that surround us, yet we can know, and that with the greatest certainty, our’ whole duty to Him that made them. And what can we reasonably desire more For “this is the whole of man,” (which is the literal rendering of Solomon’s words) his whole business, his whole happiness, In this our infant state we cannot know much: but we may love much. Let us secure this point, and we shall soon be swallowed up in the ocean both of Knowledge and Love!

London, November 16, 1777.