NEID. The most celebrated epic poem of antiquity, after the Iliad and Odyssey. It was written by Virgil in the time of Augustus Cæsar; and relates the wanderings of Æneas after the siege of Troy; his arrival in Italy, and his adventures previous to his marriage with Lavinia, with his final establishment in Latium. The poem, however, does not carry its hero so far as this, but closes with a single combat between Æneas and Turnus, and the death of the latter. In some respects Virgil has deviated from the legend related in the article Æneas. He has multiplied the Trojan ships and increased the number of the Trojans; he has carried his hero to Carthage, though we do not know whether Carthage existed at the supposed date of Æneas wanderings; he has made the death of Turnus precede the marriage of Æneas and the foundation of Lavinium, and has allowed Latinus to survive, instead of making his daughter wed the author of her father's death. The poem consists of twelve books, of which the six first are occupied in relating the wanderings of Eneas, and seem to be modelled on the Odyssey; the six last contain his descent into Italy, and the war which ensued between the Trojans and the natives, and seem to be modelled on the Iliad. In the minute details of ornament as well as in the general notions of his work, Virgil has borrowed largely from Homer. This poem was written later than his other works, the Eclogues and Georgics. It was commenced about the year A.U.C. 724, or B.C. 30; and the author continued to labour on it till his death, in B.C. 20; at which time he was so little satisfied with the state of his production that, it is said, he gave earnest injunctions on his death-bed that it should be burnt, as too imperfect to advance his fame. The order was not fulfilled, at the desire of Augustus, who intrusted the publication to two learned friends of the author, Tucca and Varus. Many lines are left imperfect; some suppose this to be one proof that the finishing hand of the master was never applied; but we doubt whether it is, and think it possible that they were purposely left so. It called forth the enthusiastic admiration of his contemporaries. Propertius wrote

Yield, Roman poets; lords of Greece, give way;
The Iliad soon shall own a greater lay;

and some writers, even in modern times, have expressed the same opinion. The merits of these poets will be better discussed under their respective names. It is enough to say that, compared with the Iliad, the neid is wanting in originality and power: it is evidently the laboured performance of a learned man, possessed of an elegant mind, who has availed himself freely of the labours of those who have preceded him. Virgil is characterized by Niebuhr as possessing a genius barren for creating, great as was his talent for embellishing. The characters of the Eneid are deficient in the individuality and freshness which mark the descriptions of those who have mingled in scenes, and been familiar with characters such as they portray. The brave Gyas, and the brave Cloanthus are hardly distinguishable, except by name: Achates, the friend of Æneas, is a mere shadow, always attending on his chief; and, indeed, with the exception of Dido, no character is well defined. Æneas himself, though the hero of the poem, neither excites any strong interest nor leaves any powerful impression. In this respect Virgil is immeasurably inferior to Homer. The former, from his own imagination, or from the writings of older authors, had to create characters and describe manners such as he had never seen; the latter was familiar with men and actions such as he described them, or at least he embodied the vivid traditions of an early and poetical age. The strength of Virgil lay in the pathetic rather than in the sublime; and many passages of the Eneid, which admitted of the former quality, are exquisitely beautiful.

The Eneid has been frequently translated into most European languages. In our own, we may notice one peculiarly interesting to the literary antiquary; a translation, by Gawin Douglas, bishop of Dunkeld, of the whole Æneid

An ænigma differs from a definition or other direct statement, not in being false, but only in being obscure and misleading. The one is an instance of the application of language to make known our thoughts, and the other of its application to the purpose of concealing them; but the words of a good ænigma, when properly understood, are as true as those of a good definition. It is also an indispensable quality of the latter, as well as of the former, that it shall be intelligible, in its whole import, only in one sense.

The object of a direct statement is to convey information, that of an ænigma is to exercise the ingenuity. The former, in its simplest and most legitimate form, has only to be received by the mind; the latter demands to be solved. An ænigma, therefore, may be regarded as one of the complex or ornamented modes of composition, that is to say, one of those which do not merely appeal to the apprehension, but excite and gratify other intellectual faculties.

In very ancient times, accordingly, the ænigma was a common and favourite medium for the conveyance even of truths of the highest importance. Formal composition in the earliest state of society, that it might be the better distinguished from ordinary speech, naturally affected an elaborately artificial character; and the ænigma or riddle presented itself among other devices for that end. It had, besides, the peculiar recommendation of giving an air of mystery to the sentiment which it involved, and so making it seem to be something still more remote than it might really be from common experience and speculation. The term ænigma, indeed, was probably used originally to describe any short composition, such as an apologue, or fable, or other portable sample of wisdom or entertainment. Enigma is something dark and obscure, and the corresponding verb (aivit7e0001) always means to speak ænigmatically, according to our meaning of the word, or to speak with a certain degree of mystery and obscurity.

In the progress of civilization and literature, it came to be felt that obscurity and difficulty were qualities, which, whatever pleasure they might convey to those who tried to master them, were inconsistent with all the higher and more appropriate objects of speaking and writing. Whether the purpose be simply to communicate information, or whether it be to appeal also to the imagination and the passions, a style is good exactly in proportion as it is expressive, that is to say, as it conveys directly and completely the thoughts of the writer or speaker. The ænigma, therefore, the very end and nature of which is the reverse of this, instead of being an ornament, must be regarded as one of the worst faults of style. Whatever approaches towards the ænigmatical, is, for the same reason, a fault in writing-whatever figure, for example, is introduced in poetry or rhetoric more in order to surprise the reader by its ingenuity than for any other purpose. Amongst those writers who have vitiated their works by what may be called an ænigmatic turn of phraseology, Young is an instance, in his Night Thoughts.

ÆOLIAN HARP, a musical instrument, the sounds of which are drawn from it by a current of air acting on the strings; hence it is named after olus, to whom in the heathen mythology is given the command of the winds.

Rather before the middle of the last century, the Æolian Harp was brought forward in London as a newly-invented instrument; and Dr. Anderson, in a note to Thomson's Ode on Eolus's Harp, ascribes the invention of it to Mr. Oswald, (the composer of Scottish songs, we presume,) adding, its properties are fully described in The Castle of Indolence. However, it is possible that an instrument of the kind was very anciently known, for the Talmudists say that the Kinnor, or harp of David, sounded of itself when the north wind blew on it. But the merit of the invention in the form it now takes, is due to Athanasius Kircher, who, in his Musurgia Universalis, (lib. ix. 352,) thus describes it: 'As the instrument is new, so also is it pleasant and easy to

VOL. I.-U

construct, and is heard in my museum to the admiration of every one. It is silent as long as the window in which it is placed remains closed, but when this is opened, a sudden harmonious sound breaks forth which astonishes the hearers, for they neither perceive whence it proceeds, nor what kind of instrument is before them, for the sounds do not resemble those of a stringed or of a pneumatic instrument, but partake of both. The instrument is made of pine wood, is five palms long, (fifteen inches,) two broad, and one deep: it may contain fifteen or more strings, all equal, and of catgut. The method of tuning it is not, as in other instruments, by 3ds, 4ths, 5ths, &c., but all the strings are to be in unison or in octaves, and it is wonderful that such different harmony should be produced from strings thus tuned.'

A modern writer gives the following more detailed directions for the construction of the Æolian harp, and such as we know, from experiment, are better calculated to produce the intended effects. Let a box be made of as thin deal as possible, of a length exactly answering to the window in which it is intended to be placed, four or five inches in depth, and five or six in width. Glue on it, at the extremities of the top, two pieces of wainscot, about half an inch high and a quarter of an inch thick, to serve as bridges for the strings; and withinside, at each end, glue two pieces of beech about an inch square, and of length equal to the width of the box, which is to hold the pegs. Into one of these bridges fix as many pegs, such as are used in a pianoforte, though not so large, as there are to be strings; and into the other, fasten as many small brass pins, to which attach one end of the strings. Then string the instrument with small catgut, or first fiddle-strings, fixing one end of them, and twisting the other round the opposite peg. These strings, which should not be drawn tight, must be tuned in unison. To procure a proper passage for the wind, a thin board, supported by four pegs, is placed over the strings, at about three inches distance from the sounding-board. The instrument must be exposed to the wind at a window partly open; and to increase the force of the current of air, either the door of the room, or an opposite window, should be opened. When the wind blows, the strings begin to sound in unison; but as the force of the current increases, the sound changes into a pleasing admixture of all the notes of the diatonic scale, ascending and descending, and these often unite in the most delightful harmonic combinations, producing

"A certain music, never known before,"

aud, by its increased velocity, pass it on to the other side, and so continue to vibrate and excite pulses in the air. which will produce the tone of the entire string. But if the current of air be too strong and rapid, when the string is bent from the rectilineal position, it will not be able to recover it, but will continue bent and bellying like the cordage of a ship in a brisk gale. However, though the whole string cannot perform its vibrations, the subordinate aliquot parts may, which will be of different lengths in different cases, according to the rapidity of the blast. Thus when the velocity of the current of air increases, so as to prevent the vibration of the whole string, those particles which strike against the middle points of the halves of the string, agitate those halves as in the case of sympathetic and secondary tones; and as these halves vibrate in half the time of the whole string, though the blast may be too rapid to admit of the vibration of the whole, yet it can have no more effect in preventing the motion of the halves, than it would have on the whole string were its tension quadruple; for the times of vibration in strings of different lengths, and agreeing in other circumstances, are directly as the lengths; and in strings differing in tensions, and agreeing in other circumstances, inversely as the square roots of the tensions: and, therefore, their vibrations may become strong enough to excite such pulses as will affect the drum of the ear; and the like may be said of other aliquot divisions of the string. In the same manner as standing corn is bent by a blast of wind, and if the wind be sufficiently rapid, it will have repeated its blast before the stem of corn can recover its perpendicular position, and therefore will keep it bent. But if it decays in rapidity or strength, the stem of corn will have time to perform a vibration before it is again impelled; and thus it will appear to wave backwards and forwards by the impulse of the wind. Those particles which strike against such points of the string as are not in the middle of the aliquot parts, will interrupt and counteract each other's vibrations, as in the case of sympathetic and secondary tones, and, therefore, will not produce a sensible effect.' With regard to those notes which cannot be produced by any exact submultiple of the string, but which, notwithstanding, are sometimes heard on the Eolian harp, Mr. Young observed that they were always transitory, gradually rising or falling to such notes, above or below them, as would be produced by exact aliquot parts of the whole string.

Mr. Young follows the principles here laid down, by a

From which, with airy fingers light,

Beyond each mortal touch the most refined,
The God of Winds draws sounds of deep delight;
Whence, with just cause, the harp of Eolus it hight.
Ah me! what hand can touch the string so fine?
Who up the lofty diapason roll

Such sweet, such sad, such solemn airs divine,
Then let them down into the soul?

Wild-warbling nature all, above the reach of art!" The learned Matthew Young, B.D., formerly of Trinity College, Dublin, has entered deeply into the nature of the Æolian harp, in his Enquiry into the principal Phænomena of Sounds, &c., and as his work is rare, we shall here avail ourselves of his remarks on this subject::

The phænomena of the Æolian lyre may be accounted for on principles analogous to those by which the phænomena of sympathetic tones are explained. [See SYMPATHETIC SOUNDS.] To remove all uncertainty in the order of the notes in the lyre, I took off all the strings but one, and on placing the instrument in a due position, was surprised to hear a great variety of notes, and frequently such as were not produced by any aliquot part of the strings: often, too, I heard a chord of two or three notes from this single string. From observing these phænomena, they appeared to me so very complex and extraordinary, that I despaired of being able to account for them on the principle of aliquot parts. However, on a more minute enquiry, they all appear to flow from it naturally and with ease.

'But let us consider what will be the effect of a current of air rushing against a stretched elastic fibre. The particles which strike against the middle point of the string will move the whole string from its rectilineal position; and as no blast continues exactly of the same strength for any considerable time, although it be able to remove the string from its rectilineal position, yet, unless it be too rapid and violent, it will not be able to keep it bent: the fibre will, therefore, by its elasticity, return to its former position;

but for these we must refer the reader to the work itself EO'LIAN ISLANDS, the ancient name of the eleven small islands north of Sicily, now generally called the LIPARI Islands.

ÆO'LIAN MODE, in ancient music, one of the five principal modes of the Greeks, which derived its name, not from the Eolian isles, but from Æolia, a country of Asia Minor. What this mode was, it is now difficult, if not impossible, to determine. Writers of all times and kinds differ most essentially from each other on the subject. Rousseau says it was grave: the Abbé Feytou contradicts him. Sir F. Stiles tells us that this mode was the same as our E flat: Dr. Burney makes it F minor; and Rousseau says F, meaning, of course, F major. See MODE.

EO'LIANS, the name of one of those various peoples, whom we are accustomed to class under the general appellalation of Greeks. We trace the name of Æolians to Thessaly, their primitive abode, as far as we know, where they appear to have been closely related to the Phthiotic Achæans of the same country. What was the nature of their relationship to the Dorians who dwelt successively in Phthia, Olympus, Pindus, Dry opis and the Peloponnesus, we cannot determine; but undoubtedly their languages were very closely allied. The Achæi of the Peloponnesus (the Achæi of Homer) were also kinsmen, and, in fact, part of the Æolians; and the great emigration, commonly called the Eolian, was an emigration of Achæan people. It seems probable that the emigration from the Peloponnesus commenced before the Dorian invasion, or return of the Heraclidæ, as it is often called, which caused so great a revolution in the Peninsula; but it cannot be doubted that this event contributed still further to the Achæan or Eolian emigration under Penthilus the son of Orestes, and others of Agamemnon's descendants. This great revolution in the Peloponnesus, caused by an invasion of hardy mountaineers and conquerors from Northern Greece, took

place, as the best-informed Greek historians believed, eighty years after the war of Troy, or B.C. 1104; and apparently caused a retrogression in the condition of southern Greece, and drove out a more civilized race. Strabo says that the Eolian settlements in Asia were four generations prior to those called the Ionian. The Eolian colonies on the Asiatic main land were widely spread, extending at least from Cyzicus along the shores of the Hellespont and the Egean to the river Caicus, and even the Hermus. Many positions in the interior were also occupied by them, as well as the fine island of Lesbos, with Tenedos, and others of smaller importance. Homer mentions all these parts as possessed by a different people; which would be a proof, if any were wanting, that the race of new settlers came after his time. There were twelve cities or states included in the older settlements in that tract of Asia Minor on the Egean, which was known in Greek geography by the name of Eolis, and formed a part of the subsequent larger division of Mysia. Smyrna, one of them, which early fell into the hands of the Ionians, the neighbours of the Eolians, still exists nearly on the old spot, with exactly the same name, thus adding one to the many instances of the durable impression made by Greek colonists wherever they settled.

But besides these twelve states, to which we have alluded, (most of which were near the coast,) there were many Æolian towns founded by the new comers along the Hellespont, the range of the Ida mountains, and on the coast of Thrace.

The name Eolic is often applied to a branch or dialect of the Greek language; but as we do not possess any entire work written in this dialect, we cannot satisfactorily compare it with the Attic, or that variety of the Greek language in which the tragedies of Eschylus. Sophocles, and Euripides, the histories of Thucydides and Xenophon, and the orations of Eschines and Demosthenes are written. There is no doubt, however, that it approached nearest to the Doric dialect of the Greek language, such as it was spoken in most parts of the Peloponnesus after the great Dorian invasion already mentioned.

ÆOLIPYLE, ÆOLIPILE, Aeoli pila, the ball of Æolus, an instrument made use of formerly in experimenting, consisting of a hollow ball, with a small orifice in which a tube might be screwed. It served to boil water in, for the purpose of creating steam. This instrument is mentioned by Des Cartes, in his treatise on Meteors, chap. iv., as used in his time. It is now entirely out of use, unless we choose to consider the boiler of a steam-engine as an æolipile. This is by no means the first instance in which a philosophical toy has been made of use to the arts.

ERA, a point of time from which subsequent years are counted, and in some instances preceding years, as in the Christian æra. The origin of the word æra is very doubtful.

All nations who have any history to record have fixed their æra at some remote period, in order to embrace in their annals as large an extent of time as practicable. The creation of the world would most naturally present itself to those who might have any means of ascertaining the time of its occurrence, and the Bible would be the source from whence the information might be obtained. But, unfortunately for chronology, the Bible is not sufficiently explicit on this subject; and, although the Jews and some Christian nations do date from the Creation, their computations of the period at which this event took place differ to the extent of nearly two thousand years. Those whom this uncertainty has deterred, or who have had no knowledge of the Scriptures, have contented themselves with more recent periods. The ancient Romans adopted the epoch of their first supposed political existence, and the Greeks that of the first celebration or revival of the Olympic Games, which were with them an important national festival. Many nations have assumed some event closely connected with their religious faith: thus, the early Christians of the East dated from the persecution under the Emperor Diocletian, and those of Europe and America, at the present day, from the birth of Christ. All the followers of Mohammed have adopted, as an æra, the retreat of their prophet from Mecca to Medina, which they call the Hegira.

Many of these æras are arbitrarily and incorrectly fixed, and even our own is erroneous by four years. But an error at the commencement will not invalidate the dates of events recorded subsequently, as any æra once assumed will be sufficient to show the succession of time, however incorrectly assigned to the period whose name it bears.

With one or two exceptions, all nations have reckoned

time in accordance with the course of the seasons; they have always begun their year at the same season, sometimes perhaps a little earlier, and sometimes later, but invariably keeping near the original commencement.

Here follows a list of the æras which have been or are most in use among the civilized nations of the world, with the year of the Christian æra in which they began :— 1. The year of the world according to the reckoning of Constantinople, which was used in Russia until the beginning of the eighteenth century, and is still employed by the Greek

church

2. The year of the world as reckoned at Antioch, now used in the Abyssinian church

B.C. 5509

B.C. 5492 [The church of Alexandria originally assumed the year B.C. 5502 as the year of the Creation, but in the year 285 A.D. they discarded ten years, and thus acceded to the computation of Antioch.]

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

The year of the world used by the Jews The Caliyuga, employed by the learned throughout India, may be called an æra of the Creation, being considered by the Hindoos as the commencement of the present state of the world, or Iron Age

The Olympiads; the æra of the victory of Corabus at the Olympic games, used chiefly by the Greek historians after the age of Alexander

- B.C. 3761

B.C. 3102

B.C. 776

The Spanish æra, from the conquest of Spain by Augustus, was employed in Spain, Portugal, Africa, and the South of France. In some provinces this æra was in use until the middle of the fifteenth century

The æra of Salivahana, in common use through the southern and western states of India The æra of Martyrs, or of Diocletian, so called from the persecution of the Christians in the reign of that emperor, was much used by the early Christians, and is still employed in the churches of the East

B. C. 38

A. D. 78

A.D. 284

A.D. 622

The Hegira, used by all Mohammedans, dates from the flight of Mohammed to Medina The Christian æra dates from the birth of Christ; the year in which he was (erroneously) supposed to be born is called 1 B.C., the following year 1 A.D. Many authors call the year of our Lord's birth 0, and consequently make the dates of all preceding events one year less than by the common practice. The following rules will serve to show the year of the Christian era cor.esponding with that of any given æra:1. When the commencement of the given era precedes the birth of Christ, subtract from the given year the number affixed to the era in the above list, and the remainder will be the year of Christ in which the given year began.

If the given year be less than the affixed number, subtract it from that number, adding one; the result will be the date before Christ.

Examples-Required the Christian date answering to the year of Rome 1754.

From 5591 Deduct 3761

The year A.D. 1314 answers to the year 1031. All the above dates may be reduced to the Christian æra by the same formula, except that of the Hegira, as the Mohammedans allow only 354 days to the year. Mohammedan reckoning is thus at variance with the course of the seasons; their year now begins in May, changes to March in 1840, and to December in 1850, and thus gains at the rate of a little more than three years in a century. It will, therefore, be necessary to prepare any given date from the Hegira by subtracting three years for every hundred, before reducing it to the Christian æra.

Required the year of 1245
the Hegira)
for every

Subtract 3 years

hundred

37

The year of the Hegira 1245 began in the year 1829 A.D. 3. The computation by Olympiads may be thus explained: for instance, Ol. lx.3 means that an event took place in the third year of the sixtieth Olympiad, and consequently in the year that followed the expiration of 59 Olympiads (or 59 periods of 4 years each), and 2 more years belonging to the sixtieth Olympiad; or after the expiration of 238 years, and therefore in the year B.C. 538.

AERIAL PERSPECTIVE, a term in painting, implies, in its simple definition, the receding of objects into distance, as seen through the medium of air. In its general application, however, it is to be understood in a more enlarged sense. Linear perspective may be considered the material guide of the artist, originating in, and governed by, mathematical science; but aërial perspective is, in whatever relates to effect, amenable to no positive law or established rule, and depends for its application on the perceptions and capacity of the artist. Although entering into every variety of subject, in graphic representation, it is in open scenery that aerial perspective is exhibited in its proper sphere. To feel this, it will only be necessary to recollect in how different an aspect the same scenery may present itself under different modifications of the atmosphere. A prospect, which at noon day, or in a clear and bleak morning, appears tame and uninteresting, shall assume an ideal character, and start into combinations of beauty, if seen at sunrise or at sunset, or under any temperature of the sky favourable to the development of picturesque effect.

It is, of course, in those schools of painting, wherein the study of external nature, especially of landscape, has been most cultivated, that we are to look for the finest examples of aerial perspective. The Roman and Florentine masters, whose object, almost exclusively, was human form and character, seem to have felt or understood but little of it. The Dutch and Flemish painters exhibit high excellence in this particular, as is shown in the works of Rubens, Rembrandt, Teniers, Ostade, Cuyp, Ruysdael, Wouvermans, Vanderveldt, &c. France, however, has the glory of having produced the artist Claude Lorraine, who, in this great quality of art, has borne off the palm from all competitors. He rarely painted any other effects than those of the rising or the setting sun, well knowing their picturesque superiority; but whatever be his subject, an ancient port, or ruins, or temples, the great and presiding charm of Claude is his consummate skill in aërial perspective. If there be any artist who, in the treatment of aerial perspective, can

His pictures are direct portraits of the scene before him,the willowy lake, the marsh, the meadow, the drowsy shepherd, and the ruminating cow. But, in spite of the simplicity of these materials, and an horizon, in general, perfectly flat, he communicates to his works an effect of air and distance, and consequently of reality, which must rank them among the most astonishing efforts of art. To these may be added a third, the English Wilson, whose breadth and brilliancy of style, and whose conspicuous mastery in the practice of aerial perspective, give him a right to rank with Claude and with Cuyp in this quality.

AERO-DYNAMICS, signifies the science which treats of the motion of the air, or of the mechanical effects of air put in motion. In its widest sense, it might be taken to include the effects of the motion of any gaseous substance or vapour; and even the properties of steam might be considered as a part of the science. We shall, however, confine ourselves to the explanation of the few general principles which can be relied upon; the applications of which will be found in the articles WIND, WINDMILL, AIR-GUN, SAIL, BELLows, RESISTANCE, GUNNERY, &c.

The air is an elastic fluid,—that is, any portion of it can be confined in a smaller, or expanded into a larger space, than it would naturally occupy. In either case a force or pressure is to be overcome; the air itself resists compression; and the pressure of the superincumbent air is to be overcome before any expansion can take place. The natural state of the air to which we have alluded, varies, as indicated by the rise or fall of the BAROMETER, which, at the level of the sea is usually between twenty-eight and thirty-one inches in height, that is, the flat bottom of any vessel is pressed by a weight, arising from the air, such as would be obtained by filling it with mercury to a height of from twentyeight to thirty-one inches. This pressure is estimated at from fourteen to fifteen pounds avoirdupois on every square inch. [See AIR.]

As soon as we begin to move, we feel, more or less, the resistance of the air. At an ordinary rate of motion, this is not very perceptible; but the jockey, who rides at the rate of from thirty to forty miles an hour, feels it sensibly, and is obliged to wear a cap which may cut the wind, as the bow of a ship cuts the water, or otherwise it would be blown off his head, though, in the common sense of the word, there might be no wind stirring at the time. Whenever we attempt to put any matter in motion, we feel what is denominated pressure or resistance, which is the greater the greater the quantity of matter we attempt to move, and the velocity we attempt to communicate to it. Thus, two violent pressures, of equal force, applied for an instant to weights of ten and twenty pounds, will make the weight of ten pounds move twice as fast as that of twenty; or, if we would have the two move equally fast, we must apply twice as much pressure to the twenty pounds weight as we do to that of ten pounds. If we now conceive a number of equal balls placed in a line, along which we move the hand uniformly, so as to set them all in motion one after the other, we might at first imagine that if we move the hand at the rate of two feet in a second, and afterwards at the rate of four feet in a second, that we exert twice as much force, and encounter twice as much resistance, in the second case, as in the first. Because, we say, we move each ball in the second case twice as fast as in the first. But there is another consideration: we not only move each ball twice as fast, but we meet with twice as many balls in a second, so that not only the velocity we communicate in a second is doubled, but also the quantity of matter to which we communicate that velocity is doubled, or, there is four times as much resistance to twice the velocity, as there was to the single velocity. Similarly, at three times the rate of motion, we meet with three times as much matter, and communicate to each portion three times the velocity: whence we meet with three times three, or nine times the quantit of resistance. If we transfer this reasoning to the case of a body moving through the air, we should infer, that the resistance is, to speak mathematically, as the SQUARE of the velocity: that is, if the velocity be suddenly made ten times as great, the resistance is made ten times ten, or a hundred times as great. And this, which was the first theory proposed on the subject, is sufficiently near the truth for practical purposes, when the velocities are not very great; for example, up to eight or nine hundred feet in a second. But one circumstance has been neglected. The success