term for accelerating the time in the middle of a piece of music; as ralantando is for retarding it.

To ACCELERATE, v. a. (accelero, Lat.) To make quick; to hasten; to quicken motion (Bacon).

ACCELERATION. s. (acceleratio, Lat.) 1. The act of quickening motion. 2. The state of the body accelerated (Haler).

ACCELERATION, in mechanics, the increase of velocity in a moving body. Accelerated motion is that which continually receives fresh accessions of velocity, and is either equally or unequally accelerated. Acceleration stands directly opposed to retardation, which denotes a diminution of velocity.

ACCELERATION is chiefly used in physics, in respect of falling bodies, i. e. of heavy bodies tending towards the centre of the earth by the force of gravity. That natural bodies are accelerated in their descent, is evident from various considerations, both a priori, and posteriori. Thus we actually find that the greater height a body falls from, the greater impression it makes, and the more vehemently does it strike the subject plane, or other obstacle. Various are the systems and opinions which philosophers have produced to account for this acceleration. But as most of them are merely visionary, or hypothetical, we think it needless to describe them. Especially, since if the reader will only admit the existence of such a force as gravity, so evidently inherent in all bodies, without regard to what may be the cause of it, the whole mystery of acceleration will be cleared up. Consider gravity then, with Galileo, only as a cause or force which acts continually on heavy bodies; and it will be easy to conceive that the principle of gravitation, which determines bodies to descend, must by a necessary consequence accelerate them in falling. A body having once begun to decsend, through the impulse of gravity; the state of descending is now, by Newton's first law of nature, become as it were natural to it; insomuch that were it left to itself, it would for ever continue to descend, even though the first cause of its descent should cease. But besides this determination to descend, impressed upon it by the first cause of motion, which would be sufficient to continue to infinity the degree of motion already begun, new impulses are continually superadded by the same cause; which continues to act upon the body already in motion, in the same manner as if it had remained at rest. There being then two causes of motion, acting both in the same direction; it necessarily follows, that the motion which they unitedly produce must be more considerable than what either could produce separately. And as long as the velocity is thus continued, the same cause still subsisting to increase it more, the descent must of necessity be

:

continually accelerated. Supposing then that gravity, from whatever principle it arises, acts uniformly upon all bodies at the same distance from the centre of the earth: dividing the time which the heavy body takes up in falling to the earth, into indefinitely small equal parts; gravity will impel the body toward the centre of the earth, in the first indefinitely short instant of the descent. If after this we suppose the action of gravity to cease, the body will continue perpetually to advance uniformly toward the earth's centre, with an indefinitely smali velocity, equal to that which resulted from the first impulse. But, if we suppose that the action of gravity still continues the same after the first impulse; in the second instant, or small part of time, the body will receive a new impulse toward the earth, equal to that which it received in the first instant; and consequently its velocity will be doubled; in the third instant it will be tripled; in the fourth quadrupled; in the fifth quintupled; and so on continually for the impulse made in any preceding instant, is no ways altered by that which is made in the following one; but they are, on the contrary, always accumulated on each other. So that the instants of time being supposed indefinitely small, and all equal, the velocity acquired by the falling body, will be at every moment proportional to the times from the beginning of the descent; and consequently the velocity will be proportional to the time in which it is produced, So that if a bedy, by this constant force acquire a velocity of 321 feet suppose in one second of time; ít will acquire a velocity of 64 feet in two seconds, 954 feet in three seconds, 1283 in four seconds, and so on. Nor ought it to seem strange that all bodies, small or large, acquire by the force of gravity the same velocity in the same time. For every equal particle of matter being endued with an equal impelling force, namely its gravity or weight, the sum of all the forces, in any compound mass of matter, will be proportional to the sum of all the weights, or quantities of matter to be moved; consequently, the force and masses moved being thus constantly increased, in the same proportion, the velocities generated will be the same in all bodies, great or small. That is, a double force moves a double mass of matter, with the same velocity that the single force moves the single mass; and so on. Or otherwise, the whole compound mass falls all together with the same velocity, and in the same manner, as if its particles were not united, but as if each fell by itself, separated all from one another. And thus all being let go at once, they would fall together, just as if they were united into one mass. The foregoing law of the descent of falling bodies, namely that the velocities are always proportional to the times of descent, as well as the laws concerning the spaces passed over, &c. were first discovered and taught by

the great Galileo in his Mechanical Diahs; the general inferences established reave to uniformly accelerated motions being ⚫ below. 1st. That the velocities acquired, a constantly proportional to the times; in a able time a double velocity, &c. 2d. That the spaces described in the whole times, each aunted from the commencement of the moton, are proportional to the squares of the tres, or to the squares of the velocities; that in twice the time, the body will describe four times the space; in thrice the time, it will describe nine times the space; in quadruple the time, sixteen times the space; and so . In short, if the times are porportional to the numbers - 1, 2, 3, 4, 5, &c, the spaces will be as 1, 4, 9, 16, 25, &c, which are the squares of the former. So that if a body, by the natural force of gravity, fall through the space of 16 feet in the first seend of time; then in the first two seconds of time it will fall through four times as much, or 14 feet; in the first three seconds it will fall Ene times as much, or 1443 feet; and so on. And as the spaces fallen through are as the cates of the times, or of the velocities; efore the times, or the velocities, are proonal to the square roots of the spaces. The spaces described by falling bodies, in arties of equal instants or intervals of time, w be as the odd

odd}

1, 3, 5, 7, 9, &c.

1, 4, 9, 16, 25, &c.

numbers which are the differtaces of the squares or whole spaces that is, the body which has run through 16 Let in the first second, will in the next second run through 48 feet, in the third second 80% and so on. 4th. If the body fall through any pace in any time, it acquires a velocity equal to double that space; that is, in an equal time with the last velocity acquired, if uniformly minued, it would pass over just double the spece. So if a body fall through 16 feet in the first second of time, then it has acquired a velocity of 32% feet in a second; that is, if the body move uniformly for one second, with the velocity acquired, it will pass over 32 feet this one second: and if in any time the body fall through 100 feet; then in another equal time, if it move uniformly with the vehty last acquired, it will pass over 200 feet, and so on. (Hutton's Dict. See also Gregory's Mechanics, vol. i. and Hauy's Natural Philo

, vol. i.)—The following theorems, for practice, are derived from the general doctrine of acceleration. Let g represent the velocity quired by a body at the end of a second or unit of time by means of the accelerating force,

the time or the number of seconds in which

the body passes over any space s, and the velocity acquired at the end of that time, then we have = g t, and s = g 12, from which two equations result the following:

And here, when the constant force is the natural force of gravity, then the distance g descended in the first second, in the latitude of London, is 16 feet: but if it be any other constant force, the value of g will be different, in proportion as the force is more or less (See FORCE). The motion of an ascending body, or of one that is impelled upwards, is diminished or retarded by the same principle of gravity, acting in a contrary direction. Such a body ascends until it has lost all its motion; which it does in the same space of time, that the body would have taken up in acquiring, by falling, a velocity equal to that with which the falling body began to be projected upwards. And consequently the heights to which bodies ascend, when projected upwards with different velocities, are to each other as the squares of those velocities.

IN

ACCELERATION OF BODIES ON CLINED PLANES. The same general laws obtain here, as in bodies falling freely, or perpendicularly; namely, that the velocities are as the times; and the spaces descended down the planes, as the squares of the times, or of the velocities. But those velocities are less, according to the sine of the plane's inclination; the sine. See INCLINED PLANE. and the spaces less, according to the square of

the force that accelerates the motion or velocity ACCELERATING FORCE, in physics, is of bodies; and it is equal to, or expressed by, the quotient arising from the motive or absolute force, divided by the mass or weight of ations respecting forces, velocities, times, and the body that is moved. In physical considerspaces gone over, the first inquiry is the acce lerating or accelerative force. This force is greater or less in proportion to the velocity it generates in the same time, and by this velocity

it is measured. All accelerating forces are the motive forces directly proportional to the equal, and generate equal velocities, that have quantities of matter: so a double motive force will move a double quantity of matter with the same velocity, as also a triple motive force a triple quantity, a quadruple force a quadruple quantity, &c. all with the same velocity. And swift by the force of gravity; for the motive this is the reason why all bodies fall equally force is exactly proportional to their weight or mass. In general, the accelerating force is in the direct ratio.of the motive force, and inverse ratio of the quantity of matter.-In the cases

3 A

laid down in a preceding article will require some modification: here we are to consider the relations of the fluxions of the time, velocity, &c Consequently taking the fluents of those expressions, in particular cases, the relations of time, space, velocity, &c. are obtained. Now if t denote the time in motion,

v the velocity generated by any force, the space passed over,

and g the variable force at any part of the motion, or the velocity the force would generate in one second of time, if it should continue invariable, like the force of gravity, during that one second; and therefore the value of this velocity g, will be in proportion to 32 feet, as that variable force, is to 1 the force of gravity. Then because the force may be supposed constant during the indefinitely small time, and that in uniform motions the spaces and velocities are proportional to the times, we from thence obtain these two general fundamental proportions,

vs: 1" t, or s = i iv;

:

ap

the planet is said to be retarded in its motion, when the mean exceeds the real diurnal motion. This inequality arises from the change in the distance of the planet from the sun, which is continually varying; the planet moving always quicker in its orbit when nearer the sun, and slower when farther off.

ACCELERATION OF THE MOON, a term used to express the increase of the moon's mean motion from the sun, compared with the diurnal motion of the earth; so that it is now a little swifter than it was formerly. Dr. Halley was the first who made this discovery, and he was led to it by comparing the ancient eclipses observed at Babylon with those observed by Albatennius in the ninth century, and some of his own time.-The moon's mean motion is deduced from a comparison of distant observations. The time between them, being divided by the number of intervening lution, or the mean lunar period. When the revolutions, gives the average time of one revoancient Chaldean observations are compared with those of Hipparchus, we obtain a certain period; when those of Hipparchus are com pared with some in the ninth century, we obtain a period somewhat shorter; when the last are compared with those of Tycho Brahe, we obtain one still shorter; and when Brahe's are compared with those of our day, we obtain the shortest period of all-and thus the moon's mean motion appears to accelerate continually; and the accelerations appear to be in the duplicate ratio of the times. The acceleration for the century which ended in 1700 is about nine seconds of a degree; that is to say, the whole motion of the moon during the 17th century must be increased nine seconds, in order to obtain its motion during the 18th; and as much must be taken from it, or added to the computed longitude, to obtain its motion during the 16th; and the donble of this must be obtain its motion during the 15th, &c. Many taken from the motion during the 16th, to conjectures have been offered as to the cause of this acceleration; and it was often looked upon as a stumbling block in the way of the Newtonian philosophy, until at length M. Laplace has happily succeeded in deducing it tion. As this is a subject of considerable imfrom the Newtonian law of planetary deflecportance, we shall enter a little into M. Laplace's explanation. The lunar period which tained, had the moon been influenced by the we observe, is not that which would have obearth alone. We should not have known that her natural period was increased, had the disturbing influence of the sun remained unchanged; but this varies in the inverse tripli

cate ratio of the earth's distance from the sun, the earth is nearer to the sun. This is the and is therefore greater in our winter, when source of the annual equation, by which the

period in January is made to exceed that in July nearly 24 minutes. The angular velarity of the moon is diminished in general and this numerical coefficient varies in the inverse ratio of the cube of the earth's distance from the sun. If we expand this inverse cube of the earth's distance into a series arranged according to the sines and cosines of the earth's mean motion, making the earth's mean distance unity, we shall find that the series contains a term equal to of the square of the eccentricity of the earth's orbit. Therefore the expression of the diminution of the moon's angular velocity contains a term equal to of this velocity, multiplied by of the square of the earth's eccentricity; or equal to the product of the square of the eccentricity, multiplied by the moon's angular velocity, and divided by 119-33 (of 179). Did this eccentricity remain constant, this product would also be constant, and would still be confounded with the general diminution, making a constant part of it: but the eccentricity of the earth's orbit is known to diminish, and its dimination is the result of the universality of the Newtonian law of the planetary deflections. Although this diminution is exceedingly small, its effect on the lunar motion becomes sensible by accumulation in the course of ages. The eccentricity diminishing, the diminution of the moon's angular motion must also diminish, that is, the angular motion must increase, -During the eighteenth century, the square of the earth's eccentricity has diminished 0-0000015325, the mean distance from the sun being 1. This has increased the angular motion of the moon in that time, 0-00000001285. As this augmentation is gradual, we must multiply the angular motion during the century by the half of this quantity, in order to obtain its accumulated effect. This will be found to be 9" very nearly, which exceeds that deduced from a most careful comparison of the motion of the last two centuries, only by a fraction of a second! While the diminution of the square of the eccentricity of the earth's orbit can be supposed proportional to the time, this effect will be as the squares of the times. When this theory is compared with observations, the coincidence is wonderful indeed. The effect on the moon's motion is periodical, as the change of the solar eccentricity is, and its period includes millions of years. Its effect on the moon's longitude will amount to several degrees before the secular acceleration change to a retardation (Encyclo. Britan.).

ACCELERATOR URINE, (accelerators sc. musculus, from accelero, to hasten). E culator seminis. Bulbo-cavernosis of Winslow. A muscle of the penis. It arises fleshy from the sphincter ani and membranous part of the urethra, and tendinous from the crus, nearly as far forwards as the beginning of the corpus cavernosum penis; the inferior fibres run more

transversely, and the superior descend in an oblique direction. It is inserted into a line in the middle of the bulbous part of the urethra, where each joins with its fellow; by which the bulb is completely closed. The use of this pair of muscles is to drive the urine or semen forward, and by grasping the bulbous part of the urethra, to push the blood towards its corpus cavernosum, and the glands by which they are distended.

To ACCEND, v. a. (accendo, Lat.) To kindle; to set on fire (Decay of Piety).

ACCENDENTES, a lower order of ministers in the Romish church, whose office is to light and trim the candles.

ACCENDONES, or ACCEDONES, in Roman antiquity, a kind of officers in the gladiatorian schools, who excited and animated the combatants during the fight.

ACCENSI, in Roman antiquity, was applied to three descriptions of persons. 1. To certain supernumerary soldiers, designed to supply the places of those who should be disabled or killed. 2. To a kind of adjutants appointed by the tribune to assist each centurian and decurian. 3. To an inferior order of officers, appointed to attend the Roman magistrates, somewhat in the manner of ushers or tipstaves among us.

ACCENSION, s. The act of kindling, or setting a body on fire. Thus the accension of tinder is effected by striking fire with flint

and steel.

A'CCENT, s. (accentus, Lat.) 1. The manner of speaking or pronouncing. 2. The sound of a syllable (Shaksp.). 3. The marks made upon syllables to regulate their pronunciation (Holder). 4. A modification of the voice, expressive of the passions or sentiments (Prior).

ACCENT, in its primitive sense, an affection of the voice, which gives each syllable of a word its due pitch, in respect of height or lowness. The word is originally Latin, accentus, a compound of ad, to; and cano, to sing. In this sense, accent is synonymous with the Greeks, the Latin tenor, or tonor, and the Hebrew gustus, taste. The accent, properly, only respects high and low, or acute and grave. Though the modern grammarians use it also in respect of loud and soft, long and short; but this confounds Accent with Quantity.

ACCENT is also used in grammar, for a character placed over a syllable, to mark the accent, i. e. to shew it is to be pronounced in a higher, or in a lower tone; and to relate the inflexions of the voice in reading. It is distinguished from emphasis, as the former regards the tone of the voice, the latter the strength of it. We reckon three grammatical agents in ordinary use, all borrowed from the Greeks, viz. the acute accent, which shews when the tone of the voice is to be raised. In modern writings it is a little line, or virgula,

placed over the vowel, a little sloping or inclined, in its descent, from right to left, as'. It is not ordinarily used, either in English or Latin: the French, indeed, retain it; but it is only to mark the close or masculine é.-The grave accent, when the note or tone of the voice is to be depressed; and is figured thus -The circumflex accent, which is composed of both the acute and the grave; it points out a kind of undulation of the voice, and is expressed thus or^. But if it be true, that the whole system of pronunciation turns on three accents, it is no less true, that each of these three admits of several degrees. The acute accent, for instance, may be either higher or lower; may be simply acute, or very acute; and the like holds of the grave and circumflex. So that each of the three common accents is, as it were, a genus, including divers particular species; though the ancient grammariaus have not thought fit to give particular names and figures to all these differences. The Hebrews have a grammatical, a rhetorical, and a musical accent; though the first and last seem, in effect, to be the same; both being comprised under the general name of tonic accents, because they give the proper tone to syllables: as the rhetorical accents are said to be euphonic; inasmuch as they tend to make the pronunciation more sweet and agreeable. There are four euphonic accents, and twentyfive tonic; however, authors are not agreed as to the number; of which some are placed above, and others below the syllables; the Hebrew accents serving not only to regulate the risings and fallings of the voice, but also to distinguish the sections, periods, and members of periods, in a discourse; and to answer the same purposes with the points in other languages. Their accents are divided into emperors, kings, dukes, &c. each bearing a title answerable to the importance of the distinction it makes. Their emperor rules over a whole phrase, and terminates the sense completely; answering to our point. Their king answers to our colon; and their duke to our comma. The king, however, occasionally becomes a duke, and the duke a king, as the phrases are more or less short. The Hebrew accents, in effect, have something common with those of the Greeks and Latins; and something peculiar to themselves. What they have in common, is, that they mark the tones; shewing how the voice is to be raised, and sunk, on certain syllables. What they have peculiar is, that they do the office of the points in other languages. It is certain that the ancient Hebrews were not acquainted with these accents: their origin and use, therefore, have been much controverted. And there has been fall as much dispute concerning the antiquity, &e. of the Greek accents as of those of the Hebrews. The use of Lecents, to prevent and Higuities, is most remarkably perceived in some eastern l..nguages, particularly the Siamese and

The

Chinese. Among the people of China, every word, or (which is the same thing) syllable, adinits of five accents, as spoken more acutely or remissly; and thus stands for many different things. The same sound ya, according to the accent affixed to it, signifies God, a wall, excellent, stupidity, and a goose. The Chinese have but 330 spoken words in their language; but these being multiplied by the different accents or tones, which affect the vowels, furnish a language tolerably copious. By means hereof, their 330 simple sounds come to denote 1650 things; but this being hardly sufficient, they are increased further by aspirates added to each word to double the number. Chinese only reckon four accents; for which the missionaries use the following marks, aá, á, à, a; to which they have added a fifth, thus a. Among the English it is found that emphasis, in particular cases, alters the seat of the accent. This is demonstrable from the following examples. He shall increase, but I shall decrease." "There is a difference between giving and forgiving." "In this species of composition, plausibility is much more essential than probability." In these examples, the emphasis requires the accent to be placed on syllables to which it does not commonly belong.

ACCENT, in music, is a modulation of the voice, to express a passion. Every bar or measure is divided into accented and unaccented parts. The accented parts are the principal; being those intended chiefly to move and affeet: it is on these the spirit of the music depends. Hence the harmony is in general to be full, and void of discords in the accented parts of the measure, while in the unaccented parts discords are allowed. In common time, of four crotchets in a bar, the accentuation will fall usually on the first and third crotchets of the bar: in triple time, on the first note of the bar. But these rules are often departed from, and with much success.

To ACCENT, v. a. (from accentus, Lat.) 1. To pronounce; to speak words with particular regard to the grammatical marks or rules (Locke). 2. In poetry, to pronounce or utter in general (Wotton). 3. To write or note

the accents.

To ACCENTUATE, v. a. (accentuer, Fr.) To place the proper accents over the vowels.

ACCENTUATION, s. (from accentuate). The act of placing the accent in pronunciation.

To ACCEPT, v. a. (accipio, Lat. accepter, Fr.) 1. To take with pleasure; to receive kindly; to admit with approbation (Dryden)2. In the language of the Bible, to accept persons, is to act with personal and partial regard.

ACCEPTABILITY, s. The quality of being acceptable (Taylor). ACCEPTABLE, a. (acceptable, French) Grateful pleasing.