+ varies as the nth power of the distance from the centre. S + &c.=s, whence r=1.2.3 1.2.3. 3·4 or, is the hyperbolic log. of s, whence s = e3, e being the base of the hyperbolic system of logarithms. Problem 4.-Find the relation of r and y from the fluxional equation (x2 + y2) j = (m y x) i. Put y2; then y + zj. By substituting these values of x and x in the proposed equation, and dividing by y3, we get z2 + 1⋅ j= = hyp. log. y + 1 j + m y 2m- 2 6, and by taking the fluents, m 2 m 2' hyp. log. (22—m—1 ̃ ̄') =log.c.(the correction); whence y · (22—m-1) m 2m Let denote the radius of the sphere, d the density at the surface, a = the area of a circle whose radius is 1, and r any distance from the centre; then 4 a x2x is the fluxion of the magdrn is the density; whence nitude, and 4 a dx" + 2 x'• is the quantity of matter in the We have given as full an account of the principles of this important branch of science, and' the method of applying them, as the space to which we are limited will admit. Happily the English language is rich in works in which the − 2 = C; an equation which by reduction student who intends to devote himself to scienti fic pursuits, may find all the aid that he can require. The treatises on fluxions by Simpson and Emerson are justly held in esteem by English mathematicians. A new edition of Simpson's treatise has lately been published, with provements in the science, by a member of the very valuable appendixes on the modern imuniversity of Cambridge. Maclaurin's work contains, perhaps, upon the whole, the most elementary exposition of the principles of the science. Indeed it was written chiefly with the view of confuting some objections which the acute and ingenious Berkeley had advanced against the metaphysics of the science. Dr Lardner of Dublin has recently published a work on the subject, marked by that elegance and originality which distinguishes whatever comes from his pen; and Mr. Jephson of Cambridge has in course of publication an elementhave seen of it, will, we are persuaded, form ary work on the subject, which, from what we a very valuable acquisition to the scientific world. We should not, however, discharge our duty to our readers if we omitted to recommend the translation of Lacroix's work on this subject by Herschel, Babbage, and Peacock, with the colpiled; nor the very elegant and methodical work lection of examples for exercise which they comof Dealtry, a work in which the subject of fluents, and the application of the science to the doctrine of forces, are expounded with remarkable perspicuity. FLY, v, a. & v. n. FLY BOAT, n. s. FLY'ER, OF FLIER, n. s. FLIGHT', n. s. For horde hath hate, and climbyng tikilaesse, Chaucer So that I mighten lyven and nat faile Id. Legend Ariadne. They hit one another with darts, as the others do with their hands, which they never throw counter, but at the back of the flier. Sandy's Journal. Pret. flew, or fled; part. fled, or flown, v. n. Sax. Fleogan. To fly is properly to use wings, and gives FLIGHT INESS, n. s. flew and flown. To flee is to escape, or to go away. Sax. Ƒlean, and makes fled they are now confounded. To move through the air with wings; to pass through the air; to pass away with the idea of swiftness or escape; to move with rapidity; applied to a violent and sudden separation of adhering parts: to shiver; to burst asunder with a sudden explosion. Sax. rlean; Germ. flichen. To run away; to attempt escape. In this sense the verb is properly to flee, when fled is formed: the verb active is used in the sense of to strain; to decline; to avoid; to refuse association with; to quit by flight; to attack by a bird of prey. It is probable that flew was originally the preterite of fly, when it signified volation, and fled when it signified escape: flown should be confined likewise to volation; but these distinctions are now confounded. We know not any book except the Scriptures in which fly and flee are carefully longer in, and not flown so dangerously abroad before For he so swift and nimble was of flight, Up to the clowdes, and thence with pineons light Upon the streaming rivers, sport to finde; And oft would dare to tempt the troublous winde. the feathers of the cause had been grown. Hooker. At the first flight of arrows sent Chery Chase. A round stone from a sling. Beaumont and Fletcher. Bondxca. The gates are ope, now prove good seconds; 'Tis for the followers fortune widens them, Not for the fliers. Shakspeare. Coriolanus. Ere the bat hath flown Id. Macbeth. His cloistered flight. kept separate. The substantives are more : Fowl that may fly above the earth in the open fir- Abiathar escaped and fled after David. As birde flyeth up in the aire, Chaucer. The Plowman's Tule. Flie, fro the prese and dwell with sothfastnesse, Id. where my chaff Shakspeare. Glad to catch this good occasion, He set up his bills here in Messina, and challenged In my school-days, when I had lost one shaft, Id. id. Love like a shadow flies, when substance love pursues; Pursuing that which flies, and flying what pursues. Id. They take great pride in the feathers of birds, and this they took from their ancestors of the mountains who were invited into it by the infinite flights of birds that came up to the high grounds. Bacon. New Atlantis. If a man can tame this monster, and with her fly other ravening fowl, and kill them, it is somewhat worth. Bacon. Here be of all sorts; flights, rovers, and butshafts. He grieves so many Britons should be lost; Taking more pains, when he beheld them yield, To save the fliers than to win the field. Waller. Sleep flies the wretch; for when with cares opprest, And his tossed limbs are wearied into rest, Then dreams invade. Dryden's Juvenal. Dedalus, to fly the Cretan shore, His heavy limbs on jointed pinions bore, The first who sailed in air. Id. Eneid. He thinks by flight his mistress must be won, And claims the prize because he best did run. Dryden. As striplings whip the top for sport, On the smooth pavement of an empty court, The wooden engine flies and whirls about. Id. Fowls, by Winter forced, forsake the floods, And wing their hasty flight to happier lands. Id. The scouts with flying speed Return, and through the city spread the news. In half-whipt muslin needles useless lie, And shuttle-cocks across the counter fly. Id. Gay. You now a more delusive art must try, And tempt their hunger with the curious fly. Id. Earth rolls back beneath the flying steed. Pope. I'll fly from shepherds, flocks, and flow'ry plains; From shepherds, flocks, and plains I may remove, Forsake mankind, and all the world but love. Id. Strange graces still, and stranger flights she had; Was just not ugly and was just not mad. Id. It is not only the utmost pitch of impiety, but the highest flight of folly, to deride these things. Tillotson. meaning. The following phrases are instanced by Dr. Johnson: To fly at. To spring with violence upon; to fall on suddenly. A servant that he bred, thrilled with remorse, Opposed against the act, bending his sword To his great master; who, thereat enraged, Flew on him, and amongst them felled him dead. Shakspeare. Though the dogs have never seen the dog-killer, yet they will come forth, and fly at him. Bacon's Natural History. No honour, no fortune, can keep a man from being miserable, when an enraged conscience shall fly at him, and take him by the throat. South. This is an age that flies at all learning, and enquires especially into faults. To fly in the face. To insult. Id. This would discourage any man from doing you good, when you will either neglect him, or fly in his face; and he must expect only danger to himself. Swift's Drapier's Letters. To fly in the face. To act in defiance. Fly in nature's face! -But how, if nature fly in my face first? To fly off. To revolt. Dryden. Deny to speak to me! They're sick, they're weary, They have travelled all the night! mean fetches; The images of revolt and flying off. The traytor Syphax Shakspeare. Flew off at once with his Numidian horse. To fly out. To burst into passion. How easy is a noble spirit discerned, Ben Jonson's Catiline. Passion is apt to ruffle, and pride will fly out into contumely and neglect. Collier of Friendship. To fly out. To break out into license. You use me like a courser spurred and reined; If I fly out, my fierceness you command. Papists, when unopposed, fly out into all the pagean Dryden. If there were any certain height where the flights tries of worship; but, when they are hard pressed by arguments, lie close intrenched behind the council of Trent. Id. of ambition end, one might imagine that the interest of France were but to conserve its present greatness. To fly out. To start violently from any direction. All bodies, moved circularly, have a perpetual endeavour to recede from the centre, and every moment would fly out in right lines, if they were not restrained. Bentley's Sermons, To let fly. To discharge. The noisy culverin, o'ercharged, lets fly, And bursts, unaiming, in the rended sky. fish, is to angle with a hook baited with a fly, either natural or artificial: a fly-flap is a fly or flapper to keep flies off. For lo the gentil kinde of the lion; Him deineth nat to wrecke him on a flie, Chaucer. Leg. of Good Women, Prologue. Earl of Surrey. Did much disdaine to subject his desire Spenser. Muiopotmos. Shakspeare. To sacrifice the honour of sacred things to our vain pleasure, being like the ridiculous fondness of that people, which, as Ælian reporteth, worshipping a fly, did offer up an ox thereto. Barrow. I am unwilling to believe that he designs to play tricks, and to flyblow my words, to make others distaste Stillingfleet. There was more need of Brutus in Domitian's days, to mend, than of Horace, to laugh at a flycatcher. them. Dryden. The swallow was a flycatcher as well as the spider. My country neighbours begin to think of being in general, before they come to think of the fly in their sheep, or the tares in their corn. Locke. To prevent the fly, some propose to sow ashes with Mortimer's Husbandry. the seed. Pope. So morning insects, that in muck begun, A constant death. Swift. None save the Spanish Fly and Attic Bee As yet are strongly stinging to be free. Byron. FLY, or Musca, in entomology, a large order of insects, the distinguishing characteristic of which is, that their wings are transparent. By this they are distinguished from beetles, butterflies, grasshoppers, &c. See ENTOMOLOGY. FLY, in mechanics, a cross, with leaden weights at its ends; or rather, a heavy wheel at right angles, to the axis of a windlass, jack, or the like; by means of which the force of the power, whatever it is, is not only preserved, but equally distributed in all parts of the revolution of the machine. See MECHANICS. FLY, ELECTRIC. See ELECTRICITY. FLY ISLAND, an island in the South Pacific Ocean, discovered by Le Maire and Schouten, in the year 1616, and so named from the number of flies seen there. It is covered with trees, and a lagoon seems to be formed in the interior by the flowing of the tide. The navigators observed a few naked inhabitants. Long. 150° 20′ W., lat. 15° S. FLY, VEGETABLE, a very curious natural production, chiefly found in the West Indies. It any resembles the drone both in size and color, excepting that it has no wings, more than other British insect. In the month of May it buries itself in the earth, and begins to vegetate. By the end of July the tree has arrived at its full growth, and resembles a coral branch: it is about three inches in height, and bears several little pods, which dropping off, become worms, and then flies, like the British caterpillar. Such was the account originally given of this extraordinary production. But several boxes of these flies having been sent to Dr. Hill, for his examination, his report was as follows: "There is in Martinique a fungus of the clavaria kind, different in species from those hitherto known. It produces soboles from its sides; I call it, therefore, clavaria sobolifera. It grows on putrid animal bodies, as our fungus ex pede equino, from the dead horse's hoof. The cicada is common in Martinique, and in its nymph state, in which the old authors call it tettigometra, it buries itself under the dead leaves to await its change; and, when the season is unfavorable, many perish. The seeds of the clavaria find a proper bed in this dead insect, and grow.' This is the solution of the mystery; though the untaught inhabitants suppose a fly to vegetate, and though there is a Spanish drawing of the plants growing into a trifoliate tree, and it has been figured with the creature flying with this tree upon its back. Mr. Edwards treats of this extraordinary production in his Gleanings of Natural History. FLY, HONEYSUCKLE. See LONICERA. FLY, HONEYSUCKLE, AFRICAN. See HALLERIA. FLYING, the progressive motion of a bird, or other winged animal in the air. The parts of birds chiefly concerned in flying are the wings and the tail; by the former, the bird sustains and wafts himself along; and, by the latter, he is assisted in ascending and descending, to keep his body poised and upright, and to obviate the vacillations thereof. It is by the largeness and strength of the pectoral muscles, that birds are so well disposed for quick, strong, and continued flying. These, muscles, which, in men, are scarcely a seventieth part of the muscles of the body, in birds exceed and outweigh all the other muscles taken together. The tail, Messrs. Willoughby, Ray, and many others, imagined to be principally employed in steering and turning the body, as a rudder; but Borelli has shown that this is the least use of it. Its chief use is to assist the bird in its ascent and descent in the air, and to obviate the vacillations of the body and wings; for, as to turning the body to this or to that side, it is performed by the wings and inclination of the body, and but very little by the help of the tail. The flying of a bird, in fact, is a very different thing from the rowing of a vessel. Birds do not vibrate their wings towards the tail, as oars are struck towards the stern, but waft them downwards; nor does the tail of the bird cut the air at right angles, as the rudder does the water; but is disposed horizontally, and preserves the same situation what way soever the bird turns. In effect, as a vessel is turned about on its centre of gravity to the right, by a brisk application of the oars to the left; so a bird, in beating the air with its right wing alone, towards the tail, will turn its fore part to the left. Thus pigeons, changing their course to the left, would labor it with their right wing, keeping the other almost at rest. Birds of a long neck, alter their course by the inclination of their head and neck, which altering the course of gravity, the bird will proceed in a new direction. The act of flying is thus performed: the bird first bends his legs, and springs with a violent leap from the ground; then opens and expands the joints of his wings, so as to make a right line perpendicular to the sides of his body: thus the wings, with all the feathers therein, constitute one continued lamina. Being now raised a little above the horizon, and vibrating the wings with great force and velocity perpendicularly against the subject air, that fluid resists those successions, both from its natural inactivity and elasticity, by means of which the whole body of the bird is protruded. The resistance the air makes to the withdrawing of the wings, and consequently the progress of the bird, will be so much the greater, as the stroke of the fan of the wing is longer; but, as the force of the wing is continually diminished by this resistance, when the two forces continue to be in equilibrio, the bird will remain suspended in the same place; for the bird only ascends so long as the arch of air the wing describes, makes a resistance greater than the excess of the specific gravity of the bird above the air. If the air, therefore, be so rare as to give way with the same velocity as it is struck withal, there will be no resistance, and consequently the bird can never mount. Birds never fly upwards in a perpendicular line, but always in a parabola. In a direct ascent, the natural and artificial tendency would oppose and destroy each other, so that the progress would be very slow. In a direct descent they would aid one another, so that the fall would be too precipitate. FLYING, ARTIFICIAL, that attempted by men, by the assistance of mechanics. The art of flying has been attempted by several persons in all ages. The Leucadians, out of superstition, are reported to have had a custom of precipitating a man from a high cliff into the sea, first fixing feathers, variously expanded, round his body, in order to break the fall. Friar Bacon not only affirms the art of flying possible, but assures us, that he himself knew how to make an engine, wherein a man sitting, might convey himself through the air like a bird; and further adds, that there was then one who had tried it with success. The secret consisted in a couple of large thin hollow copper globes, exhausted of air, which, being much lighter than air, would sustain a chair whereon a person might sit. Father Francisco Lana, in his Prodromo, proposes the same thing as his own thought. He computes that a vessel of brass, fourteen feet in diameter, weighing three ounces the square foot, will only weigh 1848 ounces, whereas a quantity of air, of the same bulk, will weigh 2155 ounces; so that the globe will not only be sustained in the air, but will carry with it a weight of 3733 ounces; and by increasing the bulk of the globe, without increasing the thickness of the metal, he adds, a vessel might be made to carry a much greater weight But a globe of the dimensions he describes, Dr. Hook shows, would not sustain the pressure of the air, but be crushed inwards. Besides, in whatever ratio the bulk of the globe were increased, in the same must the thickness of the metal, and consequently the weight be increased; so that there would be no advantage in such augmentation. See AEROSTATION. The same author describes an engine for flying, invented by the sieur Besnier, a smith, of Sable, in the county of Main. The philosophers of king Charles II.'s reign were greatly employed in endeavouring to attain this art. Bishop Wilkins was so confident of success, that he says, he does not question, but in future ages it will be as usual to hear a man call for his wings, when he is going a journey, as it is now to call for his boots. FLYING BRIDGES. See BRIDGE. FLYING FISH, a name given to several species of fish, which, by means of their long fins, keep themselves out of water a considerable time. See EXOCOETUS. FLYING PINION, a part of a clock, having a fly or fan to gather air, and so bridle the rapidity of the clock's motion, when the weight descends in the striking pace. FLY-TRAP, VENUS'S. See DIONEA. FLY-WORT, in botany. See SILENE. FO, or Fox, an idol of the Chinese, originally worshipped in the Indies, and thence transported into China. See CHINA. FOA, one of the Happaee islands, in the South Pacific Ocean, between Haano and Lefooga, to each of which it is connected by a reef. FOAL, n. s., v. a., & v. n. Sax. Fola; Goth. ful; Swed. fole; Belg. veule; qu. Lat. pullus; Gr. Twos. The offspring of a mare, or other beast of burthen. The custom now is to use colt for a young horse, and foal for a young mare; but To bring forth; to be disburthened of the fœtus. there was not, originally, any such distinction. Twenty she-asses and ten foals. Gen. xxxii. 15. The fend, quod he, you fecche body and bones, As ferforthly as ever ye were foled, So mochel wo as I have with you tholed. Chaucer. The Feeres Tale. Also flew his steed, Faerie Quecre. Such colts as are of generous race, straight when they first are foaled, Walk proudly. May's Georgicks. About September take your mares into the house, where keep them till they foal. Mortimer's Husbandry. FOAM, n. s., V. R. Sax. Fam; Teut. faum; FOAM'Y, adj. Lat. fumus, smoke. The white substance which agitation or fermentation gathers on the top of liquors; froth; spume. To froth; to gather spume. The adjective signifies covered with foam; frothy. The verb is, metaphorically, to rage; a violent agitation of mind. |