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s varies as the nth power of the distance from the +

+ &c.= s, whence r =

centre. or t, is the hyperbolic log. of s, whence s = e,

Let denote the radius of the sphere, d the e being the base of the hyperbolic system of density at the surface, a= the area of a circle logarithms.

whose radius is 1, and r any distance from the Problem 4.-Find the relation of rand

centre; then 4 a za r is the fuxion of the magy from

drn the fluxional equation (x2 + y2) j = (my x) i. nitude, and is the density; whence Put r=

y*; then i =y tj. By substituting these values of r and i in the proposed

the fuxion of the mass, the equation, and dividing by yệ, we get za + 1. j=

4 ad X1 + 3 fluent of which is


and when a my z 1 + m za j, whence +

n +3:1n у

4 a drs =,

is the quantity of matter in the -6, and by taking the fuents,

T + 3

sphere. hyp. log. y + hyp. log. (32_7-19)

We have given as full an account of the prin2

ciples of this important branch of science, and =log.c.(the correction); whencey:(z?_m=1') 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 scienti2 m 2

2 m - 2

fic pursuits, may find all the aid that he can rebecomes m

quire. The treatises on fluxions by Simpson 1 y

· y

and Emerson are justly held in esteem by Eng2 m - 2

lish mathematicians. A new edition of Simpm-1.c for z,put -., and put a for son's treatise has lately been published, with

y the constant quantity on the right of the equator,

very valuable appendixes on the modern im

provements in the science, by a member of the and after reduction we obtain m - 1.22 y'=

university of Cambridge. Maclaurin's work contains, perhaps, upon the whole, the most

elementary exposition of the principles of the y m

science. Indeed it was written chiefly with the Problem 5.-Given the height of an inclined view of confuting some objections which the plane ; required its length, so that a given power, acute and ingenious Berkeley had advanced acting on a given weight, in a direction parallel against the metaphysics of the science. to the plane, may draw it up in the least time Dr Lardner of Dublin has recently published possible.

a work on the subject, marked by that elegance Let a denote the height of the plane, r its and originality which distinguishes whatever leirgth,

р the power, and w the weight. Now, comes from his pen; and Mr. Jephson of Camby mechanics, the tendercy down the plane is bridge has in course of publication an element

ary work on the subject, which, from what we is the motive force, and have seen of it, will, we are persuaded, form P-OW

a very valuable acquisition to the scientific

world. ptw =the accelerative force f;

We should not, however, discharge our duty ptwr

to our readers if we nmitted to recommend the

translation of Lacroix's work on this subject by hence to Ef

—which must Herschel, Babbage, and Peacock, with the colpr-Iw8

lection of examples for exercise which they combe a minimum; or in fluxions 2 (prī aw) piled ; nor the very elegant and methodical work 31--23= B, or p : w:: 24: x:: double of Dealtry, a work in which the subject of the height of the plane to its length.

fluents, and the application of the science to Problem 6.-It is required to determine the the doctrine of forces, are expounded with requantity of matter in a sphere, whose density markable perspicuity.


a w

hence p

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V. n.

many adaie,


FLY, v, a. & v. n. Pret. flew, or fled; For horde hath hate, and climbyng tikilaesse, FLY'BOAT, n. s.

part. fled, or flown, Prece bath envie, and wele it brent oer all FLY'er, or FLIER, N. S. Sax. pleogan.

Chaucer FLIGHT', n. s. To fly is properly to

So that I mighten lyven and nat faile FLIGHT'Y, adj. use wings, and gives

To morowe for to taken my bataile,

I ne wolde never fro this place Aye, FLIGHT'INESS, n. s. flew and flown. To

Tyl that ye shulde the very profe yei flee is to escape, or to go away. Sax. flean, and

For, now if that the soth I shall you say, makes fled : they are now confounded. To move

I have loved you

ful through the air with wings; to pass through the

Id. Legend Ariadne. air; to pass away with the idea of swiftness or They hit one another with darts, as the others do escape; to move with rapidity; applied to a vio- with their hands, which they never throw counter, lent and sudden separation of adhering parts: but at the back of the flier. Sandy's Journal. to shiver; to burst asunder with a sudden ex For he so swift and nimble was of flight, plosion. Sax. slean; Germ. flichen. To run That from this lower tract he dared to stie away; to attempt escape. In this sense the verb Up to the clowdes, and thence with pineons light is properly to flee, when fled is formed : the verb To mount aloft unto the crystall skie, active is used in the sense of to strain; to de- To view the workmanship of heaven's height: cline; to avoid ; to refuse association with; to

Whence down descending, he along would flie quit by flight; to attack by a bird of prey. It is Upon the streaming rivers, sport to finde ; probable that flew was originally the preterite of And oft would dare to tempt the troublous winde.

Spenser. Muiopotmos. fly, when it signified volation, and fled when it

Which when the valient elf perceived, he leapt, signified escape : flown should be confined like- As lion fierce, upon the flying prey. Spenser. wise to volation; but these distinctions are now

These men's hastiness the warier sort of you do confounded. We know not any book except the

not commend : ye wish they had held themselves Scriptures in which fly and fee are carefully longer in, and not flown so dangerously abroad before kept separate. The substantives are

the feathers of the cause had been grown. Hooke, restricted, and somewhat different in their ap

At the first flight of arrows sent plication. Flyer, or flier, is one that flies, or

Full threescore Scots they slew. Chery Chasc. runs away; one that uses wings: it is used in

-A flight drawn home, mechanics and in architecture: in the one to the

A round stone from a sling. wheel in a machine of a particular use and con

Beaumont and Fletcher. Bonduca. struction; Dr. Johnson says it is that part of a The gates are ope, now prove good seconds; machine which, by being put into a more rapid 'Tis for the followers fortune widens them, motion than the other parts, equalises and regu- Not for the fliers. Shakspeare. Coriolanes. lates the motion of the rest, as in a jack; in the

Ere the bat hath flown other it is the technical name for a certain kind

His cloistered flight.

Id. Macbeth. of stairs. Stairs made of an oblong square figure,

Time thou anticipatest my dread exploits : whese fore, and back sides are parallel to each The flighty purpose never is o'ertook,

Unless the deed go with it.

Id. other, and so are their ends : the second of these

Glad to catch this good occasion, flyers stand parallel behind the first, the third behind the second, and so are said to Ay off from Most thoroughly to be winnowed, where my chaff

And corn shall fly asunder.

Shakspeare. one another.—Moxon's Mech. Exer. Flight is the act of flying, or escaping from danger; the

He set up his bills here in Messina, and challenged

id. act of using wings; removal from place to place, Cupid at the flight. by means of wings, or impelled by fear: a fock I shot his fellow of the self-same flight

In my school-days, when I had lost one shaft, If birds flying together; the birds produced in The self-same way.

Id. t'e same season; a volley; a shower : the space

Love like a shadow flies, when substance love · assed by flying ; heat of the imagination; sally of

pursues ; the soul; excursion on the wing; the power of Pursuing that which flies, and flying what pursues. flying; a shower of arrows. Flightiness is ap

Id. plied to wildness and irregularity of mind, or They take great pride in the feathers of birds, and conduct: the adjective signifies fleeting; swift; this they took from their ancestors of the mountains wild : full of imagination. Flyboat is a kind of who were invited into it by the infinite Alights of birds vessel, nimble and light for sailing.

that came up to the high grounds.

Bacon. New Atlantis. Fowl that may fly above the earth in the open fir

If a man can tame this monster, and with her fly mament of heaven.

Gen. i. 20.

other ravening fowl, and kill them, it is somewhat Abiathar escaped and fled after David.


Bacon. . 1 Sam. xxii.

Here be of all sorts ; flights, rovers, and batsbafts. Man is born unto trouble as the sparks fly upward.

Ben Jonson. Cynthian Revels.

I can at will, doubt not, Ye shall fee, as ye fled from before the earthquake.

Zech. xiv. 5.

Command a table in this wilderness ;
As birde Ayeth up in the aire,

And call swift flights of angels ministrant,
And liveth by birdes that ben meke,

Arrayed in glory, on my cup t'attend. Milton. So these ben flowe up in despair

O whither shall I run, or which way fly And shenden sely soules eke.

The sight of this so horrid spectacle ? Id. Chaucer. The Plowman's Tule.

The drowsy flighted steeds, Flie, fro the prese and dwell with sothfastnesse, That draw the litter of close-curtained sleep Suffise unto thy gode though it be small,

Id. Comu.

Job v.



No wonder that the flying roll, or quick and inevita- meaning. The following phrases are instanced ble curse, doth surprise' the swearer, and cut him off, by Dr. Johnson :as it is in the prophet.

Barrow. The conscious stag, tho' once the forests' dread,

To fly at. To spring with violence upon; to Flys to the wood and hides his armless head.

fall on suddenly. Marvell.

A servant that he bred, thrilled with remorse, Say from the golden quivers of the sky,

Opposed against the act, bending his sword Do all thy winged arrows fly?

To lis great master; who, thereat enraged, Swiftness and power by birth are thine ;

Flew on him, and amongst them felled him dead. From the great sire they came, thy sire the Word

Shakspeare. Divine.


Though the dogs have never seen the dog-killer, Old Pindar's flights by him are reacht, yet they will come forth, and fly at him. When on that gale his wings are strecht.

Bacon's Natural History. Denham.

No honour, no fortune, can keep a man from being He grieves so many Britons should be lost; miserable, when an enraged conscience shall fly at Taking more pains, when he beheld them yield, him, and take him by the throat.

South. To save the fliers than to win the field. Waller. This is an age that flies at all learning, and enquires Sleep flies the wretch ; for when with cares opprest, especially into faults.

Id. And his tossed limbs are wearied into rest,

To fly in the face. To insult. Then dreains invade.

Dryden's Juvenal.

This would discourage any man from doing you Dedalus, to fly the Cretan shore,

good, when you will either neglect him, or fly in his His heavy limbs on jointed pinions bore, The first who sailed in air.

face; and he must expect only danger to himself. Id. Æneid.

Swift's Drapier's Letters.
He thinks by flight his mistress must be won,
And claims the prize because he best did run.

To fly in the face. To act in defiance.

Fly in nature's face!
As striplings whip the top for sport,

- But how, if nature fly in my face first? On the smooth pavement of an empty court,

-Then nature's the aggressor. Dryden. The wooden engine flies and whirls about. Id. To fly off. To revolt. Fowls, by Winter forced, forsake the floods,

Deny to speak to me! They're sick, they're weary, And wing their hasty fight to happier lands.


They have travelled all the night! mean fetches; The scouts with flying speed

The images of revolt and flying off. Shaksplure. Return, and through the city spread the news.

The traytor Syphax

Flew off at once with his Numidian horse. In half-whipt muslin needles useless lie,

Addison's Cato. And shuttle-cocks across the counter fly.

To fly out. To burst into passion.
You now a more delusive art must try,

How easy is a noble spirit discerned,
And tempt their hunger with the curious fly. Id. From harsh and sulphurous matter that flies out
Earth rolls back bencath the flying steed. Pope.

In contumelies, makes a noise, and stinks.

Ben Jonson's Catiline. I'll fly from shepherds, docks, and flow'ry plains; From shepherds, flocks, and plains I may remove,

Passion is apt to ruffe, and pride will fly out into Forsake mankind, and all the world but love. Id. contumely and neglect. Collier of Friendship. Strange graces still, and stranger flights she had ;

To fly out. To break out into license. Was just not ugly and was just not mad. Id.

You use me like a courser spurred and reined; It is not only the utmost pitch of impiety, but the highest flight of folly, to deride these things.

If I fly out, my fierceness you command. Dryden. Tillotson.

Papists, when unopposed, fly out into all the pagean. If there were any certain height where the flights tries of worship; but, when they are hard pressed by of ambition end, one might imagine that the interest

lie close intrenched behind the council of arguments, Trent.

Id. of France were but to conserve its present greatness.

Temple. To fly out. To start violently from any direcAbove an hundred arrows, discharged on my left tion. hand, pricked me like so many needles; and besides All bodies, moved circularly, have a perpetual enthey shot another flight into the air as we do bombs. deavour to recede from the centre, and every moment

Swift. would fly out in right lines, if they were not restrained. The flier, tho't had leaden fect,

Bentley's Sermons, Turned so quick, you scarce could see'. Id.

To let fly. To discharge. One song employs all nations ; and all cry,

The noisy culverin, o'ercharged, lets fly, Worthy the Lamb, for he was slain for us !

And bursts, unaiming, in the rended sky. The dwellers in the vales and on the rocks

Granvillo. Shout to each other, and the mountain tops

To be light and unincumbered : as a flying From distant mountains catch the flying joy ; camp. Till nation after nation taught the strain,

FLY, n. s.

Sax. fleoge; Goth. Earth rolls the rapturous Hosanna round.


FLY BLOW, v. Q. fluga; Teut. fliege; Belg. Black Hassan from the Haram flies,

Fly'-CATCHER, n.8.

vliegen; all clearly from Nor bends on woman's form his eyes ;


the corresponding words The unwonted chase each hour employs


in those languages, signiYet shares he not the hunter's joys,

fying to fly. A small winged insect of many Not thus was Hassan wont to fly,

species : applied to a wheel, in mechanics, it has When Leila dwelt in his Seraii.

the same meaning with flier : that part of a vane Byron. Giaour.

which points from what quarter the wind blows: To fly is used in connexion with other words to fly-blow is to taint with flies; to fill with magwhich form phrases, and has in each a specific gots: a fly-catcher is one that hunts flies: to flyVol. IX.

2 B

fish, is to angle with a hook baited with a fly, resembles the drone both in size and color, exeither natural or artificial: a fly-tap is a fily or cepting that it has no wings, more than any other flapper to keep Hies off.

British insect. In the month of May it buries For lo the gentil kinde of the lion ;

itself in the earth, and begins to vegetate. By For whan a frie offendeth him or biteth,

the end of July the tree has arrived at its full He with his taile awaie the flie ysmiteth growth, and resembles a coral branch: it is Al easily, for of his genterie

about three inches in height, and bears several Him deineth nat to wrecke him on a flie, little pods, which dropping off

, become worms, As doth a curre or els another best.

and then flies, like the British caterpillar. Chaucer. Leg. of Good Women, Prologue.

Such was the account originally given of this Like as the fly that seeth the flame,

extraordinary production. But several boxes of And thiuks to play her in the fire, That found her woe and sought her game

these flies having been sent to Dr. Hill, for his Where grief did grow by her desire.

examination, his report was as follows: “There Earl of Surrey.

is in Martinique a fungus of the clavaria kina, The fresh young Flie, in whom the kindly fire different in species from those hitherto known. Of lustfull youth began to kindle fast,

It produces soboles from its sides; I call it, Did much disdaine to subject his desire

therefore, clavaria sobolifera. It grows on To loathsom sloth, or houses in ease to wast, putrid animal bodies, as our fungus ex pede But ioyd to range abroad in fresh attire

equino, from the dead horse's hoof. The cicada Through the wide compas of the ayrie coast.

is common in Martinique, and in its nymph Spenser. Muiopotmos.

state, in which the old authors call it tettigomeAs flies to wanton boys, are we to the gods;

tra, it buries itself under the dead leaves to They kill us for their sport.


await its change; and, when the season is unfaTo sacrifice the honour of sacred things to our vain pleasure, being like the ridiculous fondness of that vorable, many perish. The seeds of the clavaria people, which, as Ælian reporteth, worshipping a tiy, find a proper bed in this dead insect, and grow.' did offer up an ox thereto.


This is the solution of the mystery; though the I am unwilling to believe that he designs to play untaught inhabitants suppose a fly to vegetate, tricks, and to flyblou my words, to make others distaste and though there is a Spanish drawing of the them.

Stillingfiet. plants growing into a trifoliate tree, and it has There was more need of Brutus in Domitian's days, been figured with the creature flying with this to mend, than of Horace, to laugh at a flycatcher. tree upon its back. Mr. Edwards treats of this

Dryden. extraordinary production in his Gleanings of The swallow was a flycatcher as well as the spider. Natural History.


Fly, HoneySCCKLE. See LONICERA. My country neighbours begin to think of being in

Fly, HONEYSUCKLE, AFRICAN. See HALLERIA. general, before they come to think of the fly in their sheep, or the tares in their corn.


Flying, the progressive motion of a bird, Tu prevent the fly, some propose to sow ashes with

or other winged animal in the air. The parts of the seed.

Mortimer's Husbandry.

birds chiefly concerned in flying are the wings So morning insects, that in muck begun, and the tail; by the former, the bird sustains Shine, buz, and flyblow in the setting sun.

Pope. .

and wafts himself along; and, by the latter, he Like a fly-blown cake of tallow;

is assisted in ascending and descending, to keep Or, on parchment, ink turned yellow. Swift. his body poised and upright, and to obviate the To heedless flies the window proves

vacillations thereof. It is by the largeness and A constant death.

Thomson's Summer.

strength of the pectoral muscles, that birds are None savc the Spanish Fly and Attic Bee

so well disposed for quick, strong, and continued As yet are strongly stinging to be free. Byron.

flying. These, muscles, which, in men, are Fly, or Musca, in entomology, a large order scarcely a seventieth part of the muscles of the of insects, the distinguishing characteristic of body, in birds exceed and outweigh all the which is, that their wings are transparent. By other muscles taken together. The tail

, Messrs. this they are distinguished from beetles, butter- Willoughby, Ray, and many others, imagined flies, grasshoppers, &c. See ENTOMOLOGY.

to be principally employed in steering and turnFly, in mechanics, a cross, with leaden ing the body, as à rudder; but Borelli has weights at its ends; or rather, a heavy wheel at shown that this is the least use of it. Its chief right angles, to the axis of a windlass, jack, or use is to assist the bird in its ascent and dethe like; by means of which the force of the scent in the air, and to obviate the vacillations power, whatever it is, is not only preserved, but of the body and wings; for, as to turning the equally distributed in all parts of the revolution body to this or to that side, it is performed by of the machine. See MECHANICS.

the wings and inclination of the body, and but FLY, ELECTRIC. See ELECTRICITY.

very little by the help of the tail. The flying of Fly Island, an island in the South Pacific a bird, in fact, is a very different thing from the Ocean, discovered by Le Maire and Schouten, in rowing of a vessel. Birds do not vibrate their the year 1616, and so named from the number wings towards the tail, as oars are struck towards of flies seen there. It is covered with trees, the stern, but waft them downwards; nor does and a lagoon seems to be formed in the inte- the tail of the bird cut the air at right angles, as rior by the flowing of the tide. The naviga- the rudder does the water; but is disposed hotors observed a few naked inhabitants. Long. rizontally, and preserves the same situation what 150° 20' W., lat. 15° S.

way soever the bird turns. In effect, as a vessel Fly, VEGETABLE, a very curious natural pro- is turned about on its centre of gravity to the duction, chiefly found in the West Indies. It right, by a brisk application of the cars to the

left; so a bird, in beating the air with its right metal, he adds, a vessel might be made to carry wing alone, towards the tail, will turn its fore a much greater weight But a globe of the dipart to the left.

Thus pigeons, changing their mensions he describes, Dr. Hook shows, would course to the left, would labor it with their right not sustain the pressure of the air, but be crushwing, keeping the other almost at rest. Birds ed inwards. Besides, in whatever ratio the bulk of a long neck, alter their course by the inclina- of the globe were increased, in the same must tion of their head and neck, which altering the the thickness of the metal, and consequently the course of gravity, the bird will proceed in a weight be increased; so that there would be no new direction. The act of flying is thus per- advantage in such augmentation. See Aerosformed: the bird first bends his legs, and springs TATION, The same author describes an engine with a violent leap from the ground; then opens for flying, invented by the sieur Besnier, a smith, and expands the joints of his wings, so as to of Sable, in the county of Main. The philosomake a right line perpendicular to the sides of his phers of king Charles II.'s reign were greatly body: thus the wings, with all the feathers there- employed in endeavouring to attain this art. in, constitute one continued lamina. Being now Bishop Wilkins was so confident of success, raised a little above the horizon, and vibrating that he says, he does not question, but in future the wings with great force and velocity perpen- ages it will be as usual to hear a man call for dicularly against the subject air, that fluid resists his wings, when he is going a journey, as it is those successions, both from its natural inactivity now to call for his boots. and elasticity, by means of which the whole FLYING BRIDGES. See BRIDGE. body of the bird is protruded. The resistance FLYING Fish, a name given to several species the air makes to the withdrawing of the wings, of fish, which, by means of their long fins, keep and consequently the progress of the bird, will themselves out of water a considerable time. be so much the greater, as the stroke of the fan See Exocoetus. of the wing is longer; but, as the force of the Flying Pinion, a part of a clock, having a wing is continually diminished by this resist- fly or fan to gather air, and so bridle the rapiance, when the two forces continue to be in dity of the clock's motion, when the weight deequilibrio, the bird will remain suspended in the scends in the striking pace. same place; for the bird only ascends so long FLY-Trap, Venus's. See DIONÆA. as the arch of air the wing describes, makes a Fly-Wort, in botany. See SILENE. resistance greater than the excess of the specific FO, or Foe, an idol of the Chinese, originally gravity of the bird above the air. If the air, worshipped in the Indies, and thence transtherefore, be so rare as to give way with the ported into China. See China. same velocity as it is struck withal, there will be

FOA, one of the liappaee islands, in the South Do resistance, and consequently the bird can Pacific Ocean, between Haano and Lefooga, to never mount. Birds never fly upwards in a each of which it is connected by a reef. perpendicular line, but always in a parabola. In a direct ascent , the natural and artificial ten- Swed. fole ; Belg. veule ; qu. Lat. pullus ; Gr.

FOAL, n. s., v.Q., & v.n. Sax. fola; Goth. ful; dency would oppose and destroy each other, so thai the progress would be very slow. In a'di- twos. The offspring of a mare, or other beast

of burthen. The custom now is to use colt for fect descent they would aid one another, so that the fall would be too precipitate.

a young horse, and foal for a young mare; but FLYING, ArtiFICIAL, that attempted by men,

there was not, originally, any such distinction. by the assistance of mechanics. The art of Aying To bring forth; to be disburthened of the fætus. has been attempted by several persons in all Twenty she-asses and ten foals. Gen. xxxii. 15. ages. The Leucadians, out of superstition, The fend, quod he, you fecche body and bones, are reported to have had a custom of precipi- As ferforthly as ever ye were foled, tating a man from a high cliff into the sea, first Su mochel wo as I have with you tholed. fixing feathers, variously expanded, round his

Chancer. The Feeres Tale. body, in order to break the fall. Friar Bacon

Also Rew his steed, not only affirms the art of flying possible, but And with his winged heels did tread the wind, assures us, that he himself knew how to make an As he had been a foal of Pegasus's kind. engine, wherein a man sitting, might convey

Faerie Quecne. himself through the air like a bird; and further

Give my horse to Timon : it foals me slraight

Shakspeare. Timon. adds, that there was then one who had tried it Ten able horses.

Such colts as are with success. The secret consisted in a couple of large thin hollow copper globes, exhausted of Of generous race, straight when they first are foaled,

Walk proudly.

May's Georgicks. air, which, being much lighter than air, would sustain a chair whereon a person might sit.

About September take your mares into the house, Father Francisco Lana, in his Prodromo, pro

where keep them till they foal. Mortimer's Husbandry. poses the same thing as his own thought. He FOAM, n. s., 4. n. Sax. fam; Teut. faum; computes that a vessel of brass, fourteen feet in FOAM'y, adj. 3 Lat. fumus, smoke. The diameter, weighing three ounces the square foot, white substance which agitation or fermentation will only weigh 1848 ounces, whereas a quantitý Fathers on the top of liquors; froth; spume. of air, of the same bulk, will weigh 2155

To froth; to gather spume. The adjective sig

nifies covered with foam ; frothy. The verb is, ounces; so that the globe will not only be sustained in the air, but will carry with it'a weight metaphorically, to rage; a violent agitation of of 3731 ounces; and by increasing the bulk of mind. the globe, without increasing the thickness of the The foam upon the waters. Hosea *. 7.

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