method they defend is an incommodious one." Ts remark we think uncandid: the prolixity is ccasioned not by want of simplicity in the method they defend, but by the tortuous intricacy and scurity of many of the objections, which required much time to be pursued throughout, and, as several of them was subtile and spacious, much Lbar and room to refute them completely With regard to the comparative perspicuity of the two methods of establishing the principles, from the doctrine of motion and from pure analysis, we cabut besitate to say that the former has the preference: and we are convinced that every unbissed reader of the treatises of Maclaurin and Simpson on the one hand, and of Bossut and Lamos on the other, will agree with us in opinion. Ye, we are constrained to acknowledge, notwithoding this, that the principal improvements and extensions of the modern analysis, during the hat forty years, have been made by continental, A by British, mathematicians.

For the various applications of fluxions to practical purposes, see the articles ASYMPTOTE, FLEXION, MAXIMA, TANGENT, &c. To FLY. v. n. pret, flew or fled; part. fled ar flown: fled is properly from flee. (Fleogan.) 1. To move through the air with wings (Shakspeare). 2. To pass through the air (Job). 3. To pass away (Prior). 4. To pass swiftly (Pope) 5. To move with rapidity (Dryden). 6. To part with violence (Shakspeare). 7. To break; to shiver; to burst asunder with a sudden explosion (Swift). 8. To run away; to flee (Prior). 9. To FLY at. To spring with violence upon; to fall on suddenly (South). 10. To FLY in the face. To insult (Swift). 11. To FLY in the face. To act in defiance. 12. To FLY off. To revolt (Addison). 13. To FLY out. To burst into passion (Ben Jonson). 14. To FLY out. To break cut into licence. 15. To FLY out. To start violently from any direction (Bentley). 16. To let FLY. To discharge (Glanville).

To FLY. v. a. 1. To shun; to avoid; to decline (Shakspeare). 2. To refuse association with (Dryden). 3. To quit by flight (Dryden). 4. To attack by a bird of prey (Bacon).

FLY, in entomology. See MuSCA.
FLY (Honeysuckle), in botany. See Loxi-

FLY (Spanish). See CANTHARIDES. FLY-TRAP (Venus's). See DIONEA. FLY THE HEELS, in the manage, is when a berse obeys the spurs.

FLY (Vegetable), a very curious natural production, chiefly found in the West Indies, and thus improperly denominated. Excepting that it has no wings, it resembles the drone both in size and colour more than any other British insect. In the month of May it buries itself in the earth, and begins to vezetate. By the latter end of July, the tree is arrived at its full growth, and resembles a coral branch; and is about three inches high, and bears several little pods, which dropping VOL. V.

off become worms, and thence flies, like the British caterpillar. Such was the account ori ginally given of this extraordinary production. But several boxes of these flies having been sent to Dr. Hill for examination, his report was this: "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 nympha state, in which the old authors call it tettigometra: it buries itself under dead leaves to wait its change; and, when the season is unfavourable, many perish. The seeds of the clavaria find a proper bed in this dead insect, and grow. The tettigometra is among the cicada in the British museum; the clavaria is just now known. This is the fact, and all the fact; 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." Edwards has taken notice of this extraordinary production in his Gleanings of Natural History.

FLY, in mechanics, is a name given to a certain appendage to many machines, either as a regulator of their motions, or as a collector of power. In the first case the fly is a heavy disk or hoop, or other mass of matter balanced on its axis, and so connected with the machinery as to turn briskly round with it. This may done with the view of rendering the motion of the whole more regular, notwithstanding unavoidable inequalities occasioned by the work. It becomes a REGULATOR. Suppose the resistance extremely unequal, and the impelling power perfectly constant; as when a bucket wheel is employed to work one pump. When the piston has ended its working stroke, and while it is going down the barrel, the power of the wheel being scarcely oppose, it accelerates the whole machine, and the piston arrives at the bottom of the barrel with a considerable velocity. But in the rising again, the wheel is opposed by the column of water now pressing This immediately retards the on the piston. wheel; and when the piston has reached the top of the barrel, all the acceleration is undone, and is to begin again. The motion of such a machine is very hobbling but the superplus of accelerating force at the beginning of a returning stroke will not make such a change in the motion of the machine if we connect the fly with it. For the accelerating momentum is a determinate quantity. Therefore, if the radius of the fly be great, this momentum will be attained by communicating a small angular motion to the machine. The momentum of the fly is as the square of its radius; therefore it resists acceleration in this proportion; and although the overplus of power generates the chine as before, it makes but a small addition to its velocity. If the diameter of the fly he doubled, the augmentation of rotation will be reduced to one-fourth. Thus, by giving a rapid notion to a small quantity of matter, the great acceleration, during the returning stroke of the piston, is prevented. This acceleration continues, however,

of the accelerating forces, or of the resistances

same momentum of rotation in the whole ma

C

during the whole of the returning stroke, and at the end of it the machine has acquired its greatest velocity. Now the working stroke begins, and the overplus of power is at an end. The machine accelerates no more; but if the power is just in equilibrio with the resistance, it keeps the velocity which it has acquired, and is still more accelerated during the next returning stroke. But now, at the beginning of the subsequent working stroke, there is an overplus of resistance, and a retardation begins, and continues during the whole rise of the piston; but it is considerable in comparison of what it would have been without the fly; for the fly, retaining its acquired momentum, drags forward the rest of the machine, aiding the impelling power of the wheel. It does this by all the communications taking into each other in the opposite direction. The teeth of the intervening wheels are heard to drop from their former contact on one side, to a contact on the other. By considering this process with attention, we easily perceive that, in a few strokes, the overplus of power during the returning stroke comes to be so adjusted to the deficiency during the working stroke, that the accelerations and retardations exactly destroy each other, and every succeeding stroke is made with the same velocity, and an equal number of strokes is made in every suc ceeding minute. Thus the machine acquires a general uniformity with periodical inequalities. It is plain, that by sufficiently enlarging either the diameter or the weight of the fly, the irregularity of the motion may be rendered as small as we please. It is much better to enlarge the diameter. This preserves the friction more moderate, and the pivot wears less. For these reasons, a fly is in general a considerable improvement in machinery, by equalising many exertions that are naturally very irregular. Thus, a man working at a common windlass exerts a very irregular pressure on the winch. In one of his positions in each turn he can exert a force of near 70 pounds without fatigue, but in another he cannot exert above 25; nor must he be loaded with much above this in general. But if a large fly be connected properly with the windlass, he will act with equal ease and speed against 30 pounds.

This regulating power of the fly is without bounds, and may be used to render uniform a motion produced by the most desultory and irregular power. It is thus that the most regular motion is given to mills that are driven by a single-stroke steam engine, where for two or even three seconds there is no force pressing round the mill.

The communication is made through a massive fly of very great diameter, whirling with great rapidity. As soon as the impulse cases, the fly, continuing its motion, urges round the whole machinery with almost unabated speed, At this instant all the teeth, and all the joints, between the fly and the first mover, are heard to catch in the opposite direction.

If any permanent change should happen in the impelling power, or in the resistance, the fly makes no obstacle to its producing its full effect on the machine; and it will be observed to accelerate or retard uniformly, till a new general speed is acquired exactly corresponding with this new pover and resistance.

Many machines include in their construction movements which are equivalent to this intentional regulator. A four-mul, for example, canfot be better regulated than by its millstone; but

in the Albion Mills, a heavy fly was added with great propriety; for if the mills had been regulated by their millstones only, then at every change of stroke in the steam engine, the whole train of communications between the beam, which is the first mover, and the regulating millstone, which is the very last mover, would take in the opposite direction. Although each drop in the teeth and joints be but a trifle, the whole, added together, would make a considerable jolt. This is avoided by a regulator immediately adjoining to the beam. This continually presses the working machinery in one direction. So judiciously were the movements of that noble machine contrived, and so nicely were they executed, that not the least noise was heard, nor the slightest tremor felt in the building.

Mr. Valoué's beautiful pile engine employed at Westminster Bridge is another remarkable instance of the regulating power of a fly. When the ram is dropped, and its follower disengaged immediately after it, the horses would instantly tumble down, because the load, against which they had been straining hard, is at once taken off; but the gin is connected with a very large fly, which checks any remarkable acceleration, allowing the horses to lean on it during the descent of the load; after which their draught recommences immediately. The spindles, cards, and bobbins of a cotton mill, are also a sort of flies. Indeed all bulky machines of the rotative kind tend to preserve their motion with some degree of steadiness, and their great momentum of inertia is as useful in this respect as it is prejudicial to the acceleration or any reciprocation when wanted.

There is another kind of regulating fly, consisting of wings whirled briskly round till the resistance of the air prevents any great acceleration. This is a very bad one for a working machine, for it produces its effect by really wasting a part of the moving power. Frequently it employs a very great and unknown part of it, and robs the pro prietor of much work. It should never be introduced into any machine employed in manufac

tures.

Some rare cases occur where a very different regulator is required: where a certain determined velocity is found necessary. In this case the machine is furnished, at its extreme mover, with a conical pendulum, consisting of two heavy balls hanging by rods, which move in very nice and steady joints at the top of a vertical axis. It is well known, that when this axis turns round, with an angular velocity suited to the length of those pendulums, the time of a revolution is determined. Thus, if the length of each pendulum be 39! inches, the axis will make a revolution in two seconds very nearly. If we attempt to force it more swiftly round, the balls will recede a little from the axis, but it employs as long time for a revolution as before; and we cannot make it turn swifter, unless the impelling power be increased beyond all probability; in which case the pendulum will fly out from the centre till the rods are horizontal, after which every increase of power will accel rate the machine very sensibly. Watt and Boulton have applied this contrivance with great ingenuity to their steam engines, when they are employed for driving machinery for manufactures which have a very changeable resistance, and where a certam speed cannot be much de parted from without great inconvenience. They have connected this recess of the balls from the

minished by this resistance, when the two forces come 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 equal to the excess of the specific gravity of the bird above the air. If the air, therefore, is so rare as to give way with the same velocity as it is struck with, 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-FISH, in ichthyology. See Exo

FOAL, the produce of a horse and mare in a general sense; though more usually applied to the colt or male produce; the female being commonly called a filly foal. It is said to be no difficult matter to know the shape that a foal is likely to be of when full grown; for the same shape that he carries at a month he will carry at six years old, if he be not abused in after keeping; and as the good shape, so will be the defects also. As to the height, it is observed, that a large shin-bone, long from the knee to the pastern, indicates a tall horse. Another way of judging is, to see what space he has between his knee and withers; which being doubled, it will be his height when he is a competent horse. There are also means to know the probable goodness of foals in a subsequent period; for if they be stirring, not apt to be frighted, active, and striving for mastery, some writers assert, they generally prove good mettled horses.

FOAL-TEETH. See the article AGE. To FOAL. v. a. (from the noun.) To bring forth a foal (May).

FOAM. s. (Fam, Saxon.) The white substance which agitation or fermentation gathers on the top of liquors; froth; spume (Ho

sea).

To FOAM. v. n. (from the noun.) 1. To froth to gather foam (Shakspeare). 2. To be in rage; to be violently agitated (Mark).

FO AMY. a. (from foam.) Covered with foam; frothy (Sidney).

FOB. s. (fuppe, German.) A small pocket (Addison).

To FOB. v. a. (fuppen, German.) 1. To cheat; to trick; to defraud (Shakspeare). 2. To FOB of To shift off; to put aside with an artifice (Addison).

FOCAL. a. (from focus, Latin.) Belonging to the focus (Denham).

FOCAL DISTANCE, the distance of the focus, which is sometimes understood as its distance from the vertex, as in the parabola ; and

sometimes its distance from the centre, as in the ellipse or hyperbola.

FO-CHAN, a village of China, in the province of Quangtong. It is called a village, because it has no walls nor a presiding governor, although it has a great trade, and contains more houses and inhabitants than Canton. It is reckoned to be nine miles in circumference, and to contain 1,000,000 inhabitants. It is 12 miles from Canton.

FOCHIA NOVA, a seaport of Natolia, with a good harbour, and a castle. It is seated on the gulf of Sanderly. Lat. 38. 44 N. Lon. 26. 39 E.

FO CIL. s. (focile, French.) The greater or less bone between the knee and ankle, or elbow and wrist (Wiseman).

FOCILLATION. s. (focillo, Lat.) Comfort; ; support.

FOCOSO, in music, with fire and spirit. FOCUS, in geometry and the conic scctions, is applied to certain points in the ellipse, hyperbola, and parabola, where the rays reflected from all parts of these curves do concur or meet; that is, rays issuing from a luminous point in the one focus, and falling on all points of the curves, are reflected into the other focus, or into the line directed to the other focus, viz. into the other focus in the ellipse and parabola, and directly from it in the hyperbola. Which is the reason of the name focus, or burning-point. Hence, as the one focus of the parabola is at an infinite distance; and consequently all rays drawn from it, to any finite part of the curve about the vertex, are parallel to one another; therefore if rays from the sun, or any other object so distant as that those rays may be accounted parallel, fall upon the curve of a parabola or concave surface of a paraboloidal figure, those rays will all be reflected into its focus.

In all the three curves the double ordinate drawn through the focus is the parameter of the axis, or a third proportional to the transverse and conjugate. If there be any tangent to these curves, and two lines drawn from the foci to the point of contact, these two lines will make equal angles with that tangent.

In the parabola, the distance from the focus to the vertex is equal to of the parameter, or the ordinate at the focus.

For other properties of the foci, see the dif. ferent authors on Conics.

Focus, in optics, is a point in which seve ral rays meet, and are collected, after being either reflected or refracted. It is so called. because the rays being here brought together and united, their force and effect are increased, insomuch as to be able to burn; and therefore it is that bodies are placed in this point to be burnt, or to shew the effect of burning glasses, or mirrors. It is to be observed, however, that in practice, the focus is not an absolute point, but a space of some small breadth, over which the rays are scattered; owing to the different nature and refrangibility of the rays of light, and to the imperfections in the

fcure of the lens, &c. However, the smaller ts space is, the better, or the nearer to pertection the machine approaches. Huygens shews that the focus of a lens convex on both sales, has its breadth equal to † of the thickness of the lens.

Firtual Focus, or Point of Divergence, so called by Mr. Molyneux, is the point from whence rays tend, after refraction or reflection; being in this respect opposed to the ordinary focus, or point of concurrence, where rays are made to meet after refraction or reflection. Thus, the foci of an hyperbola are mutually virtual foci to each other: but, in an ellipse, they are common foci to each other: for the rays are reflected from the other focus in the hyperbola, but towards it in the ellipse. Practical Rules for finding the Faci of Glasses.

1: To find, by experiment, the focus of a convex spherical glass, being of a small sphere; apply it to the end of a scale of inches and decimal parts, and expose it before the sun; upon the scale may be seen the bright intersection of the rays measured out: or, expose it in the hole of a dark chamber; and where a white paper receives the distinct representation of distant objects, there is the focus of the glass. 2. For a glass of a pretty long focus, ebserve some distant object through it, and rerede from the glass till the eye perceives all in confusion, or the object begins to appear in verted; then the eye is in the focus. 3. For a plano-convex glass: make it reflect the sun against the wall: on the wall will then be seen two sorts of light, a brighter within another more obscure; withdraw the glass from the wall, till the bright image be in its least dimensions; then is the glass distant from the wall about a fourth part of its focal length. 4. For a double convex: expose each side to the sun in like manner; and observe both the distances of the glass from the wall: then is the first distance about half the radius of the convexity turned from the sun; and the second is about half the radius of the other convexity. The radii of the two convexities being thus known, the focus is then found by this rule; As the sum of the radii of both convexities : is to the radius of either convexity: so is double the radius of the other convexity: to the distance of the focus.

Dr. Halley gave general methods of finding the foci of all kinds of glasses, both geometrically and algebraically. See Phil Trans. No. 205, &c. The same is also shewn by the principal writers on optics; as by Emerson, Martin, Smith, Wood, &c. See also our articles CATOPTRICS and DIOPTRICS.

FØDDER. s. (fodre, foder, Saxon.) Dry food stored up for cattle against winter (Knolles).

Te FODDER. v. a. (from the noun.) To feed with dry food (Evelyn).

FODDERER. s. He who fodders cattle. FODWAR, a town of Hungary. Lat. 46. 39 N. Lon. 19. 36 E.

FOE s. (Fah, Saxon.) 1. An enemy in

war (Spenser). 2. A persecutor; an enemy in common life. 3. An opponent; an illwisher (Watts).

FOEMAN. s. (from foe and man.) Enemy in war; antagonist: obsolete (Spenser) FŒNICULUM. (fœniculum, quasi fxnum osulorum, the hay or herb good for the sight; so called because it is thought good for the eyes.) Fennel. See ANETHUM.

FENICULUM AQUATICUM. Water fennel. Fine-leaved water hemlock. The plant which bears this name in the pharmacopoeias is the phellandrium aquaticum; foliorum ramificationibus divaricatis, of Linnéus. It possesses vertiginous and poisonous qualities, which are best counteracted by acids, after clearing the primæ viæ. The seeds are recommended by some, in conjunction with peruvian bark, in the cure of pulmonary phthisis. See PHELLANDRIUM.

FONICULUM DULCE. Common fennel. Anethum foeniculum fructibus ovatis of Linnéus. Class pentandria. Order digynia. The seeds and root of this indigenous plant are directed by the colleges of London and Edinburgh. The seeds have an aromatic smell, and a warm sweetish taste, and contain a large proportion of essential oil. They are stomachic and carminative. The root has a sweet taste, but very little aromatic warmth, and is said to be pectoral and diuretic.

FENICULUM PORCINUM. See PEUCEDANUM and ANETHUM,

FONICULUM VULGARE. Common fenne or fenckle. A variety of the anethum fœniculum. See FONICULUM DULCE.

FOENUGREEK, in botany. See TRIGO

NELLA.

FOENUM GRÆCUM. (fænum, hay, and græcus, belonging to Greece, because in Greece it grew in the meadows like hay.) Fenugreek. Trigonella fænum græcum leguminibus sessilibus strictis erectiusculis subfalcatis acuminatis, caule erecto, of Linnéus. Diadelphia. Decandria. A native of Montpelier. The seeds are brought to us from the southern parts of France and Germany; they have a strong disagreeable smell, and an unctu ous farinaceous taste, accompanied with a slight bitterness. They are esteemed as assisting the formation of pus in inflammatory tumours; and the meal, with that intention, is made into a poultice with milk; though the meal of linseed is at present more frequently resorted to, as a better emollient and sedative."

FOENUM CAMELORUM. See JUNCUS ODORATUS.

FOETIDIA. In botany, a genus of the class icosandria, order monogynia. Calyx su. perior, four-cleft; corolless; capsule woody, four-celled; the cells one or two-seeded. A tree of Mauritius, with one-flowered terminal peduncles.

FOETUS. (fætus.) The child enclosed in the uterus of its mother is called a foetus from the fifth month after pregnancy until the time of its birth. This term should rather be spelt fetus, as derived from the old Latin feo, whence fio, and is so spelt by ail the old