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in this case, neither the Leibnitzian nor the Cartesian propositions take place. But this force of percussion depends chiefly on the hardness of the bodies; the greater this is, the greater will the force of percussion be. If M : N, this force will be as of Mcc x Aa, that is, in a compound subduplicate ratio of the vis vica of the striking body, of the hardness, and of the plane of contact. But if M, the hardness of one of the bodies, be infinite, the force of percussion will be as Nec × Aa; at the same time, if M = N, this force will be as

in a second; according to Mr. Enler, the greatest
berce of compression will be equivalent to 400lb.
and this force will produce, in each of these bodies,
impression equal to of a foot; and the dura-
tom of the collision, that is, till the bodies arrive
at her greatest compression, will be about
a second. Mr. Euler, in his calculations, supposes
the hardness of a body to be proportional to the
tarce or pressure requisite to make a given im-
pression on it; so that the force by which a given
impression is made on a body, is in a compound
s of the hardness of the body and of the quan-
uty of the impression. But he observes, that re-
gard must be had to the magnitude of the bodies,
is the same impression cannot be made on the
let bodies as on the greatest, from the defect of
space through which their component particles
must be driven: he considers, therefore, only the
least impression, and supposes the bodies of such
magnitudes, that with respect to them, the im-
pressions may be looked upon as nothing. What
be supposes concerning the hardness of bodies,
Bether implies elasticity nor the want of it, as
rancity only produces a restitution of figure and
impression when the pressing force ceases; but

ms restitution need not be here considered. It
is also supposed, that the bodies which strike each
ther have plain and equal bases, by which they
roach each other in the collision; so that the im-
pression hereby made diminishes the length of
ach body. It is farther to be observed, that in
Mr. Euler's calculations, bodies are supposed so
constituted, that they may not only receive im-
pressions from the forces pressing them, but that
a greater force is requisite to make a greater im-
pression. This excludes all bodies, fluid or solid,
in which the same force may penetrate farther and
fanber, provided it have time, without ever being
in equilibrio with the resistance: thus a body may
continually penetrate farther into soft wax, al-
though the force impelling it be not increased: in
these, and the like cases, nothing is required but
to surmount the first obstacles; which being once
done, and the connection of parts broken, the pene-
Tating body always advances, meeting with the
same obstacles as before, and destroying them by
an equal force. But Mr. Euler only considers the
first obstacles which exist before any separation of
parts, and which are doubtless such, that a greater
impression requires a greater force. Indeed, this
chicly takes place in elastic bodies; but it seems
Lacwise to obtain in all bodies, when the impres-
sions made on them are small, and the contexture
of their parts is not altered.

These things being premised, let the mass or weight of the body A be expressed in general by A. and let its velocity before the shock be that which it might acquire by falling from the height Farther, let the hardness of A be expressed by M, and that of B by N, and let the area of the base, on which the impression is made, be ce; then will the greatest compression be made with the

furce

MNec
M÷N

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pression received by the body B, in this case, will be to the impression it receives in the former, as to 2.

Mr. Euler has likewise considered and computed the case where the striking body has its anterior surface convex, with which it strikes an immoveable body, whose surface is plain. He has also examined the case, when both bodies are supposed immoveable: and from his formula he deduces the known laws of the collision of elastic and nonelastic bodies. He has also determined the greatest pressures the bodies receive in these cases; and likewise the impressions made on them. In particular he shews, that the impressions received by the body struck, or B, if moveable, is to the impression received by the same body when immoveable, as B to A + B.

There are several curious as well as useful observations in Desaguliers's Experimental Philosophy, concerning the comparative forces of men and horses, and the best way of applying them. A horse draws with the greatest advantage when the line of direction is level with his breast; in such a situation, he is able to draw 200lb. for eight hours a day, walking about 24 miles an hour. But if the same horse be made to draw 2401b. he can work only six hours a day, and cannot go quite so fast. On a carriage, indeed, where friction alone is to be overcome, a middling horse will draw 1000lb. But the best way to try the force of a × Aa. Therefore, if the hardness horse, is to make him draw up out of a well, over a single pulley or roller; and, in that case, an ordinary horse will draw about 200lb. as before observed.

of the two bodies, and the plane of their contact Curing the whole time of their collision be the ae, this force will be as Aa, that is, as the quare root of the vis viva of the striking body A. And as a is proportional to the velocity of the body A, the force of percussion will be in a compound ratio of the velocity, and of the subduplicate ratio of the mass of the body striking; so that

It is found, that five men are of equal force with 1 horse, and can, with equal ease, push round the horizontal beam of a mill, in a walk 40 feet wide; whereas, three men will do it in a walk only 19 feet wide.

The worst way of applying the force of a horse

is, to make him carry or draw up hill: for if the hill be steep, three men will do more than a horse, cach man climbing up faster with a burden of 100lb. weight, than a horse that is loaded with 300lb.: a difference which is owing to the position of the parts of the human body being better adapted to climb, than those of a horse.

On the other hand, the best way of applying the force of a horse, is the horizontal direction, in which a man can exert the least force: thus, a man that weighs 140lb. when drawing a boat along by means of a rope coming over his shoulders, cannot draw above 271b, or exert above 4th part of the force of a horse employed to the same purpose; so that, in this way, the force of a horse is equal to that of seven men.

The best and most effectual posture in a man, is that of rowing; when he not only acts with more muscles at once, for overcoming the resist ance, than in any other position, but also as he pulls backwards, the weight of his body assists by way of lever. See Desaguliers's Exp. Philos, v. 1. F. 241, where several other observations are made relative to force acquired by certain positions of the body; from which that author accounts for most feats of strength and activity. See also a Memoir on this subject by M. De la Hire, in the Mem. Roy. Acad. 1729; or in Desaguliers's Exp. &c. p. 267, &c. who has published a translation of part of it with remarks.

Force is distinguished into motive and accelerative or retardive.

Motive force, otherwise called momentum, or force of percussion, is the absolute force of a body in motion, &c. and is expressed by the product of the weight or mass of matter in the body multiplied by the velocity with which it moves. But, Accelerative force, or retardive force, is that which respects the velocity of the motion only, accelerating or retarding it; and it is denoted by the quotient of the motive force, divided by the mass or weight of the body. So,

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In centripetal forces, the absolute quantity is defined from the magnitude, or at least from the strength and efficacy of the central body. The accelerating is that force as perpetually decreasing in the increase of the distance, et contra. The moving force is the weight itself, which arises from the body or mass drawn into the accelerating force. From whence, the absolute force being given, the moving force in a given body will be as the accelerating; and the accelerating being given it will be as the body. These three forces, therefore, are referred to three things, to bodies, to the places of bodies, and to the centre of force. The motive force respects the body, and the endeavour and propension thereof to the centre, as compounded of the endeavours and propensions of all the parts. The accelerating reters to the place of the body in the medium, as the efficacy of the same absolute force, according to divers distances from the centre: and the absolute force respects the centre or central body itself, as endowed with some power, without which the moving forces are no propagated round about; whether that power be the central body (as the magnet in the magnetic force, or the carth in

the centre of the gravitating force), or be seme other thing which does not appear.

Again, forces are either constant or variable. Constant forces are such as remain and act continually the same for some determinate time. Such, for example, is the force of gravity, which acts constantly the same upon a body while it continues at the same distance from the centre of the earth, or from the centre of force, wherever that may be.

Here the following nine propositions will often be of utility:

1. If different forces are successively applied to accelerate equal quantities of matter from quiescence, the spaces described in any given time will be in the same proportion with the forces.

2. If the same force impels different quantities of matter, for any given time, the spaces described from quiescence will be inversely as the quantities of matter moved.

3. If the force be increased or diminished, in the same proportion with the mass moved, the spaces. described from rest, in the same time, will be equal.

4. If a body is moved from quiescence, during any given time, it will, at the end of that time, have acquired such a velocity as will, if continued uniform, carry it, in the same time, through double the space which the body has already described to acquire that velocity.

5. If the same force acts on the same mass, for different times, the velocities generated will be respectively in the same proportion with the times in which the given force acts.

6. If any given quantity of matter is moved from quiescence by different forces, during a given time, the velocities acquired will be in the same proportion with the forces.

7. If a given force impels different quantities of matter for the same time, the velocities generated will be inversely as the quantities of matter.

8. If a body be moved from quiescence, through the same space by different forces, the velocities generated will be in a subduplicate ratio of the forces.

9. If a given quantity of matter is impelled from quiescence, through different spaces, by the action of the same force, the velocities generated will be in a subduplicate ratio of the spaces described.

In the case of a constant force F, acting upon a body b, for any time t, we have these following theorems; putting

f = the constant accelerating force = F÷b, the velocity at the end of the time t,

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s = the space passed over in that time, by the constant action of that force on the body: and g 16 feet, the space generated by gravity, in one second, and calling the accelerating force of gravity 1; then is

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as the square of the distance increases. In variable forces, theorems, similar to those above, may be exhibited by using the fluxions of quantities, and afterwards taking the fluents of the given fusional equations. And herein consists one of the great excellencies of the Newtonian or modern analysis, by which we are enabled to manage, and compute the effects of all kinds of variable forces, whether accelerating or retarding. Thus, using the same notation as above, for constant forces, viz. f the accelerating force at any instant, the time a-body has been in motion by the action of the variable force, v the velocity generated in that time, the space run over in that time, and g = 32} feet, then is

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gs

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In these four theorems, the foreef, though variable, is supposed to be constant for the indefinitely small time i; and they are to be used in all cases of variable forces, as the former ones in constant forces; viz. from the circumstances of the problem under consideration, deduce a general expression for the value of the force f, at any indefinite time ; then substitute it in one of these theorems, which shall be proper to the case in hand; and the equation, thence resulting, will determine the corresponding values of the other quantities in the problem.

It is also to be observed, that the foregoing theorems equally hold good for the destruction of motion and velocity, by means of retarding or resisting forces, as for the generation of the same by

means of accelerating forces.

FORCES, CENTRAL, CENTRIFUGAL, &c. See the respective words.

FORCE COERCITIVE, the name given by Coulomb to the resistance opposed by the molecule of certain bodies to the motion of the electric fluid, when it endeavours to escape from them. This force augments with the defect of the conducting power.

FORCE OF COMBINATION, is that in virtue of which the particles of two or more heterogeneous bodies become so intimately united, that the result of their union is a body which has none of the properties of the constituents.

FORCE EXPANSIVE. See EXPANSION. FORCE OF TORSION, the effort made by a thread cr wire, which has been twisted, to return to its former state.

FORCE PROJECTILE. See PROJECTILES.

FORCEDLY. ad. (from force.) Violently; constrainedly; unnaturally (Burnet). FORCEFUL. a. (force and full.) Violent; strong; impetuous (Pope).

FORCEFULLY. ad. (from forceful.) Violently; impetuously.

FORCELESS. a. (from force.) Having little force; weak; feeble; impotent.

FORCEPS. (forceps, cipis, quasi ferrireps, as being the iron with which we seize any thing hot, from ferrum, iron, and ca

pio, to take.) A surgical instrument with which extraneous bodies or other substances are extracted: al-o an instrument used occasionally by men midwives to bring the head of the fetus through the pelvis.

FO'RCER. s. (from force.) 1. That which forces, drives, or constrains. 2. The embolus of a pump working by pulsion (Wilkins).

For an account of Trevithick's temporary forcer to produce a constant stream, consult Nicholson's Journal, No. 9. N. S., or Gregory's Mechanics, vol. ii. p. 197.

FORCHEIM, a strong town of Franconia, in the bishopric of Bamberg. It is seated at the confluence of the Wisent and Rednitz. Lat. 49. 44 N. Long. 11. 2 E.

FORCIBLE. a. (from force.) 1. Strong; mighty (Milton). 2. Violent; impetuous (Prior). 3. Efficacious; active; powerful (Bacon). 4. Prevalent; of great influence (Raleigh). 5. Done by force; suffered by force (Swift). 6. Valid; binding; obliga

tory.

For

FORCIBLE ENTRY AND DETAINER. cible entry, is a violent actual entry into a house or land, &c. or taking a distress of any person, armed, whether he offer violence or fear of hurt to any there, or furiously drive any out of the possession; if one enter another's house, without his consent, although the doors be open, this is a forcible entry punishable by the law.

And an indictment will lie at common law for a forcible entry, though generally brought on the several statutes against forcible entry. The punishment for this offence is by fine and imprisonment.

FORCIBLE MARRIAGE. If any person shall take away any woman having lands or goods, or that is heir apparent to her ancestors, by force and against her will, and afterwards she be married to him, or to another by his procurement; or defiled; he, and also the procurers, and receivers of such a woman, shall be adjudged principal felons. And by 39 Eliz. c. 9, the benefit of clergy is taken from away the principals, procurers, and accessaries before. And by 4 and 5 Phil. and Mary, c. 8, if any person shall take or convey away any unmarried woman, under the age of sixteen (though not attended with force), he shall be imprisoned two years, or fined, at the discre tion of the court; and if he deflower her, or contract matrimony with her without the consent of her parent or guardian, he shall be imprisoned five years, or fined in like manner. And the marriage of any person under the age of twenty one, by licence, without such con

sent, is void.

1.

FORCIBLENESS. $. Force; violence. FORCIBLY. ad. (from forcible.) Strongly; powerfully (Tillotson). 2. Impetuously; with great strength. 3. By violence; by force (Hammond).

FORCING, in gardening, the art of raising and producing plants, flowers, and fruits, by means of artificial heat. It is accomplished, either by the gentle moist heat that is evolved

during the fermentation and decomposition of stable dung, tanner's bark, and other similar materials, or by the use of actual fire in stoves, Alues, and other contrivances for the purpose. The former of these methods is principally employed in raising cucumbers, melons, and some other fruits, and the latter in producing pine apples, various kinds of wall fruits, and several other sorts of vegetable productions. The great difficulty in the management of this process, is that of adapting and regulating the heat, of whatever sort it may be, in such a manner as to promote and bring forward the plants in the most perfect and healthy growth, without their sustaining injury either by a deficiency or excess. The various methods of effecting this in the most perfect manner are fully described under the culture of the different trees, plants, and vegetables that require such treatment in their cultivation. It is by this process that different sorts of vegetable productions, fruits, and flowers, are afforded at much earlier periods than could otherwise be the case, and it of course constitutes an important branch of practical gardening.

FORCING FRAME, that kind of large frame work or erection which is made use of in procuring different sorts of vegetables, fruits, and flowers at an early period, by the application of artificial heat in some of the above modes. It is a construction covered with sloping glass sliding frames on the top, and sometimes in the front. It may be either fixed or moveable; but in the former case the walls are most ly made of brick-work.

These sorts of forcing frames are usually placed full to the south sun, and the length may be from ten to fifty, or one hundred feet; the width from five to fifteen, and from five to ten high; having an upright back wall of wood, where small, but where large, of brick; and a front of glass-work, made sometimes in one continued range of slope to the top of the back wall; and sometimes with upright glasswork, head high, ranging immediately along the front, and from the top of which a glass roof is carried to the top of the back or main wall: when wrought by dung heat, it is chiefly applied against the outside of the back wall, and by being formed into a bed internally; when by bark heat, by forming it into a bed in a pit withinside; and when by fire heat, by having several returns of flues against the inside of the back wall, and that of the front and both ends, for the heat to pass along, constructed according to the sorts of plants chiefly intended to be forced, and the nature of the materials to be employed in producing the

heat.

Where the first kind of materials is employed in affording heat, the frame is usually formed with an upright back and ends of deal planking, and a sloping front of moveable glass lights; the length may be ten, twenty, or thirty feet, or more; the width from three to five (or sere), and five or six high; the frame-work be of inch and half deal planking, 1, and closely joined, that no steam from

the dung may penetrate into the frame; raised five, six, or seven feet high behind, and only ten or twelve inches high in front, raising both ends answerable to the front and back; the glass work to range, from the upright in front, sloping upward towards the back wall, to about a foot width at top, there resting the ends upon proper frame work of wood; and bars or bearers, three inches in width, ranged sloping from the back to front, for the support of the lights, as in common hot-bed frames, and the top of all boarded wind and water tight; having sometimes withinside two or three ranges of narrow shelves, along the back and ends, for pots of small plants, and the bottom levelled, on which to place pots of larger kinds; or shelves may be made, rising one above another, quite from the front, half way up the back wall, in order to place the lowest plants in front, the others in order behind them, rising gradually to the tallest in the back

rows.

In working these frames, after having placed the pots of plants in regular order, the lights are put on, and a sufficient quantity of fresh, hot, stable dung, prepared as for common dung hot-beds, is to be piled up close against the outside of the back and ends, a yard wide at bottom, drawing it gradually into a foot width at top, finishing it somewhat sloping, to throw off wet; and as the dung settles or sinks down, a fresh supply must be added at top, to maintain the lining to the full height of the frame, additions being occasionally made of fresh dung as the heat declines; by this means a fine growing heat will be thrown in. See HOT-BED.

Where bark is made use of in producing heat, the frame may be constructed either of wood or brick work, and fronted, &c. with sashes of glass as the former; the length may be ten, twenty, or thirty feet, or more; eight or ten wide, and six or eight high; and like the dung heat frame, be six or eight feet high behind, and one in front, the ends conformable and sloping, having glass work frames raised from the front, sloping either quile to the top of the back wall, or inclmed only about one half towards that part, meeting a tiled roof at top half way, which should be raised high enough in front to throw the water off behind, as well as to admit as much sun as possible to every part of the frame; it may likewise be constructed with an upright front of glass, head high, and a sloping roof of glass work, ranging from the upright front to the top of the back wall, which is the most eligible form, both for convenience and benefit of the plants; either of which constructions may be erected detached, or against a south wail already built, which will serve for the back, and save some expense; the ends may either be of wood or brick, and should be glazed like the front, &c. and the glass work in every part be made to move on and off, as well as to slide backward and forward, to give air, and perform other necessary work. At one end, near the back wall, a door should be made to enter occasionally at, and withinside,

apit formed for the bark bed, three feet deep, part sunk, the greater part raised, continued the whole length and width, except about a foot and half alley to pass in to perform the necessary culture, as well as view and gather the procace of the different plants.

The pit within is to be filled with new tan, in order to afford a proper heat for the growth and support of the plants that are to be cultirated. See HOT-BED.

Where fire heat is to be employed, the frame must be formed of brick work, at least the back or main wall, for the convenience of having fre Blues, and the whole front, &c. be glass like the other sorts; the length may be from twenty to forty or fifty feet, or more, though one fire will not warm more than that length; the width from five or six to tclve or fifteen feet, an eight or ten high. In this case the fre is burned in a furnace behind, one end micole, thence communicating e het by internal flues or funnels ronning the whole length of the back wall, in rury, jour returns one above another, and condoued in one or two flues in the fut Aud frames thus constructed may be couped ither of moderate width, for one row of trees only, to range against the back wall, or may be capacious enough to have a range of trained wall trees bebird, and some small half or full standards, targing also from the back to the front, or endrely for standards, especially those of cher

ries.

Where it is intended to have a narrow frame for only a row of trained trees behind, the width of from four to five or six feet is sufcient, having the back or main wall formed of brick or stone, as just observed, eight or ten feet high, with several flues withinside, returned over each other, running the whole length of the wall; in the front must be a low wall a foot high, on which to lay a plate of timber, and from which are ranged glass frames or lights in one continued slope to the top of the back wall, there received into proper frame work; but, for the greater convenience, the lights may be in two tiers or ranges, an under and upper tier, the upper range made to slide up and down over the others, but so that all the glass work can be moved away occasionally, to admit the full air to the trees after the work of forcing is over: the whole bottom space within the frame should be of good loamy earth, or any good garden mould, two spades deep, which should be dug or trenched in the commop way; then a range of trees planted behind, towards the wall, two or three yards asunder, erecting a trellis behind them, upon which to train the branches, as against a wall respalier. Other inferior plants may likewise be set in the border, or in pots, in front of the

trees.

la forcing frames of this construction, from Eny or fifty feet long may be sufficient; but if longer, two furnaces for fires are necessary. SHOT-HOUSE.

Diderent sorts of frames of this naturę may

be seen in the plates on forcing frames, hot. houses, &c.

In the first deseription of forcing frame, various kinds of fruits may be produced both of the dwarf fruit tree, and other sorts, as well as different sorts of vegetables and plants of the flowery and other kinds.

Fraines of this sort may have such dimensions as to have substantial hot-beds prepared within them, for the purpose of receiving many different sorts of potted plants.

And in the second sort of frame, from the heat being more regular and lasting, a still greater variety of the finer sorts of fruits, and the more tender flowers and other vegetable productions, may be produced, not only long before they could be raised in any other way, but with much greater ease and convenience, as well as with greater certainty.

The last kind of forcing frame is employed in furnishing many of the finer sorts of fruits, that require high degrees of heat to produce them in the utmost perfection, such as pineapples, grapes, apricots, peaches, nectarines, and various others, as well as many tender sorts of vegetables, and numerous plants of the curious flower and other kinds.

FORCING GROUND, the portion of ground in a garden that is destined to the purpose of forcing or raising vegetable productions by means of artificial heat. Grounds of this sort should always be detached from the garden, and situated as near to the stable as the nature of the land will admit, in order that dung may be conveyed to them with as much ease and convenience as possible, litter prevented, and the disagreeable appearance of the beds concealed.

It is necessary in most situations, and particularly in such as are exposed, to have them inclosed with a fence, either of brick work or paling, six or eight feet in height. They should have sufficient space for containing a suitable number of frames and pits, and such linings as may be necessary in the working of them. And it is of great advantage in raising many sorts of tender crops, both of the vegeta ble and fruit kind, to have four or six feet borders made round them in a raised manner. Where melons are raised; it is usual to have brick pits coped with stone or wood. Those which are most convenient, according to Mr. Forsyth, are such as are about twelve feet in width, and two and a half in depth; the length in proportion to the number of frames employed. They are, however, often made of much smaller dimensions, especially where the extent of forcing ground is but small.

In regard to the size of the lights for early melons, the above author advises, that they should be five feet in length, and three in breadth; and for others six feet in length, and four in breadth, the fornier being four, and the latter three light boxes. See FRAME.

In constructing the pits, nine inch walls will be sufficient, square spaces of wood being

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