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preservation of: he cannot for his life do it FORBIDDER. s. (from forbid.) One that (Addison). 39. For all. Notwithstanding prohibits (Brown). (South).
FORBIDDING. particip.a.(from forlid.) For. conj. 1. The word by which the rea- Raising abhorrence (Aaron Hill). son is given of something advanced before FORCE. s. (force, French.) 1. Strength; (Cowley). 2. Because; on this account that vigour; might (Donne). 2. Violence (Dry(Spenser). 3. For as much. In regard to den). 3. Virtue ; efficacy (Locke). 4. Vas that; in consideration of (Hooker). 4. For Jidvess; power of law (Denham). 5. Armasky. Because ; for this reason that (Knoll.). ment; warlike preparation (Waller). 6. Des
TO FOʻRAGE. v. a. (from foris, abroad, tiny; necessity; fatal compulsion, Lat.) 1. To wander far; to rove at a distance: Tó Force. v. a. (from the noun.) 1. To not in use (Shakspeare). 2. To wander in compel; to constrain (Swifi). 2. To oversearch of provisions (Denham). 3. To ra- power by strength (Milton). 3. To impel; rage; to feed on spoil (Shakspeare).
to press; to draw or push by main strength To FO'R AGE. v. a. To plunder ; to strip; (Dryden). 4. To enforce; to urge (Milton). to spoil (South).
5. To drive by violence or power (Decay of FO'RAGE. 5. (fourage, Germ. and French, Piety). 6. To gain by violence or power from foris, Latin.) 1. Search of provisions; (Dryden). 7. To storm ; to enter by violence the act of feeding abroad (Millon). 2. Provi- (Waller). 8. To ravish; to violate by force sions sought abroad (Dryden). 3. Provisions (Dryden). 9. To constrain; to distort (Ad. in general (Dryden).
dison). 10. To man; to strengthen by sol. FORAMEN. (foramen, from foro, to diers' (Raleigh). 11. To Force out. To pierce.) A little opening.
extort (Atterbury). FOR AMEN Cæcum. A single opening in To Force. vin, To lay stress upon (Camthe basis of the cranium between the ethnioid den). and the frontal bone, that gives exit to a small
Force, or Power, in physics, is that vein. FORAMEN OVALE. The opening between whether that state be rest or motion.
which causes a change in the state of a body, the two auricles of the heart of the fætus. See
We speak here of proximate causes, for it is not also INNOMINATUM OS.
the business of mechanics to search into the cssenFORAMINA LACERA IN BASI CRANIT, tial and hidden causes of motion. The enquiry A pair of foramina in the basis of the cranium, whether they are material or spiritual may exerthrough which the internal jugular veins and cise the talents of ingenious speculatists, and may, the eighth pair of accessory nerves pass.
perhaps, be of some importance in a moral point FORAMINOUS. a. (from foramen, Lat.) of view; but certainly forms no part of the prinFull of holes ; porous (Bacon).
ciples of mechanical science. The muscular power T. FORBE'AR. v. no pret. I forbore, an
of animals, as likewise pressure, impact, gravity,
electricity, &c. are by us looked upon as forces, ciently forbare; part. forborn. (Forbæran,
or sources of motion; for it is an incontrovertible Saxon.) 1. To cease from any thing; to in- fact that bodies exposed to the free action of either termit. 2. To panse; to delay (Shakspeare). of these are put into motion, or have the state of 3. To omit voluntarily; to abstain (Denham). their motion changed. All forces, however vari4. To restrain any violence of temper; to be ous, are measured by the effects they produce in patient (Proverls).
like circumstances; whether the effects be creat. T. FORBE'AR. 1. a. 1. To decline; to avoid ing, accelerating, retarding, or deflecting motions: voluntarily (Waller). 2. To abstain from; to the effect of some general and commonly observed omit (Clarendon). 3. To spare; to treat with force is taken for unity; and with this any others clemency (Ephesians). 4. To withhold (Chro. may be compared, and their proportions reprenicles).
sented by numbers or by lines: in this point of FORBE'ARANCE. s. (from forlear.) 1.
view they are considered by the mathematician;
all else falls within the province of the universal The care of avoiding or shuoning any thing; philosopher or the inetaphysician. When we say negation of practice (South). 2. Intermission that a force is represented by a right line AB it is of something. 3. Command of temper (Shake to be understood that it would cause a material speare). 4. Lenity; delay of punishment; point situated' at rest in A, to run over the line AB mildness (Rogers).
(which we name the direction of the power) so as FORBE'ARER. s. (from forbear.) An in- to arrive at B, at the end of a given time, while termitter; interceptor of any thing (Tusser). another power should cause the same point to
T. FORBID. v. a. pret. I forbade; part. have moved a greater or less distance from A in forbidden or forbid (forbeodan, Sax.) 1. To the same time. prohibit; to interdict any thing (Shaksp.). 2.
Mechanical forces may be reduced to two sorts; To command to forbear any thing (Sidney). 3.
one of a body at rest, the other of a body in
motion. To oppose; to hinder (Dryden). 4. To ac
The force of a body at rest, is that which we curse; to blast: obsolete (Shakspeare).
conceive to be in a body lying li on a table, or To For Bl'd. v. n. To utter a prohibition hanging by a rope, or supported by a spring, &c.; (Shakspeare).
and this is called by the vames of pressure, tenFORBIDDANCE. s. (from forbid.) Pro- sion, force, or vis mortua, solicilatio, cunalus movendi, hibition ; edict against any thing (Milton). conamen, &c.; which kind of force may be always,
FORBI'DDENLY. ad. (from forbid.) In measured by a weight, viz.the weight that sustaing an unlawful manner (Shakspeare).
it. To this class of forces may also be referred VOL. V.
dentripetal and centrifugal forces, though they re- double velocity in the body on rhich it acts. The Leibs side in a body in motion; because these forces are nitrian calls that a quadruple force which makes a homogeneous to weights, pressures, or tensions of quadruple penetration. The reasonings of both in the any kind. The pressure, or force of gravity in any demonstration of a proposition in dynamics may body, is proportional to the quantity of matter be the same, as also the result, though expressed in it.
in different numbers, The force of a body in motion, is a power re- But the two measures are far from being equally siding in that body, so long as it continues its mo- proper; for the Leibnitzian measure obliges us to tion, by means of which, it is able to remove ob- do continual violence to the common use of words. stacies lying in its way; to lessen, destroy, or When two bodies moving in opposite directions overcome the force of any other moving body, meet, strike each other, and stop, all men will say tvhich meets it in an opposite direction; or to sur- that their forces are equal, because they have the mount any the largest dead pressure or resistance, best test of equality which we can devise. Or as tension, gravity, friction, &c. for some time; when two boilies in motion strike the parts of a but which will be lessened or destroyed by such machine, such as the opposite arms of a lever, and resistance as lessens or destroys the motion of the are thus brought completely to rest, we and all body. This is called vis motrir, moving force, or men will pronounce their mutual energies by the motive force, and by some late writers vis vioa, to intervention of the machine to be equal. Now, distinguish it from the vis mortua, spoken of be- in all these cases, it is well known that a perfect fore.
equality is found in the products of the quantities Concerning the measure of moving force mathe. of matter and velocity. Thus a ball of two pounds, maticians have been divided into two parties. It is moving with the velocity of four feet in a second, allowed on both hands, that the measure of this force will stop a ball of eight pounds moving with the depends partly upon the mass of matter in the body, velocity of one foot per second. But the followers and partly upon the velocity with which it moves: of Leibnitz say, that the force of the first ball is the point in dispute is, whether the force varies as four times that of the second. the velocity, or as the square of the velocity, All parties are agreed in calling gravity an unio
Descartes, and all the writers of his time, as- form or invariable accelerating force; and the desumed the velocity produced in a body as the mea- finition which they give of such a force is, that it sure of the force which produces it; and observing always produces the same acceleration, that is, that a body, in consequence of its being in motion, equal accelerations in equal times, and therefore produces changes in the state or motion of other produces augmentations of velocity proportionable bodies, and that these changes are in the propor- to the times in which they are produced. The tion of the velocity of the changing body, they as. only effect ascribed to this force, apil consequently serted that there is in a moving body a vis insita, the only thing which indicates, characterises, and an inherent force, and that this is proportional to measures it, is the augmentation of velocity. its velocity; saying that its force is twice or thrice What is this velocity, considered not merely as a as great, when it moves twice or thrice as fast at mathematical term, but as a phenomenon, as an one time as at another. But Leibnitz observed, event, a production by the operation of a natural that a body which moves twice as fast, rises four cause? It cannot be conceived any other way times as high, against the uniform action of gra- than as a determination to move on for ever at a vity; that it penetrates four times as deep into a certain rate, if nothing shall change it. We can. piece of uniform clay; that it bends four times not conceive this very clearly. We feel ourselves as many springs, or a spring four times as strong forced to animate, as it were, the body, and give to the same degree; and produces a great many it not only a will and intention to move in this effects which are four times greater than those pro- manner, but a real exertion of some faculty in duced by a body which has half the the initial ve- consequence of this determination of mind. We locity. If the velocity be triple, quadruple, &c. are conscious of such a train of operations in ourthe effects are nine times, 16 times, &c. greater; selves; and the last step of this train is the exerand, in short, are proportional, not to the velocity, tion or energy of some natural faculty, which we, but to its square. This observation had been made in the utmost propriety of language, call force. before by Dr. Hooke, who has enumerated a pro- By such analogical conception we suppose a soniedigious variety of important cases in which this thing, an energy inherent in the moving body; proportion of effect is observed. Leibnitz, there- and its only office is the production and continua. fore, affirmed that the force inherent in a moving tion of this motion, as in our own case. Scientific body is proportional to the square of the velocity. curiosity was among our latest wants,' and lan
It is evident that a body, moving with the same guage was formed long before its appearance: as velocity, has the same inherent force, whether this we formed analogical conceptions, we contented be employed to move another body, to bend springs, ourselves with the words already familiar to us, to rise in opposition to gravity, or to penetrate a and to this something we gave the name FORCE, mass of soft matter. Therefore these measures, which expressed that energy in ourselves which which are so widely different, while each is agree- bears some resemblance (in office at least) to the able to a numerous class of facts, are not measures determination of a body to move on at a certain of this something inherent in the moving body rate. This sort of allegory pervades the whole of which we call its force, but are the measures of its our conceptions of natural operations, and we can exertions when modified according to the circum. hardly think or speak of any operation without a stances of the case; or, to speak still more cau- language, which supposes the animation of matter. tiously and securely, they are the measures of cer- And, in the present case, there are so many points tain classes of phenomena consequent on the action of resemblance between the effects of our exertions of a moving body. It is in vain, therefore, to at. and the operations of nature, that the language is tempt to support either of them by demonstration, most expressive, and has the strongest appearance The measure itself is nothing but a definition. The of propriety. By exerting our force, we not only Cartesian calls that a double force which produces move and keep in motion, but we more other bodies. Just so a ball not only moves, but puts collision of bodies, perfectly hard, there was 116 other bodies in motion, or penetrates them, &c.- such conservatio virium vitarum; and that, in this This is the origin of that conception which so for- case, the forces must be acknowledged to be procibly obtrudes itself into our thoughts, that there portional to the velocities. The objections were is inherent in a moving body a force by which it unanswerable. But John Bernoului evaded their produces changes in other bodies. No such thing force, by affirming, that there were and could be appears in the same body if it be not in motion. no budies perfectly hard. This was the origin of We therefore conclude, that it is the production of another celebrated doctrine, on which Leibnitz the moving force, whatever that has been. If so, greatly plumed himself, the Law of Continuity, it must be conceived as proportional to its pro- viz. that nothing is observed to change abruptly, ducing cause. Now this force, thus produced or or per saltum. But no one will pretend to say that exerted in the moving body, is only another way a perfectly hard body is an inconceivable thing; of conceiving that determination which we call on the contrary, all will allow, that softness and velocity, when it is conceived as a natural event, compressibility are adjunct ideas, and not in the We can form no other notion of it. The vis insita, least necessary to the conception of a particle of the determination to move at a certain rate, and matter; nay, totally incompatible with our notion tbe velocity, are one and the same thing, considered of an ultimate atom. in different relations.
Sir Isaac Newton never could be provoked to Therefore the ois insita corpori moventi, the deter- engage in this dispute. He always considered it mination to move at a certain rate, and the velo. as a wilful abuse of words, and unworthy of his atcity, should have one and the same measure, or tention. He guarded against all possibility of any one of them may be taken for the measure of cavil, by giving the most precise and perspicuous the other. The velocity being an object of per- definitions of those measures of forces, and all other ception, is therefore a proper measure of the inhe- quantities wbich he had occasion to consider, and rent force; and the propriety is more evident by by carefully adhering to them. And in one prothe perfect agreement of this use of the words with position of about 20 lines, viz. the 39th of the 1st common language. For we conceive and express book of the Principia, he explained every phenothe action of gravity as uniform, when we think and menon adduced in support of the Leibnitzian docsay that its effects are proportional to the times of trine, shewing them to be immediate consequences its action. Now all agree, that the velocity pro- of the action of a force measured by the velocity duced by gravity is proportional to the time of its which it produces or extinguishes. There it apaction. And thus the measure of force, in refer- pears that the heights to which bodies will rise in ence to its producing cause, perfectly agrees with opposition to the uniform action of gravity are as its measure, independent of this consideration. the squares of the initial velocities : so are the
But this agreement totally lost in the Leib- depths to which they will penetrate uniforınly renitzian doctrine; for the body which has fallen sisting matter: so is the number of equal springs four times as far, and has sustained the action of which they will bend to the same degree, &c. We gravity twice as long, is said to have four times have had occasion to mention this proposition as ibe force.
the most extensively useful of all Newton's discoThe quaintness and continual paradox of ex- veries. It is this which gives the immediate appression which this measure of inberent force leadsplication of mechanical principles to the explanaus into, would have quickly exploded it, had it not tion of natural phenomena. It is incessantly embeen that its chief abettors were leagued in a keen ployed in every problem by the very persons who and acrimonious warfare with the British mathe- hold by the other measures of forces, although such maticians who supported the claim of Sir Isaac conduct is virtually giving up that measure. They Newton to the invention of Auxions. They re- all adopt, in every investigation, the two theorems joiced to find in the elegant writings of Huyghens ri=v, and fi=v; both of which suppose an acce. a physical principle of great extent, sucb as this lerating force s proportional to the velocity o which is, which could be set in comparison with some of it produces by its uniform action during the the wonderful discoveries in Newton's Principia. The fact, that in the mutual actions of bodies on time t, and the theorem f js=o is the 39th 1. each other, the products of the masses and the Princip. and is the conservatio virium vivarum. squares of the velocities remain always the same Let a certain force Q, such, for instance, as (which they call the conservatio virium vivarum), is would propel a body B with a velocity U, be caof almost universal extent; and the knowledge of pable, by its instantaneous action, of raising a it enabled them to give ready and elegant solutions, mass M, whose weight is W to a certain height of the most abstruse and intricate problems, by H; and let g denote the force of gravity, while which they acquired a great and deserved cele- iis an evanescent element of time. Then, that brity. Dr. Robert Hooke, whose observation which has been employed to raise W, to the height hardly any thing escaped, was the first (long be. will be equivalent to WH, this being the effect fore Huyghens) who remarked that in all the cases produced. But H, being a space run over
, may be of the gradual production and extinction of motion, expressed by the product of a velocity V and a the sensible phenomenon is proportional to the time T; and, on the other hand, we have W=gM square of the produced or extinguished velocity. John Bernoulli brought all these facts together,
' is manifestly the velocity V', and systematized them according to the principle advanced by Huyghens in bis treatise on the centre which would be generated by gravity in the eleof oscillation. He, and Daniel Bernoulli, gave most beautiful specimens of the prodigious use of this ment of time i. Consequently WH=>
XVT principle, for the solution of difficult physical pro
t blems, in their dissertations on the motion and
т impulse of faids, and on the communication of
** M u being the mean propose motion. It was, however, very early objected to them (we think by Marquis Poleni), that in the
tional between the velocities V and V': and since and mortua, or living and dead force, will tanishi
by their shock, does not happen in an instant, ap-
dency by this instance: suppose that the hardness, A second observation which has been made by of the two bodies, A and B, is equal; and sucha, some eminent writers, is, that the effect of a shock that being pressed together with the force of 100lb. of two or more bodies is not produced in an io- the impression made on each is of the depth of staut, but requires a certain interval of time. If both part of a foot. Suppose also that B is fixed, this bu so, the heterogeneity between the via vive" and that A strikes, it with the velocity of 100 feet
in a second; according to Mr. Euler, the greatest in this case, neither the Leibnitzian nor the Carte. force of compression will be equivalent to 4001b. sian propositions take place. But this force of and this force will produce, in each of these bodies, percussion depends chiefly on the bardness of tie an impression equal to f of a foot ; and the dura- bodies; the greater this is the greater will the force ration of the collision, that is, till the bodies arrive of percussion be. If M=N, this force will be as at their greatest compression, will be about adó of Mcc Aa, that is, in a compound subduplicate a second. Mr. Euler, in his calculations, supposes ratio of tbe vis vita of the striking body, of the the bardness of a body to be proportional to the hardness, and of the plane of contact. But if M, force or pressure requisite to make a given im- the hardness of one of the bodies, be infinite, the pression on it; so that the force by which a given impression is made on a body, is in a compound force of percussion will be as „Ncc * Aa; ratio of the hardness of the body and of the quan- at the same time, if M-N, this force will be as tity of the impression. But he obseryes, that re- „ANcc * Aa. Therefore, all other things being gard must be had to the magnitude of the bodies, equal, the force of percussion, if the striking body as the same impression cannot be made on the be infinitely hard, will be to the force of perleast bodies as on the greatest, from the defect of cussion when both the bodies are equally hard, as space through which their component particles 72 to 1. imust be driven: he considers, therefore, only the Mr. Euler farther deduces from his calculation, least impressions, and supposes the bodies of such that the impression received by the bodies A and anagnitudes, that with respect to them, the im- B will be as follows; viz. as pressions may be looked upon as nothing. What Νx Αα
Μ και Αα be supposes concerning the hardness of bodies,
respecte neither implies elasticity nor the want of it, as
M + N X MCC
M+N Ncc elasticity only produces a restitution of figure and ively. If, therefore, the hardness of A, that is M, impression when the pressing force ceases; but be infinite, it will suffer no impression; whereas, this restitution need not be here considered. It is also supposed, that the bodies which strike each that on B will extend to the depth of
Noc other hare plain and equal bases, by which they touch cach other in the collisiou; so that the inn. But if the hardness of the two bodies be the same, pression hereby inade, diminishes the length of or M=N, they will each receive equal impresrach body. It is farther to be observed, that in
So that the im. Mr. Luler's calculations, bodies are supposed so sions of the depth
2Ncc constituted, that they may not only receive impressions from the forces pressing them, but that pression received by the body B, in this case, will a greater force is requisite to make a greater im. be to the impression it receives in the former, as pression. This excludes all bodies, Anid or solid, i to v2. in which the same force may penetrate farther and
Mr. Euler has likewise considered and computed farther, provided it have time, without ever being the case where the striking body has its anterior in equilibrio with the resistance: thus a body may surface convex, with which it strikes an immovecontinually penetrate farther into soft wax, al- able body, whose surface is plain. He has also though the force impelling it be uot increased: in examined the case, when both bodies are supposed these, and the like cases, nothing is required but immoveable; and from his formulæ he deduces the to surmount the first obstacles; which being once known laws of the collision of elastic and nondone, and the connection of parts broken, the pene. elastic bodies. He has also determined the greate trating body always advances, meeting with the est pressures the bodies receive in these cases; same obstacles as before, and destroying them by and likewise the impressions made on them. In an equal force, But Mr. Euler only considers the particular he shews, that the impressions received first obstacles which exist before any separation of by the body struck, or B, if moveable, is to the parts, and which are doubtless such, that a greater impression received by the same body when imimpression requires a greater force. Indeed, this moveable, as v B to A + B. chietly takes place in elastic bodies; but it seems likewise to obtain in all bodies, when the impresservations in Desaguliers's Experimental Philoso
There are several curious as well as useful ob. sions made on them are small, and the contexture phy, concerning the comparative forces of men of their parts is not altered.
and horses, and the best way of applying them. These things being premised, let the mass or weight of the body A be expressed in general by the line of direction is level with his breast; in
A horse draws with the greatest adıautoge when A, and let its relocity before the shock be that such a situation, he is able to draw 2001b, for eight Which it might acquire by falling from the height hours a day, walking about 24 miles an hour. But A. Farther, let the hardness of A be expressed by M, and that of B by N, and let the area of the if the same borse be made to draw 24016, he can base, on which the impression is made, be ce; then work only six hours a day, and cannot go quite so will the greatest compression be made with the is to be overcome, a middling horse will draw
fast. On a carriage, indeed, where friction alone MNCC
1000lb. But the best way to try the force of a force
* Aa. Therefore if the hardness horse, is to make him draw up out of a well, over M+N
a șingle pulley or roller; and in that case, an of the two bodies, and the plane of their contact ordinary horse will draw about 2001b, as before during the whole time of their collision be the observed.. same, this force will be as Aa, that is, as the It is found, that five men are of eqnal force with square root of the vis pica of the striking body A, 1 horse, and can, with equal ease, push round the And as Va is proportional to the velocity of the horizontal beam of a mill, in a walk, 40 feet wide; body A, the force of percussion will be in a com- whereas, three men will do it in a walk only 19 feet pound ratio of the velocity, and of the subduplia wide. este ratio of the mass of the body striking ; so that The worst way of applying the force of a borse