FOR
FOR
comes to the f?mc thing, when the fucceeding one is in a per pendicular direction to the furface of the water. As to the length of thefe float-boards ■, it may be regulated ac- cording to the breadth of the flream. See Defaguliers, vol. ii p. 425, feq, "
FLOAT-grafs, in botanv. See the article Grass, Append. FLOWER of Brijlol, 'a name ibmetimes ufed for the lychnis of
botanical writers. See the article Lychnis, SuppL Gentle Flower, the Englifh name of agenus of plants called by botanical writers amaranthus. See the article Amaranthus, SuppL Eternal Flower, a name by which fome call the xeranthemum of botanical writers. See the article Xeranthemum, SuppL Everlafling Flower, a term by which fome call the gnaphali urn, or cud-weed, of Linnxus and Tournefort. See the ar tide Gnaphalium, SuppL F Low EK- fc-ncc, a term fometimes ufed for a genus of plants known among authors by the name of poinciana. Sec the ar- ticle Poinciana, SuppL Four o' clod Flower, a name given by fome to jalap. Sec the
article Jalap, SuppL S'ule-faddle Flower, the name ufed by fome for the Sarracena
of botanifts. Seethe article Sarracena, SuppL Sultan-F 'lower, a name (bmetimes ufed for the cyanus, or blue- bottle. See the article Cyanus, SuppL Sun-F lower, the Engliili name of a genus of plants, called by botanical writers helianthus and corona foils. See the article Svx-flozvcr, Sic pi. FXUELLIN, in botany, a name fometimes given to fpeed-well called by authors veronica. See the article Veronica, SuppL FLY (CycL and SuppL)— Humble-bee Fly, the Englifh name of a fpecies of adex. See the articles Humble, SuppL and Culex, Append. FLY-wort, in botany, a name by which fome call the lychnis
of authors. See the article Lychnis, SuppL Fly, in mechanics, a crofs with leaden weights at its ends, or rather a heavy wheel at right angles to the axis of a heavy windlas or roller, by means of which the force of the power is not only preferved, but equally diftributed in all the parts of the revolution.
The fly may be applied to fevcral forts of engines, whe'ther moved by men, horfes, wind, or water; and is of great ufe in thofe parts of an engine, which have a quick circular mo- tion, and where the power or refiftance act unequally in the different parts of a revolution. In this cafe the/^> becomes a moderator, making the motion of revolution almolt every where equal.
The force of a fly, when joined with the fcrew, for damp- ing the image upon coins, maybe calculated thus: fuppofe its two arms to be each 15 inches long, meafuring from the center of the weights to the axis of motion, and the weights to be 501b. each, and the diameter of the axis preffing up- on the dye to be 1 inch ; if every ftroke be made in half a fe- conJ, and the weights defcribe an half circumference, which will in this cafe be of 4 feet, the velocity will at the inftant of the ftroke be at the rate of 8 feet in a fecond, and therefore the momentum 8co ; but the arms of the fly being as leavers, one brachium of which is 15 inches long, whilft the other, viz. the feml-axis, is but of half an inch, we muft increafe this force 30 times, which will give 24000 ; an immenfe force, equal to that of 100 lb. weight falling 1 20 feet, or near 3 feconds in time ; or to that of a body of 7501b. fall- ing i6 T 'i feet, or one fecond in time.
Some of thefe engines for coining crown-pieces have the arms or the flits five times as long, and the weights twice as heavy as thofe here mentioned, fo that the effect is ten times greater. Defaguliers, Exper. Philofoph. p. 245, 339. ICENUM fanStum, jaint Foin, in botany, a name by which the Onobrychis of anatomifts is fometimes called. See the ar- ticles Onobrychis and SAi^i-foin, SuppL FCETUS (CycL) — 7 he qucftion about the circulation of the blood in the fetus feems not yet determined. See A-lem. Acad. Scienc. 1699, 1701, 1703, 1 7 1 7, 1725, and 1739. POLDAGE, among farmers, denotes the liberty of penning
fheep by night. Diet. Ruft. in voc. FOND, the fame with fund. See the article Fund, CycL FOOL's-flones, in botany, an appellation given by fome to a genus of plants called orchis by botanical writers. See the article Orchis, SuppL FOOT-kyK-;, among herbalifts, the fame with the cup of a
flower. See the article Calyx, SuppL FORCE, (CycL) in mechanics. — Whenever a body, which was at reft begins to move, or has a motion which is either not uniform, or not direct, the caufe of this change in the ftate of the body is called force .
While a body remains in the fame ftate, either of reft, or of uniform and rectilinear motion, the caufe of its remaining in fuch a ftate, is in the nature of the body, and it cannot be faid, that any extrinfic force has acted on it: this internal caufe or principle is called inertia b . [a Mr. Euler, in Mem. Acad. Berlin. 1745, p . 21. b Ibid.]
Mechanical forces may be reduced to two forts j one of a body at reft, the other of a body in motion. The force of a body at reft, is that which we conceive to be in a body lying ftill on a table, or hanging by a rope, or
fupportcd by a fpring, &c. And this is called by the name* of preffure, tenflon, foi'ce, or vis mortua, folicitatio, conatus movendi, conamen, &c. To this clafs alfo of forces we muft refer centripetal and centrifugal forces, though they refide in a body in motion ; becaufe thefe forces are homogeneous to weight 1 ;, preffures, or tenfions of any kind. Butof this more particularly farther on.
The meafure of this force is the weight with which the table is prefled, or the rope ftretched, or the fpring is bent. And as to this meafure there is no difpute, notwithftanding the di- verfity of appellations by which it is called. The force of a body in motion is on all hands agreed to be a power refiding in that body, fo long as it continues its mo- tion, by means of which it is able to remove obftacles lying in its way; to leften, deftroy, or overcome the force of any other moving body, which meet it in an oppofite direction ; or to furmount any dead preffure or refiftance, as tenfion, gravity, friction, ike. for fome time ; but which will be lef- fened or deftroyed by fuch refiftance as leffens or deftroys the motion of the body.
This is called moving force, vis matrix, and by fome late 1 writers vis viva, to diftinguifh it from the vis mortua fpoken of before : and by thefe appellations, however different, the fame thing is underftood by ali mathematicians ; namely^ that power of difplacing, of withftanding oppofite moving forces, or of overcoming any dead refiftance, which refides in a moving body, and which, in whole or in part, continues to accompany it, fo long as the body moves. But about the meafure of this fort of force, mathematicians are divided into two parties. Both fides agree that the mea- fure of this force depends partly upon the mafs, or weight, of the body, and partly upon its velocity ; fo that upon any increafe either of weight or velocity, the moving force will be- come greater. It is alfo agreed that the velocity being given, or being the fame in two bodies, their forces will be in pro- portion to their maffes or weights.
But when two bodies are equal, and the velocities with which they move are different, the two parties no longer agree about the meafure of the moving force.
The Newtonians and Cartefians maintain, that the moving force is in proportion to the velocity with which the bodies move. But the Leibnitians aflert, that the moving force is in, proportion to the fquare of the velocity ; fo that if the ve- locity of a moving body be double, triple, quadruple, l$c. of that of another equal body, the force of the former will be fourtimes, nine times, fixteen times as great as that of the latter. Hence the Newtonians pretend that the vis matrix, or mov- ing force of bodies is in the compound ratio of their weights and velocities ; and the Leibnitians maintain it to be in the compound ratio of the weights and the fquares of the velocities. This controvcrfy was firft ftarted by the famous Mr. Leibnitz, and has been carried on by him and his followers near feventy years, during whith time a great number of pieces have been publifhed on both fides of the quefrion, and a great number of experiments have been made, or propofed to be made in order to decide it : but tho' both parties agree in the event of the ex- periments, whether actually made or only propofed, yet as the writers on each fide have found a way of deducing from thofe experiments a conclufion fuitabie to their own opinion, the difagreement ftill continues as wide as ever. Now it muft be owned that thefe oppofite conclufions from the fame experiments are not fo much owing to falfe reafonino- on either fide, as to their difagreement in the principles on which the reafoningis founded. See Dr. Jurln, in Phil. Tranf. N°. 476. Thofe who maintain that the movingy"or« is as the weight into the velocity, lay down for a principle or axiom, that when two bodies meet one another in contrary directions, if their moving forces be equal, neither body will prevail over each other: and if their moving forces be unequal, the ftrono-er will always prevail over the weaker. This is maintained by Mr. Mac Laurin, among others, in his piece which gained the prize in the Royal Academy of Sciences, in 1724, in his Fluxions, and lately in his Account of Sir Ifaac Newton's dis- coveries ; it is alfo agreed to by all the oppofers of the Leib- nitian doctrine, though fome do not formally lay it down as an axiom, but pretend to derive it from the more general principles of preffure and the time it acts.
But the followers of Leibnitz deny the truth of this principle, and lay down others, which, as they pretend, are more clear and fatisfactory, fuch as, that it always requires a determi- nate degree^of/orrf to bend a given fpring to a given degree, whether this be performed in a longer or fhortcr time, or vice verfa ; that a given fpring bent to a given degree, always communicates the fame force to a body, by unbendino- itfelf whether the time it takes to unbend itfeif be longer orfhorter! Mr. 'S Gravefande's words are exprefs : Idem elafleriwn, co- dem modo flexum, dum relaxatur equalem femper vim carport communkat, five lentius five velocius relaxetur. 'S Gravefande^ Phyf. Elem.Math. § 731. edit. 1742. It is true, he does not afTume it as a principle, but derives it from a more general principle, that the force communicated by a preffure is in a compound ratio of the preffure and the fpace through which it paffes. But thefe proportions are alikedeniedbytheNewtonians. Now if it be admitted, that thofe bodies have* equal forces, 7 whi-ih
