have eight; flies, grass-hoppers, and butterflies have six feet; animals destined to swim, and water-fowl, have their toes webbed together, as the phoce, goose, duck, &c.; the fore-feet of the mole, rabbit, &c. are wonderfully formed for digging and scratching up the earth, in order to make way for their head. FOOT. See ANATOMY. FOOT, in the Latin and Greek poetry, a metre or measure, composed of a certain number of long and short syllables. These feet are commonly reckoned twenty-eight, of which some are simple, as consisting of two or three syllables, and therefore called disyllabic or trisyllabic feet; others are compound, consisting of four syllables, and are therefore called tetrasyllabic feet. Foor is also a long measure, consisting of twelve inches. Geometricians divide the foot into ten digits, and the digit into ten lines. See DIGIT and LINE. FOOT square, is the same measure both in breadth and length, containing 144 square or superficial inches. FOOT cubic, or solid, is the same measure in all the three dimensions, length, breadth, and depth or thickness, containing 1728 cubic inches. The foot is of different lengths in different countries. The Paris royal foot exceeds the English by nine lines; the ancient Roman foot of the Capitol consisted of four palms, equal to 11 inches English; Rhineland or Leyden foot, by which the northern nations go, is to the Roman foot, as 950 to 1000. See MEAsure. Foor gell, or Faut-geld, in our old eustoms, an amercement laid upon those who live within the bounds of a forest, for not lawing or cutting out the ball of their dog's feet. To be free of a foot-geld, was a privilege to keep dogs unlawed, within the bounds of a forest. Foor level, among artificers, an instrument that serves as a foot-ruie, a square, and a level. See LEVEL. FORAGE, in military affairs, implies hay, straw, and oats, for the subsistence of the army horses. It is divided into rations, of which one is a day's allowance for a horse, and contains 20lb. of hay, 10lb. of oats, and 5lb. of straw. When cavalry is stationed in barracks in Great Britain, the number of rations of forage is, to field-officers four, supposing them to have four effective horses; to captains three; to staff officers two; to quarter-masters, non-commissioned officers, and privates, each one. On foreign service, this article is governed by circumstances. FORAMEN, in anatomy, a name given to several apertures, or perforations in di'vers parts of the body; as, the foramen lachrymale, &c. See ANATOMY. FORCE, in mechanics, denotes the cause of the change in the state of a body when being at rest it begins to move, or has a motion which is either not uniform, or not direct. Mechanical forces may be reduced to two sorts, one of a body at rest, the other of a body in motion. See MECHANICS. The force of a body at rest is that which we conceive to be in a body lying still on a table, or hanging by a rope, or supported by a spring, and is called by the names of pressure, vis mortua, &c. The which the table is pressed, or the spring measure of this force being the weight with bent. The force of a body in motion, called moving force, vis motrix, and vis vica, to distinguish it from the vis mortuu, is allowed to be a power residing in that body so long as it continues its motion, by means of which it is able to remove obstacles lying in its way, to surmount any resistance, as tension, gravity, friction, &c. and which, in whole or in part, continues to accompany it so long as the body moves. We have several curious, as well as useful observations, in Desagulier'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. eight hours a-day, walking about two miles and a half an hour. And if the same horse is made to draw 240lb. he can work but 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 a horse's force, is by making him draw up out of a well, over a single pulley or roller; and, in such a case, one horse with another will draw 200lb., as already observed. Five men are found to be equal in strength to one horse, and can, with as much ease, push round the horizontal beam of a mill, in a walk forty feet wide; whereas three men will do it in a walk only nineteen 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, each 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 in a horizontal direction, wherein a man can exert least force; thus a man weighing 140lb., and drawing a boat along by means of a rope coming over his shoulders, cannot draw above 27 lb., or exert above one-seventh part of the force of a horse employed to the same purpose. The very best and most effectual posture in a man, is that of rowing, in which he not only acts with more muscles at once, for overcoming the resistance, than in any other position; but, as he pulls backward, the weight of his body assists by way of lever. m of the distance increases. In variable feet; then is s= = 2 g fi; i = ;; ข v v 2gs 2gt. In these four theorems, the force f, 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 expres FORCE accelerative, 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, if m denote the motive force, and b the body, or its weight, and ƒ the accelerating or retarding force, then is fassion for the value of the force ƒ, at any inAgain, 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. In the case of a constant force F, acting upon a body h, for any time t, we have these following theorems; puttingf= the constant accelerating force = F÷b; the velocity at the end of the time t; 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 1 second, and calling the accelerating force of gravity 1; then is s = to=gft2 = ;; v = 2 gft = 8 definite time t; 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. FORCEPS, a pair of nippers, or pinchers, for laying hold of and pulling out any thing forced into another body. FORCEPS, in surgery, &c. a pair of scissars for cutting off, or dividing, the fleshy or membraneous parts of the body, as occasion requires. Forceps are commonly made of steel, but those of silver are much neater. 4gJ FORCER, or forcing pump, in mechanics, = == is a kind of pump in which there is a forcer or piston without a valve. See PUMP. 2gJ 4g s 2$ FORCES variable, are such as are continnally changing in their effect and intensity; such as the force of gravity at different distances from the centre of the earth, which decreases in proportion as the square FORCIBLE entry and detainer. Forcible 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, al though 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 forcibly 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 away from 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 discretion 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 twentyone, by licence, without such consent, is void. FORECASTLE, in naval affairs, a short deck placed in the fore-part of the ship above the upper deck, it is usually terminated both before and behind in vessels of war by a breast work, the foremost part forming the top of the beak-head, and the hind part reaching to the after part of the fore chains. Forecastle men, are sailors stationed there, and are of the best kind as to experience and discipline. FORE foot, in ship-building, a piece of timber which terminates the keel at the fore-end; it is connected by a scarf to the extremity of the keel, and the other end of it which is incurvated upwards into a sort of knee, is attached to the lower end of the stem; it is also called a gripe. FORE foot, in the sea-language, signifies one ship's lying, or sailing, across another's way: as if two ship's being under sail, and in ken one of another, one of them lying in her course with her stem so much a weather the other, that holding on their several ways, neither of them altering their courses, the windward ship will run a head of the other: then it is said, such a ship lies with other's fore foot. FOREIGN seamen serving two years on board British ships, whether of war, trade, or privateers, during the time of war, shall be deemed natural born subjects. FORELORN hope, in the military art, signifies men detached from several regiments, or otherwise appointed, to make the first attack in day of battle, or, at a siege, to storm the counterscarp, mount the breach, or the like. They are so called from the great danger they are unavoidably exposed to; but the word is old, and begins to be obsolete. FOREMAST of a ship, a large, round piece of timber, placed in her fore-part, or forecastle, and carrying the fore-sail and fore-top-sail yards. Its length is usually of the main-mast. And the foretop-gallant-mast is the length of the foretop-mast. See MAST. FOREMAST men are those on board a ship that take in the top sails, fling the yards, furl the sails, bowse, trice, and take their turn at the helm, &c. FORE reach, in the sea language, a ship is said to fore reach upon another, when both sailing together, one sails better, or outgoeth the other. FORESCHOKE, in our old authors, signifies the same with forsaken, and is particularly used in one of our statutes for lands or tenements seised by the lord for want of services performed by his tenant, and quietly held by such lord above a year and a day, without any due course of law taken by the tenant for recovery thereof; here he does in presumption of law disavow or forsake all the rights he has thereto, for which reason those lands shall be called foreschoke. FORESKIN, in anatomy, the same with prepuce. See PREPUCE. FORE staff, or cross-staff, an instrument used at sea for taking the altitude of the sun, moon, or stars, It is called fore-staff, because the observer, in using it, turns his face towards the object; whereas in using 2 thod, belong to such and such kinds of flowing quantities: thus, for example, the fluent of 2 x x is known to be x2; because, by the direct method, the fluxion of x is found to be 2x: but the fluent of yx is unknown, since no expression has been discovered that produces y x for its fluxion. Be this as it will, the following rules are those used by the best mathematicians, for finding the fluents of given fluxions. 1. To find the fluent of any simple fluxion, you need only write the letters without the dots over them: thus, the fluent of x is x, and that of ax+b ỷ, is ax + by. 2. To assign the fluent of any power of a variable quantity, multiplied by the fluxion of the root; first divide by the fluxion of the root, add unity to the exponent of the power, and divide by the exponent so increased: for dividing the fluxion n x-1 by x, it becomes nx-1; and adding 1 to the exponent (n-1) we have nx"; which, divided by n, gives x", the true fluent of nx-x. Hence, by the same rule, the fluent of 3x2x will be=x3; 1 that of 2 xx= ; and that of y y = . ; that of mxn+1 -; whence the equation or flu ent, properly corrected, is y = am+xn+1. amn+m - mxn+1 Hitherto x and y are both supposed equal to nothing, at the same time; which will not always be the case: thus, for instance, or a xx-"- though the sine and tangent of an arch are both equal to nothing, when the arch itself is so; yet the secant is then equal to the radius. It will therefore be proper to add some examples, wherein the value of y is equal to nothing, when that of x is equal to any given quantity a. Thus, let the equa tion = x2, be proposed; whereof the fluent first found is y = but when y = 3 that of a+3×2 = that of a 2" x 2"-12= am 4 ; and + mxn+1 In assigning the fluents of given fluxions, it ought to be considered, whether the flowing quantity, found as above, requires the addition or subtraction of some constant quantity, to render it complete : thus, for instance, the fluent of nx-x may be either represented by a" or by x a; for a being a constant quantity, the fluxion of xa, as well as of xa, is n x”—1x. Hence it appears, that the variable part of a fluent only can be assigned by the common method, the constant part being only assignable from the particular nature of the problem. Now to do this, the best way is to consider how much the variable part of the fluent, first found, differs from the truth, when the quantity which the whole rected is y = fluent ought to express, is equal to nothing; then that difference, added to, or subtracted y= ་ But it seldom happens that these kinds of fluxions, which involve two variable quantities in one term, and yet admit of known and perfect fluents, are to be met with in practice. Having thus shewn the manner of finding such fluents as can be truly exhibited in algebraic terms, it remains now to say something with regard to those other forms of expressions involving one variable quantity only; which yet are so affected by compound divisors and radical quantities, that their fluents cannot be accurately determined by any method whatsoever. The only method with regard to these, of which there are innumerable kinds, is to find their fluents by approximation, which, by the method of infinite series, may be done to any degree of exactness. See SERIES. Thus, if it were proposed to find the fluent ax of it becomes necessary to throw the fluxion into an infinite series, by dividing a x by a-x: thus, a x÷a -x ++++ +, &c. α xx a a Now the fluent of each term of this series, may be found by the foregoing rules to be x+ + + 2 a 3a2 5 a* +,&c. In order to shew the usefulness of fluxions, we shall give an example or two. 1. Suppose it were required to divide any given right line AB into two such parts, A C, C B, that their products are rectangles, may be the greatest possible. Let A B = a, and let the part A C, considered as variable (by the motion of C towards B) be denoted by r. Then B C being a-x, we have ACX BC=ax-xx, whose fluxion a r -2xx being put = 0, we get ax=2xx; and, consequently, xa. Hence it appears that A C (or x) must be exactly one half of A B. Ex. 2. To divide a given number a into two parts, x, y, so that x y may be a maximum. Cor. Hence, to divide a quantity a into three parts, x, y, z, so that x y z may be a max. the parts must be equal. For sup pose x to remain constant, and y, z, to vary; the product yz, and consequently xyz, will be greatest when y=z. Or if y remain constant, the product xz, and conse. quently y x z, will be greatest when x=z. Thus it appears that the parts must be equal. And in like manner it may be shewn, that whatever be the number of parts, they will be equal. Ex. 3. Given x+y+za, and x y2 z3 a maximum, to find x, y, z. As x, y, z, must have some certain determinate values to answer these conditions, let us suppose such a value of y to remain constant, whilst x and z vary till they answer the conditions, and then x+2=0 and z3x+3x z2 = 0; hence, x=3 x ż 3 x z ż 23 -, ..z = 3 x. Now let us suppose the value of 2 to remain constaut, and x and y to vary, so as to satisfy the conditions; then += 0, y2 x+ 2xy=0; hence, x=-&=· 2 x y ÿ y' == 2 x y ..y=2x; substitute in the given equation, these values of y and z in terms of x, and x+2x+3x=a,or 6x=a 1 hence, x= = 1; a; . . y = {};a; z = a. In વ; 2 |