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np fester with a burden of lOOJi. weight, than a horse that is loaded with 300/6.; 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 140/6., and drawing a boat along by means of a rope coming over his shoulders, cannot draw above "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.
Force occeleratire, or Retardice 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/the accelerating or retarding force, then is/as -r.
Agaiu, forces are either constant or variable. Constant forces are such as remain and act continually the same for some dc♦ei initiate 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; putting/ = the constant accelerating force = F-^-4; 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 = lfrj'j feet, the space generated by gravity in 1 second, and calling the accelerating force of gravity 1 j then is
v .« v*
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
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 fluxional 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. /, the accelerating force at any instant; t, the time a body has been in motion by the action of the variable force; r, the velocity generated in that time; », the space run over in that time; and g = lti.L
feet; then is » = ——. = 11 ; v = ■ *•*
In the«e four theorems, the force/, 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; ri:. from the circumstances of the problem under consideration, deduce a general expression for the value of the force /, at any indefinite time t; then substitute it in one of these theorems, which shall be proper to the case in hand; and the equation thence resulting wilt 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, Sec. a pair of scissors 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.
FORCER, or forcing pump, in mechanics, is a kind of pump in which there is a forcer or piston without a valve. See Pump.
Forcible entry and detainer. Forcible entry, is a violent actual entry into a house or land, Stc, 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 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.
FORCING, among gardeners, signifies the making trees produce ripe fruit before their usual time. This is done by planting them in a hot-bed against a southwall, and likewise defending them from the injuries of the weather by a glass frame. They should always be grown trees, as young ones are apt to be destroyed by this management. The glasses must be taken off at proper seasons, to admit the benefit of fresh air, and especially of gentle showers.
FORECASTLE, in naval affairs, a short deck placed in the fore-part of the 'hip 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/oot, in ship-building, a piece of timber which terminates the keel at the tore-end ; it is connected by a scarf to the extremity of the keel, and the other end of it which is incurvatcd 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 ll 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 seized 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 tliod, belong to such and such kind, of flowing quantities: thus, for example, the fluent of 2 x x is known to be x1; because, by the direct method, the fluxion of x' is found to be 2 x x: but the fluent of y x 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. expressions as involve two or more variable quantities, substitute, instead of such fluxion, its respective flowing quantity; and, adding all the terms together, divide the sum by the number of terms, and the quotient will be the fluent. Thus
1. To find the fluent of any simple fluxion, you need only write the letters without the dots over them: thus, the threat of x is x, and that of a x + by, is nx-\-by.
j. 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 ax"-' x by x, it becomes 'tar-'; and adding 1 to the exponent (n—l)we have n x"; which, divided by n, gives x", the true fluent of xxx. Hence, by the same rule, the fluent of 3x" x will be=x';
that of 3x- x=~; that of y \y = » yi; that
that of a" +z"!"X s"
mx» + l
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 xx x may be either represented by x" or by r ± a ; for a being a Constant quantity, the fluxion of x'± a, as well as of P, is a **-'*•.
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 ot 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 truthjWhen the quantity which the whole fluent ought to express, is equal to nothing , then that difference, added to, or subtracted
m X » +1
ter part of the equation becomes
— _-___^; whence the equation or flii
«Xn+l ent, properly corrected, is y =
a«i_|_ I""!'"!-1 0<nt! + m
m x n+T Hitherto x and y are both supposed equal to nothing, at the same time; which will not always be the case: thus, for instance, 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 equation _y = x1 x, be proposed; whereof the
fluent first found is y = 5 ; but when y =
0, then - = «, by the hypothesis;
therefore the fluent, corrected, is y =9
—- . Again, suppose y = x" x;
x"+' then will y — —Ft! which, corrected,
becomes y = r-r-: . And lastly,
the fluent of xy +y x = ?* + *?>=-%*
= Ij; and the fluent ofxyz -\-y x z -f- z y x
_-ry: +rV z-\-ry z _3xyz _
— ii ~ 3 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
of , it becomes necessary to throw
the fluxion into an infinite series, by dividing a x by a — x: thus, Dario — x xx , xx
Now the fluent of each term of this series, may be found by the foregoing rules
10 ***+?«+ T*+77>+£?+>*<■
In order to shew the usefulness of fluxions, we shall give an example or two. l. Suppose it were required to divide any given nsrlit line A B into two such parts, A C, C, B, that their products are rectangles, may be the greatest possible. Let AB = o, and let the part A C, considered as variable (by the motion of C towards B) be denoted by x. Then B C being = a — x, we have ACx BC = n—xx, whose fluxion n — 2 xx being put = 0,wegct ax = 2xx; and, consequently, x = $ a. Hence it appears that the C (or x) must be exactly one half of A B.
Ex. 9. To divide a given number a into two parts, x, >;, so that x" y"1 may be a maximum.
given equation, these values of y and z in terms of x, and x -\- 2 x -f- 3 x = a, or 6 x = a
hence, x = - a; .". y = - a ; z z= - a. In
like manner, whatever be the number of unknown quantities, make any one of them variable with each of the rest, aud the values of each in terms of that one quantity will be obtained; and by substituting the values of each in terms of that one, in the given equation, you will get the value of