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FORCE, in mechanics, denotes that unknown cause which produces a change in the state of a body, as to motion, rest, pressure, &c.; that is, whatever produces According to this definition, the muscular denned: If two or more forces, differ power of animals, as likewise pressure, ently directed, act upon the same body, at impact, gravity, &c, are considered as the same time, as the body in question forces, or sources of motion, it being evi cannot obey them all, it will move in a di dent, from daily experience, that bodies rection somewhere between them. This exposed to the free action of any of these is called the composition and resolution of are either put into motion, or have their forces or of motion, and may be illustrated state of motion changed. All forces, in the following manner: Suppose a body, however various, are meas ired by the A, to be acted upon by a effects which they produce in like circum force in the direction A B, c D stances, whether the effect be creating, while, at the same time, accelerating, retarding or deflecting mo it is impelled by another tions; the result of some general and com force in the direction A C,_______ monly observed force is taken for unity, it will then move in the A B and with this any others may be com direction A D ; and if the ared, and their proportions represented lines A B, A C, be made of lengths proy numbers or lines. Under this point of portionate to the forces, and the lines C D, view they are considered by the mathe D B, be drawn parallel to them, so as to matician ; all else falls within the prov complete the parallelogram ABDC, then ince of the universal philosopher, or the the line which the body A will describe, metaphysician. When we say that a will be the diagonal A D; and the length force is represented by a right line, A B, of this line will represent the force with it is to be understood that it would cause w7hich the body will move. But if the a material point, situated at rest in A, to body be impelled by equal forces, acting run over the line A B, which is called the at right angles to each other, it will move direction of the force, so as to arrive at B in the diagonal of a square. Instances in at the end of a given time, while another nature, of motion produced by several force would cause the same point to have powers acting at the same time, are innumoved a greater or less distance from A merable. A ship impelled by the wind and in the same time. (See the figure below.) tide is one well known ; a paper kite actMechanical forces may be reduced to two ed upon in one direction by the wind, and sorts; one of a body at rest, the other of a in another by the string, is another instance, body in motion. The former is that which Animal Force, as applied to Machinery. we conceive as residing in a body when it All machines are impelled either by the is supported by a plane, suspended by a exertion of animal force or by the applirope, or balanced by the action of a spring, cation of the powers of nature. The lat&c, being denominated pressure, tension, ter comprise the potent elements of water, force, or vis nwrtua, solicitatio, conatus air and fire. The former is more commovendi, and which may always be esti mon, yet so variable as hardly to admit of mated or measured by a weight, viz., the calculation. It depends not only on the weight that sustains it. To this class of vigor of the individual, but on the differ forces may also be referred centripetal and ent strength of the particular muscles em centrifugal forces, though they reside in a ployed. Every animal exertion is attendbody in motion, because these forces are ed by fatigue; it soon relaxes, and would homogeneous to weights, pressures, or speedily produce exhaustion. The most tensions of any kind. The force of a profitable mode of applying the labor of body in motion is a power residing in that animals, is to vary their muscular action, body so long as it continues its motion; and revive its tone by short and frequent by means of which, it is able to remove * intervals of repose. The ordinary method obstacles lying in its way, to lessen, de of computing the effects of human labor stroy, or overcome the force of any other is, from the weight which it is capable of moving body, which meets it in an oppo elevating to a certain height, in a given site direction; or to surmount the larg time, the product of these three numbers est dead pressure or resistance, as ten expressing the absolute quantity of persion, gravity, friction, &c, for some time, formance. This was reckoned by Daniel but which will be lessened or destroyed Bernoulli and Desaguliers at 2,000,000 by such resistance as lessens or destroys lbs. avoirdupois, which a man could raise the motion of the body. This is called one foot in a day. But our civil engineers inn motrix, moving force, or motive force, have gone much farther, and are accusan d, by some late writer?, vis viva, to dis tomed, in their calculations, to assumeIis able to continue such exertion for ten hours each day, thus accumulating the performance of 3,600,000. But this estimate seems to be drawn from the produce of momentary exertions, under the most favorable circumstances; ^ and it therefore greatly exceeds the actual results, as commonly depressed by fatigue, and curtailed by the unavoidable waste of force. Coulomb has furnished the most accurate and varied observations on the measure of human labor. A man will climb a stair, from 70 to 100 feet high, at the rate of 45 feet in a minute. Reckoning his weight at 155 lbs., the animal exertion for one minute is 6975, and would amount to 4,185,000 if continued for ten hours. But such exercise is too violent to be often repeated in the course of a day. A person may clamber up a rock 500 feet high, by a ladderstair, in 20 minutes, and, consequently, at the rate of 25 ft. each minute ; his efforts are thus already impaired, and the performance reaches only 3875 in a minute. But, under the incumbrance of a load, the quantity of action is still more remarkably diminished. A porter, weighing 140 lbs., was found willing to climb a stair 40 feet high 266 times in a day; but he could carry up only 66 loads of firewood, each of them 163 lbs. weight. In the former case, his daily performance was very nearly 1,500,000; while, in the latter, it amounted only to 808,000. The quantity of permanent effect was hence only about 700,000, or scarcely half the labor exerted in mere climbing. In the driving of piles, a load of 42 lbs., called the ram, is drawn up 3<| feet high 20 times in a minute; but the work has been considered so fatiguing as to endure only three hours a day. This gives about 530,000 for the daily performance. Nearly the same result is obtained, by computing the quantity of water which, by means of a double bucket, a man drew UD from only to the fourth part of that di 7k miles. Assuming his own ^ be 140 lbs., the quantity of 1 action would amount to 42,7C 28 times the vertical performa the share of it in conveying th 20,961,780, or about 30 times ^ spent in its elevation. The gr< vantage is obtained by reducinj den to 102 lbs., the length of jour augmented in a higher ratio, suits are apparently below the a English labor, which is not o vigorous, but, in many cases, q strained. Moderate exertion of joined to regularity and pen would be more conducive to robi and the comfortable duration < life. A porter in London is ac to carry a burden of 200 lbs. at t three miles an hour. In the s tropolis, a couple of Irish chain tinue, at the pace of four miles under a load of 300 lbs. These are greatly inferior, however, tc performed by porters in Turke vant, and generally on the she Mediterranean. At Constanti Albanian porter will carry 800 < on his back, stooping forward, t ing his steps by a sort of staff, seilles, four porters commonly immense load of nearly two means of soft hods passing < heads, and resting on their shou] the ends of poles, from which are suspended. According to periments of the late Mr. Bucr exertions of a man in working a turning a winch, in ringing a bi rowing a boat, are as the nun 167, 227, and 248. But tho appear to have been continui great length of time. The Gree in the Dardanelles, are esteer skilful and vigorous in the act < marks, that the French soldiers, employed on the fortifications of the Isle of Martinique, became soon exhausted, and were unable to perform half the work executed by them at home. The most violent and toilsome exertion of human labor is performed in Peru, by the carriers, or cargueros, who traverse the loftiest mountains, and clamber along the sides of the most tremendous precipices, with travellers seated on chairs strapped to their backs. In this manner, they convey loads of 12, 14, or even 18 stone; and possess such strength and action, as to be able to pursue their painful task eight or nine hours, for several successive days. These men are a vagabond race, consisting mostly of mulattoes, with a mixture of whites, who prefer a life of hardship and vicissitude to that of constant though moderate labor. When a man stands, he pulls with the greatest effect; but his power of traction is much enfeebled by the labor of travelling. If v denote the number of miles which a person walks in an hour, the force which he exerts in dragging forward a load will be expressed nearly by J (12-2vf. Thus, when at rest, he pulls with a force of about 29 lbs. avoirdupois; but if he walks at the rate of two miles an hour, his power of traction is reduced to 14 lbs.; and if he quicken his pace to four miles an hour, he can draw only 3 lbs. There is, consequently, a certain velocity which procures the greatest effect, or when the product of the traction by the velocity becomes a maximum. This takes place ;when he proceeds at the rate of two miles an hour. The utmost exertion which a man, walking, might continue to make, in drawing up a weight by means of a pulley, would amount, therefore, in a minute, only to 2430; but if he applied his entire strength, without moving from the spot, he could produce an effect of 3675. The labor of a horse in a day is commonly reckoned equal to that of five men; but then he works only eight hours, while a man easily continues his exertions for ten hours. Horses, likewise, display much greater force in carrying than in pulling; and yet an active walker will beat them on a long journey. Their power of traction seldom exceeds 144 pounds, but they are capable of carrying more than six times as much weight. The packhorses in the West Riding of Yorkshire are accustomed to transport loads of 420 lbs. over a hilly country. But, in many parts of England, the millhorses will carry the ordinary power of draught, the formula (12-vf, where v denotes the velocity in miles an hour, will perhaps be found sufficiently near the truth. Thus a horse, beginning his pull with the force of 144 lbs., would draw 100 lbs. at a walk of two miles an hour, but only 64 lbs. when advancing at double that rate, and not more than 36 lbs. if he quickened his pace to six miles an hour. His greatest performance would hence be made with the velocity of four miles an hour. The accumulated effort in a minute will then amount to 22,528. The measure generally adopted for computing the power of steam engines is much higher, the labor of a horse being reckoned sufficient to raise, every minute, to the elevation of one foot, the weight of 32,000 lbs. But this estimate is not onty greatly exaggerated, but should be viewed as merely an arbitrary and conventional standard. Wheel carriages enable horses, on level roads, to draw, at an average, loads about 15 times greater than the power exerted. The carriers between Glasgow and Edinburgh transport, in a singlehorse cart, weighing about 7 cwt., the load of a ton, and travel at the rate of 22 miles a day. At Paris, one horse, in a small cart, conveys along the streets half a cord of wood, weighing two tons; but three horses, yoked in a line, are able to drag 105 cwt. 5£ lbs., or that of a heavy cart loaded with building stones. The Normandy carriers travel from 14 to 22 miles a day, with twowheeled carts, weighing each 11 cwt., and loaded with 79 cwt., or nearly 4 tons, of goods, drawn by a team of four horses. The French draught horses, thus harnessed to light carriages, are more efficient, perhaps, than the finer breeds of England. They perform very nearly as much work as those in the singlehorse carts used at Glasgow, and far greater than those heavy animals which drag the lumpish and towering English wagons. The London drayhorses, in the mere act of ascending from the wharfs, display a powerful effort, but they afterwards make little exertion, their force being mostly expended in transporting their own ponderous mass along. Oxen, on account of their steady pull, are in many countries preferred for draught. They were formerly employed universally in the various labors of husbandry. The tenderness of their hoofs, unless shod, however, makes them unfit for pulling on paved roads, and they can work only with advantage in soft grounds. But they want all the pliancy and animation which are the favorite qualities of the horse. The patient drudgery of the ass renders him a serviceable companion of the poor. Much inferior in strength to the horse, he is maintained at far less cost. In this country, an ass will carry about two hundred weight of coals or limestone twenty miles a day. But, in the warmer climates, he becomes a larger and finer animal, and trots or ambles briskly under a load of 150 pounds. The mule is still more powerful and hardy, being fitted equally for burden and draught. In the hotter parte of Asia and Africa, the ponderous strength of the elephant has been long turned to the purposes of war. He is reckoned more powerful than six horses, but his consumption of food is proportionally great. The elephant carries a load of three or four thousand pounds ; his ordinary pace is equal to that of a slow trot; he travels easily over forty or fifty miles in a day, and has been known to perform, in that time, a journey of one hundred and ten miles. His sagacity directs him to apply his strength according to the exigency of the occasion. The camel is a most useful beast of burden in the arid plains of Arabia. The stronger ones carry a load of ten or twelve hundred weight, and the weaker ones transport six or seven hundred; they walk at the rate of two miles and a half in an hour, and march about thirty miles every day. The camel travels often eight or nine days, without any fresh supply of water. When a caravan encamps in the evening, he is, perhaps,\ turned loose, for the space of an hour, to browze on the coarsest herbage, which serves him to ruminate during the rest of the night. In this manner, without making any other halt, he will perform a dreary and monotonous journey of two thousand miles. Within the arctic circle, the reindeer is a domesticated animal, not less valuable. He not only feeds and clothes the poor Laplander, but transports his master, with great swiftness, in a covered sledge, over the snowy and frozen tracts. The reindeer subsist on the scanty vegetation of moss or lichens, and are docile, but not powerful. Two of them are required to draw a light sledge : so harnessed, they will run fifty or sixty miles on a stretch, and sometimes perform a journey of a hundred and twelve miles in the course of a day. But such exertions soon wear them out. A sort of dwarf camel was the only animal of burden possessed by the ancient Peruvians. The lama is, in deed, peculiarly fitted for the lofty regions of the Andes. The strongest of them carry only from 150 to 200 pounds, but perform about fifteen miles a day over the roughest mountains. They generally continue this labor during five days, and are then allowed to halt two or three days before they renew their task. The paco is another similar animal, employed likewise in transporting goods in that singular country; it is very stubborn, however, and carries only from fifty to seventy pounds. Even the exertions of goats have, in some parts of Europe, been turned to useful labor. They are made to tread in a wheel which draws water, or raises ore from the mine. Though a very light animal, the goat exerts much force, as he climbs at a high angle. Supposing this soaring creature, though only the fourth part of the weight of a man, to march as fast along an ascent of 40°, as he does over one of 18°,^the sine of the former being double that of the latter,it must perform half as much work.