FORCE. 



229 



point, situated at rest in A, to run over the line A 13 

 which is called the direction of the force, so as t 

 arrive at B at the end of a given time, while anothe 

 force would cause the same point to have moved 

 greater or less distance from A in the same time 

 (See the figure below.) Mechanical forces may b 

 reduced to two sorts ; one of a body at rest, the 

 other of a body in motion. The former is that whicl 

 we conceive as residing in a body when it is sup- 

 ported by a plane, suspended by a rope, or balanced 

 by the action of a spring, &c., being denominate( 

 pressure, tension, force, or vis mortua, solicitatio 

 conatus movendi, and which may always be estimatec 

 or measured by a weight, viz., the weight that sustain: 

 it. To this class of forces may also be referrec 

 centripetal and centrifugal forces, though they reside 

 in a body in motion, because these forces are homo- 

 geneous to weights, pressures, or tensions of any kind. 

 The force of a oody in motion is a power residing in 

 that body so long as it continues its motions, by 

 means of which, it is able to remove obstacles lying 

 in its way, to lessen, destroy, or overcome the force oi 

 any other moving body, which meets it in an opposite 

 direction ; or to surmount the largest dead pressure 01 

 resistance, as tension, gravity, friction, &c., for some 

 time, but which will ue lessened or destroyed by 

 such resistance as lessens or destroys the motion oJ 

 the body. This is called vis matrix, moving force, 

 or motive force, and, by some late writers, vis viva, 

 to distinguish it from the vis mortua, spoken ol 

 before. 



Composition of Forces may be thus defined : If two 

 or more forces, differently directed, act upon the 

 same body, at the same time, as the body in question 

 cannot obey them all, it will move in a direction 

 somewhere between them. This is called the com- 

 position and resolution of forces or of motion, and 

 may be illustrated in the following manner : Suppose 

 a body, A, to be acted 

 upon by a force in the di- A 

 rection A B, while, at 

 the same time, it is im- 

 pelled by another force 

 in the direction A C, it 

 will then move in the di- 

 rection A D ; and if the lines A B, A C, be made 

 of lengths proportionate to the forces, and the lines 

 C D, I) B, be drawn parallel to them, so as to com- 

 plete the parallelogram A B D C, then the line which 

 the body A will describe, will be the diagonal A D ; 

 and the length of this line will represent the force 

 with which the body will move. But if the body be 

 impelled by equal forces, acting at right angles to 

 each other, it will move in the diagonal of a square. 

 Instances in nature, of motion produced by several 

 powers acting at the same time, are innumerable. 

 (See Gunnery and Projectiles.) A ship impelled by 

 the wind and tide is one well known ; a paper kite 

 acted upon in one direction by the wind, and in an- 

 other by the string, is another instance. 



Animal Force, as applied to Machinery. All ma- 

 chines are impelled either by the exertion of animal 

 force or by the application of the powers of nature. 

 The latter comprise the potent elements of water, 

 air, and fire. The former is more common, yet so 

 variable as hardly to admit of calculation. It depends 

 not only on the vigour of the individual, but on the 

 different strength of the particular muscles employed. 

 Every animal exertion is attended by fatigue ; it soon 

 relaxes, and would speedily produce exhaustion. 

 The most profitable mode of applying the labour of 

 animals, is to vary their muscular action, and revive 

 its tone by short and frequent intervals of repose. 

 The ordinary method of computing the effects of 

 human labour is, from the weight which il is capable 



of elevating to a certain height, in a given time, the 

 prod net of these three numbers expressing the abso- 

 lute qiiiintity of performance. This was reckoned by 

 Daniel Bernoulli and Desaguliers nt 2,000,000 Ibs. 

 avoirdupois, which a man could raise one foot in a 

 day. But our civil engineers have gone much far- 

 ther, and are accustomed, in their calculations, to 

 assume that a labourer will lift ten Ibs. to the height 

 of ten feet every second, and is 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 favourable 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 labour. A man will climb a stair, 

 from 70 to 100 feet high, at the rate of forty-five feet 

 in a minute. Reckoning his weight at 155 Ibs., 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 ladder-stair, in twenty mi- 

 nutes, and, consequently, at the rate of twenty-five 

 feet each minute ; his efforts are thus already im- 

 paired, 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 Ibs., was found willing to 

 climb a stair forty feet high 266 times in a day ; but 

 tie could carry up only sixty-six loads of firewood, 

 each of them 163 Ibs. weight. In the former case, 

 tiis 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 labour exerted in 

 nere climbing. In the driving of piles, a load of 

 forty-two Ibs., called the ram, is drawn up three and 

 a half feet high twenty 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 

 br the daily performance. Nearly the same result 

 s obtained, by computing the quantity of water which, 

 jy means of a double bucket, a man drew up from a 

 well. He lifted thirty-six Ibs. 120 times in a day, from 

 a depth of 120 feet, the total effect being 518,400. A 

 skilful labourer, working in a field with a large hoe, 

 creates an effect equal to 728,000. When the agency 

 of a winch is employed in turning a machine, the 

 >erformance is still greater, amounting to 845,000. 

 n all these instances, a certain weight is heaved up, 

 >ut a much smaller effort is sufficient to transport a 

 oad horizontally. A man could, in the space of a 

 day, scarcely reach an altitude of two miles by climb- 

 ng a stair ; though he will easily walk over thirty 

 mues on a smooth and level road. But he would, in 

 he same time, carry 130 Ibs. only to the fourth part 

 f that distance, or seven and a lialf miles. Assuming . 

 lis own weight to be 140 Ibs., the quantity of hori- 

 ontal action would amount to 42,768,000, or twenty- 

 eight times the vertical performance ; but the share 

 :>f it in conveying the load is 20,961,780, or about 

 hirty times what was spent in its elevation. The 

 greatest advantage is obtained by reducing the bur- 

 len to 102 Ibs., the length of journey being aug- 

 iiented in a higher ratio. These results are appa- 

 ently below the average of British labour, which is 

 iot only more vigorous, but, in many cases, quite 

 verstrained. Moderate exertion of strength, joined 

 o regularity and perseverance, would be more con- 

 ucive to robust health, and the comfortable dura- 

 ion of human life. A porter, in London, is accus- 

 ouied to carry a burden of 200 Ibs. at the rate of 



