MECHANICS. 



743 



body must fall to acquire tliat velocity. The pheno- 

 mena of accelerated anil retarded motion are beauti- 

 fully exhibited by Atwood's machine for that purpose. 



In moving- down an inclined plane, a solid body 

 is urged by a portion of the- force of gravitation, 

 which is continually smaller as the plane is nearer to 

 a horizontal position. (See Inclined Plane.) When 

 it is horizontal, the whole weight of the body is sus- 

 tained by the plane. The velocity acquired 

 by bodies moving down any plane, is the same 

 as they would have acquired by falling freely 

 from the perpendicular height of the plane. 

 If a body be allowed to fall down the inclined 

 plane C A, the velocity it acquires when it A B 

 arrives at B, having moved from C, will be the 

 same as it would have acquired, had it fallen freely 

 in the perpendicular line C B, from C. 



It is necessary, in the construction of machines, 

 carriages, buildings, bridges, and ships, and in many 

 tittier cases, to ascertain exactly the centre of gravity 

 of the whole and of each part ; since, if the centre of 

 gravity, in any body or system of bodies, be supported, 

 the whole must remain firm, and in a state of rest, in 

 every possible position. (See Gravity, Centre of.) 

 The various problems arising from this necessity 

 have been solved with great accuracy, and on fixed 

 principles. In all regular solids, of uniform density, 

 whether bounded by straight or curve lines, the 

 centre of gravity coincides with the centre of mag- 

 nitude. If a body of any shape be suspended, freely, 

 from any one point of its surface, the straight line 

 extending from that point to the centre of the earth 

 will pass through the centre of gravity. This line is 

 called the line of direction. The centre of gravity 

 may, therefore, sometimes be found practically, by 

 suspending a body successively from two of its points, 

 and observing the point where the lines of direction 

 cross each other. The centre of gravity of a triangle 

 is at one third the distance from the middle of the 

 br.se to the vertex ; that of a cone and of a pyramid, 

 at one fourth the same distance. Stability, in every 

 case, depends upon the position of the centre of gra- 

 vity in reference to the base. The nearer it is to the 

 base, and the farther the line of direction falls from 

 each part of the perimeter of the base, the greater is 

 the stability. The sphere rests equally in every 

 position, because the centre of gravity is at the same 

 distance from every part of the surface. It is unstable 

 in every position, as it rests on a single point of the 

 plane ; and it yields to the smallest force, as the 

 centre of gravity does not rise when the sphere 

 revolves. In order that the pyramid or cone may be 

 overturned, the centre of gravity must rise almost 

 perpendicularly, and move for a great distance before 

 it ceases to tend to fall back to its place. Hence 

 their stability, and hence the propriety of giving to 

 steeples, monuments, and other buildings of great 

 height, a pyramidical or conical figure. Those car- 

 riages are most secure which are hung low, and have 

 the wheels far apart. Whatever raises the centre of 

 gravity or narrows the base, allows the line of direc- 

 tion more easily to pass without it, and diminishes 

 stability. Hence we see the imprudence of rising 

 in carriages or boats which are in danger of being 

 overset, and hence the danger of high loads on 

 wagons, where the roads are not perfectly level. 



The force of gravity is not often employed directly 

 as a mechanical agent, or prime mover. Those most 

 frequently employed to give motion to machinery are 

 water, wind, heat, and the strength of animals. Water 

 acts by its weight and by the velocity which it acquires 

 from falling, in consequence of its weight. /Find 

 acts by its volume or mass and its velocity. Botli 

 these agents are variable, and both act in a straight 

 line. Heat, as given out by combustible material--, 



produces steam, or gas ; or gives motion to air by mak- 

 ing it lighter, and thus causing it to rise. The 

 steam, or gas, when formed, has a tendency to 

 expand itself, presses against the sides of the vessel 

 which contains it, and endeavours to escape with a 

 force proportioned to the heat and pressure to which 

 it was exposed. When allowed to escape in only one 

 direction, it necessarily generates motion in a straight 

 line. Steam, as usually employed, generates motion, 

 which is alternately in one direction and the opposite. 

 The strength of animals is commonly made to act 

 upon some centre of resistance, by drawing, pushing, 

 or pressing, and produces variable motions, naturally 

 in a straight line, but often in a curve. The motions 

 or pressures produced by all these agents are capable 

 of being compared with those produced by weights. 

 They might all be referred to a common standard, 

 the unit of which should be the force required to raise 

 a given weight a certain number of feet in a given 

 time. 



1'he mechanical agents are employed to measure 

 time, to move ships and carriages, to raise weights, to 

 shape wood and work metals, to overcome the resist- 

 ance of air, of water, and of cohesion, to draw out and 

 form materials, and to combine them into new fabric . 

 To apply them to accomplish any one of these t Heels 

 requires the intervention of some mechanical contri- 

 vance. Such a mechanical contrivance, whether 

 consisting of a few or of many parts, is called a 

 machine. A machine has been defined, " a system 

 of bodies, fixed or movable, so connected together 

 that a movement impressed on one of them shall be 

 transmitted to the others." The object of a machine 

 is often vaguely supposed to be to produce or aug- 

 ment power. It can never have this effect. The 

 resistance of the fixed and the friction of the movable 

 parts will always consume a part of the power of the 

 prime mover. The real object of every machine is 

 to increase or diminish the velocity of the moving 

 force, to change its direction, to accumulate its action 

 and expend it at a single effort, to distribute the force 

 among a great number of small resistances, or to 

 divide the force of a resistance so that it may be 

 overcome by a series of actions, or by the continued 

 action of the moving power. A machine may com- 

 bine the action of several movers, and employ one to 

 regulate the others, so that the final effect shall be 

 perfectly uniform. The pendulum, the governor, and 

 the fly-wheel are employed for this purpose. 



By the mechanical powers, are signified the simple 

 machines, to which all machines, however complex, 

 may be referred. They are essentially three in num- 

 ber, but usually considered seven : 1 . The lever, the 

 wheel and axis ; 2. the inclined plane, the screiv, the 

 wedge; 3. the rope and the pulley. 



The Lever is a bar, resting on a support, called a 

 fulcrum, or prop, for the purpose of raising, by a 

 power applied to one end, a weight at the other. An 

 iron crow used by workmen to raise heavy stones, 

 affords a good instance of a lever. The stone is the 

 weight ; the block on which the crow rests is the 

 fulcrum ; the strength of the men, the power. To 

 gain any advantage by its use, the fulcrum must be 

 nearer to the weight than to the power. If the dis- 

 tance from the power to the fulcrum be five times 

 greater than the distance from the weight to the ful- 

 crum, a force of one pound in the power will balance 

 a pressure of five pounds in the weight. But in this 

 case the end of the long arm of the lever will, as it 

 turns on the prop, pass through a space five times 

 greater than that of the short arm. By such a lever 

 a man could raise 1000 pounds with the same exer- 

 tion as would be required to raise 200 without a lever, 

 but he could raise it only a fifth part so high in the 

 >anie time. Wliat he would gain therefore in power, 



