lies in the lower block by two. A pair of blocks with a rope is called a tackle.

Of compound Machines.

389. Though any one of the mechanical powers is capable of overcoming the greatest possible resistance, in theory; yet, in practice, if used singly, for producing great effects, they are unwieldy and unmanageable, it is found more advantageous to combine them; by which means the power is more easily applied, and many other advantages obtained. In all machines, simple as well as compound, what is gained in power is lost in time.

Suppose a man, by a fixed pulley, raises a beam to the top of a house in two minutes, he will be able to raise six beams in twelve minutes: but by means of a tackle, with three lower pullies, he will raise the six beams at once, with the same ease that he raised one; but he will be twelve minutes about it; the work is performed in the same time, whether the mechanical power is used or not. But the convenience gained by the power is very great; for if the six beams be joined in one, they may be raised by the tackle, though it would be impossible to move them by the unassisted strength of one man.

Consequently, if by any power you are able to raise a pound with a given velocity, it will be impossible, by the help of any machine, without increasing the power, to raise two pounds with the same velocity: yet, by the assistance of a machine, you may raise two pounds with half that velocity, or even one thousand with the thousandth part of that velocity; but still there is no greater quantity of motion produced, when a thousand pounds are moved, than when one pound is moved; the thousand pounds moving proportionally slower.

No real gain of force is, therefore, obtained by mechanical 'contrivances; on the contrary, from friction, and other causes force is always lost; but by machines we are able to give a more convenient direction to the moving power, and to apply its action at some distance from the body to be moved. By machines also, we can so modify the energy of the moving power, as to obtain effects which it could not produce without this modification.

In machines composed of several of the mechanical powers, the power will be to the weight, when they are in equili brio, in a ratio formed by the multiplication of the several

proportions which the power bears to the weight in every separate mechanical power of which the machine consists.

Suppose a machine, for instance, composed of the axle in the wheel, and pullies: let the axle and wheel be such, that a power consisting of one-sixth of the weight will balance it; and let the pullies be such, that by means of them alone, a power equal to one-fourth of the weight would support it: then, by means of the axle in the wheel, and the pullies combined, a power equal to one-fourth of one-sixth, that is, of the weight, will be in equilibrio with it.

In contriving machines, simplicity ought to be attended to; for a complicated machine is more expensive, and more apt to be out of order, and the friction is in proportion to the number of rubbing parts.

Whatever be the construction of a machine, the advantage gained by it will be in proportion as the velocity of the power is to that of the weight; and so that this is obtained in the great est degree that circumstances will admit, or are necessary, then the fewer parts the better.

The velocity of a wheel is to that of a pinion, or smaller wheel driven by it, in proportion to the diameter, circumference, or number of teeth in the pinion to that of the wheel.

Thus, if the number of teeth in a wheel be 60, and those of the pinion 5, then the pinion will go 12 times round while the wheel goes once round, because 605 give 12 for a quotient. Hence, if you have any number of wheels acting on so many pinions, you must divide the product of the teeth in the wheels by the product of those in the pinions; and the quotient will give the number of turns of the last pinion in one turn of the first wheel. Thus, if a wheel of 48 teeth acts on a pinion of 8, on whose axis there is a wheel of 40, driving a pinion of 6, carrying a wheel of 36, which moves a pinion of 6, carrying an index; then the number of turns made by the index will be found in this manner: 48 x 40 x 3669120-240, the number of turns which the index will make while the wheel goes once round.

Any number of teeth on the wheels and pinions having the same ratio, will give the same number of revolutions to an axis thus, 50+36-115200-240, as before. It therefore depends on the skill of the engineer, or mechanic, to determine what numbers will best suit his design.

It is evident that the same motion may be performed, either by one wheel and pinion, or by many wheels and pinions, provided the number of turns of all the wheels bear the same proportion to all the pinions which that one wheel bears to its pinion.

When a wheel is moved immediately by the power, it is

called a leader; if there is another wheel on the same axis, it is called the follower.

Thus A being moved immediately by the power is to be considered a leader, and B a follower; the wheel C driven by B becomes a leader, and Da follower; E is a leader and the cylinder F a follower. Sometimes the same wheel acts both as a leader and a follower. Thus if the ends of the cylinder were reversed, and the teeth of the wheel E worked in the teeth of C, then would C be a follower to B and a leader to E: that is, when these wheels work in succession, the middle one is both a leader and a follower. Therefore, as to multiply both the divisors and dividend by the same number, does not alter the quotient; in mechanical

B

calculations, every wheel that is both a leader and a follower, may be entirely omitted.

The power of a machine is not at all altered by the size of the wheels, provided the proportions to each other are the same. Formerly the wheels of engines being mostly of wood, were of a large size, on account of strength; but now that castiron wheels are so easily made, the size of them is very much diminished, and they occupy much less room.

Of Fly Wheels.

390. In all machines, the moving power acts with more or less irregularity, being sometimes stronger, and at other times weaker. But to correct this, and render the motion uniform, an additional part, called a fly, is applied.

This fly is generally either a heavy wheel, or a cross bar loaded with equal weights, made to revolve about its axis, and keep up the force of the power by distributing it equally in all parts of its revolution: for on account of its inertia, a small variation in force does not sensibly alter its motion; whilst friction, and the resistance of the machine, prevent it from accelerating. If the motion of the machine slackens, it helps it forward: if it moves too fast, it will keep it back. The truth of this is easily understood from considering the inequality of the motion in a clock, when the pendulum is off, and how very uniformly it goes when regulated by a pendulum, which here acts as a fly. Every regulating-wheel should be

fixed upon that axis where the motion is swiftest, and should be heavy when the motion is designed to be slow, and light when it is designed to be swift. In all cases, the centre of motion should coincide with the centre of gravity of the wheel. The axis may be either perpendicular, or parallel to the horizon. Fly-wheels, in general, are employed to equalize the motion of a machine; they cannot add to its power. Of Friction.

391. Friction in its primitive sense signifies the act of rubbing two bodies together; in machinery it implies the resistance caused by the motion of the different parts against each other; and in the application of all the mechanical powers, one third is allowed to overcome the friction of the surface, and other obstacles to which machines are liable.

If a horizontal plane were perfectly smooth, a body would be free to move upon it in any direction, by the least force applied to it. But however smooth bodies appear to the eye, if you examine their surfaces with a microscope, you will discover numberless inequalities; in consequence of which, the prominent parts of one body fall into the hollows of another, so as to be locked together; and therefore, in moving them over each other, one of the bodies must be raised up, or its prominences broken off: this is a philososophical definition of friction.

Friction is greater in bodies, in proportion to their weight or pressure against each other. It does not increase much in proportion to the surface, but in proportion to the velocity of the moving bodies. Wood slides more easily upon the ground, or earth, in wet weather than in dry, and more easily than iron in dry weather, but iron more easily than wood in wet weather. A cubic piece of smooth soft wood, eight pounds in weight, moving upon a smooth plane of soft wood, at the rate of three feet every second, has a friction equal to above two-thirds of its weight. Soft wood upon hard wood, has a friction equal to one-sixth part of its weight: and hard wood upon hard wood, has a friction equal to about one-eighth part of its weight. In wood rubbing upon wood, oil, grease, or black-lead, properly applied, makes the friction two-thirds less. Wheel-naves, when greased, have only one-fourth of the friction they would have if wet. Hence the propriety of so contriving wheel naves as to keep the grease from being dissipated.

When polished steel moves on steel, or pewter properly oiled, the friction is about one-fourth of the weight; on cop

per or lead, one-fifth; on brass one-sixth; and metals have more friction when they move on metals of the same kind, than on different metals.

The friction of a single lever is very little. The friction of the wheel and axle is in proportion to the weight, velocity, and diameter of the axle; the smaller the diameter of the axle, the less the friction.

The friction of pullies is great, on account of the smallness of their diameters, in proportion to that of their axes; because they often bear against the blocks, and from the wearing of their holes and axles.

In the wedge and screw there is much friction. Screws with sharp threads, have more friction than those with square threads, and endless screws have most.

Men and Horses considered as first Movers.

392. A horse draws with the greatest advantage, when the line of draught is not level with his breast, but inclines upwards, making a small angle with the horizontal plane. When a horse works in a circle, it should not be less than forty feet in diameter. A horse exerts most strength, when drawing horizontally.

In turning a winch, a man exerts his strength in different proportions at different parts of the circle. The greatest force is when he pulls the handle upwards from the height of his knee; and the least, when he thrusts from him horizontally.

The handles at each end of a winch should be put on at right angles to each other, and not opposite, as they often

are.

The Mill and Mill Work....

393. In the strictest sense of the word, a mill sig nifies a machine for grinding corn, though the term mill-work is frequently applied to all kinds of machinery where large wheels are used. They are distinguished into various kinds, either according to the powers by which they are moved, or the uses to which they are applied. Such as water-mills, horse, wind, corn, fulling, powder, and boring-mills, &c.

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