The practical object of this science is, to teach the best modes of overcoming resistances by means of mechanical powers, and to apply motion to useful purposes, by means of machinery.

A machine is any instrument by which power, motion, cr velocity, is applied, or regulated.

A machine may be very simple, or exceedingly complex. Thus, a pin is a machine for fastening clothes, and a steam engine is a machine for propelling mills and boats.

Ås machines are constructed for a vast variety of purposes, their forms, powers, and kinds of movement, must depend on their intended uses.

Several considerations ought to precede the actual construction of a new or untried machine; for if it does not answer the purpose intended, it is commonly a total loss to the builder.

Many a man, on attempting to apply an old principle to a new purpose, or to invent a new machine for an old purpose, has been sorely disappointed, having found, when too late, that his time and money had been thrown away, for want of proper reflection, or requisite knowledge.

If a man, for instance, thinks of constructing a machine for raising a ship, he ought to take into consideration the inertia, or weight, to be moved the force to be applied-the strength of the materials, and the space, or situation, he has to work in. For, if the force applied, or the strength of the materials, be insufficient, his machine is obviously useless; and if the force and strength be ample, but the space be wanting, the same result must follow.

If he intends his machine for twisting the fibres of flexible substances into threads, he may find no difficulty in respect to power, strength of materials, or space to work in, but if the velocity, direction, and kind of motion he obtains, be not ap plicable to the work intended, he still loses his labour.

Thousands of machines have been constructed, which, so far as regarded the skill of the workmen, the ingenuity of the contriver, and the construction of the individual parts, were models of art and beauty; and, so far as could be seen without trial, admirably adapted to the intended purpose. But on putting them to actual use, it has too often been found, that their only imperfection consisted in a stubborn refusal to do any part of the work intended.

What is the object of this science? What is a machine? Mention onə of the most simple, and one of the most complex of machines.

Now, a thorough knowledge of the laws of motion, and the principles of mechanics, would, in many instances at least, have prevented all this loss of labour and money, and spared him so much vexation and chagrin, by showing the projector that his machine would not answer the intended pur

pose.

The importance of this kind of knowledge is therefore obvious, and it is hoped will become more so as we proceed.

In mechanics, as well as in other sciences, there are words which must be explained, either because they are common words used in a peculiar sense, or because they are terms of art, not in common use. All technical terms will be as much as possible avoided, but still there are a few, which it is necessary here to explain.

Force is the means by which bodies are set in motion, kept in motion, and, when moving, are brought to rest. The force of gunpowder sets the ball in motion, and keeps it moving, until the force of resisting air, and the force of gravity, bring it to rest.

Power is the means by which the machine is moved, and the force gained. Thus we have horse power, water power, and the power of weights.

Weight is the resistance, or the thing to be moved by the force of the power. Thus, the stone is the weight to be moved by the force of the lever, or bar.

Fulcrum, or prop, is the point or part on which a thing is supported, and about which it has more or less motion. In raising a stone, the thing on which the lever rests, is the ful

In mechanics, there are a few simple machines, called the mechanical powers, and however mixed, or complex, a combination of machinery may be, it consists only of these few individual powers.

We shall not here burthen the memory of the pupil with the names of these powers, of the nature of which he is at present supposed to know nothing, but shall explain the action. and use of each in its turn, and then sum up the whole for his accommodation.

What is meant by force, in mechanics? What is meant by power? What is understood by weight? What is the fulcrum? Are the mechanical powers numerous, or only few in number?

The Lever.

Any rod, or bar, which is used in raising a weight, or sur mounting a resistance, by being placed on a fulcrum, or prop, becomes a lever.

This machine is the most simple of all the mechanical powers, and is therefore in universal use.

Fig. 40.

and c, the fulcrum.

Fig. 40 represents a a straight lever, or hand spike, called also a crowbar, which is commonly used in raising and moving stone and other heavy bodies. The block b is the weight, or resistance, a is the lever,

The power is the hand, or weight of a man applied at a, to depress that end of the lever, and thus to raise the weight.

It will be observed, that by this arrangement, the applica tion of a small power may be used to overcome a great re sistance.

The force to be obtained by the lever, depends on its length, together with the power applied, and the distance of the weight and power from the fulcrum.

a

Fig. 41.

Δ

Suppose, fig. 41, that a is the lever, b the fulcrum, d the weight to be raised, and c the power. Let d be considered three times as heavy as c, and the fulcrum three times as far from c as it is from d; then the weight and power will exactly balance each other. Thus, if the bar be four feet long, and the fulcrum three feet from the end, then three pounds on the long arm, will weigh just as much as nine pounds on the short arm, and these proportions will be found the same in all cases.

What is a lever? What is the simplest of all mechanical powers? Explain fig. 40. Which is the weight? Where is the fulcrum? Where is the power applied? What is the power in this case? On what does the force to be obtained by the lever depend? Suppose a lever 4 feet long, and the fulcrum one foot from the end, what number of pounds will balance each

other at the ends?

When two weights balance each other, the fulcrum is always at the centre of gravity between them, and therefore, to make a small weight raise a large one, the fulcrum must be placed as near as possible to the large one, since the greater the distance from the fulcrum the small weight or power is placed, the greater will be its force.

Fig. 42.

Suppose the weight b, fig. 42, to be sixteen pounds, an sup pose the fulcrum to be placed so near it, as to be raised by the power a, of four pounds, hanging equally distant from the fulcrum and the end of the lever. If now the power a, be remov

ed, and another of two pounds, c, be placed at the end of the lever, its force will be just equal to a, placed at the middle of the lever.

But let the fulcrum be moved along to the middle of the lever, with the weight of sixteen pounds still suspended to it, it would then take another weight of sixteen pounds, instead of two pounds, to balance it, fig. 43.

Fig. 43.

Thus the power which would balance 16 pounds, when the fulcrum is in one place, must be exchanged for another power weighing 8 times as much, when the fulcrum is in another place.

From these investigations, we may draw the following general truth, or proposition, concerning the lever : "That the force of the lever increases in proportion to the distance of the power from the fulcrum, and diminishes in proportion as the distance of the weight from the fulcrum

increases."

From this proposition may be drawn the following rule, by which the exact proportions between the weight, or resistance, and the power, may be found. Multiply the weight by its

When weights balance each other, at what point between them must the fulcrum be? Suppose a weight of 16 pounds on the short arm of a lever is counterbalanced by 4 pounds in the middle of the long arm, what power would balance this weight at the end of the lever? Suppose the fulcrum to De moved to the middle of the lever, what power would then be equal to the 16 pounds? What is the general proposition drawn from these results?

distance from the fulcrum; then multiply the power by its distance from the same point, and if the products are equal, the weight and the power will balance each other.

Suppose a weight of 100 pounds on the short arm of a lever, 8 inches from the fulcrum, then another weight, or power, of 8 pounds, would be equal to this, at the distance of 100 inches from the fulcrum; because 8 multiplied by 100 is equal to 800; and 100 multiplied by 8 is equal to 800, and thus they would mutually counteract each other.

Fig. 44.

Pincers, forceps, and sugar cutters, are examples of this kind of lever.

A common scale-beam, used for weighing, is a lever, suspended at the centre of gravity, so that the two arms balance each other. Hence the machine is called a balance. The fulcrum, or what is called the pivot, is sharpened, like a wedge, and made of hardened steel, so as much as possible to avoid friction.

Fig. 45.

a

A dish is suspended by cords to each end or arm of the lever, for the purpose of holding the articles to be weighed. When the whole is suspended at the point a, fig. 45, the beam or lever ought to remain in a horizontal position, one of its ends being exactly as high as the other. If the weights in the two dishes are equal, and the support exactly in the centre, they will always hang as represented in the figure.

A very slight variation of the point of support towards one

What is the rule for finding the proportions between the weight and power? Give an illustration of this rule. What instruments operate on the principle of this lever? When the scissors are used, what is the resistance, and what the power? In the common scale-beam, where is the fulerum? In what position ought the scale-beam to hang ?