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modified in a thousand different ways. It is, indeed, this same simple principle, which lies at the foundation of all the ingenious and often complicated machinery included under the general name of wheel-work.
The pulley, the third in importance of the mechanical powers, consists essentially of a cord passing over a wheel which turns on an axis. We often speak of the wheel as if it were itself the pulley, but it is upon the cord that the mechanical effect depends, the wheel being introduced to lessen the effects of friction. When the wheel merely turns on its axis, without moving from its place, it is said to be fixed; but when it is suspended by means of the cord, so as to rise and fall with the weight, it is called a movable pulley.
If the cord of the fixed pulley A have a weight suspended at each end, it is obvious that these weights, to balance Fig. 34. each other, must be equal. Hence
the fixed pulley gives no additional
by a downward force, or indeed by w ØP
a force acting in any direction what
ever. It is evident that a hand will have the same effect in raising the weight W, whether it act at P, or at Q, or at R. Thus, a moving power, of whatever kind, may, by the use of one or more fixed pulleys, produce a motion in any desired direction by acting itself in the direction in which it can be most conveniently applied.
A movable pulley, however, affords mechanical assistance. Suppose the weight W to be attached to Fig. 35. the movable pulley A, and one end of the cord of the pulley fastened to a hook at B. If we fasten the other end to a similar hook at C, each hook will support onehalf of the weight. But if, instead of being fastened at C, that end of the cord is either held by the hand, or passed over a fixed pulley, and stretched by a weight P, the hook at B will still support its half of the weight W, so that the weight P, or the hand which holds the cord, will have to support only the other half. If the hand now pull the string, the hook at B will continue to afford the same assistance. Hence the power of the hand will be doubled. But it is to be observed that the weight will move with only one-half the velocity with which the hand moves; for, in order to raise it one inch, the cord must be pulled till it is one inch shorter on each side of the pulley, that is, till the hand has moved through two inches. Thus the advantage of a movable pulley consists in dividing the difficulty. The weight is raised through a certain space, by pulling the cord through a space twice as great, but only one-half the strength is required which would be necessary without the aid of the machine. The effect is almost the same as if the weight were divided into two equal parts, and these parts raised successively.
Here, then, we have another example of the principle on which all mechanical power is founded. The deficiency of strength in the moving power is compensated by superior velocity. In every machine, however powerful, and however ingenious, what is gained in power must be lost in time. It would be a great mistake, however, to suppose that the loss is equal to the gain, and that we derive no advantage from the mechanical powers. Since our strength is not great, and we cannot augment it, that science is of wonderful utility which enables us to reduce to its level any
resistance we may have to overcome, or any heavy body we may have to raise. This we accomplish very much in the same way as if we divided the body into parts, and raised these parts successively; but with this important difference, that, at the conclusion of our task, the body remains whole and uninjured. If it requires a sacrifice of time to attain this end by means of a machine, it must be remembered that without the machine it could not be attained at all. It is with great advantage, then, that time is thus exchanged for power.
If two or more movable pulleys be connected together, Fig. 36. the effect will be increased. Sometimes one
cord is passed round several wheels, as in the system represented in fig. 36. Here the weight is supported by four cords, or, to speak more correctly, by the four parts or folds into which the cord is divided by the wheels. The power P therefore supports only one-fourth of the weight W. For instance, a boy strong enough to lift 1 cwt., either without a machine, or by means of a fixed pulley, would be able, by such a system as this, to lift 4 cwt. There are other methods of arranging pulleys in which several
distinct cords are employed. In these, the
1. mechanical effect is still greater, but the appaw Op ratus is more complicated, and less convenient.
The pulley is chiefly used for the purpose of raising hcavy bodies. It is by means of pulleys that the sailor hoists his sails. They are in this case doubly convenient; for, besides affording him mechanical assistance, they enable him to accomplish his purpose without leaviny the deck.
THE INCLINED PLANE, WEDGE, AND SCREW. The inclined plane is the simplest of the mechanical powers. It is a plain sloping surface, used for the purpose of moving weighits from one level to anothor. Thus, if a heavy cask
has to be put into a cart, it may be difficult to lift it perpendicularly; but, by laying a broad plank in a sloping position, with one end
Fig. 37. resting on the ground, and the other on the cart, the difficulty is easily overcome. In this and similar cases, the power necessary for raising a weight, will bear the same proportion to the weight itself, as the perpendicular height, through which the weight has been raised, does to the length of the plane along which it has actually moved. By lengthening the plane, therefore, we render the work easier. Thus, on an inclined plane of 20 feet in length, and 4 feet in perpendicular height, a weight of 500 lbs. will be balanced by a force equal to 100 lbs. urging it up the plane. If the plane is 40 feet long, the height remaining the same, the same force will balance a weight of 1000 lbs. It is for this reason that we do not make a road right up a hill, but give it a winding course, so as to increase the length, and thereby lessen the difficulty of the ascent. Roads, it may be observed, are usually inclined planes, and the same may be said of railways, though both are in some parts horizontal.
The wedge may be considered as made up of two inclined planes united at their bases. The back of the wedge corresponds to the perpendicular height of the FIG. 38. inclined planes of which it is composed; hence the mechanical advantage gained by it is in proportion as the breadth of the back is less than the lengths of the two sides added together. But in the case of this instrument, the friction is usually so enormous, that calculations based on the supposition of perfect smoothness are really of little or no value. The principal use of the wedge is for cleaving timber and other
hard substances. It is also employed, as well as the screw, to join the parts of machines firmly together; pins and nails being modified wedges, which are retained in their places by friction. Knives, and other cutting instruments in daily use among us, may be referred to the principle of the wedge.
The screw, as well as the wedge, is to be regarded as a variety of the inclined plane. It is in fact nothing more than an inclined plane rolled round a cylinder. A staircase winding round a pillar is a rough example on a large Fig. 39.
scale. If a piece of paper be cut so that its edge AC shall be in the position of an inclined plane, and then rolled round a pencilor other cylindrical body AB, the edge AC will form a
spiral round the pencil, which will answer to the thread of a screw, as seen in the figure EF. Hence, in calculating the mechanical advantage which it gives, the screw may be treated exactly as an inclined plane. In practice, however, the power of this instrument is greatly increased by the handle which works it, and which is usually a lever or a winch.
It must never be forgotten that, in all the foregoing explanations, the effects of friction and other disturbing influences have been left out of account. The results arrived at, therefore, are by no means absolutely correct, but they may be taken, in most cases, as a pretty near approximation to the truth.
CONCLUSION. Such are the leading principles of the science of machinery, the knowledge and application of which have done so much for man. In a savage state, ignorant of the arts which depend on mechanical combinations, he is exposed, without shelter, to the inclemencies of the weather; he is unable to