and are the same in principle with the lever. It is apparent, therefore, that the simple machines may be reduced to three classes: 1. The lever, and the wheel and axle. 2. The inclined plane, screw, and wedge. 3. The pulley and rope machine. It is by combining these machines, in various ways, that the machinery now employed in the arts, which is so various, and in many places so intricate, has been constructed. We propose, in this Chapter, to consider the several objects, some one or more of which it is always proposed to attain, by the use of machinery. ; or 1. The first is, to divide a resistance too great to be overcome by a single effort of the moving power, so that it may be overcome by a series of actions, or by the continual action of the moving power. If a man were to apply all his strength directly to a rock or to a box of merchandise, which he wishes to elevate to some point, he might not be able to move it at all at least might not be able to raise it to the required height. But with a lever, or a wheel and axle, or a pulley, he effects his object with ease. Here, he does not actually gain power. He gains the means of acting upon the resistance by degrees. It is like taking this rock to pieces, and carrying up the parts separately; and a little reflection must convince us, that when we employ a machine, we exert not only all the force which would be requisite in such a case, if we had not used the machine, but also as much more, as is necessary to overcome the friction and weight of that machine. It is a great error, and one to which we cannot too often advert, to suppose that, by any mechanical device, force can be generated, or even augmented. Misled by such a notion, projectors have imagined that they could adjust levers, pendulums, &c., that would act with a power greater than that which they derived from some external source. It is obvious, and should ever be kept in mind, that the inertia of matter, in virtue of which, no particle of it ever moves, except in obedience to some force impressed upon it, and in pro portion to that force, renders all such projects entirely impracticable. Universally, to overcome a resistance, a force must be exerted equal to that resistance; and, as we have already said, if it be exerted through a machine, the force must be absolutely greater than the resistance. But, on the other hand, force is made up of velocity and the quantity of matter; and hence, if the mass to be moved, or the resistance to be overcome, be much heavier than the moving power, we equalize them, if we can, by giving to the resistance a much slower motion than that which the power has; thus making the greater velocity of the power compensate for its inferior weight, or mass. In all these cases, however, time must be lost; and it must be remembered, as a general principle, that whatever advantage is gained in respect to power is lost in respect to time.* A man with a machine does no more than in the same time he would have done without a machine, provided he could have divided the resistance into separate parts. In many cases, however, this is impossible; and hence we are enabled, by the aid of machines, to effect what, without them, would have been altogether beyond our power. 2. The second use of machinery is to enable us, by changing the direction of a force, to apply it more advantageously. Thus, in lifting a weight out of a well, or raising ore out of a mine, it is obvious, with how much more effect a man can work, at the arm of a windlass, than he could draw directly upon the rope, stooping over the well. There are other cases, in which machinery, by changing the direction of a force that, in its natural state, is useless, enables us to apply it to important purposes. For example in a steam * Archimedes is said to have boasted, that, if he had a place on which to stand, he would move the earth. Had such a place been furnished him, and had he been able, moreover, to move with the velocity of a cannon ball, it would have taken him a million of years to have shifted the earth only the twenty-seven hundred thousandth part of an inch. boat, the piston of a steam-engine alternately ascends and descends, along a perpendicular;* whereas, the vessel, which it serves to propel, is required to move in a continued horizontal line. On the other hand, the stream of a saw-mill moves in a continued horizontal or perpendicular line, while the saw, which it drives, is required to have an alternating perpendicular movement. In the first case, the rectilinear alternating motion is converted into a circular one, by means of the crank, a contrivance which, in principle, is much like the common winch, or like the key which winds a clock; and then the circular motion of the waterwheels, acting against the water, carries the vessel forward in a continued right line. As a general rule, a circular can be converted into a continuous rectilinear motion, and vice versa, by means of a toothed wheel and rack, as in Fig. 30; a continuous circular into an alternate rectilinear, as in the saw-mill, Fig. 31; or Fig. 30. Fig. 31. - into an alternate circular, as in the balance-wheel of a watch, Fig. 32, and the pendulum of a clock, Fig. 33, (see page 95,) by means of cams, racks, &c. 3. The third object for which machinery is employed is, to change the velocity. In some cases, the work to be done, as spinning, turning, &c., requires a great velocity. In others, the velocity requires to be smaller than that of the moving power, as in the smoke-jack. This change may be effected in various ways; for ex *We speak here of the engines common in this part of the country. On the Mississippi and its tributaries, the piston has a horizontal motion. ample, by the lever. If it be a lever of the first kind,* it diminishes or increases velocity, according as the arm, to which the power is applied, is longer or shorter than the other arm. In a lever of the third kind, velocity is always increased, since the resistance is further from the fulcrum than the power. Hence, in the human arm, sheep-shears, tongs, &c., which are levers of the third kind, a great part of the power is expended in procuring velocity, and the resistance, therefore, must be proportionally diminished. If a The machine most frequently employed, however, in transmitting force and regulating velocity, is the wheel and axle. band pass from the circumference of one wheel to that of another and a smaller one, as in Fig. 34, it is evident, that, while the first and greater revolves once, the second must revolve as many times as its circumference is less than that of the larger. This is the Fig. 34. * See pages 89, 90, Figs. 18, 19, 20, for representations of the different kinds of levers. case with the spinning-wheel. Here, if the thread were twisted directly by the fingers, little work could be done. But, by applying the power to a large wheel, which, by means of a band, gives motion to a small one, called the spindle, a great velocity is created, and not only more work is done, but it is done much better. Sometimes, the band passes from the circumference of one wheel to the axle of another, when there is a much greater gain in velocity. As bands are liable to slip, and cannot be employed where the resistance is very great, In the larger and more important machinery, means are sometimes adopted, to increase velocity, different from any that I have yet mentioned. For example: in converting cast into wrought iron, a mass of metal, of about a hundred weight, is heated almost to a white heat, and placed under a heavy hammer, moved by water or steam power. This is raised by a projection on a revolving axis, and if the hammer derived its momentum only from the space through which it fell, it would require a considerably greater time to give a blow. But, as it is important that the softened mass of red-hot iron should receive as many blows as possible before it cools, the form of the cam or projection on the axis is such, that the hammer, instead of being lifted to a small height, is thrown up with a jerk, and almost the instant after it strikes against a large beam, which acts as a powerful spring, and drives it down on the iron, with such velocity, that by these means, about |