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lever. Scissors, snuffers, and pincers are double levers of the first kind; the nail that unites the two parts of the instrument being the fulcrum of both.
We have a very important application of this class of levers in the various kinds of balances used for weighing goods. In the
FIG. 28. balance, the arms are equal, so that the power and the weight, or rather the two weights, must also be equal, in order to secure equilibrium. The steel-yard differs from the common balance in having arms of unequal length, on the longer of which is marked a scale of divis,
Fig. 29. ious. A known weight (P) is slid along these divisions, until it balances the substance to be weighed (W). Its position on the scale will then indicate the weight of that substance.
The second kind of lever has the weight between the fulcrum and the power. It is obvious that, in this case, the power will be always less than
FIG. 30. the weight, because it pulls by a longer arm, that is, at a greater distance from the ful
It is equally clear that the power must move through a greater space than the weight, and therefore with greater speed. Hence this kind of lever is best adapted to produce an effect which requires great force rather than velocity of motion. An oar is a good example. The water against which its blade is pressed may be regarded as the fulcrum, the weight is the boat, and the hand of the boatman is the power.
Gates and doors are often mentioned as examples of this kind of lever. A porter, rolling a heavy cask along the street, thrusts the point of a handspike below
it, and shoves it from him, pressing it upwards. The earth is here the fulcrum; the power and weight are easily distinguished. Nut-crackers are double levers of the second kind. The hinge is the fulcrum of each half, the nut is the weight or resistance to be overcome, and the hand is the power. In levers of the third kind, the power takes the middle FIG, 31.
place and, being nearer the fulcrum, must always be greater than the weight. Hence they are adopted only where rapid
ity and despatch are required more than power. One of the best examples is the treadle of a turning-lathe, in which the hinge is the fulcrum, the foot the power, and the crank of the wheel with which the treadle is connected the weight. Common tongs and the shepherd's shears are familiar examples of double levers of the third kind. Many striking examples are found in the animal economy. The limbs of animals are generally levers of this description. The forearm, for instance, has its fulcrum in the elbow-joint; the weight is the forearm itself and the hand, together with anything which they may be employed to move; and the power is a strong muscle proceeding from the shoulder, and attached to the forearm a little below the elbow. The advantage is, that a slight contraction of the muscle gives a considerable motion to the limb. Here, surely, we see displayed the goodness and wisdom of the Creator; for it is of much less consequence to man to be able to exert a great force or overcome a great resistance with his hand and arm, than to move these and the other members of his body with sufficient nimbleness and rapidity.
THE WHEEL AND AXLE.
Almost every one has seen a draw-well, into which the bucket is let down empty, and then drawn up full, by
means of a rope coiled round a cylinder. This cylinder is worked by a handle
Fig. 32 called winch (HIK), and the hand which drives the winch makes one revolution for every coil of the rope. Suppose now that for the winch a wheel is substituted,* of such a size that its circumference
may coincide with the circle described by the hand in working the machine. The apparatus will then be a wheel and axle, in the simplest form which it can assume. The cylinder, round which the rope is coiled, is called the axle.
In this, the second of the mechanical powers of which all machinery is composed, the moving power acts at the circumference of the wheel, and tends to make it revolve, The weight or resistance acts in the same way at the circumference of the axle, and pulls it round in the opposite direction to that in which the wheel is pulled. But the whole machine is either of one piece, or at least the wheel and axle are so connected, that if the one revolves, the other must revolve with it. Hence the power and the weight act against each other.
Suppose the circumference of the wheel to be ten feet, and that of the axle one foot. The weight, in one revolution, will thus pass through one tenth of the space described
power in the same time; consequently it will be ten times as large as the power, if they are in equilibrium. A force of 1 lb., for example, will balance in the case supposed a resistance of 10 lbs. But it will be observed that the circumference of the wheel, which carries the smaller weight, moves ten times more rapidly than that of the axle, which carries the greater. Accordingly, where the object is to increase, or rather to accumulate power—in other words, to make a feeble power overcome a great resistance —the
* In the figure given above, there is both a wheel and a winch; but generally it is not necessary to have both in the same machine,
power must be applied to the wheel, and the resistance to the axle, in the mode already described. But when, on the other hand, it is desirable to secure velocity of motion, even at the expense
power, the order of the parts must be reversed. The moving power will then act on the axle, which, in its turn, will communicate motion to the wheel. In either case, the two forces will balance each other, when they are inversely proportional to the lengths of the circumferences in which they act.
It may be remarked, that the principle of this machine is exactly identical with that of the lever. The common axis round which both wheel and axle turn, may be regarded as the fulcrum. The weight acts at a distance from that fulcrum equal to the radius of the axle, and the power at a distance equal to the radius of the wheel. Now, these distances form, as it were, the two arms of a lever of the first kind. Every successive instant, as the machine revolves, cach of the forces acts at the extremity of a new radius, so that every conceivable radius, both of the wheel and axle, becomes an arm of the lever in its turn. Hence the wheel and axle has sometimes been called the perpetual lever.
We have an example of the wheel and axle in the apparatus used for steering a ship. In boats and other small vessels, the helm is moved by a lever, but in larger vessels a wheel and axle is employed. Hence we hear the helmsman spoken of as “the man at the wheel. In this case, the rim of the wheel is set round with handles for the helmsman to pull by; the chain that moves the helm is coiled round the axle. In practice, it is not always necessary that the wheel should be complete; for the same effect will be produced if spokes are inserted into the axle without being connected by a rim, and these may be turned by the hand, or by any other power acting at their extremities. This is the principle of the capstan, a powerful instrument used in ships for hauling up anchors. The axle is a strong vertical cylinder, and is moved by the sailors pressing against the spokes, which are taken out and laid aside when the instrument is not in use. In one case already referred to, the wheel is wanting altogether, its place being supplied by a winch. The length of the rod or lever KI (fig. 32) is to be regarded as the radius of the wheel, and the circle described by the hand its circumference. This form of the machine is called a windlass.
When great power, or great velocity is required, wheels and axles are often combined so as to impart motion to one another. The modes of combination are extremely various. Sometimes a strap or cord is placed in a groove in the circumference of an axle, and carried round a similar groove in the circumference of a wheel. This is called an endless band. But the most common mode of connecting two wheels, or a wheel and an axle, is to surround the circumference of both with teeth or cogs fitting into each other. In this case, the axles are usually
called pinions, and the teeth raised upon
them are called leaves. Thus, in the system represented in fig. 33, the power moves the wheel C; the axle of that wheel is a
Fig. 33. pinion whose leaves fit into the teeth of the wheel B, and set it in motion; the axle of the wheel B, again, imparts motion, in the same way, to the wheel A. Now, if the wheel A has p fifty teeth, and the pinion which drives it ten, the latter must evidently make five revolutions for every revolution of the former. The wheel B will therefore move five times as fast as the wheel A; and, on a similar supposition in regard to the wheel B and the pinion which drives it, the wheel C will be found to move five times as fast as the wheel B.
By this system, then we lose velocity and time, but gain power. It is clear however, that the arrangement might be reverscd, or