Every-day Science: Volume 6. The Conquest of Nature

by Henry Smith Williams; Edward Huntington Williams

This practical knowledge no doubt sufficed for a vast number of generations of men who used the lever habitually, without making specific study of the relations between the force expended, the lengths of the two ends of the lever, and the weight raised. Such specific experiments were made, however, more than two thousand years ago by the famous Syracusan, Archimedes. He discovered—or if some one else had discovered it before him, he at least recorded and so gains the credit of discovery—the specific laws of the lever, and he also pointed out that levers, all acting on the same principle, may be different as to their practical mechanism in three ways.

First, the fulcrum may lie between the power and the weight, as in the case of the balance with which we were just experimenting. This is called a lever of the first class, and familiar illustrations of it are furnished by the poker, steelyard, or a pair of scissors. The so-called extensor muscles of the body—those for example, that cause the arm to extend—act on the bones in such a way as to make them levers of this first class.

The second type of lever is that in which the weight lies between the force and the fulcrum, as illustrated by the wheelbarrow, or by an ordinary door.

In the third class of levers the power is applied between weight and fulcrum, as illustrated by a pair of tongs, the treadle of a lathe, or by the flexor muscles of the arm, operating upon the bones of the forearm.

But in each case, let it be repeated, precisely the same principles are involved, and the same simple law of the relations between positions of power, weight, and fulcrum are maintained. The practical result is always that a weight of indefinite size may be moved by a power indefinitely long. If one arm of the lever is ten times as long as the other, the power of one pound will lift or balance a ten-pound weight; if the one arm is a thousand times as long as the other the power of one pound will lift or balance a thousand pounds. If the long arm of the lever could be made some millions of miles in length, the power that a man could exert would balance the earth.

How fully Archimedes realized the possibilities of the lever is illustrated in the classical remark attributed to him, that, had he but a fulcrum on which to place his lever, he could move the world. As otherwise quoted, the remark of Archimedes was that, had he a place on which to stand, he could move the world, a remark which even more than the other illustrates the full and acute appreciation of the laws of motion; since, as we have already pointed out, action and reaction being equal, the most infinitesimal push must be considered as disturbing even the largest body.

Tremendous as is the pull of gravity by which the earth is held in its orbit, yet the smallest push, steadily applied from the direction of the sun, would suffice ultimately to disturb the stability of our earth's motion, and to push it gradually through a spiral course farther and farther away from its present line of elliptical flight. Or if, on the other hand, the persistent force were applied from the side opposite the sun, it would suffice ultimately to carry the earth in a spiral course until it plunged into the sun itself. Indeed it has been questioned in modern times whether it may not be possible that precisely this latter effect is gradually being accomplished, through the action of meteorites, some millions of which fall out of space into the earth's atmosphere every day. If these meteorites were uniformly distributed through space and flying in every direction, the fact that the sun screens the earth from a certain number of them, would make the average number falling on the side away from the sun greater, and thus would in the course of ages produce the result just suggested. All that could save our earth from such a fate would be the operation of some counteracting force. Such a counteracting force is perhaps found in solar radiation. It may be added that the distribution of meteorites in space is probably too irregular to make their influence on the earth predicable in the present state of science; but the principle involved is no less sure.

WHEELS AND PULLEYS

Returning from such theoretical applications of the principle of motion, to the practicalities of every-day mechanisms, we must note some of the applications through which the principle of the lever is made available. Of these some of the most familiar are wheels, and the various modifications of wheels utilized in pulleys and in cogged and bevelled gearings. A moment's reflection will make it clear that the wheel is a lever of the first class, of which the axle constitutes the fulcrum. The spokes of the wheel being of equal length, weights and forces applied to opposite ends of any diameter are, of course, in equilibrium. It follows that when a wheel is adjusted so that a rope may be run about it, constituting a simple pulley, a mechanism is developed which gives no gain in power, but only enables the operator to change the direction of application of power. In other words, pound weights at either end of a rope passed about a simple pulley are in equilibrium and will balance each other, and move through equal distances in opposite directions.