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

by Henry Smith Williams; Edward Huntington Williams

It is obvious all along, of course, since action and reaction are equal, that all of the relations in question are reciprocal. When, for example, we speak of a pound weight on the long end of a lever balancing a ten-pound weight on the short end, it is equally appropriate to speak of the ten-pound weight as balancing the one-pound weight. Similarly, when power is applied to the lever, it may be applied at either end. Ordinarily, to be sure, the power is applied at the long end, since the object is to lift the heavy weight; but in complicated machinery it quite as often happens that these conditions are reversed, and then it becomes desirable to apply strong power to the short end of the lever, in order that the relatively small weight may be carried through the long distance. In the inter-relations of gearing wheels, such conditions very frequently obtain, practical ends being met by a series of wheels of different sizes. But the single rule, already so often outlined, everywhere holds—wherever there is gain of power there is loss of distance, and we can gain distance only by losing power. The words gain and loss in this application are in a sense misnomers, since, as we have already seen, gain and loss are only apparent, but their convenience of application is obvious.

A familiar case in which there is first loss of speed and gain of power, and then gain of speed at the expense of power in the same mechanism, is furnished by the bicycle, where (1) the crank shaft turns the sprocket wheel that constitutes a lever of the second class with gain of power; where (2) power is further augmented through transmission from the relatively large sprocket wheel to the small sprocket of the axle; and where (3) there is great loss of power and corresponding gain of speed in transmitting the force from the small sprocket wheel at the axle to the rubber rim of the bicycle proper, this last transmission representing a lever of the third class. The net gain of speed is tangibly represented by the difference in distance traversed by the man's feet in revolving the pedals, and the actual distance covered by the bicycle.

INCLINED PLANES AND DERRICKS

A less obvious application of the principle of reciprocal equivalence of distance and weight is furnished by the inclined plane, a familiar mechanism with the aid of which a great gain of power is possible. The inclined plane, like the lever, has been known from remotest antiquity. Its utility was probably discovered by almost the earliest builders. Diodorus Siculus tells us that the great pyramids of Egypt were constructed with the aid of inclined planes, based on a foundation of earth piled about the pyramids. Diodorus, living at a period removed by some thousands of years from the day of the building of the pyramids, may or may not have voiced and recorded an authentic tradition, but we may well believe that the principle of the inclined plane was largely drawn upon by the mechanics of old Egypt, as by later peoples.

The law of the inclined plane is that in order to establish equilibrium between two weights, the one must be to the other as the height of the inclined plane is to its length. The steeper the inclined plane, therefore, the less will be the gain in power; a mechanical principle which familiar experience or the simplest experiment will readily corroborate.

In its elemental form the inclined plane is not used very largely in modern machinery, but its modified form of the wedge and the screw have more utility. The screw, indeed, which is obviously an inclined plane adjusted spirally about a cylinder or a cone, is familiar to everyone, and is constantly utilized in applying power.

The crane or derrick furnishes a familiar but relatively elaborate illustration of a mechanism for the transmission of power, in which all the various devices hitherto referred to are combined, without the introduction of any new principle.

Derricks have been employed from a very early day. The battering-rams of the ancient Egyptians and Babylonians, for example, were virtually derricks; and no doubt the same people used the device in raising stones to build their temples and city walls, and in putting into position such massive sculptures as the obelisks of Egypt and the monster graven bulls and lions of Nineveh and Babylon.