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of the beam has two rods, by which is suspended the movable part, AB. In order to relieve the knife edge which supports the platform, and to avoid a shock when it is unloaded, after a weighing has been made, the arm, OR, is lifted by raising a support, r, which is below the beam, by means of the handle, M. The horizontality of the beam is ascertained by means of two indicators, m and n, the first fixed to the frame and the second to the beam.

To understand the working of the mechanism reference must be made to fig. 36, in which the principal pieces only are represented. A lever, ih, which bifurcates underneath the platform, rests at one end on a double knife edge, i, and at the other, on the lower end of the rod, Lh, which is fixed to the beam. A-second lever, eg, rests at s on the lever ih, attached at g to the rod ag, which is also supported by the beam. Lastly, the distance is being

the fifth of ih, aO is also a fifth of OL.

From this division of the two levers, ih and OL, into propor'tional parts two important consequences follow. First, that when the beam oscillates, the points a and g being lowered by a certain amount, the points L and h are lowered five times as much. But for a similar reason, since the lever ih oscillates upon the knife edge i, the knife edge s is lowered one-fifth as much as the point, h, and therefore just as much as g. The lever eg therefore descends parallel to itself, and therefore also the platform A.

Secondly it follows moreover, from the proportional division of the levers OL and ih, that the pressure at the points of suspension, exercised by the load g on the platform, is independent of the place which it occupies on the latter, so that it just acts as if it were applied along the rod ag. This may be deduced from the properties of the lever by a simple calculation, which cannot however be given here.

Lastly, since the weight is applied at a, the longer the arm of the lever OC as compared with Oa, the smaller need be the weight in the scale D, in order to produce equilibrium. In most weighing machines Oa is the tenth of OC. Hence the weights in the scale D represent one-tenth the weight of the body on the platform.

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51. Laws of falling bodies.-When bodies fall in a vacuumthat is, when they experience no resistance—their fall is subject to the following laws :

I. In a vacuum all bodies fall with equal rapidity.

II. The space which a falling body traverses is proportional to the square of the time during which it

has fallen; that is, that if the space traversed in a second is 16 feet, in two seconds it will be 64 feet; that is, 4 times as much, and in 3 seconds 9 times as much, or 144 feet, and so on.

III. The velocity acquired by a falling body is proportional to the duration of its fall; that is, that if the velocity at the end of a second is 16 feet, at the end of two seconds it is twice 16, or 32 feet, at the end of 3 seconds 48 feet, and so forth.

To demonstrate the first law by experiment a glass tube about two yards long (fig. 37) may be taken, having one of its extremities completely closed, and a brass cock fixed to the other. After having introduced bodies of different weights and densities (pieces of lead, paper, feather, &c.) into the tube, the air is withdrawn from it by an air-pump, and the cock closed. If the tube be now suddenly reversed, all the bodies will fall equally

Fig. 37.

quickly. On introducing a little air and again inverting the tube, the lighter bodies become slightly retarded, and this retardation increases with the quantity of air introduced.

It is, therefore, concluded that terrestrial attraction which is the cause to which the fall of bodies is due, is equally exerted on all substances, and that the difference in the velocity with which bodies fall is occasioned by the resistance of the air, which is more perceptible the smaller the mass of bodies and the greater the surface they present.

The resistance opposed by the air to falling bodies is especially remarkable in the case of liquids. The Staubbach in Switzerland is a good illustration; an immense mass of water is seen falling over a high precipice, but before reaching the bottom it is shattered by the air into the finest mist. In a vacuum, however, liquids fall like solids, without separation of their molecules. The water hammer illustrates this; the instrument consists of a thick glass tube about a foot long, half filled with water, the air having been expelled by ebullition previous to closing one extremity with the blow-pipe. When such a tube is suddenly inverted the water falls in one undivided mass against the other extremity of the tube, and produces a sharp dry sound, resembling that which accompanies the shock of two solid bodies.

The two other laws are verified by the aid of the inclined plane, and of Attwood's machine (fig. 40).

52. Inclined plane.-Any plane surface more or less oblique in

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reference to the horizon is an inclined plane. Such is the surface (fig. 38), and also that of an ordinary desk.

When a body rests on a horizontal plane, the action of gravitation is entirely counteracted by the resistance of this plane. This, however, is not the case when it is placed upon an inclined plane;

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Attwood's Machine.

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the action of gravity is then decomposed into two forces (25), one perpendicular to the inclined plane, that is, acting along its surface, and the other parallel to the plane. The only effect of the first force is to press the first on the plane without imparting to it any motion; while the second makes the body descend along the plane. This latter, however, is only one component of gravity; it is only a fraction, a third, or a quarter, according to the degree of inclination of the plane. Hence a body will roll down an inclined plane, but more slowly than if it fell vertically; and the velocity is indeed less the smaller the angle which the plane makes with the horizon.

53. Demonstration of the second law of falling bodies by the inclined plane.-The above property which the inclined plane possesses, of slackening the fall of bodies, has been used to demonstrate the second law of their fall (51), that the space traversed by a falling body is proportional to the square of the time during which it has been falling.

To make this experiment an inclined plane is taken, along which is traced a scale graduated in inches; then taking a well-polished ivory ball, a position is found by trial, at which it just takes a second to reach the bottom of the inclined plane A. Let us suppose that this is at the eleventh division. The experiment is then repeated by making the ball traverse four times the distance, that is, placing it at the forty-fourth division, and it will then be found to take two seconds in so doing. In like manner it will be found that, in passing through nine times the distance, or through ninety-nine divisions, three seconds are re

quired. Hence it is concluded, that the spaces traversed increase as the squares of the times.

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Fig. 39.

motion, H, regulated in the usual way by a seconds' pendulum, P.

On the right of the column is a graduated the spaces traversed by the falling bodies.

scale which measures Along this scale two

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