Fig. 13.
a. The centre ball, representing the earth's centre of gravity. w w w w. Four wires fixed into centre ball, and passing through and secured in the hoop, projecting about one foot from the circumference. b b b b. Two balls—a model ship and toy—working on the wires like beads, with vulcanized India-rubber straps attached to them and the circumference of the hoop.
With this simple apparatus we may illustrate the upward, downward, and sideway movement of bodies from the earth, and the counteraction by the force of gravitation of any tendency of matter to fall away from the globe, which is represented in the model by the india-rubber springs pulling the balls and toys back again to the circumference of the hoop.
The attraction of gravitation decreases (quoting the remainder of Newton's definition) as the squares of the distances which separate the particles increase—i.e., it obeys the principle called "inverse proportion"—viz., the greater the distance, the less gravitating power; the less the distance, the greater the power of gravitation. Gravitation is like the distribution of light and other radiant forces, and may be thus illustrated.
Fig. 14.
Place a lighted candle, marked a, at a certain distance from No. 1, a board one foot square; at double the distance the latter will shadow another board, No. 2, four feet square; at three times, No. 3, nine feet square; at four, No. 4, sixteen feet; and so on.
To make the comparison between the propagation of light and the attraction of gravitation, we have only to imagine the candle, a, to represent the point where the force of gravity exists in the highest degree of intensity; suppose it to be the sun—the great centre of this power in our planetary system. A body, as at No. 1, at any given distance will be attracted (like iron-filings to a magnet) with a certain force; at twice the distance, the square of two being four, and by inverse proportion, the attraction will be four times less; at thrice the distance, nine times less; at the fourth distance, sixteen times less; and so on. With the assistance of this law, we may calculate, roughly, the depth of a well, or a precipice, or a column, by ascertaining the time occupied in the fall of a stone or other heavy substance. A falling body descends about 16 feet in one second, 64 feet in two seconds, 144 feet in three seconds, 256 feet in four seconds, 400 feet in five seconds, 576 feet in six seconds; the spaces passed over being as the squares of the times.
Suppose a stone takes three seconds in falling to the surface of the water in a well, then 3 × 3 = 9 × 16 = 144 feet would be a rough estimate of the depth. The calculation will exceed the truth in consequence of the stone being retarded in its passage by the resistance of the air.