LAWS OF FALLING BODIES.
Since a body falls to the ground in consequence of the earth’s attraction on each of its molecules, it follows that, all other things being equal, all bodies, great and small, light and heavy, ought to fall with equal rapidity, and a lump of sand without cohesion should during its fall retain its original form as perfectly as if it were compact stone. The fact that a stone falls more rapidly than a feather is due solely to the unequal resistances opposed by the air to the descent of these bodies; in a vacuum all bodies fall with equal velocity.
In a vacuum, however, liquids fall like solids without separation of their molecules. The water-hammer, a model used in scientific schools, 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 metallic sound, resembling that which accompanies the shock of two solid bodies coming suddenly together.
Note.—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. See Parker’s Philosophy, pp. 69-70.
It has been ascertained, by experiment, that from rest, a body falling freely will descend 161⁄12 feet in the first second of time, and will then have acquired a velocity, which being continued uniformly, will carry it through 321⁄6 feet in the next second. Therefore if the first series of numbers be expressed in seconds, 1″, 2″, 3″, &c., the velocities in feet will be 321⁄6, 641⁄3, 961⁄2, &c.; the spaces passed through as 161⁄12, 641⁄3, 1443⁄4, &c., and the spaces for each second, 161⁄2, 481⁄4, 805⁄12, &c.
TABLE.
Showing the Relation of Time, Space and Velocity.
| Time in seconds of the body’s fall. | Velocity acquired at the end of that time. | Squares. | Space fallen through in that time. | Space. | Whole Space fallen through in the last second of the fall. |
|---|---|---|---|---|---|
| 1 | 32·16 | 1 | 16·08 | 1 | 16·08 |
| 2 | 64·33 | 4 | 64·33 | 3 | 48·25 |
| 3 | 96·5 | 9 | 144·75 | 5 | 80·41 |
| 4 | 128·66 | 16 | 257·33 | 7 | 112·58 |
| 5 | 160·83 | 25 | 402·08 | 9 | 144·75 |
| 6 | 193· | 36 | 579· | 11 | 176·91 |
| 7 | 225·17 | 49 | 788·08 | 13 | 209·08 |
| 8 | 257·33 | 64 | 1029·33 | 15 | 241·25 |
| 9 | 289·5 | 81 | 1302·75 | 17 | 273·42 |
| 10 | 321·66 | 100 | 1946·08 | 19 | 305·58 |
Experience has shown that the measurement of all physical quantities may be expressed in terms of three fundamental magnitudes. Those commonly chosen for this purpose are time, length and mass or quantity of matter. It may be assumed that our ideas of time and space are sufficiently exact for all practical purposes. The subject of matter, however, requires more particular consideration. Of the three magnitudes named, matter alone is directly cognizable by the senses, and invested with a variety of interesting properties.
For present purposes matter may be defined as anything that can be weighed, and the quantity of matter as proportional to its weight; i.e., its attraction towards the earth. The weight of a body is the force it exerts in consequence of its gravity, and is measured by its mechanical effects, such as bending a spring. We weigh a body by ascertaining the force required to hold it up, or to keep it from descending. Hence, weights are nothing more than measures of the force of gravity in different bodies.