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.
Again, Gravitation, the most feeble of physical actions between small masses, is almost imperceptible; yet it is an energy abundant in proportion to the quantity of matter in the universe, and fully competent, by its gradual condensing agency, to account for the origination of planetary systems and their movements. It is not strange, therefore, that by some physicists this energy is supposed to be the beginning of that of which all other forms of force are residues or metamorphoses. Gravity is the name especially given to its terrestrial manifestations. A particle or body without a sphere or spheroid, solid or hollow, is attracted to the center of the mass of such body; within a hollow sphere, it will remain at rest at any point. At different depths below the earth’s surface, a body will be attracted with a force diminishing as the distance from its center decreases. The slight variation in the gravitating force of the same falling body at different heights is in practice usually disregarded. The weight of a body, as the measure of its gravitating tendency, must vary both with mass and with the force acting on it; hence, from the form of the earth, the same body at the sea level will weigh less and less as it is removed from either pole toward the equator. An elevation above the sea level gives a like result. A stone falls through a less distance in a given time on a mountain than in the valley below, less at the equator than at either pole. The loss of weight in these cases cannot be tested by lever scales, in which this loss is equal on both sides; but it may be by the spring balance, in which bodies are weighed by the pull they exert against the elasticity of a coiled wire. The effect of centrifugal force, increasing from the pole to the equator, co-operates with increasing removal from the earth’s center to lessen weight; the result of the combined action of these two causes is, that a body weighing 195 lbs. at either pole will weigh but 194 over the equator. The line of a falling body, called also the line of direction, is interesting as being that direction in space at any point of the earth’s surface with reference to which all other directions are named, and by which they are to be determined.
A few points remain to be named. The flow of water is the result of the force of gravity; the importance of this fact and its wide influence cannot be over stated; the gently falling dew, the mighty currents in the unfathomable depths of the ocean, as well as the rivulet merrily falling over the rocks to a lower level are all subject to the laws of terrestrial gravity.
The upper surface of a liquid in a vessel exposed to the atmosphere is called the free surface and is pressed downwards by the air under about 15 lbs. pressure per square inch. The free surface of a small body of a perfect liquid, at rest, is horizontal and perpendicular to the action of gravity although in large bodies of liquid, as lakes and ponds, the free surface is spherical, assuming the curvature of the earth’s surface.