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.
RULES RELATING TO THE VELOCITY OF FALLING BODIES.
1.—To find the Velocity a falling Body will acquire in any given time.
Multiply the time, in seconds, by 321⁄6, and it will give the velocity acquired in feet, per second.
Example. Required the velocity in seven seconds.
321⁄6 × 7 = 2251⁄6 feet. Ans.
2.—To find the Velocity a Body will acquire by falling from any given height.