Figs. 15 and 16.
A body falling, then, descends sixteen feet in the first second, and for every succeeding second it assumes a greater velocity. The distance the body travels has been calculated, and the space it passes through has been found to increase in proportion to the square of the time it takes to fall. For instance, suppose you drop a stone from the top of a cliff to the beach, and it occupies two seconds in falling, if you multiply 2 × 2, and the result by sixteen, you will find how high the cliff is: in this (supposed) case it is (omitting decimals) sixty-four feet high. The depth of a well can also be ascertained in the same way, leaving out the effect of air resistance.
But if we go up into the air, the force of gravity will be diminished. The attraction will be less, because we are more distant from the centre of the earth. This decrease is scarcely, if at all, perceptible, even on very high mountains, because their size is not great in comparison with the mass of the earth’s surface. The rule for this is that gravity decreases in proportion to the square of the distance. So that if at a certain distance from the earth’s surface the force of attraction be 1, if the distance be doubled the attraction will be only one quarter as much as before—not one-half.
Gravity has exactly the same influence upon all bodies, and the force of the attraction is in proportion to the mass. All bodies of equal mass will fall in the same time in a given distance. Two coins (or a coin and a feather in vacuo) will fall together. But in the air the feather will remain far behind the coin, because nearly all the atoms of the former are resisted by the air, while in the coin only some particles are exposed to the resistance, the density of the latter preventing the air from reaching more than a few atoms, comparatively speaking. The theory of weight and gravitation, and experiments relating to the falling of bodies, may be easily demonstrated with ordinary objects that we have at hand. I take a halfpenny and a piece of paper, which I cut in the shape of the coin, and holding them side by side, I drop them simultaneously; the halfpenny reaches the ground some time before the paper, a result quite in accordance with the laws of gravitation, as one must bear in mind the presence of air, and the different resistance it offers to two bodies differing in density. I next place the paper disc on the upper surface of the piece of money, and then drop them simultaneously. The two objects now reach the ground at the same time, the paper, in contact with the halfpenny, being preserved from the action of the air. This experiment is so well known that we need not further discuss it; but it must be plainly evident that it is capable of development in experiments on phenomena relating to falling bodies.[7] When a body influenced by the action of a force acts, in its turn, upon another, the latter reacts in an opposite manner upon the first, and with the same intensity.
The Attraction of Cohesion is the attraction of particles of bodies to each other at very small distances apart. Cohesion has received various names in order to express its various degrees. For instance, we say a body is tough or brittle, or soft or hard, according to the degrees of cohesion the particles exercise. We know if we break a glass we destroy the cohesion; the particles cannot be reunited. Most Liquid particles can be united, but not all. Oil will not mix with water.
The force of cohesion depends upon heat. Heat expands everything, and the cohesion diminishes as temperature increases.
There are some objects or substances upon the earth the particles of which adhere much more closely than others, and can only, with very great difficulty, be separated. These are termed Solids. There are other substances whose particles can easily be divided, or their position altered. These are called Fluids. A third class seem to have little or no cohesion at all. These are termed Gases.
Adhesion is also a form of attraction, and is cohesion existing on the surfaces of two bodies. When a fluid adheres to a solid we say the solid is wet. We turn this natural adhesion to our own purposes in many ways,—we whitewash our walls, and paint our houses; we paste our papers together, etc.