Fig. 135.
206. Reflection of Motion.—If an elastic body be thrown perpendicularly upon a surface it rebounds in the same path in which it is thrown. But if it hit the surface obliquely it is thrown off or reflected in a different direction. Thus a ball thrown from b upon c, Fig. 135 (p. 158), will return in the line drawn to b. But if it be thrown from d it will be reflected in the line c a. Now the angle d c b, called the angle of incidence, is always equal to b c a, the angle of reflection. The same, you will find in other parts of this book, is true of sound and light and heat.
207. Uniformity of Motion.—Since motion, when once begun, is disposed to continue unless arrested by obstacles, it is naturally uniform both in its velocity and its direction. I will speak now only of velocity. Suppose a body to be set in motion, and to meet with no opposition from friction, or the resistance of air, or attraction, it would move on forever, and with the same velocity with which it began. Now precisely these circumstances we have in the motion of the heavenly bodies in their orbits. They are, it is true, under the influence of attraction, but in such a way, as you will soon see, as not to interfere with the uniformity of their motion. Were it not for this uniformity we should have no regularity of times and seasons. It is only by the uniform motion of the earth round the sun, and round its own axis, that we can calculate for to-morrow, or next week, or next year. If these motions were irregular it would throw confusion into all our calculations for the future and all our recollections of the past. We can measure time by nothing else but regular motion, and were there no regular motion we should have merely the very inaccurate measure furnished by our sensations. To measure time with accuracy we take some great and extensive uniform motion as our standard. Thus, the revolution of the earth around the sun we take as one division of time, and call it a year. We observe that during this time it whirls around on its own axis 365 times, and the time occupied by each of these revolutions we call a day.
208. The Pendulum.—Various modes of measuring time have been adopted by mankind. At first time was inaccurately divided by merely observing the sun. But after a while man resorted to various contrivances to measure short periods of time with accuracy. All of these depend upon the uniformity of motion alone. The sun-dial measures time by the uniform movement of the shadow on its face, caused by the uniform movement of the earth in relation to the sun. The hour-glass measures time by the uniform fall of sand produced by the attraction of gravity. The best measurement of time is by the comparatively modern invention of clocks and watches, in which time is divided into very minute periods by the uniform motion of the pendulum or the balance-wheel. The pendulum furnishes an interesting example of motion kept up by the influence of gravity. It was not till the time of Galileo, less than three centuries ago, that its operation was understood and appropriated to the measurement of time. He observed that chandeliers hanging from lofty ceilings vibrated very long and uniformly after they were accidentally agitated, and the thought of the philosopher evolved from this phenomenon the most important results. Though it had been before men's eyes in some shape or other since the creation, it was reserved for Galileo to observe its significance, and the result is that the pendulum has become man's time-keeper over the whole earth.
Fig. 136.
209. Explanation of its Operation.—A pendulum consists commonly of a ball or weight at the end of a rod suspended so as to vibrate with little friction at the point of the suspension. Let a b, Fig. 136, represent such a pendulum. When it is at rest it makes a plumb-line hanging toward the centre of the earth. If it be raised to c and be left to fall, the force of gravity will not only carry it to b, but, by the accelerated velocity or accumulated momentum which it gives it in its descent, it will carry it to d. The same would be true of its return from d. And it would vibrate forever in this way if it could be entirely freed from the resistance of the air and friction. But, as it is, the pendulum left to itself gradually loses its motion from these obstacles. In the common clock the office of the weight is to counteract the influence of these obstacles, and keep the pendulum vibrating. In the watch the mainspring performs the same office to the balance-wheel.
Fig. 137.
The times of the vibrations of a pendulum are nearly equal whether the arc it describes be great or small. For when the vibration is a large one the velocity which the pendulum acquires in falling is greater than when the vibration is of small extent. The reason is that the higher it rises the more steep is the beginning of its descent. Thus a c, Fig. 137, is steeper than c b.