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pernican system was fully established by the discoveries of Galileo with his telescope. Philosophers gradually adopted this view, and the Ptolemaic theory became a relic of the past. In 1666, Newton, a young man of twenty-four years, was spending a season in the country, on account of the plague which prevailed at Cambridge, his place of residence. One day, while sitting in a garden, an apple chanced to fall to the ground near him. Reflecting upon the strange power that causes all bodies thus to descend to the earth, and remembering that this force continues, even when we ascend to the tops of high mountains, the thought occurred to his mind, "May not this same force extend to a great distance out in space? Does it not reach the moon?"

Laws of Motion.—To understand, the philosophy of the reasoning that now occupied the mind of Newton, let us apply the laws of motion as we have learned them in Philosophy. When a body is once set in motion, it will continue to move forever in a straight line, unless another force is applied. As there is no friction in space, the planets do not lose any of their original velocity, but move now with the same speed which they received in the beginning from the Divine hand. But this would make them all pass through straight, and not circular orbits. What causes the curve? Obviously another force. For example: I throw a stone into the air. It moves not in a straight line, but in a curve, because the earth constantly bends it downward.

Application.—Just so the moon is moving around the earth, not in a straight line, but in a curve. Can it not be that the earth bends it downward, just as it does the stone? Newton knew that a stone falls toward the earth sixteen feet the first second. He imagined, after a careful study of Kepler's laws, that the attraction of the earth diminishes according to the square of the distance. He knew (according to the measurement then received) that a body on the surface of the earth is four thousand miles from the centre. He applied this imaginary law. Suppose it is removed four thousand miles from the surface of the earth, or eight thousand miles from the centre. Then, as it is twice as far from the centre, its weight will be diminished 2J, or 4 times. If it were placed 3, 4, 5, 10 times further away, its weight would then decrease 9, 16, 25, 100 times. If, then, the stone at the surface of the earth (four thousand miles from the centre) falls sixteen feet the first second, at eight thousand mile3 it would fall only four feet; at 240,000 miles, or the distance of the moon, it would fall only about one-twentieth of an inch (exactly .053). Now the question arose, "How far does the moon fall toward the earth, t. c, bend from a straight line, every second?" For seventeen years, with a patience rivalling Kepler's, this philosopher toiled over interminable columns of figures to find how much the moon's path around the earth curves each second. He reached the result at last. It was nearly, but not quite exact. Disavpointed, he laid aside his calculations. Repeatedly he reviewed them, but could not find a mistake. At length, while in London, he learned of a new and more accurate measurement of the distance from the circumference to the centre of the earth. He hastened home, inserted this new value in his calculations, and soon found that the result would be correct. Overpowered by the thought of the grand truth just before him, his hand faltered, and he called upon a friend to complete the computation.

From the moon, Newton passed on to the other heavenly bodies, calculating and testing their orbits. At last he turned his attention to the sun, and, by reasoning equally conclusive, proved that the attraction of that great central orb compels all the planets to revolve about it in elliptical orbits, and holds them with an irresistible power in their appointed paths. At last he announced this grand Law of Gravitation:



We now in imagination pass into space, which stretches out in every direction without bounds or measures. We look up to the heavens and try to locate some object among the mazes of the stars. We are bewildered, and immediately feel the necessity of some system of measurement. Let us try to understand the one adopted by astronomers.

The Celestial Sphere.—The blue arch of the sky, as it appears to be spread above us, is termed the Celestial Sphere. There are two points to be noticed here. First, that so far distant is this imaginary arch from us, that if any two parallel lines from different parts of the earth are drawn to this sphere, they will apparently intersect. Of course this cannot be the fact; but the distance is so immense, that we are unable to distinguish the little difference of four or even eight thousand miles, and the two lines will seem to unite: so we must consider this great earth as a mere speck or point at the centre of the Celestial Sphere. Second, that we must even neglect the entire diameter of the earth's orbit, so that if we should draw two parallel lines, one from each end of the earth's orbit, to the sphere, although these lines would be 183,000,000 miles apart, yet they would be extended so far that we could not separate them, and they would appear to pierce the sphere at the same point; which is to say, that at that enormous distance, 183,000,000 miles shrink to a point. Consequently, in all parts of the earth, and in every part of the earth's orbit, we see the fixed stars in the same place. This sphere of stars surrounds the earth on every side. In the daytime we cannot see the stars because of the superior light of the sun; but with a telescope they can be traced, and an astronomer will find certain stars as well at noon as at midnight. Indeed, when looking at the sky from the bottom of a deep well or lofty chimney, if a bright star happens to be directly overhead, it can be seen with the naked eye even at midday. In this way it is said a celebrated optician was first led to think of there being stars by day as well as by night. One half of the sphere is constantly visible to us; and so far distant are the stars, that we see just as much of the sphere as we would if the upper part of the earth were removed, and we were to stand four thousand miles further away, or at the very centre of the earth, where our view would be bounded by a great circle of the earth. On the concave surface of the celestial sphere there are imagined to be drawn three systems of circles: the HoriZon, the Equinoctial, and the Ecliptic Systems. Each of these has (1) its Principal Circle, (2) itg Subordinate Circles, (3) its Points, and (4) its Measurements.

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