and waited for months, until, once more, his patience triumphed, and he reached the third law

THE SQUARES OF THE TIMES OF REVOLUTION OF THE PLANETS ABOUT THE SUN, ARE PROPORTIONAL TO THE CUBES OF THEIR MEAN DISTANCES FROM THE SUN.*

In rapture over the discovery of these three laws, so marked by that divine simplicity which pervades all the laws of nature, Kepler exclaimed, "Nothing holds me. The die is cast. The book is written, to be read now or by posterity, I care not which. It may well wait a century for a reader, since God has waited six thousand years for an observer."+

Galileo.-Contemporary with Kepler was the great Florentine philosopher, Galileo. He discovered the laws of the pendulum and of falling bodies, as we have already learned in Natural Philosophy. He, however, was educated in and believed the Ptolemaic theory. A disciple of the Copernican theory happening to come to Pisa, where Galileo was teaching

* For example: The square of Jupiter's period is to the square of Mars' period, as the cube of Jupiter's distance is to the cube of Mars' distance; or, representing the earth's time of revolution by P, and her distance from the sun by p, then letting D and d represent the same in another planet, we have the proportion P: D' :: p3: ď3.

Kepler, strangely enough, believed in the "Music of the Spheres." He made Saturn and Jupiter take the bass, Mars the tenor, Earth and Venus the counter, and Mercury the treble. This shows what a streak of folly or superstition may run through the character of the noblest man. However, as Johnson says, a mass of metal may be gold, though there be in it a little vein of tin.

as professor in the University, drew his attention to its simplicity and beauty. His clear discriminating mind perceived its perfection, and he henceforth advocated it with all the ardor of his unconquerable zeal. Soon after he learned that one Jansen, a Dutch watchmaker, had invented a contrivance for making distant objects appear near. With his profound knowledge of optics and philosophical instruments, Galileo instantly caught the idea, and soon had a telescope completed that would magnify thirty times. It was a very simple affair-only a piece of lead pipe with glasses set at each end; but it was the first telescope ever made, and destined to overthrow the old Ptolemaic theory, and revolutionize the whole science of Astronomy.

Discoveries made with the telescope.-Galileo now examined the moon. He saw its mountains and valleys, and watched the dense shadows sweep over its plains. On January 8, 1610, he turned the telescope toward Jupiter. Near it he saw three bright stars, as he considered them, which were invisible to the naked eye. The next night he noticed that those stars had changed their relative positions. Astonished and perplexed, he waited three days for a fair night in which to resume his observations. The fourth night was favorable, and he again found the three stars had shifted. Night after night he watched them, discovered a fourth star, and finally found that they were all rapidly revolving around Jupiter, each in its elliptical orbit, with its own rate

of motion, and all accompanying the planet in its journey around the sun. Here was a miniature Copernican system, hung up in the sky for all to see and examine for themselves.

Reception of the discoveries.-Galileo met with the most bitter opposition. Many refused to look through the telescope lest they might become victims of the philosopher's magic. Some prated of the wickedness of digging out valleys in the fair face of the moon. Others doggedly clung to the theory they had held from their youth up. As a specimen of the arguments adduced against the new system, the following by Sizzi is a fair instance. "There are seven windows in the head, through which the air is admitted to the body, to enlighten, to warm, and to nourish it,-two nostrils, two eyes, two ears, and one mouth. So in the heavens there are two favorable stars, Jupiter and Venus; two unpropitious, Mars and Saturn; two luminaries, the Sun and Moon; and Mercury alone, undecided and indifferent. From which, and from many other phenomena of Nature, such as the seven metals, etc., we gather that the number of planets is necessarily seven. Moreover, the satellites are invisible to the naked eye, can exercise no influence over the earth, and would be useless, and therefore do not exist. Besides, the week is divided into seven days, which are named from the seven planets. Now, if we increase the number of planets, this whole system falls to the ground."

NEWTON. As we have seen, the truth of the Co

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 22, 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 miles 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, i. e., 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. Disap