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to the length of the string we use,—the longer the string, the nearer a circle will the figure become. This figure is the ellipse. The two points F F are called the foci (singular, focus). We can now understand Kepler's attempt, and the glorious triumph which crowned his seventeen years of unflagging toil
First Law.—With this figure be constructed an orbit, having the sun at the centre, and again followed the planet Mars in its course. But very soon there was as great discrepancy between the observed and computed places as before. Undismayed by this failure, Kepler assumed another hypothesis. He determined to place the sun at one of the foci of the ellipse, and once more "hunted down" the theory. For a whole year he traced the planet along the imaginary orbit, and it did not diverge. The truth was discovered at last, and Kepler announced his first great law—
Planets Revolve In Ellipses, With The Sun At One Focus.
Second Law.—Kepler knew that the planets do not move with equal velocity in the different parts of their orbits. He next set about establishing some law 1 y which this speed could be determined, and the place of the planet computed. He drew an ellipse, and marked the various positions of the planet Mars once more. He soon found that when at its 'perihelion (point nearest the sun) it moves the fastest, but when at its aphelion (point furthest from the sun) it moves the slowest. Once more he "hunted down" various hypotheses, until at last he discovered that while in going from B to A the planet moves very slowly, and from D to 0
very rapidly; yet the space inclosed between the lines SB and SA is equal to that inclosed between S D and S C. Hence the second law—
A LINE CONNECTING THE CENTRE OF THE EARTH WITH THE CENTRE OF THE SUN, PASSES OVER EQUAL SPACES IN EQUAL TIMES.
Third Laiv.—Kepler, not satisfied with the discovery of these laws, now determined to ascertain if there were not some relation existing between the times of the revolution of the planets about the sun and their distances frdm that body. With the same wonderful patience, he took the figures of Tycho Brahe, and began to compare them. He tried them in every imaginable relation. Next he took their squares, then he attempted their cubes, and lastly he combined the squares and the cubes. Here was the secret; but he toiled around it, made a blunder, 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, "t
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 i represent the same in another planet, we have the proportion P*: D' :: p% : cC.
t 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 JohnBon 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