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struments. Clad in his robes of state, he watched the heavens with the intelligence of a philosopher and the splendor of a king. His indefatigable industry and zeal resulted in the accumulation of a vast fund of astronomical knowledge, which, however, he lacked the wit to apply to any further advance in science. His pupil, Kepler, saw these facts, and in his fruitful mind they germinated into three great truths, called Kepler's laws. These constitute almost the sum of astronomical knowledge, and form one of the most precious conquests of the human mind. They are the three arches of the bridge over which Astronomy crossed the gulf between the Ptolemaic and Copernican systems.

Kepler's Laws.—Kepler, taking the investigations of his master, Tycho Brahe, determined to find what is the exact shape of the orbits of the planets. He adopted the Copernican theory, that the sun is the centre of the system. At that time all believed the orbits to be circular. Since, as they said, the circle is perfect, is the most beautiful figure in nature, has neither beginning nor ending, therefore it is the only form worthy of God, and He must have used it for the orbits of the worlds He has made. Imbued with this romantic view, Kepler commeitced with a rigorous comparison of the places of the planet Mars, as observed by Brahe, with the places as stated by the best tables that could be computed on the circular theory. For a time they agreed, but in certain portions of the orbit the observations of Brahe would not fit the computed place by eight minutes of a degree. Believing that so good an astronomer could not be mistaken as to the facts, Kepler exclaimed, "Out of these eight minutes we will construct a new theory that will explain the movements of all planets." He resumed his work, and for eight years continued to imagine every conceivable hypothesis, and then patiently to test it—"hunt it down," as he called it. Each in turn proved false, until nineteen had been tried. He then determined to abandon the circle and adopt another form. The ellipse suggested itself to his mind. Let us see how this figure is made.

Pig. 2.

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Attach a thread to two pins, as at F F in the figure; next move a pencil along with the thread, the latter being kept tightly stretched, and the point will mark a curve which is flattened in proportion 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. 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

First Law.—With this figure he 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 by 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

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Fig. 3.

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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 Law.—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 from 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,

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

The Squares Of The Times Of Reyolution 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 - d represent the same in another planet, we have the proportion V: D" :: p': (f.

f 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.

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