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added to account for the fact. Thus the system became more and more complicated, until a combination of nve cranks and circles was necessary to make the planet Mars keep pace with the Ptolemaic theory. No wonder that Alfonso, king of Castile, and a very celebrated patron of Astronomy, revolted at the cumbersome machinery, and cried out, "If I had been consulted at the creation, I could have done the thing better than that!"

Astrology.—After the death of Ptolemy, Astronomy ceased to be cultivated as a science. The Romans, engrossed with schemes of conquest, never produced a single great astronomer. Indeed, when Julius Csesar reformed the calendar, he obtained the assistance, not of a Soman, but of Sosigenes an Alexandrian. The Arabians studied the stars merely for purposes of soothsaying and prophecy. They professed to foretell the future by the appearance of the planets or stars. All of the ancient astronomers shared more or less in this superstition. Tiberius, emperor of Rome, practised Astrology. Hippocrates himself, the "Father of Medicine" who flourishes in the 4th century B. C, ranked it among the most important branches of knowledge for the physician. Star-diviners were held in the greatest estimation. The system continued to increase in credit until the Middle Ages, when it was at its height of popularity. The issue of any important undertaking, or the fortunes of an individual, were foretold by the astrologer, who drew up a Horoscope

representing the position of the stars and planets at the beginning of the enterprise, or at the birth of the person. It was a complete and complicated system, and contained regular rules, which guided the interpretation, and which were so abstruse that they required years for their entire mastery. Venus foretold love; Mars, war; the Pleiades,* storms at sea. The ignorant were not alone the dupes of this visionary system. Lord Bacon believed in it most firmly. As late even as the reign of Charles II., Lilly, a famous astrologer of that time, was called before a committee of the House of Commons to give his opinion on the probable issue of some enterprise then under consideration. However foolish the system of Astrology itself may have been, it preserved the science of Astronomy during the Dark Ages, and prompted to accurate observation and diligent study of the heavens.

The Copernican System.—About the middle of the sixteenth century, Copernicus, breaking away from the theory of Ptolemy, which was still taught in all the institutions of learning in Europe, revived the theory of Pythagoras. He saw how beautifully simple is the idea of considering the sun the grand centre about which revolve the earth and all the planets. He noticed how constantly, when we are riding swiftly, we forget our own motion, and think that the trees and fences are gliding by us in

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the contrary direction. He applied this thought to the movements of the heavenly bodies, and maintained that, instead of all the starry host revolving about the earth once in twenty-four hours, the earth simply turns on its own axis: that this produces the apparent daily revolution of the sun and stars; while the yearly motion of the earth about the sun, transferred in the same manner to that body, would account for its various movements. Though Copernicus thus simplified so greatly the Ptolemaic theory, he yet found that the idea of circular orbits for the planets would not explain all the phenomena; he therefore still retained the "cycles and epicycles" that Alfonso had so heartily condemned. For forty years this illustrious astronomer carried on his observations in the upper part of a humble, dilapidated farm-house, through the roof of which he had an unobstructed view of the sky. The work containing his theory was at last published just in time to be laid upon his death-bed.

Tycho Brahe, a celebrated Danish astronomer, next propounded a modification of the Copernican system. He rejected the idea of cycles and epicycles, but, influenced by certain passages of Scripture, maintained, with Ptolemy, that the earth is the centre, and that all the heavenly bodies revolve about it daily in circular orbits. Brahe was a nobleman of wealth, and, in addition, received large sums from the Government. He erected a magnificent observatory, and made many beautiful and rare instruments. 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 commenced 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.

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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

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