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TABLE ILLUSTRATING KEPLER'S THIRD LAW. (CHAMBERS.)
In the first column are the relative distances of the planets from the sun; in the second, the periodic times of the planets; and in the third, the squares of the periodic times divided by the cubes of the mean distances. The decimal points are omitted in the third column for convenience of comparison. The want of exact uniformity is doubtless due to errors in the observations.
Arago, speaking of Kepler's Laws, says: "These interesting laws, tested for every planet, have been found so perfectly exact, that we do not hesitate to infer the distances of the planets from the sun from the duration of their sidereal periods; and it is obvious that this method possesses considerable advantages in point of exactness."
These are the questions which the author has used in his own classes for review and examination. In the historical portion, he has "required his pupils to write articles upon the character and life of the various persons named, gathering materials from every attainable source. He has also introduced whatever problems the class could master, taking topics from the article on Celestial Measurements and the various mathematical treatises.
Introduction.—Define Astronomy. Is the earth a planet? What is the difference in the appearance of a fixed star and a planet? What is the Milky Way ?—HISTORY. What can you say of the antiquity of astronomy? How far back do the Chinese records extend? Name some astronomical phenomena they contain.
17. Why should the Chaldeans have become versed in this study? How ancient are their records? What discoveries did they make? What Grecian philosopher early acquired a reputation in this science? What other discovery did Thales make (Phil., p. 261)? What did he teach? What memorable eclipse did he predict? What were the names of two of his pupils? What did Anaximander teach?
18. Anaxagoras? What was his fate? In what century did Pythagoras live? What was his characteristic trait? Did he have any proof of his system? Explain his theory. How does it differ from ours? What strange views did he hold? What theory did Eudoxus advance?
19. What is the theory of the crystalline spheres? What has Hipparchus been styled? What addition did he make to astronomical knowledge? How many stars in our present catalogue (p. 228)? How did Egypt rank in science at an early day? What preparation did the Grecian philosophers make to fit themselves for teachers? How long did Pythagoras travel for this purpose? What can you say of the school at Alexandria? What great work did Ptolemy write there? What theory did he expound?