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 BRAHÉ, 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. Brahé 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 in

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 Brahé, 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 Brahé, 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 Brahé 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.

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.

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

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 C

Fig. 3.

very rapidly; yet the space inclosed between the lines SB and SA is equal to that inclosed between SD and SC. 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 Brahé, 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,