CH. XII.

KEPLER'S THREE LAWS.

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of the planet A has the sun for one focus and the dot for the other, while the orbit of the planet в has the sun for one focus and the dot d for the other, and this makes the two orbits lie in a different di

rection. Kepler's first law,

then, was that planets move

in ellipses.

Kepler's Second Law,

1609. His second law was about the rate at which B planets move. He found

from Tycho's tables that they all moved more

FIG. 10.

FIG. II.

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m

quickly when they were near the sun than when they were far from it, and after an immense number of calculations he found the following rule. If you could draw a line from the sun to any planet on the first day of each month of the year, you would enclose a number of spaces, such as a, b, c, d, &c., in Fig. 11, and each of these spaces would be the same size, although not the same shape. For instance, the planet, when travelling from 1 to 2 near the sun, would go very quickly and pass over a number of miles,

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while when travelling from 6 to 7 it would go slowly and pass over comparatively few miles. And yet the space f will be exactly the same size as the space a, only it will be long and thin instead of short and broad. Kepler's

second law, therefore, was that planets describe equal areas about their centre in equal times.

Not many months after Kepler published these two laws, he heard of Galileo's discoveries with his telescope— that Jupiter had four satellites, and that Venus was proved to move round the sun by having phases like our moon. You may imagine how delighted he was to find the Copernican theory made so much more certain, and to see that the telescope was opening the way for so many new discoveries. Such a fit of wonder,' he said, 'seized me at this report, and I was thrown into such agitation, that between the joy of the friend who told me, my imagination, and the laughter of both, confounded as we were by such a novelty, we were hardly capable, he of speaking or I of listening.'

For many years after this Kepler was beset with troubles. The Emperor, being at war with his brother Matthias, had no money to spare for salaries. Kepler was thus harassed by poverty; his favourite son died of the small-pox, which the troops had brought into the city, and his wife died of grief not long afterwards. It was not till the year 1618, after he had re-married and had been rescued from his poverty by the new Emperor Matthias, that the unfortunate astronomer had energy and leisure to turn again to his favourite planets.

Kepler's Third Law, 1618.—It was in that year that he worked out with immense labour his third and most famous law-by which he showed how much longer the planets were going round the sun, according as they were farther off from it. This is difficult to understand, but we must try to form some idea of it. He did not know in figures how far each planet was from the sun, but he knew the proportion of their distances, as for example, that Mars is 4 times and

CH. XII. TYCHO BRAHE, Galileo, AND KEPLER. ΙΟΙ

Jupiter 13 times farther off from the sun than Mercury, and he also knew how long each one was in going round the sun, and from these two facts he worked the following rule.

If you take any two planets and cube their distances from the sun and then square the time each takes in going round the sun, the two squares of the time will bear the same proportion to each other as do the two cubes of the distance. For instance, Mars is 4 times as far from the sun as Mercury, and therefore it is 8 times as long going round it, because the cube of 4 (or 4 × 4 × 4) is 64, and the square of 8 (or 8 x 8) is also 64. Thus the cube of Mercury's distance as compared with that of Mars is 1 to 64, and the square of their periodic times of going round is also as 1 to 64. This law holds equally true of all the planets, and is expressed in scientific language thus: The squares of the periodic times of the planets are proportional to the cubes of their distances.

These three laws of Kepler were very great discoveries; especially the last one, which cost him years of labour and calculation. He was so astonished and delighted when he proved it, that he told a friend he thought at first it must be only a happy dream that he should have succeeded at last after so many failures.

After this Kepler wrote and published many books, but he made no more important discoveries. The Rudolphine Tables were at last published in 1628, and Kepler received a gold chain from the Grand Duke of Tuscany for his services to Astronomy; but still he could not obtain the payment of his salary, and money difficulties pressed upon him. His anxiety threw him into a violent. fever, and he died in 1630 at sixty years of age.

Work done in Science by Tycho Brahe, Galileo, and

Kepler. It will be instructive to notice here how very different these three astronomers, Tycho, Galileo, and Kepler were, and yet how they each did their own part to add to our knowledge. Tycho was a man who collected facts his work was dry, and his tables a mass of figures, such as most people would think very uninteresting; yet if Tycho had not spent his life in this dry conscientious work, Kepler could never have discovered his laws. Galileo was a warmhearted enthusiastic observer: he loved the beauty of the heavens, and knew how to make others love it too; every observation he made he told in popular language to the world, and taught people the truth of the Copernican theory by showing them plainly how they could prove it for themselves, if they chose to look at the heavens. Kepler was quite different from either Tycho or Galileo; he was a mathematician, and worked everything out in his own brain by accurate methods. He took Tycho's observations, which he knew were true, and turned them this way and that way, working out now one calculation, now another, and always throwing them aside if they were not exactly true. He spent years over his attempts, but it was worth while, for he arrived at three true laws, which will remain for ever. There was only one point he had not reached; he knew that his laws were true, but he did not know why they were true. This was left for Newton to demonstrate nearly fifty years afterwards.

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Chief Works consulted. -Brewster's 'Martyrs of Science;' Herschel's Astronomy;' Denison's 'Astronomy without Mathematics;' Airy's 'Popular Astronomy;' Drinkwater's Life of Kepler;' Baden Powell's 'History of Natural Philosophy.'

CH. XIII. FRANCIS BACON.-' NOVUM ORGANUM. 103

CHAPTER XIII.

SCIENCE OF THE SEVENTEENTH CENTURY (CONTINUED). Francis Bacon, 1561-1626-He teaches the true method of studying Science in his 'Novum Organum'-René Descartes, 1596-1650-He teaches that Doubt is more honest than Ignorant Assertion— Willebrord Snellius discovers the Law of Refraction, 1621Explanation of this Law.

Bacon's Influence upon Science. Although this book is a history of scientific discovery and not of philosophy, yet we must now mention in passing two philosophers who lived about this time, and whose writings had great influence upon science. These were Francis Bacon in England, and René Descartes in France.

Francis Bacon, commonly known as Lord Bacon, was born in London in 1561, and died in 1626. He was made Lord Chancellor of England in 1618, in the reign of James I., with the title of Lord Verulam and afterwards Viscount St. Alban's, and was a great political character. Bacon devoted much of his time to science, and, like his namesake Roger Bacon in the fifteenth century, he seems to have foreseen many of the discoveries which were afterwards made. But his most useful work was a book called the 'Novum Organum,' or 'New Method,' published in 1620, in which he sketched out very fully how science ought to be studied. He insisted that no knowledge can be real but that which is founded on experience, and that the only