CH. XIL TYCHO BRAHE, GALILEO, <Sr KEPLER. 99 



the sun, the two squares of the time will bear the same pro- 

 portion to each other as do the two cubes of the distance. 

 For instance, Mars is 4 times as far from the sun as Mer- 

 cury, and therefore it is 8 times as long going round it, 

 because the cube of 4 (or 4 x 4 x 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 i to 64, and the 

 square of their periodic times of going round is also as i 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 

 had 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 ser- 

 vices to Astronomy ; but still he could not obtain the pay- 

 ment 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 were a mass of figures, 

 such as most people would think very uninteresting ; yet if 

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