CH. xii. TYCHO BRAHE, GALILEO, AND KEPLER. 101 



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 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, be- 

 cause 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 dis- 

 tance 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 

 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 Rudolph- 

 ine 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 ob- 

 tain 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 



