SCIENCE AS MEASUREMENT 91 



the astronomer's assistant, to the Bohemian capital 

 in 1600 and in a few months fell heir to Tycho's 

 data in reference to 777 stars, which he made the 

 basis of the Rudolphine tables of 1627. Kepler's 

 genius was complementary to that of his predecessor. 

 He was gifted with an imagination to turn observa- 

 tions to account. His astronomy did not rest in mere 

 description, but sought the physical explanation. He 

 had the artist's feeling for the beauty and harmony, 

 which he divined before he demonstrated, in the 

 number relations of the planetary movements. After 

 special studies of Mars based on Tycho's data, he set 

 forth in 1609 (Astronomia Novct) (1) that every 

 planet moves in an ellipse of which the sun occupies 

 one focus, and (2) that the area swept by the ra- 

 dius vector from the planet to the sun is proportional 

 to the time. Luckily for the success of his investi- 

 gation the planet on which he had concentrated his 

 attention is the one of all the planets then known, 

 the orbit of which most widely differs from a circle. 

 In a later work {Harmonica Mundi, 1619) the title 

 of which, the Harmonics of the Universe, proclaimed 

 his inclination to Pythagorean views, he demon- 

 strated (3) that the square of the periodic time of 

 any planet is proportional to the cube of its mean 

 distance from the sun. 



Kepler's studies were facilitatejijby the invention, 

 in 1614 by John Napier, of f logarithm!, which have 



v A V^ ^J 



been said, by abridging tedious-calculations, to dou- 

 ble the life of an astronomer. About the same time 

 Kepler in purchasing some wine was struck by the 

 rough-and-ready method used by the merchant to de- 

 termine the capacity of the wine-vessels. He applied 



