mathematician, allowing him at the same time to accept the 

 professorship of mathematics at Linz. 



Perhaps the greatest service rendered to science by the 

 Emperor Rudolph was bringing about the association of the 

 two astronomers Tycho Brahe and John Kepler; they were 

 unlike in disposition and mental gifts, yet their cooperation 

 proved most fruitful. Brahe had clung to the Ptolemaic 

 astronomy that made the earth the centre of the celestial 

 universe, but Kepler early accepted the theory of Copernicus 

 that placed the sun in the centre; Brahe had gathered an 

 immense number of careful, systematic observations with a 

 view to overthrowing the Copemican system, and Kepler 

 used these very facts to establish it. 



While in the service of Rudolph, Kepler wrote some of his 

 most valuable works; in the treatise on "Optrics and Di- 

 optrics" (1604) he explained the physics of the eye and the 

 action of lenses; in his "New Astronomy" (1609) he deter- 

 mined the elliptical orbit of the planets, since called Kepler's 

 First Law; in the same year he announced his discovery of 

 the rate at which the planets move (Kepler's Second Law); 

 but the third law, on the relation between the distances of 

 the planets from the sun and their periods of revolution about 

 it, was not promulgated until 1618, after the death of 

 Rudolph. These three laws have remained unchallenged as 

 absolute scientific truths and form the foundation of the 

 modern system of astronomy. The telescope, in the hands 

 of Galileo was marking a new era in astronomy, and Kepler 

 greatly improved it by inserting two convex lenses which 

 yielded a much larger field of view. The Rudolphine Tables 

 were not published until 1628, at the expense of Ferdinand, 

 who succeeded Matthias after his brief reign of seven years. 



Pecuniary embarrassments obliged Kepler to cast nativi- 

 ties for his friends, but his heart was never in the business 



86 



