44 GREAT MEN OF SCIENCE 



over this discovery was of short duration. The agreement 

 with reahty as known through Tycho's observations was 

 certainly better than hitherto, but it was not complete; small 

 discrepancies remained. Kepler was not the man to be 

 satisfied with partial success; it also fell to him to give us a 

 first great example in the history of science, of how discre- 

 pancies between calculation and observation are to be judged. 

 The departures were small, but - and this was the essential 

 point - they were nevertheless greater than the possible 

 errors of Tycho's observation. As soon as a case of this kind 

 occurs, the conclusion must be drawn that an unknown 

 factor is concerned. Kepler now began to seek the 

 unknown element in the shape of the planetary orbits. 

 Hitherto only the circle had been seriously considered as the 

 path of permanent heavenly bodies; the comets however had 

 already betrayed the fact that other paths are possible. The 

 departure from the circular path could not be great in the 

 case of Mars; Kepler tried, one after another, all sorts of 

 other closed paths of different curvature. The ellipse was 

 at that time no more likely than any other possibility; but 

 only elliptical orbits with the sun at the focus satisfied 

 Tycho's observations; and this they did completely when 

 the law of equal surfaces for the radius was taken into 

 account. With this the problem of the path of Mars had 

 been conquered after six years, and the two first laws had 

 been found, which now could be taken to hold for the other 

 planets as well as for Mars and the Earth. The publication 

 followed in his New Astronomy founded on True Causes 

 (1609). 



At the same time, Kepler was busy with optical investiga- 

 tions. Galileo's Messenger, which had just appeared with the 

 successes of the first telescopic observations of the heavens, 

 led him to investigate closely the path of the light rays in the 

 telescope, and further, the behaviour of light rays generally. 

 The results are collected in two works {Paralipomena and 



