JOHANNES KEPLER 43 



successor, with the title " Imperial Mathematician." Un- 

 fortunately, however, the effects of political confusion in 

 Germany, from which he never succeeded in escaping, 

 followed him also to Prague. His salary, nominally ample, 

 was only paid rarely or in part, so that his domestic life was 

 very uncomfortable, the more so when later the war came to 

 his neighbourhood, and epidemics broke out. 



Nevertheless, it was just in the eleven years of his stay in 

 Prague that Kepler did the main part of his life's work. He 

 became the scientific heir of Tycho, taking over the extensive 

 records of Tycho's fine measurements, extending over many 

 years, of the positions of the planets, together with the task of 

 making scientific use of these observations, and of finishing 

 the Rudolfine Tables, which were to give the positions of the 

 planets at future times. Kepler attacked this task in the 

 most thorough manner possible; he wished above all to find 

 the true paths of the planets from Tycho's observations, 

 with the greatest possible accuracy which the observations 

 permitted. He soon found that the circular paths performed 

 at constant speed, which alone had been considered hitherto, 

 would not suffice. Further advance was very difficult, for 

 the planetary motions are observed from a moving position, 

 namely the planet Earth, of which the exact path and mode 

 of motion were just as unknown as those of the other 

 planets. 



Kepler expended six years of tireless labour upon the 

 path of Mars alone. After all kinds of eccentric paths around 

 the sun for Mars and the Earth had been tried, whereby the 

 diameters of the paths had also to be altered by trial, and after 

 all this had not led to the desired goal, various non-uniform 

 motions in the circles were tried one after another. One of 

 these appeared satisfactory, namely the one in which the line 

 joining sun and planet swept over equal surfaces in equal 

 times. With this the substance of what was afterwards 

 called the second law was discovered, but Kepler's delight 



