302 TYCHO AND HIS SUCCESSOR. 



very near to Mars when she passes between that planet and 

 the sun, that is to say, when she is in opposition, while she 

 retires from it triple the distance when in conjunction, that 

 is, when the sun is between her and Mars. Hence arise cer- 

 tain variations of aspect, particularly adapted to make manifest 

 the form of the orbit, and the law of the real movement of the 

 " red planet, Mars." As for the other planets, as far as they 

 were then known, their orbits differ so little from the circle, 

 that the nature of the curve which they describe in reality 

 would never have been exactly recognised by any inexperienced 

 star-gazer. 



For these reasons Kepler regarded as providential the choice 

 he had been led to make of Mars at the outset of his astrono- 

 mical career. Before the close of 1601, Tycho died, bequeath- 

 ing to his young fellow-worker a treasury of observation. 

 Thenceforth Kepler undertook to finish without assistance 

 the famous Rudolphine Tables. They cost him five-and- 

 twenty years of assiduous labour. Looking upon Tycho's 

 observations, because of their exactness, as " a gift from the 

 Divine Goodness," he employed them, in the first place, as 

 a test of the old hypotheses of planetary orbits and move- 

 ments. Let us do our best to grasp the range and bearing 

 of this part of his work. 



In the system of Copernicus, which Kepler ardently adopted, 

 the earth revolves around the sun. Now, observation having 

 shown that the sun remains seven or eight days longer in the 

 northern than in the southern signs of the Zodiac, we must of 



