212 A SHORT HISTORY OF SCIENCE 



The Copernican theory like the Ptolemaic involved the resolu- 

 tion of the motion of each planet into a main circular motion, 

 modified by superimposing other circular motions epicycles 

 successively upon it, each circle being the path of the centre of the 

 next. Even after disentangling the essential irregularities of 

 Mars' orbit from those merely due to irregular motion of the earth, 

 he could still obtain no satisfactory agreement with Tycho's 

 records, of which, as has been said, he refused to doubt the ac- 

 curacy. Taking advantage of his own failure - - as happens to 

 men of true genius - - he abandoned the restriction of circular 

 motions, and experimented with other closed curves, of which 

 the ellipse is simplest. Taking the sun at a focus, the problem 

 was at last solved, theory and observation reconciled within due 

 limits of error. At the same time uniform motion was naturally 

 abandoned, for with a non-circular orbit, it was evident that the 

 planet could not describe both equal distances and equal areas 

 in equal times. Here, again, Kepler's scientific imagination led 

 him to the great discovery that the planet traverses its orbit in 

 such a manner that a line joining it to the sun w r ould describe 

 sectors of equal area in equal times, the planet thus moving 

 fastest when nearest the sun. 



Of Kepler's celebrated three laws, the first two are: 



The planet describes an ellipse, the sun being in one focus. 



The straight line joining the planet to the sun sweeps out 

 equal areas in equal intervals of time. 



These results were published in 1609 as part of extended Com- 

 mentaries on the Motions of Mars. 



The great problem was solved at last, the problem which had 

 baffled the genius of Eudoxus and had been a stumbling-block to the 

 Alexandrian astronomers, to such an extent that Pliny had called 

 Mars the inobservabile sidtis. The numerous observations made 

 by Tycho Brahe, with a degree of accuracy never before attained, 

 had in the skilful hand of Kepler revealed the unexpected fact that 

 Mars describes an ellipse, in one of the foci of which the sun is situated, 

 and that the radius vector of the planet sweeps over equal areas in 

 equal times. And the genius and astounding patience of Kepler had 



