300 KEPLER'S GOOD WORK. 



comprehensive, these and other theories, however fine in 

 appearance, teres atque rotundus, gradually disappeared, if 

 fundamentally erroneous. By the invention of micrometers, 

 we were enabled to measure more exactly than had formerly 

 been possible the variations of diameter or the modifications 

 of distance, and afterwards to compare them with the changes 

 of velocity. From this comparison it results that the latter 

 are not greater than is compatible with the alterations of 

 distance indicated by the variations of diameter ; in a word, 

 that the hypothesis of epicycles is decidedly insufficient to 

 account for all the inequalities detected by careful investi- 

 gation. 



Kepler was the first to break the charm which had held 

 captive the mind of astronomers, including even Copernicus 

 and Tycho Brand Ptolemaeus had considered the mean 

 positions of the stars to be real. Kepler, strong in his 

 researches, declared that they were but a factitious mode of 

 calculation by which the true positions might be ascertained ; 

 that the mean movement is simply an artifice representing the 

 star's place, if no inequality existed ; in fine, that we must 

 take the movements as they are in nature, the true move- 

 ments, given by observation, and not the mean movements, 

 deduced from an erroneous hypothesis. 



This declaration of principles met, at the time, with the 

 hostility of all astronomers of any reputation, but it has 

 become the starting-point of the discovery of the laws on 

 which the whole edifice of astronomy reposes. Had Kepler, 



