INDUCTIVE EPOCH OF KEPLER. 449 



5. The physical hypothesis on the supposition 

 of a perfect circle. 



6. The physical hypothesis on the supposition 

 of a perfect ellipse. 



By the physical hypothesis, he meant the doc- 

 trine that the time of a planet's describing any 

 part of its orbit is proportional to the distance of 

 the planet from the sun, for which supposition, as 

 we have said, he conceived that he had assigned 

 physical reasons. 



The two last hypotheses came the nearest to 

 the truth, and differed from it only by about eight 

 minutes, the one in excess and the other in defect. 

 And, after being much perplexed by this remaining 

 error, it at last occurred to him 11 that he might 

 take another ellipsis, exactly intermediate between 

 the former one and the circle, and that this must 

 give the path and the motion of the planet. Making 

 this assumption, and taking the areas to represent 

 the times, he now saw 12 that both the longitude 

 and the distances of Mars would agree with ob- 

 servation to the requisite degree of accuracy. The 

 rectification of the former hypothesis, when thus 

 stated, may, perhaps, appear obvious. And Kepler 

 informs us that he had nearly been anticipated in 

 this step. (c. 55.) "David Fabricius, to whom I 

 had communicated my hypothesis of cap. 45, was 

 able, by his observations, to show that it erred in 

 11 De Stella Martis, c. 58. " Ibid. p. 235. 



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