136 DISSERTATION SECOND. [part «. 



found that the same thing is true of the earth's orbit round 

 the sun ; hence by analogy it was reasonable to think, 

 that all the planetary orbits are elliptical, having the sun 

 in their common focus. 



The industry and patience of Kepler, in this investiga- 

 tion, were not less remarkable than his ingenuity and in- 

 vention. Logarithms were not yet known, so that arith- 

 metical computation, when pushed to great accuracy, was 

 carried on at a vast expense of time and labour. In the 

 calculation of every opposition of Mars, the work filled ten 

 folio pages, and Kepler repeated each calculation ten 

 times, so that the whole work for each opposition exiended 

 to one hundred such pages ; seven oppositions thus calcu- 

 lated produced a large folio volume. 



In these calculations the introduction of hypotheses was 

 unavoidable, and Kepler's candour in rejecting them, 

 whenever they appeared erroneous, without any other re- 

 gret than for the time which they had cost him, cannot be 

 sufficiently admired. He began with hypothesis, and ended 

 with rejecting every thing hypothetical. In this great as- 

 tronomer we find genius, industry, and candour, all uniting 

 together as instruments of investigation. 



Though the angular motion'of the planet was not found 

 to be uniform, it was discovered that a very simple law 

 connected that motion with the rectilineal distance from 

 the sun, the former being every where inversely as the 

 square of the latter ; and hence it was easy to prove, that 

 the area, described by the line drawn from the planet to 

 the sun, increased at a uniform rate, and, therefore, that 

 any two such areas were proportional to the times in which 

 Ihey were described. The picture presented of the hea- 

 vens was thus, for the first time, cleared of every thing 

 hypothetical. 



