184 A Short History of Astronomy [Cn. vn. 



results of which could be compared with observation. The 

 places of Mars as seen on the sky being a combined result 

 of the motions of Mars and of the earth in their respective 

 orbits round the sun, the irregularities of the two orbits 

 were apparently inextricably mixed up, and a great simpli- 

 fication was accordingly effected when Kepler succeeded, 

 by an ingenious combination of observations taken at suit- 

 able times, in disentangling the irregularities due to the 

 earth from those due to the motion of Mars itself, and 

 thus rendering it possible to concentrate his attention on 

 the latter. His fertile imagination suggested hypothesis 

 after hypothesis, combination after combination of eccentric, 

 epicycle, and equant ; he calculated the results of each and 

 compared them rigorously with observation ; and at one 

 stage he arrived at a geometrical scheme which was capable 

 of representing the observations with errors not exceeding 

 8'.* A man of less intellectual honesty, or less convinced 

 of the necessity of subordinating theory to fact when the 

 two conflict, might have rested content with this degree 

 of accuracy, or might have supposed Tycho's refractory 

 observations to be in error. Kepler, however, thought 

 otherwise : 



11 Since the divine goodness has given to us in Tycho Brahe a 

 most careful observer, from whose observations the error of 8' 

 is shewn in this calculation, ... it is right that we should with 

 gratitude recognise and make use of this gift of God. . . . For if 

 I could have treated 8' of longitude as negligible I should have 

 already corrected sufficiently the hypothesis . % . discovered in 

 chapter xvi. But as they could not be neglected, these 8' 

 alone have led the way towards the complete reformation of 

 astronomy, and have been made the subject-matter of a great 

 part of this work." f 



140. He accordingly started afresh, and after trying a variety 

 of other combinations of circles decided that the path of 

 Mars must be an oval of some kind. At first he was in- 

 clined to believe in an egg-shaped oval, larger at one end than 

 at the other, but soon had to abandon this idea. Finally 



* Two stars 4' apart only just appear distinct to the naked eye of 

 a person with average keenness of sight. 



f Commentaries on the Motions of Mars, Part II., end of chapter xix. 



