504 ADDITIONS. 



omy, when further advanced, would be able to render an account of 

 many things for which she has not accounted even to this day. Thus, 

 in the passage in the seventh Book of the Republic, he says that the 

 philosopher requires a reason for the proportion of the day to the 

 month, and the month to the year, deeper and more substantial than 

 mere observation can give. Yet Astronomy has not yet shown us 

 any reason why the proportion of the times of the earth's rotation on 

 its axis, the moon's revolution round the earth, and the earth's revolu- 

 tion, round the sun, might not have been made by the Creator quite 

 different from what they are. But in thus asking Mathematical As- 

 tronomy for reasons which she cannot give, Plato was only doing what 

 a great astronomical discoverer, Kepler, did at a later period. One 

 of the questions which Kepler especially wished to have answered was, 

 why there are five planets, and why at such particular distances from 

 the sun? And it is still more curious that he thought he had found 

 the reason of these things, in the relations of those Five Regular Solids 

 which, as we have seen, Plato was desirous of introducing into the phi- 

 losophy of the universe. We have Kepler's account of this, his im- 

 aginary discovery, in the Mysterium Cosmoyraphicum, published in 

 1596, as stated in our History, Book v. Chap. iv. Sect. 2. 



Kepler regards the law which thus determines the number and 

 magnitude of the planetary orbits by means of the five regular solids 

 as a discovery no less remarkable and certain than the Three Laws 

 which give his name its imperishable place in the history of astronomy. 



We are not on this account to think that there is no steady criterion 

 of the difference between imaginary and real discoveries in science. 

 As discovery becomes possible by the liberty of guessing, it becomes 

 real by allowing observation constantly and authoritatively to deter- 

 mine the value of guesses. Kepler added to Plato's boldness of fancy 

 his own patient and candid habit of testing his fancies by a rigorous 

 and laborious comparison with the phenomena ; and thus his discover- 

 es led to those of Newton. 



