200 CHILDHOOD OF SCIENCE. 



of them would give him the true place within eight minutes. 

 Ten of the best years of Kepler's life were thus spent in trying 

 to reconcile the planetary motions to the mystic and divine prop- 

 erties of the circle. At last, from the simple circumstance of 

 his happening to use the ellipse to facilitate his calculations, 

 came his first great discovery, that the planets all revolve in 

 elliptical orbits, witli the sun in one of the foci or centers. 



The second law of planetary motion discovered by Kepler, 

 which is, that a line connecting the sun with any planet would 

 pass over equal areas in equal time, was rather in the nature of a 

 mathematical corollary from the first law, and therefore did not 

 require much time or eifort for its discovery. 



But the intuitions, the almost inspirations of Kepler's mind, 

 that there were definite relations between the distances from the 

 sun and the periods of revolution of the planets, were not yet 

 realized ; and so long as those "harmonies of the universe" were 

 unascertained, he accounted all his other discoveries as nothing. 

 He therefore commenced at once and over again his dreary wan- 

 derings in the fields of conjecture. He followed up each 

 shadowy indication of a relation, till hope was exhausted in that 

 direction, then turned off to another with the simple regret that 

 the last had been such a sad thief of his time. He ran down to 

 their farthest absurdity the vague conjectures of Greek philoso- 

 phy, dozed with Plato and dreamed with Aristotle. For a long 

 time he held by the numerical harmonies of Pythagoras ; then 

 by the five regular geometrical solids of Plato. But his longest, 

 dreariest wanderings were in the endeavor to fix the musical 

 gamut in the skies, to guage the motions of the planets by some 

 relations of concords of sounds. 



Over twenty years were thus spent in these baffled efforts, till 

 at last it occurred to him to compare the various powers as the 

 square and cube of the planetary elements. He eventually hit 

 upon the very relation which afterward became the law. But 

 this time, with his usual ill-luck, the poor man made a mistake 

 in his figures, and was again tossing on the sea of uncertainty. 

 Months afterwards, however, he was induced to recur to the same 

 figures, namely, the ratio of the squares of the periodic times 



