INDUCTIVE EPOCH OF KEPLER. 291 



In the first place, we may observe that the leading thought which 

 suggested and animated all Kepler's attempts was true, and we may 

 add, sagacious and philosophical ; namely, that there must be some 

 numerical or geometrical relations among the times, distances, and 

 velocities of the revolving bodies of the solar system. This settled and 

 constant conviction of an important truth regulated all the conjectures, 

 apparently so capricious and fanciful, which he made and examined, 

 respecting particular relations in the system. 



In the next place, we may venture to say, that advances in knowl- 

 edge are not commonly made without the previous exercise of some 

 boldness and license in guessing. The discovery of new truths re- 

 quires, undoubtedly, minds careful and scrupulous in examining what 

 is suggested ; but it requires, no less, such as are quick and fertile in 

 suggesting. What is Invention, except the talent of rapidly calling 

 before us many possibilities, and selecting the appropriate one ? It is 

 true, that when we have rejected all the inadmissible suppositions, 

 they are quickly forgotten by most persons ; and few think it neces- 

 sary to dwell on these discarded hypotheses, and on the process by 

 which they were condemned, as Kepler has done. But all who dis- 

 cover truths must have reasoned upon many errors, to obtain each 

 truth ; every accepted doctrine must have been one selected out of 

 many candidates. In making many conjectures, which on trial proved 

 erroneous, Kepler was no more fanciful or unphilosophical than other 

 discoverers have been. Discovery is not a " cautious" or " rigorous" 

 process, in the sense of abstaining from such suppositions. But there 

 are great differences in different cases, in the facility with which guesses 

 are proved to be errors, and in the degree of attention with which the 

 error and the proof are afterwards dwelt on. Kepler certainly was 

 remarkable for the labor which he gave to such self-refutations, and 

 for the candor and copiousness with which he narrated them ; his 

 works are in this way extremely curious and amusing ; and are a very 

 instructive exhibition of the mental process of discovery. But in this 

 respect, I venture to believe, they exhibit to us the usual process 

 (somewhat caricatured) of inventive minds : they rather exemplify the 

 rule of genius than (as has generally been hitherto taught) the excep- 

 tion. We may add, that if many of Kepler's guesses now appear 

 fanciful and absurd, because time and observation have refuted them, 

 others, which were at the time equally gratuitous, have been confirmed 

 by succeeding discoveries in a manner which makes them appear 

 marvellously sagacious ; as, for instance, his assertion of the rotation of 



