INDUCTIVE EPOCH OF KEPLER. 441 



the answer must have been, that they are propor- 

 tional to the square of the cube root. This ex-post- 

 facto obviousness of discoveries is a delusion to 

 which we are liable with regard to many of the 

 most important principles. In the case of Kepler, 

 we may observe, that the process of connecting two 

 classes of quantities by comparing their powers, is 

 obvious only to those who are familiar with general 

 algebraical views ; and that in Kepler's time, alge- 

 bra had not taken the place of geometry, as the 

 most usual vehicle of mathematical reasoning. It 

 may be added, also, that Kepler always sought his 

 formal laws by means of physical reasonings; and 

 these, though vague or erroneous, determined the 

 nature of the mathematical connexion which he 

 assumed. Thus in the Mysterium he had been led 

 by his notions of moving virtue of the sun to this 

 conjecture, among others, that, in the planets, the 

 increase of the periods will be double of the dif- 

 ference of the distances; which supposition he 

 found to give him an approach to the actual pro- 

 portion of the distances, but one not sufficiently 

 close to satisfy him. 



The greater part of the fifth Book of the Har- 

 monics of the Universe consists in attempts to ex- 

 plain various relations among the distances, times, 

 and eccentricities of the planets, by means of the 

 ratios which belong to certain concords and dis- 

 cords. This portion of the work is so complex and 

 laborious, that probably few modern readers have 



