INDUCTIVE EPOCH OF KEPLER. 445 



failures, explaining, at length, the various suppo- 

 sitions which he had made, the notions by which he 

 had been led to invent or to entertain them, the 

 processes by which he had proved their falsehood, 

 and the alternations of hope and sorrow, of vexa- 

 tion and triumph, through which he had gone. It 

 will not be necessary for us to cite many passages of 

 these kinds, curious and amusing as they are. 



One of the most important truths contained in 

 the motions of Mars is the discovery that the plane 

 of the orbit of the planet should be considered 

 with reference to the sun itself, instead of referring 

 it' to any of the other centers of motion which the 

 eccentric hypothesis introduced; and that, when 

 so considered, it had none of the librations which 

 Ptolemy and Copernicus had attributed to it. The 

 fourteenth chapter of the second part asserts, 

 " Plana eccentricorum esse ardXavra ;" that the 

 planes are unlibrating ; retaining always the same 

 inclination to the ecliptic, and the same line of 

 nodes. With this step Kepler appears to have been 

 justly delighted. His reflections on it are very phi- 

 losophical. "Copernicus," he says, "not knowing 

 the value of what he possessed (his system), under- 

 took to represent Ptolemy, rather than Nature, to 

 which, however, he had approached more nearly 

 than any other person. For being rejoiced that 

 the quantity of the latitude of each planet was in- 

 creased by the approach of the earth to the planet, 

 according to his theory, he did not venture to 



