INDUCTIVE EPOCH OF HIPPARCHUS. 155 



the application of distinct and appropriate Ideas to a real series of 

 Facts. The distinctness of the geometrical conceptions which enabled 

 Hipparchus to assign the Orbits of the Sun and Moon, requires no 

 illustration ; and we have just explained how these ideas combined 

 into a connected whole the various motions and places of those lumi- 

 naries. To make this step in astronomy, required diligence and care, 

 exerted in collecting observations, and mathematical clearness and 

 steadiness of view, exercised in seeing and showing that the theory 

 was a successful analysis of them. 



Sect. 3. — Discovery of the Precession of the JZquinoxes. 



The same qualities which we trace in the researches of Hipparchus 

 already examined, — diligence in collecting observations, and clearness 

 of idea in representing them, — appear also in other discoveries of his, 

 which we must not pass unnoticed. The Precession of the Equinoxes, 

 in particular, is one of the most important of these discoveries. 



The circumstance here brought into notice was a Change of Longi- 

 tude of the Fixed Stars. The longitudes of the heavenly bodies, being 

 measured from the point where the sun's annual path cuts the equator, 

 will change if that path changes. Whether this happens, however, 

 is not very easy to decide; for the sun's path among the stars is made 

 out, not by merely looking at the heavens, but by a series of infer- 

 ences from other observable facts. Hipparchus used for this purpose 

 eclipses of the moon ; for these, being exactly opposite to the sun, 

 afford data in marking out his path. By comparing the eclipses of 

 his own time with those observed at an earlier period by Timocharis, 

 he found that the bright star, Spica Virginis, was six degrees behind 

 the equinoctial point in his own time, and had been eight degrees be- 

 hind the same point at an earlier epoch. The suspicion was thus sug- 

 gested, that the longitudes of all the stars increase perpetually ; but 

 Hipparchus had too truly philosophical a spirit to take this for granted. 

 He examined the places of Regulus, and those of other stars, as he had 

 done those of Spica ; and he found, in all these instances, a change of 

 place which could be explained by a certain alteration of position in 

 the circles to which the stars are referred, which alteration is described 

 as the Precession of the Equinoxes. 



The distinctness with which Hipparchus conceived this change ot 

 relation of the heavens, is manifested by the question which, as we are 

 told by Ptolemy, he examined and decided ; — that this motion of the 



