TEE PREDECESSORS OF COPERNICUS. 321 



we now know, twenty tho^^sand times as far from us as Saturn, and 

 it is this fact — which was not finally established till 1837 — that ex- 

 plains why the miniature apparent orbits of the stars were not seen- 

 by the Greeks or by their successors. They were too minute to be 

 discoverable. 



All the important writings of Hipparchus, who lived in the second 

 century B. C, are lost, and the doctrines of this 'most truth-loving and 

 labor-loving man' are known to us only through Ptolemy, his expositor 

 and ardent admirer. Hipparchus was an indefatigable observer, a 

 mathematician of tact and insight, an astronomer of original and 

 profound genius. By his own observations, made at Rhodes (188-127 

 B. C), he fixed the positions (the celestial longitudes and latitudes) 

 of the principal fixed stars. Comparing their present places with 

 their past positions as determined by Timocharis and Aristillus, he 

 discovered that backward motion of the equinoctial points which causes 

 the epoch of the sun's passage through the equinox to recur earlier 

 and earlier each year — the precession of the equinoxes — and fixed its 

 probable annual amount. Comparing his own determinations of the 

 date of the vernal equinoctial passage of the sun with those of 

 Aristarchus, he determined the length of the year with accuracy.* It 

 is by systematic comparisons of the sort that many of his discoveries 

 were made. 



It is very noteworthy that he gives not only his results, but like- 

 wise an estimate of their probable errors. His observations of the 

 time of the sun's arriving at a solstice might be erroneous, he says, 

 by about three fourths of a day; at an equinox by about one fourth. 

 Comparisons made in this systematic fashion, and estimates of error 

 of this sort, we are apt to think of as 'modern.' Certainly they are 

 not characteristic of observational astronomy till the eighteenth cen- 

 tury, two thousand years after Hipparchus showed the way. Some 

 of his most important researches related to measures of time. What 

 was the length of the year ? Were all years of the same length ? His 

 observations showed him no difference between one year and another. 

 It is interesting to note how he formulates his conclusions. He does 

 not say that all years are, without doubt, of one and the same length; 

 he asserts simply that the differences, if any, must be very small, so 

 small that his observations are not delicate enough to detect them. 



In the year 134 B. C. a new star suddenly appeared in Scorpio, and 

 Hipparchus began the formation of a catalogue of stars visible to him. 

 With such a conspectus of the present state of the sky no new appear- 

 ances could subsequently occur without detection. His catalogue gave 

 the position and magnitude (brightness) of 1,080 stars for the epoch 

 128 B. C, and arranged them in the constellation figures that have 



* Hipparchus fixed the length of the tropical year at 365 days 5 hours 55 

 minutes. Its true length is 365 days 5 hours 48 minutes 45.51 seconds (1900). 



VOL. LXIV.— 21. 



