5 6 A Short History of Astronomy [CM. n. 



enough to show definitely the invariability of the year, there 

 was no evidence to suppose that it had changed. 



The length of the tropical year being thus evaluated at 

 365 days 5 hours 55 minutes, and the difference between 

 the two kinds of year being given by the observations of 

 precession, the sidereal year was ascertained to exceed 

 365! days by about 10 minutes, a result agreeing almost 

 exactly with modern estimates. That the addition of two 

 erroneous quantities, the length of the tropical year and the 

 amount of the precession, gave such an accurate result was 

 not, as at first sight appears, a mere accident. The chief 

 source of error in each case being the erroneous times of 

 the several equinoxes and solstices employed, the errors 

 in them would tend to produce errors of opposite kinds 

 in the tropical year and in precession, so that they would in 

 part compensate one another. This estimate of the length 

 of the sidereal/ year was probably also to some extent 

 verified by Hipparchus by comparing eclipse observations 

 made at different epochs. 



43. The great improvements which Hipparchus effected 

 in the theories of the sun and moon naturally enabled him 

 to deal more successfully than any of his predecessors with 

 a problem which in all ages has been of the greatest interest, 

 the prediction of eclipses of the sun and moon. 



That eclipses of the moon were caused by the passage 

 of the moon through the shadow of the earth thrown by 

 the sun, or, in other words, by the interposition of the 

 earth between the sun and moon, and eclipses of the sun 

 by the passage of the moon between the sun and the 

 observer, was perfectly well known to Greek astronomers 

 in the time of Aristotle ( 29), and probably much earlier 

 (chapter I., 17), though the knowledge was probably 

 confined to comparatively few people and superstitious 

 terrors were long associated with eclipses. 



The chief difficulty in dealing with eclipses depends 

 on the fact that the moon's path does not coincide 

 with the ecliptic. If the moon's path on the celestial 

 sphere were identical with the ecliptic, then, once every 

 month, at new moon, the moon (M) would pass exactly 

 between the earth and the sun, and the latter would be 

 eclipsed, and once every month also, at full moon, the 



