80 PRECESSION. SECT. XI. 



the equinoctial points a slow but direct motion on the ecliptic of 

 0"'31 annually, which is entirely independent of the figure of 

 the earth, and would be the same if it were a sphere. Thus the 

 sun and moon by moving the plane of the equator cause the 

 equinoctial points to retrograde on the ecliptic : and the planets 

 by moving the plane of the ecliptic give them a direct motion, 

 though much less than the former. Consequently the difference 

 of the two is the mean precession, which is proved both by 

 theory and observation to be about 50"'l annually (N. 146). 



As the longitudes of all the fixed stars are increased by this 

 quantity, the effects of precession are soon detected. It was 

 accordingly discovered by Hipparchus in the year 128 before 

 Christ, from a comparison of his own observations with those of 

 Timocharis 155 years before. In the time of Hipparchus the 

 entrance of the sun into the constellation Aries was the beginning 

 of spring ; but since that time the equinoctial points have re- 

 ceded 30, so that the constellations called the signs of the zodiac 

 are now at a considerable distance from those divisions of the 

 ecliptic which bear fcheir names. Moving at the rate of 50"'l 

 annually, the equinoctial points will accomplish a revolution in 

 25,868 years. But, as the precession varies in different centuries, 

 the extent of this period will be slightly modified. Since the 

 motion of the sun is direct, and that of the equinoctial points 

 retrograde, he takes a shorter time to return to the equator than 

 to arrive at the same stars ; so that the tropical year of 365 d 5 h 

 48 49*' 7 must be increased by the time he takes to move 

 through an arc of 50"'l, in order to have the length of the side- 

 real year. The time required is 20 m 19 8 '6, so that the sidereal 

 year contains 36 5 d 6 h 9 m 9 g< 6 mean solar days. 



The mean annual precession is subject to a secular variation ; 

 for, although the change in the plane of the ecliptic in which the 

 orbit of the sun lies be independent of the form of the earth, yet, 

 by bringing the sun, moon, and earth into different relative posi- 

 tions from age to age, it alters the direct action of the two first 

 on the prominent matter at the equator : on this account the 

 motion of the equinox is greater by CT'455 now than it was in 

 the time of Hipparchus. Consequently the actual length of the 

 tropical year is about 4 < 21 shorter than it was at that time. 

 The utmost change that it can experience from this cause amounts 

 to 43 seconds. 



