90 PRECESSION. [SECT. xi. 



and the equinoxes would always correspond with the same 

 points of the ecliptic, at least as far as this kind of motion 

 is concerned. But another and totally different cause which 

 operates on this motion has already been mentioned. The 

 action of the planets on one another and on the sun occasions 

 a very slow variation in the position of the plane of the 

 ecliptic which affects its inclination to the plane of the 

 equator, and gives the equinoctial points a slow but direct 

 motion on the ecliptic of 0"'31 annually, which is entirely in- 

 dependent 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 retro- 

 grade 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"' 1 annually (N. 143). 



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 receded 30, so that the constella- 

 tions called the signs of the zodiac are now at a considerable 

 distance from those divisions of the ecliptic which bear their 

 names. Moving at the rate of 50"- 1 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 m 49 8< 7 must be increased by the time he takes to move 

 through an arc of 50"' 1, in order to have the length of the 



