SCT. XI. PRECESSION. 75 



tion of the two planes remains constant, as a top spin- 

 ning preserves the same inclination to the plane of the 

 horizon. Were the earth spherical, this effect would 

 not be produced, and the equinoxes would always cor- 

 respond 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 va- 

 riation in the position of the plane of the ecliptic, which 

 uffects 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 inde- 

 pendent 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 mo- 

 tion, 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 de- 

 tected. 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 constellations 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 equinoc- 

 tial 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, 



