76 LENGTH OF THE YEAR. SECT. XI. 



in order to have the length of the sidereal year. The 

 time required is 20 m 19 s - 6, so that the sidereal year con- 

 tains 365 d 6 h 9 m 9 8 -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 positions 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 0"-455 now than it 

 was in the time of Hipparchus. Consequently the ac- 

 tual length of the tropical year is about 4 S> 21 shorter 

 than it was at that time. The utmost change that it 

 can experience from this cause amounts to 43 seconds. 



Such is the secular motion of the equinoxes. But it 

 is sometimes increased and sometimes diminished by 

 periodic variations, whose periods depend upon the 

 relative positions of the sun and moon with regard to 

 the earth, and which are occasioned by the direct ac- 

 tion of these bodies on the equator. Dr. Bradley discov- 

 ered that by this action the moon causes the pole of the 

 equator to describe a small ellipse in the heavens, the 

 axes of which are 18"-5 and 13"-674, the longer being 

 directed toward the pole of the ecliptic. The period 

 of this inequality is about 19 years, the time employed 

 by the nodes of the lunar orbit to accomplish a revolu- 

 tion. The sun causes a small variation in the descrip- 

 tion of this ellipse ; it runs through its period in half a 

 year. Since the whole earth obeys these motions they 

 affect the position of its axis of rotation with regard to 

 the starry heavens, though not with regard to the sur- 

 face of the earth; for in consequence of precession 

 alone the pole of the equator moves in a circle round 

 the pole of the ecliptic in 25,868 years, and by nutation 

 alone it describes a small ellipse in the heavens every 

 19 years, on each side of which it deviates every half 

 year from the action of the sun. The real curve traced 

 in the starry heavens by the imaginary prolongation of 

 the earth's axis is compounded of these three motions 

 (N. 144). This nutatiou in the earth's axis affects both 

 tho precession and obliquity with small periodic varia- 



