SECT.xr.] LENGTH OF THE YEAR. 91 



sidereal year. The time required is 2G m 19 S> 6, so that the 

 sidereal year contains 365a 6 h 9 m 9 8- 6 mean solar days. 



The mean annual precession is subject to a secular vari- 

 ation ; 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. Con- 

 sequently the actual length of the tropical year is about 4 8> 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 action of these bodies on the equator. 

 Dr. Bradley discovered 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 towards 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 revolution. The 

 sun causes a small variation in the description 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 surface 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 nuta- 

 tion 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 



