SECT. XL NUTATION. 81 



Such is the secular motion of the equinoxes. But it is some- 

 times 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 dis- 

 covered 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 

 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. 147). This nutation in 

 the earth's axis affects both the precession and obliquity with 

 small periodic variations. But in consequence of the secular 

 variation in the position of the terrestrial orbit, which is chiefly 

 owing to the disturbing energy of Jupiter on the earth, the 

 obliquity of the ecliptic is annually diminished, according to M. 

 Bessel, by 0"'457. This variation in the course of ages may 

 amount to 10 or 11 degrees ; but the obliquity of the ecliptic to 

 the equator can never vary more than 2 42' or 3, since the 

 equator will follow in some measure the motion of the ecliptic. 



It is evident that the places of all the celestial bodies are 

 affected by precession and nutation. Their longitudes estimated 

 from the equinox are augmented by precession ; but, as it affects 

 all the bodies equally, it makes no change in their relative posi- 

 tions. Both the celestial latitudes and longitudes are altered to 

 a small degree by nutation ; hence all observations must be 

 corrected for these inequalities. In consequence of this real 

 motion in the earth's axis, the pole-star, forming part of the con- 



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