A good notion of precession may be got from observiug the spin ning of a top. As long as the axis of the top is not vertical, thin axis itself revolves, hut much more slowly than the top revolves round its axis. Let the top be supposed to remain with its axis at one angle to the vertical, except only a alight balancing motion to and from the vertical, and let the milled motion of the axis be slightly tuscelemted and retarded : this will give a complete notion of the phenomena of precession and notation.
Before proceeding to the mathematical and physical description of those phenomena, we shall show the manner in which they may have an historical and chronological importance. Let the reader take a globe or a map of the stars, he will see that the ecliptic crosses the equator under time tail of one of the Fishes, so that the vernal equinox is nearly in a line with the eters a Andromeche and y l'egasi rat and Algenib). These stars then are invisible at the beginning of the spring, being in the region of the heavens nearest to the sun. Let from twelve to thirteen thousand year's elapse, and the slow pre cessional motion of the equinoctial points will reverse the positions of the equinoxes, so that the above-named stars will be near the me ridian at midnight at the commencement of spring, as the stars in the head of Virgo are now. An Aratus of our day would celebrate the brightness of Virgo in the nights of spring, while one of thirteen thousand years hence must choose Pisces for that purpose, The Demons of the year at which different stars begin to be distant enough from the sun to shine brightly is undergoing a gradual alteration. liesiod, for instance, says that in his time and country Arcturus rose at sunset in sixty days after the winter solstice ; Newton micte Wed that this took place about n.c. S70, which is one of his reasons for supposing that the poet was alive about that time. The phe nomenon however is itself rather vague, and Healed may ho supposed not very exact in his description. It is generally considered that Newton attached too much importance to such data in settling his system of chronology.
About two thousand years ago the equinox was twenty-eight degrees more advanced among the signs, and was near the beginning of the constellation Aries. It was about this time that the precession of the equinoxes was discovered by Ilipparchtm [Asenosoler ; Hirrencrirs, in Bloo. Div.), and since that time the vernal equinox has preserved
the title which it properly held at the time when its motion was discovered, namely, the first point of Aries. Certain astronomical fictitious constellations have been made to move with the equinox, at least until lately; counting from the equinox, the first thirty degrees of the ecliptic have been always called Arica, the second thirty Taurus, and so on. Thus when an astronomer of the middle ages asserts the longitude of a star to be -se_ 18° 22', be recalls that it is in 18* 22' of the astronomical Libra, a constellation supposed to begin at 6 x 30' or 180° distance from the vernal equinox. An astronomer of our day would say the star's longitude was 198° 22'.
Taking the beginning of the year 1750 as the starting point (as is generally done since the publication of the Mecanique Celeste '), and calling it the number of years elapsed, the whole motion of the equinoxes from precession, including the effect of the planetary action on the ecliptic, is 50".176068 t +0".00012214S3 while the precession in one year is 50'176068 4-0'0002442966 t.
M. Besse] substitutes 50".21129 for 50".176068.
The obliquity of the ecliptic, assumed at 23° 28' 18" in 1750, is 23° 28' 18" 0"48368 t 0'00000272295 its yearly diminution, arising front the planetary action, independently of notation, being 0"48368 + 0'4000054459 t.
M. Beasel takes 23° 28' 17"63 for the obliquity in 1750, and uses 0"457 instead of 0"48368.
The nutatiott affects both tho place of the equinoxes and the ob liquity of tho ecliptic. Let AA denote the mutation in longitude, AV the effect upon the obliquity of the ecliptic. Then, according to Pro fessor Peters (` Nnmerus Constans Nutationisl, AA=-17"'2491 sin 68 sin 2 68 0".2041 sin 2 ( +0".0677 aim((1 re) 1" -2692 sin 2 0 +0"1277 sin (0 (0 +s). con b3-0"0807 cos 2 68 +0"08S6 cos 2 ( +0'5508 x cos 2 0 + 0'0093 cue (CD -I- pr), in which expressions 68 dcnotea the longitude of the moon's ascending node, C the longitude of the moon, 0 the longitude of the sun, s, the longitude of the perihelion of the earth'a orbit, and tr', the longi tude of the moon's perigee.