at the end of so many sidereal years, he will be found again at S: but at the end of so many Julian years, he will be found at M, short of S, and at the end of so many tropical years, he will be found short of M in the 30th degree of Taurus at T, which has receded back from S to Tin that time, by the precession of the equinoctial points y Aries and Libra.

The arc ST will be equal to the amount of the precession of the equinox in 2160 years at the rate of 50" of a degree, or 20 min. 17 sec. of time annually this, in so many years, makes 30 days 101 hours which is the difference between 2160 sidereal and tropical years. And the arc MT will be equal to the space moved through by the Sun in 2160 times 11 min. 3 sec. or 16 days 13 hours 48 minutes, which is the difference between 2160 Julian and tropical years.

248. From the shifting of the equinoctial points, and with them all the signs of the ecliptic, it follows that those stars which in the infancy of astronomy were in Aries are now got into Taurus: those of Taurus into Gemini, &c. Hence likewise it is, that the stars which rose or set at any particular season of the year, in the times of HESIOD, EUDOXUS, VIRGIL, PLINY, &c. by no means answer at this time to their descriptions. The preceding table shews the quantity of this shifting both in the heavens and on the Earth, for any number of years to 25,920; which completes the grand celestial period within which any number and its quantity is easily found, as in the following example, for 5763 years; which at the autumnal equinox, A. D. 1756, is thought to be the age of the world. So that with regard to the fixed stars, the equinoctial points in the heavens have receded 2$ 20° 2' 30" since the creation; which is as much as the Sun moves in in 81 5h 0m 52. And since that time, or in 5763 years, the equinoxes with us have fallen back 44 5 21m 9; hence, reckoning from the time of the Julian equinox, A. D. 1756, viz. Sept. 11th, it

appears that the autumnal equinox at the creation was on the 25th of October.

Precesssion of the Equinoctial | Anticipation

Points in the Heavens.

of the Equi

noxes on the

5763 2 20 2 30 81 5 0 52 44 5 21 9

seasons.

249. The anticipation of the equinoxes, and con- The antisequently of the seasons, is by no means owing to the equicipation of the precession of the equinoctial and solstitial points noxes and in the heavens (which can only affect the apparent motions, places and declinations of the fixed stars) but to the difference between the civil and solar year, which is 11 minutes 3 seconds; the civil year containing 365 days 6 hours, and the solar year 365 days 5 hours 48 minutes 57 seconds. The next following table, page 189, shews the length, and consequently the difference of any number of sidereal, civil and solar years, from 1 to 10,000.

son for al

tering the

250. The above 11 minutes 3 seconds, by which The reathe civil or Julian year, exceeds the solar, amounts to 11 days in 1433 years: and so much our seasons style. have fallen back with respect to the days of the months, since the time of the Nicene council in A. D. 325; and therefore, in order to bring back all the fasts and festivals to the days then settled, it was requisite to suppres 11 nominal days. And that the same seasons might be kept to the same times of the year for the future, to leave out the Bissex

PLATE

VI.

tile-day in February at the end of every century of years where the significant figures are not divisible by 4; reckoning them only common years, as the 17th, 18th, and 19th centuries, viz. the years 1700, 1800, 1900, &c. because a day intercalated every fourth year was too much, and retaining the Bissextile-day at the end of those centuries of years which are divisible by 4, as the 16th, 20th and 24th centuries: viz. the years 1600, 2000, 2400, &c. Otherwise, in length of time, the seasons would be quite reversed with regard to the months of the year; though it would have required near 23,783 years to have brought about such a total change. If the Earth had made exactly 3654 diurnal rotations on its axis, while it revolved from any equinoctial or solstitial point to the same again, the civil and solar years would always have kept pace together, and the style would never have required any alteration. 251. Having already mentioned the cause of the cesssion of precession of the equinoctial points in the heavens, the equi 246, which occasions a slow deviation of the Earth's axis from its parallelism, and thereby a change of the declination of the stars from the equa tor, together with a slow apparent motion of the stars forward with respect to the signs of the ecliptic, we shall now explain the phenomena by a diagram.

The pre

noctial

points.

Fig. VI.

Let NZSVL be the Earth, SONA its axis produced to the starry heavens, and terminating in A, the present north pole of the heavens, which is vertical to N, the north pole of the Earth. Let EOQ be the equator, TZ the tropic of Cancer, and VT the tropic of Capricorn: VOZ the ecliptic, and BO its axis, both which are immoveable among the stars. But as * the equinoctial points recede in

*The equinoctial circle intercepts the ecliptic in two opposite points; namely, the first points of the signs Aries and Libra. They are called the equinoctial points, because when the Sun is in either

the ecliptic, the Earth's axis SON is in motion upon the Earth's centre O, in such a manner as to describe the double cone NOn and Sos, round the axis of the ecliptic, BO, in the time that the equinoctial points move quite round the ecliptic, which is 25,920 years, and in that length of time the north pole of the Earth's axis produced, describes the circleABC DA, in the starry heavens, round the pole of the ecliptic, which keeps immoveable in the centre of that circle, the Earth's axis being 23 degrees inclined to the axis of the ecliptic, the circle ABC DA, described by the north pole of the Earth's axis produced to A, is 47 degrees in diameter, or double the inclination of the Earth's axis. In consequence of this motion, the point A, which at present is the north pole of the heavens, and near to a star of the second magnitude in the tail of the constellation called the Little Bear, must be deserted by the Earth's axis; which moving backward a degree every 72 years, will be directed toward the star or point B in 6480 years from this time; and in twice that time, or 12960 years, it will be directed toward the star or point C: which will then be the north pole of the heavens, although it is at present 8 degrees south of the zenith of London L. The present position of the equator EOQ will then be changed into e0q, the tropic of Cancer T Z into Vt and the tropic of Capricorn VT vs into t vs Z; as is evident by the figure; and the Sun, when in that part of the heavens, where he is now over the terrestrial tropic of Capricorn, and makes the shortest days and longest nights in the northern hemisphere, will then be over the terrestrial tropic of Cancer, and make the days longest and nights shortest. And it will require 12,960 years more, or 25,920 from the pre

of them, he is directly over the terrestrial equator: and then the days and nights are equal.

sent time, to bring the north pole N quite round, so as to be directed toward that point of the heavens which is vertical to it at present. And then, and not till then, the same stars, which at present describe the equator, tropics, polar circles, &c. by the Earth's diurnal motion, will describe them over again.