CHAP. XIV.
 
Of the Precession of the Equinoxes.

246. It has been already observed, § 116, that by the Earth’s motion on it’s Axis, there is more matter accumulated all round the equatoreal parts than any where else on the Earth.

The Sun and Moon, by attracting this redundancy of matter, bring the Equator sooner under them in every return towards it than if there was no such accumulation. Therefore, if the Sun sets out, as from any Star, or other fixed point in the Heavens, the moment he is departing from the Equinoctial or either Tropic, he will come to the same again before he compleats his annual course, so as to arrive at the same fixed Star or Point from whence he set out.

When the Sun arrives at the same [56]Equinoctial or Solstitial Point, he finishes what we call the Tropical Year, which, by long observation, is found to contain 365 days 5 hours 48 minutes 57 seconds: and when he arrives at the same fixed Star again, as seen from the Earth, he compleats the Sidereal Year; which is found to contain 365 days 6 hours 9 minutes 141⁄2 seconds. The Sidereal Year is therefore 20 minutes 171⁄2 seconds longer than the Solar or Tropical year, and 9 minutes 141⁄2 seconds longer than the Julian or Civil year, which we state at 365 days 6 hours: so that the Civil year is almost a mean betwixt the Sidereal and Tropical.

PLATE VI.

247. As the Sun describes the whole Ecliptic, or 360 degrees, in a Tropical year, he moves 59ʹ 8ʺ of a degree every day; and consequently 50ʺ of a degree in 20 minutes 171⁄2 seconds of time: therefore, he will arrive at the same Equinox or Solstice when he is 50ʺ of a degree short of the same Star or fixed point in the Heavens from which he set out in the year before. So that, with respect to the fixed Stars, the Sun and Equinoctial points fall back (as it were) 30 degrees in 2160 years; which will make the Stars appear to have gone 30 deg. forward, with respect to the Signs of the Ecliptic in that time: for the same Signs always keep in the same points of the Ecliptic, without regard to the constellations.

A Table shewing the Precession of the Equinoctial Points in the Heavens, both in Motion and Time; and the Anticipation of the Equinoxes on Earth.
Julian years. Precession of the Equinoctial Points in the Heavens.   Anticipation of the Equinoxes on the Earth.
Motion. Time.
S. ° ʹ ʺ Days H. M. S. D. H. M. S.
1 0 0 0 50 0 0 20 171⁄2 0 0 11 3
2 0 0 1 40 0 0 40 35 0 0 22 6
3 0 0 2 30 0 1 0 521⁄2 0 0 33 9
4 0 0 3 20 0 1 21 10 0 0 44 12
5 0 0 4 10 0 1 41 271⁄2 0 0 55 15
6 0 0 5 0 0 2 1 45 0 1 6 18
7 0 0 5 50 0 2 22 21⁄2 0 1 17 21
8 0 0 6 40 0 2 42 20 0 1 28 24
9 0 0 7 30 0 3 2 371⁄2 0 1 39 27
10 0 0 8 20 0 3 22 55 0 1 50 30
20 0 0 16 40 0 6 45 50 0 3 41 0
30 0 0 25 0 0 10 8 45 0 5 31 30
40 0 0 33 20 0 13 31 40 0 7 22 0
50 0 0 41 40 0 16 54 35 0 9 12 30
60 0 0 50 0 0 20 17 30 0 11 3 0
70 0 0 58 20 0 23 40 25 0 12 53 30
80 0 1 6 40 1 3 3 20 0 14 44 0
90 0 1 15 0 1 6 26 15 0 16 34 30
100 0 1 23 20 1 9 49 10 0 18 25 0
200 0 2 46 40 2 19 38 20 1 12 50 0
300 0 4 10 0 4 5 27 30 2 7 15 0
400 0 5 33 20 5 15 16 40 3 1 40 0
500 0 6 56 40 7 1 5 50 3 20 5 0
600 0 8 20 0 8 10 55 0 4 14 30 0
700 0 9 43 20 9 20 44 10 5 8 55 0
800 0 11 6 40 11 6 33 20 6 3 20 0
900 0 12 29 0 12 16 22 30 6 21 45 0
1000 0 13 53 20 14 2 11 40 7 16 10 0
2000 0 27 46 40 28 4 23 20 15 8 20 0
3000 1 11 40 0 42 6 35 0 23 0 30 0
4000 1 25 33 20 56 8 46 40 30 16 40 0
5000 2 9 26 40 70 10 58 20 38 8 50 0
6000 2 23 20 0 84 13 10 0 46 1 0 0
7000 3 7 13 20 98 15 21 40 53 17 10 0
8000 3 21 6 40 112 17 33 20 61 9 20 0
9000 4 5 0 0 126 19 45 0 69 1 30 0
10000 4 18 53 20 140 21 56 40 76 17 40 0
20000 9 7 46 40 281 19 53 20 153 11 20 0
25920 12 0 0 0 365 6 0 0 198 21 36 0
Fig. IV.

To explain this by a Figure, let the Sun be in conjunction with a fixed Star at S, suppose in the 30th degree of ♉, on the 20th day of May 1756. Then, making 2160 revolutions through the Ecliptic VWX, 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 deg. of Taurus at T, which has receded back from S to T in that time, by the Precession of the Equinoctial points ♈ 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 50ʺ of a degree, or 20 min. 171⁄2 sec. of time, annually: this, in so many years, makes 30 days, 101⁄2 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 time 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 compleats 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 2s 20° 2ʹ 30ʺ since the creation; which is as much as the Sun moves in 81d 5h 0m 52s. And since that time, or in 5763 years, the Equinoxes with us have fallen back 44d 5h 21m 9s; hence, reckoning from the time of the Julian Equinox, A. D. 1756, viz. Sept. 12th, it appears that the Autumnal Equinox at the creation was on the 26th of October.

Julian years. Precession of the Equinoctial Points in the Heavens.   Anticipation of the Equinoxes on the Earth.
Motion. Time.
S. ° ʹ ʺ D. H. M. S. D. H. M. S.
5000 2 9 26 40 70 10 58 20 38 8 50 0
700 0 9 43 20 9 20 44 10 5 8 55 0
60 0 0 50 0 0 20 17 30 0 11 3 0
3 0 0 2 30 0 1 0 52 0 0 33 9
5763 2 20 2 30 81 5 0 52 44 5 21 9
The anticipation of the Equinoxes and Seasons.

PLATE VI.

249. The anticipation of the Equinoxes, and consequently of the seasons, is by no means owing to the Precession of the Equinoctial and Solsticial points 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 following table shews the length, and consequently the difference of any number of Sidereal, Civil, and Solar years from 1 to 10,000.

The reason for altering the Style.

250. The above 11 minutes 3 seconds, by which the Civil or Julian year exceeds the Solar, amounts to 11 days in 1433 years: and so much our seasons 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 suppress 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 Bissextile day in February at the end of every century of years 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 have been quite reversed with regard to the months of the years; though it would have required near 23,783 years to have brought about such a total change. If the Earth had made exactly 3651⁄4 diurnal rotations on its axis, whilst 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 needed any alteration.

The Precession of the Equinoctial Points.

251. Having already mentioned the cause of the Precession of the Equinoctial points in the heavens, § 246, which occasions a flow deviation of the earth’s axis from its parallelism, and thereby a change of the declination of the Stars from the Equator, together with a slow apparent motion of the Stars forward with respect to the Signs of the Ecliptic; we shall now describe the Phenomena by a Diagram.

Fig. V.

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, T♋Z 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 [57]the Equinoctial points recede in the Ecliptic, the Earth’s Axis SON is in motion upon the Earth’s center 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 Circle ABCDA in the starry Heavens, round the Pole of the Ecliptic, which keeps immoveable in the center of that Circle. The Earth’s Axis being 231⁄2 degrees inclined to the Axis of the Ecliptic, the Circle ABCDA, 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, 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 backwards a degree every 72 years, will be directed towards the Star or Point B in 6480 years hence: and in double of that time, or 12,960 years, it will be directed towards the Star or Point C; which will then be the North Pole of the Heavens, although it is at present 81⁄2 degrees south of the Zenith of London L. The present position of the Equator EOQ will then be changed into eOq, the Tropic of Cancer T♋Z into Vt♋, and the Tropic of Capricorn VT♑ into t♑Z; as is evident by the Figure. And the Sun, in the same part of the Heavens where he is now over the earthly Tropic of Capricorn, and makes the shortest days and longest nights in the Northern Hemisphere, will then be over the earthly Tropic of Cancer, and make the days longest, and nights shortest. So that it will require 12,960 years yet more, or 25,920 from the present 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, and Poles, by the Earth’s diurnal motion, will describe them over again.

A TABLE shewing the Time contained in any number of Sidereal, Julian, and Solar Years, from 1 to 10000.
Sidereal Years.   Julian Years.   Solar Years.
Years Days H. M. S. Days H. Days H. M. S.
1 Contain 365 6 9 141⁄2 Contain 365 6 Contain 365 5 48 57
2 730 12 18 29 730 12 370 11 37 54
3 1095 18 27 431⁄2 1095 18 1095 17 26 51
4 1461 0 36 58 1461 0 1460 23 15 48
5 1826 6 46 121⁄2 1826 6 1826 5 4 45
6 2191 12 55 27 2191 12 2191 10 53 42
7 2556 19 5 411⁄2 2556 18 2556 16 42 39
8 2922 1 13 56 2922 0 2921 22 31 36
9 3287 7 23 101⁄2 3287 6 3287 4 20 33
10 3652 13 32 25 3652 12 3652 10 9 30
20 7305 3 4 50 7305 0 7304 20 19 0
30 10957 16 37 15 10957 12 10957 6 28 30
40 14610 6 9 40 14610 0 14609 16 38 0
50 18262 19 42 5 18262 12 18262 2 47 30
60 21915 9 14 30 21915 0 21914 12 57 0
70 25567 22 46 55 25567 12 25566 23 6 30
80 29220 12 19 20 25220 0 29219 9 16 0
90 32873 1 51 45 32872 12 32871 19 25 30
100 36525 15 24 10 36525   36524 5 35  
200 73051 6 48 20 73050   73048 11 10  
300 109576 22 12 30 109575   109572 16 45  
400 146102 13 36 40 146100   146096 22 20  
500 182628 5 0 50 182625   182621 3 55  
600 219153 20 25   219150   219145 9 30  
700 255679 11 49 10 255675   255669 15 5  
800 292205 3 13 20 292200   292193 20 10  
900 328730 18 37 30 328725   328718 2 15  
1000 365256 10 1 40 365250   365242 7 50  
2000 730512 20 3 20 730500   730484 15 40  
3000 1095769 6 5   1095750   1095726 23 30  
4000 1461025 16 6 40 1461000   1460969 7 20  
5000 1826282 2 8 20 1826250   1826211 15 10  
6000 2191538 12 10   2191500   2191453 14 40  
7000 2556794 22 11 40 2556750   2556696 6 50  
8000 2922051 8 13 20 2922000   2921938 14 40  
9000 3287037 18 15   3287250   3287180 22 30  
10000 3652564 4 16 40 3652500   3652423 6 20  
A TABLE shewing the Sun’s true Place, and Distance from his Apogee, for the second Year after Leap-year.
Days January February March April May June
Sun’s Place. Sun’s Anom. Sun’s Place. Sun’s Anom. Sun’s Place. Sun’s Anom. Sun’s Place. Sun’s Anom. Sun’s Place. Sun’s Anom. Sun’s Place. Sun’s Anom.
D. M. S. D. D. M. S. D. D. M. S. D. D. M. S. D. D. M. S. D. D. M. S. D.
1 11♑ 7 6 2 12♒ 39 7 3 10♓ 53 8 0 11♈ 40 9 1 10♉ 57 10 0 10♊ 46 11 1
2 12 8 6 3 13 40 7 4 11 53 8 1 12 39 9 2 11 55 10 1 11 44 11 2
3 13 9 6 4 14 41 7 5 12 53 8 2 13 38 9 3 12 53 10 2 12 41 11 3
4 14 10 6 5 15 42 7 6 13 53 8 3 14 37 9 4 13 51 10 3 13 38 11 4
5 15 11 6 6 16 43 7 7 14 53 8 4 15 36 9 5 14 49 10 4 14 35 11 5
6 16 12 6 7 17 43 7 8 5 53 8 5 16 35 9 6 15 47 10 5 15 33 11 6
7 17 14 6 8 18 44 7 9 16 53 8 6 17 34 9 7 16 45 10 6 16 30 11 7
8 18 15 6 9 19 45 7 10 17 53 8 7 18 33 9 8 17 43 10 7 17 28 11 8
9 19 16 6 10 20 46 7 11 18 53 8 8 19 32 9 9 18 41 10 8 18 25 11 9
10 20 17 6 11 21 46 7 12 19 53 8 9 20 30 9 10 19 39 10 9 19 22 11 10
11 21 18 6 12 22 47 7 13 20 52 8 10 21 29 9 11 20 37 10 10 20 20 11 11
12 22 19 6 13 23 47 7 14 21 52 8 11 22 28 9 12 21 34 10 11 21 17 11 12
13 23 21 6 14 24 48 7 15 22 52 8 12 23 26 9 13 22 32 10 12 22 14 11 13
14 24 22 6 15 25 48 7 16 23 52 8 13 24 25 9 14 23 30 10 13 23 11 11 14
15 25 23 6 16 26 49 7 17 24 51 8 14 25 24 9 15 24 28 10 14 24 8 11 15
16 26 24 6 17 27 49 7 18 25 51 8 15 26 22 9 16 25 26 10 15 25 6 11 16
17 27 25 6 18 28 50 7 19 26 51 8 16 27 21 9 17 26 23 10 16 26 3 11 17
18 28 26 6 19 29 50 7 20 27 50 8 17 28 19 9 18 27 21 10 17 27 0 11 18
19 29 27 6 20 ♓ 51 7 21 28 50 8 18 29 18 9 19 28 19 10 18 27 58 11 18
20 ♒ 28 6 21 1 51 7 22 29 49 8 19 ♉ 16 9 20 29 16 10 19 28 55 11 19
21 1 29 6 22 2 51 7 23 ♈ 49 8 20 1 15 9 21 ♊ 15 10 20 29 52 11 20
22 2 30 6 23 3 52 7 24 1 48 8 21 2 13 9 22 1 11 10 21 ♋ 49 11 21
23 3 31 6 24 4 52 7 25 2 47 8 22 3 11 9 23 2 9 10 22 1 46 11 22
24 4 32 6 25 5 52 7 26 3 47 8 23 4 10 9 24 3 6 10 23 2 44 11 23
25 5 33 6 26 6 52 7 27 4 46 8 24 5 8 9 25 4 4 10 24 3 41 11 24
26 6 34 6 27 7 53 7 28 5 45 8 25 6 6 9 26 5 2 10 25 4 38 11 25
27 7 35 6 28 8 53 7 29 6 45 8 26 7 4 9 27 5 59 10 26 5 35 11 26
28 8 36 6 29 9 53 8 0 7 44 8 27 8 3 9 28 6 56 10 27 6 32 11 27
29 9 37 7 0         8 43 8 28 9 1 9 29 7 54 10 28 7 30 11 28
30 10 38 7 1         9 42 8 29 9 59 9 29 8 51 10 29 8 27 11 29
31 11 39 7 2         10 41 9 0         9 48 11 0