_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 14-1/2 seconds. The _Sidereal Year_ is therefore 20
minutes 17-1/2 seconds longer than the Solar or Tropical year, and 9
minutes 14-1/2 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.
[Sidenote: 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 17-1/2 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_. |
+--------+--------------------------------------++-----------------+
| | Precession of the Equinoctial || Anticipation of |
| | Points in the Heavens. || the Equinoxes |
| Julian +----------------+---------------------++ on the Earth. |
| years. | Motion. | Time. || |
| +----------------+---------------------++-----------------+
| | S. ° ʹ ʺ | Days H. M. S. || D. H. M. S. |
+--------+----------------+--------------------++------------------+
| 1 | 0 0 0 50 | 0 0 20 17-1/2 || 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 52-1/2 || 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 27-1/2 || 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 2-1/2 || 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 37-1/2 || 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 |
+--------+----------------+---------------------++-----------------+
[Sidenote: 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.
17-1/2 sec. of time, annually: this, in so many years, makes 30 days,
10-1/2 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 2^s 20° 2ʹ 30ʺ since the
creation; which is as much as the Sun moves in 81^d 5^h 0^m 52^s. And
since that time, or in 5763 years, the Equinoxes with us have fallen
back 44^d 5^h 21^m 9^s; 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_.
+---------+----------------------------------++----------------+
| | Precession of the Equinoctial || Anticipation |
| | Points in the Heavens. || of the |
| Julian +-----------------+----------------+| Equinoxes on |
| years. | Motion. | Time. || the Earth. |
| +-----------------+----------------++----------------+
| | 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 |
+---------+-----------------+----------------++----------------+
[Sidenote: The anticipation of the Equinoxes and Seasons.