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four days of the year; namely, when the Sun enters Aries, Cancer, Libra, and Capricorn : but the other cause, now explained, would make the Sun and clock equal only twice in a year; that is, when the Sun is in his apogee, and in hisperigee. Consequently, when these two points fall in the beginnings of Cancer and Capricorn, or of Aries and Libra, they concur in making the Sun and clock equal in these points. But the apogee at present is in the 9th degree of Cancer, and the perigee in the 9th degree of Capricorn; and therefore the Sun and clock cannot be equal about the beginnings of these signs, nor at any time of the year, except when the swiftness or slowness of the equation resulting from one cause just balances the slowness or swiftness arising from the other.
243. The second table in the following chapter shews the Sun's place in the ecliptic at the noon of every day by the clock, for the second year after leap-year; and also the Sun's anomaly to the nearest degree, neglecting the odd minutes of that de. gree. Its use is only to assist in the method of making a general equation-table from the two forementioned tables of equation depending on the Sun's place and anomaly, $ 229, 241; concerning which method we shall give a few examples presently. The next tables which follow them are made from those two; and shew the absolute equation of time resulting from the combination of both its causes; in which the minutes as well as degrees, both of the Sun's place and anomaly, are considered. The use of
. these tables is already explained, $ 225: and they serve for every day in leap-year, and the first, second, and third years after: For on most of the same days of all these years the equation differs, because of the odd six hours more than the 365 days of which the year consists.
Example I. On the 14th of April, the Sun is in for maks the 25th degree of r Aries and his anomaly is 9 ing equasigns 15 degrees; the equation resulting from the tion-tables.
former is 7 minutes 22 seconds of time too fast, ý 229; and from the latter, 7 minutes 24 seconds too slow, 1241; the difference is 2 seconds that the Sun is too slow at the noon of that day, taking it in gross for the degrees of the Sun's place and anomaly, without making proportionable allowance for the odd minutes. Hence at noon, the swiftness of the one equation balancing so nearly the slowness of the other, makes the Sun and clock equal on some part of that day.
EXAMPLE II. On the 16th of June, the Sun is in the 25th degree of a Gemini, and his anomaly is 11 signs 16 degrees; the equation arising from the former is 1 minute 48 seconds too fast; and from the latter 1 minute 50 seconds too slow; which balancing one another at noon to 2 seconds, the Sun and clock are again equal on that day.
Example III. On the 31st of August, the Sun's place is 8 degrees 11 minutes of me Virgo (which we call the 8th degree, as it is so near), and his ano. maly is 1 sign 29 degrees; the equation arising from the former is 6 minutes 40 seconds too slow; and from the latter, 6 minutes 32 seconds too fast; the difference being only 8 seconds too slow at noon, and decreasing toward an equality, will make the Sun and clock equal in the evening of that day.
EXAMPLE IV. On the 23d of December, the Sun's place is 1 degree 58 minutes (call it 2 degrees of vs Capricorn), and his anomaly is 5 signs 23 de. grees; the equation for the former is 43 seconds too slow, and for the latter 58 seconds too fast; the difference is 15 seconds too fast at noon; which decreasing will come to an equality, and so make the Sun and clock equal in the evening of that day.
And thus we find, that on some part of each of the above-mentioned four days, the Sun and clock are equal; but if we work examples for all other days of the year, we shall find them different. And,
244. On those days which are equidistant from any equinox or solstice, we do not find that the cquation is as much too fast or too slow on the one side, as it is too slow or too fast on the other. The reason is, that the line of the apsides, $ 238, does Remark, not, at present, fall either into the equinoctial or the solstitial points, | 242.
245. The four following equation-tables, for leap. The rea. year, and the first, second, and third years after, son why would serve for ever, if the Sun's place and anomaly tables are were always the same on every given day of the year, but temas on the same day four years before or after. But porary. since that is not the case, no general equation-tables can be so constructed as to be perpetual.
Of the Precession of the Equinoxes.
T has been already observed, § 116, that by 246.
the Earth's motion on its axis, there is more matter accumulated all around the equatorial 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 from any star, or other fixed point in the heavens, the moment when he is departing from the equinoctial, or from either tropic; he will come to the same cquinox or tropic again 20 min. 17° sec. of time, or 50 seconds of a degree, before he completes his course, so as to arrive at the same fixed star or point from whence he set out. For the equinoctial points recede 50 seconds of a degrec westward cvery year, contrary to the Sun's annual progressive motion.
When the Sun arrives at the same * equinoctial or solstitial point, he finishes what we call the tropi. cal year; which, by observation, is found to con. tain 365 days 5 hours 48 minutes 57 seconds : and when he arrives at the same fixed star again, as seen from the Earth, he completes the sidereal year, which contains 365 days 6 hours 9 minutes 14 seconds. The sidereal year is therefore 20 minutes 174 seconds longer than the solar or tropical year, and 9 minutes 14 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 the tropical.
247. As the Sun describes the whole ecliptic, or 360 degrees, in a tropical year, he moves 59' 8" of a degree every day at a mean rate: and consequently 50' of a degree in 20 minutes 173 seconds of time: therefore he will arrive at the same equinox or sol. stice when he is 50' of a degree short of the same star or fixed point in the heavens from which he set out 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.
To explain this by a figure, let the Sun be in conjunction with a fixed star at S, suppose in the 30th degree of 8, on the 21st day of May 1756. Then making 2160 revolutions through the ecliptic VWX,
* The two opposite points in which the ecliptic crosses the equinoctial, are called the equinoctial points: and the two points where the ecliptic touches the tropics (which are likewise opposite, and 90 degrees from the former) are called the solstitial points.
runs A TABLE shewing the Precession of the Equinoctial Points in the
Heavens, both in Motion and Time; and the Anticipation of the
Equinoxes on Julian
the Earth. years. Motion.
8O 9 O 10 O
Days H. M.
D. H. M. S. 0 50 0
11 1 40 0 0 40 35 O 0 22 6 2 301 0 1 0
0 0 33 9 3 20 1 21 10 O O 44
12 4 10
0 55 15 5 0
45 O 1 6 18 5 50
2 22 21 0 1 17 21 6 40
20 0 1 28 24 7 30 O 3
0 1 39 27 8 201 O 3 22
1 50 30 16 401 0 6
45 50 0 3 41 25 0 0
8 45 0 5 31 30 33 20 0 13 31
0 7 22
0 9 12 30 50 0 0 20 17 30 0 11 8 O 58 20 0 23 40 25 0 12 53 SO 6 40 1 3 3 20 0 14
44 0 15 0 1 6 20 15 0 16
34 30 23 20 1 9 49 10 0
20 5 15 16 40 3 i 40
10 5 8 55
23 0 SO
13 10 0 46 1 0
61 9 20
0 198 21 36 0
300 O 4 4001 O 5 500 0 6 600 O 8 700 O 9 8001 O 11 9001 O 12 1000 O
23 70001 3 7 8000! 3 21 9000 4 5 100001 4 18 20000 9 7 2592012 0