Mean Anomaly, what.

239. The distance that the Sun has gone in any time from his Apogee (not the distance he has to go to it though ever so little) is called his mean Anomaly, and is reckoned in Signs and Degrees, allowing 30 Degrees to a Sign. Thus, when the Sun has gone suppose 174 degrees from his Apogee at A, he is said to be 5 Signs 24 Degrees from it, which is his mean Anomaly: and when he is gone suppose 355 degrees from his Apogee, he is said to be 11 Signs 25 Degrees from it, although he be but 5 Degrees short of A in coming round to it again.

240. From what was said above it appears, that when the Sun’s Anomaly is less than 6 Signs, that is, when he is any where between A and C, in the half ABC of his orbit, the true noon precedes the fictitious; but when his Anomaly is more than 6 Signs, that is, when he is any where between C and A, in the half CDA of his Orbit, the fictitious noon precedes the true. When his Anomaly is 0 Signs 0 Degrees, that is, when he is in his Apogee at A; or 6 Signs 0 Degrees, which is when he is in his Perigee at C; he comes to the Meridian at the moment that the fictitious Sun does, and then it is noon by them both at the same instant.

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A Table of the Equation of Time, depending on the Sun’s Anomaly.

241. The annexed Table shews the Variation, or Equation of time depending on the Sun’s Anomaly, and arising from his unequal motion in the Ecliptic; as the former Table § [229] shews the Variation depending on the Sun’s place, and resulting from the obliquity of the Ecliptic: this is to be understood the same way as the other, namely, that when the Signs are at the head of the Table, the Degrees are at the left hand; but when the Signs are at the foot of the Table the respective Degrees are at the right hand; and in both cases the Equation is in the Angle of meeting. When both the above-mentioned Equations are either faster or slower, their sum is the absolute Equation of Time; but when the one is faster, and the other slower, it is their difference. Thus, suppose the Equation depending on the Sun’s place, be 6 minutes 41 seconds too slow, and the Equation depending on the Sun’s Anomaly, be 4 minutes 20 seconds too slow, their Sun is 11 minutes 1 second too slow. But if the one had been 6 minutes 41 seconds too fast, and the other 4 minutes 20 seconds too slow, their difference had been 2 minutes 21 seconds too fast, because the greater quantity is too fast.

242. The obliquity of the Ecliptic to the Equator, which is the first mentioned cause of the Equation of Time, would make the Sun and Clocks agree on four days of the year; which are, when the Sun enters Aries, Cancer, Libra, and Capricorn: but the other cause, now explained, would make the Sun and Clocks equal only twice in a year; that is, when the Sun is in his Apogee and Perigee. 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 Clocks 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 Clocks cannot be equal about the beginning of these Signs, nor at any time of the year, except when the swiftness or slowness of Equation resulting from one cause just balances the slowness or swiftness arising from the other.

243. The last Table but one, at the end of this 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 a degree. Their use is only to assist in shewing the method of making a general Equation Table from the two fore-mentioned Tables of Equation depending on the Sun’s Place and Anomaly § [229], [241]; concerning which method we shall give a few examples presently. The following Tables are such as might be made from these two; and shew the absolute Equation of Time resulting from the combination of both it’s 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.

Examples for making Equation Tables.

Example I. On the 15th of April the Sun is in the 25th degree of ♈ Aries, and his Anomaly is 9 Signs 15 Degrees; the Equation resulting from the former is 7 minutes 23 seconds of time too fast § [229]; and from the latter, 7 minutes 27 seconds too slow, § [241]; the difference is 4 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 Clocks equal on some part of that day.