Example II. On the 16th of June, the Sun is in the 25th degree of ♊ 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 Clocks are again equal on that day.
Example III. On the 31st of August the Sun’s place is 7 degrees 52 minutes of ♍ Virgo (which we shall call the 8th degree, as it is so near) and his Anomaly is 2 Signs 0 Degrees; the Equation arising from the former is 6 minutes 41 seconds too slow; and from the latter 6 minutes 39 seconds too fast; the difference being only 2 seconds too slow at noon, and decreasing towards an equality will make the Sun and Clocks equal in the afternoon of that day.
Example. IV. On the 23d of December the Sun’s place is 1 degree 41 minutes (call it 2 degrees) of ♑ Capricorn, and his Anomaly is 5 Signs 23 Degrees; 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 Clocks 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 Clocks are equal; but if we work examples for all other days of the year we shall find them different. And,
Remark.
244. On those days which are equidistant from any Equinox or Solstice, we do not find that the Equation 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 not, at present, fall either into the Equinoctial or Solsticial points § [242].
The reason why Equation Tables are but temporary.
245. If the line of the Apsides, together with the Equinoctial and Solsticial points, were immoveable, a general Equation Table might be made from the preceding Equation Tables, which would always keep true, because these Tables themselves are permanent. But, with respect to the fixed Stars, the line of the Apsides moves forwards 12 seconds of a degree every year, and the above points 50 seconds backward. So that if in any given year, the Equinoctial points, and line of the Apsides were coincident, in 100 years afterward they would be separated 1 degree 43 minutes 20 seconds; and consequently in 5225.8 years they would be separated 90 degrees, and could not meet again, so that the same Equinoctial point should fall again into the Apogee in less than 20,903 years: and this is the shortest Period in which the Equation of Time can be restored to the same state again, with respect to the same seasons of the year.
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.