229. The annexed Table shews how much the Sun is faster or slower than the clock ought to be, so far as the difference depends upon the obliquity of the Ecliptic; of which the Signs of the first and third quadrants are at the head of the Table, and their Degrees at the left hand; and in these the Sun is faster than the Clock: the Signs of the second and fourth quadrants are at the foot of the Table, and their degrees at the right hand; in all which the Sun is slower than the Clock: so that entering the Table with the given Sign of the Sun’s place at the head of the Table, and the Degree of his place in that Sign at the left hand; or with the given Sign at the foot of the Table, and Degree at the right hand; in the Angle of meeting is the number of minutes and seconds that the Sun is faster or slower than the clock: or in other words, the quantity of time in which the real Sun, when in that part of the Ecliptic, comes sooner or later to the Meridian than the fictitious Sun in the Equator. Thus, when the Sun’s place is ♉ Taurus 12 degrees, he is 9 minutes 49 seconds faster than the clock; and when his place is ♋ Cancer 18 degrees, he is 6 minutes 2 seconds slower.

Sun faster than the Clock in
Degrees♈♉♊1st Q.
♎♏♐3d Q.
ʹʺʹʺʹʺDeg.
00082484630
102083583629
204084582528
31085481427
4119938126
513991174925
615991873524
721892472123
82379317622
925693665121
1031694163520
1133494561919
123539496218
1341195154517
1442995352716
154479545915
165495545014
1752195543113
1853895441212
1955495235211
2061095033210
216269473129
226419432518
236559382307
2479933296
257239271485
267369201274
27749913153
2881950432
298138560221
30824846000
2d Q.♍♌♋Deg.
4th Q.♓♒♑
Sun slower than the Clock in

Fig. III.

230. This part of the Equation of time may perhaps be somewhat difficult to understand by a Figure, because both halves of the Ecliptic seem to be on the same side of the Globe; but it may be made very easy to any person who has a real Globe before him, by putting small patches on every tenth or fifteenth degree both of the Equator and Ecliptic; and then, turning the ball slowly round westward, he will see all the patches from Aries to Cancer come to the brazen Meridian sooner than the corresponding patches on the Equator; all those from Cancer to Libra will come later to the Meridian than their corresponding patches on the Equator; those from Libra to Capricorn sooner, and those from Capricorn to Aries later: and the patches at the beginnings of Aries, Cancer, Libra, and Capricorn, being also on the Equator, shew that the two Suns meet there, and come to the Meridian together.

A machine for shewing the sidereal, the equal, and the solar
Time.
[PLATE VI].

231. Let us suppose that there are two little balls moving equably round a celestial Globe by clock-work, one always keeping in the Ecliptic, and gilt with gold, to represent the real Sun; and the other keeping in the Equator, and silvered, to represent the fictitious Sun: and that whilst these balls move once, round the Globe according to the order of Signs, the Clock turns the Globe 366 times round it’s Axis westward. The Stars will make 366 diurnal revolutions from the brasen Meridian to it again; and the two balls representing the real and fictitious Sun always going farther eastward from any given Star, will come later than it to the Meridian every following day; and each ball will make 365 revolutions to the Meridian; coming equally to it at the beginnings of Aries, Cancer, Libra, and Capricorn: but in every other point of the Ecliptic, the gilt ball will come either sooner or later to the Meridian than the silvered ball, like the patches above-mentioned. This would be a pretty-enough way of shewing the reason why any given Star, which, on a certain day of the year, comes to the Meridian with the Sun, passes over it so much sooner every following day, as on that day twelvemonth to come to the Meridian with the Sun again; and also to shew the reason why the real Sun comes to the Meridian sometimes sooner, sometimes later, than it is noon by the clock; and, on four days of the year, at the same time; whilst the fictitious Sun always comes to the Meridian when it is twelve at noon by the clock. This would be no difficult task for an artist to perform; for the gold ball might be carried round the Ecliptic by a wire from it’s north Pole, and the silver ball round the Equator by a wire from it’s south Pole, with a few wheels to each; which might be easily added to my improvement of the celestial Globe, described in No 483 of the Philosophical Transactions; and of which I shall give a description in the latter part of this Book, from the 3d Figure of the 3d plate.

Fig. III.

232. ’Tis plain that if the Ecliptic were more obliquely posited to the Equator, as the dotted Circle ♈x♎, the equal divisions from ♈ to x would come still sooner to the Meridian Z0♈ than those marked A, B, C, D, and E do: for two divisions containing 30 degrees, from ♈ to the second dott, a little short of the figure 1, come sooner to the Meridian than one division containing only 15 degrees from ♈ to A does, as the Ecliptic now stands; and those of the second quadrant from x to ♎ would be so much later. The third quadrant would be as the first, and the fourth as the second. And it is likewise plain, that where the Ecliptic is most oblique, namely about Aries and Libra, the difference would be greatest: and least about Cancer and Capricorn, where the obliquity is least.

The second part of the Equation of Time.
[PLATE VI].

234. Having explained one cause of the difference of time shewn by a well-regulated Clock and a true Sun-dial; and considered the Sun, not the Earth, as moving in the Ecliptic; we now proceed to explain the other cause of this difference, namely, the inequality of the Sun’s apparent motion § [205], which is slowest in summer, when the Sun is farthest from the Earth, and swiftest in winter when he is nearest to it. But the Earth’s motion on it’s Axis is equable all the year round, and is performed from west to east; which is the way that the Sun appears to change his place in the Ecliptic.