227. As the Equation of time, or difference between the time shewn by a well regulated Clock and a true Sun-dial, depends upon two causes, namely, the obliquity of the Ecliptic, and the unequal motion of the Earth in it, we shall first explain the effects of these causes separately considered, and then the united effects resulting from their combination.

[PLATE VI].
The first part of the Equation of time.

228. The Earth’s motion on it’s Axis being perfectly equable, or always at the same rate, and the [[55]]plane of the Equator being perpendicular to it’s Axis, ’tis evident that in equal times equal portions of the Equator pass over the Meridian; and so would equal portions of the Ecliptic if it were parallel to or coincident with the Equator. But, as the Ecliptic is oblique to the Equator, the equable motion of the Earth carries unequal portions of the Ecliptic over the Meridian in equal times, the difference being proportionate to the obliquity; and as some parts of the Ecliptic are much more oblique than others, those differences are unequal among themselves. Therefore, if two Suns should start either from the beginning of Aries or Libra, and continue to move through equal arcs in equal times, one in the Equator, and the other in the Ecliptic, the equatoreal Sun would always return to the Meridian in 24 hours time, as measured by a well regulated clock; but the Sun in the Ecliptic would return to the Meridian sometimes sooner, and sometimes later than the equatoreal Sun; and only at the same moments with him on four days of the year; namely, the 20th of March, when the Sun enters Aries; the 21st of June, when he enters Cancer; the 23d of September, when he enters Libra; and the 21st of December, when he enters Capricorn. But, as there is only one Sun, and his apparent motion is always in the Ecliptic, let us henceforth call him the real Sun, and the other which is supposed to move in the Equator the fictitious; to which last, the motion of a well regulated clock always answers.

Fig. III.

Let Z♈z♎ be the Earth, ZFRz it’s Axis, abcde &c. the Equator, ABCDE &c. the northern half of the Ecliptic from ♈ to ♎ on the side of the Globe next the eye, and MNOP &c. the southern half on the opposite side from ♎ to ♈. Let the points at A, B, C, D, E, F, &c. quite round from ♈ to ♈ again bound equal portions of the Ecliptic, gone through in equal times by the real Sun; and those at a, b, c, d, e, f, &c. equal portions of the Equator described in equal times by the fictitious Sun; and let Z♈z be the Meridian.

As the real Sun moves obliquely in the Ecliptic, and the fictitious Sun directly in the Equator, with respect to the Meridian, a degree, or any number of degrees, between ♈ and F on the Ecliptic, must be nearer the Meridian Z♈z, than a degree, or any corresponding number of degrees on the Equator from ♈ to f; and the more so, as they are the more oblique: and therefore the true Sun comes sooner to the Meridian whilst he is in the quadrant ♈ F, than the fictitious Sun does in the quadrant ♈ f; for which reason, the solar noon precedes noon by the Clock, until the real Sun comes to F, and the fictitious to f; which two points, being equidistant from the Meridian, both Suns will come to it precisely at noon by the Clock.

Whilst the real Sun describes the second quadrant of the Ecliptic FGHIKL from ♋ to ♎; he comes later to the Meridian every day, than the fictitious Sun moving through the second quadrant of the Equator from f to ♎; for the points at G, H, I, K, and L being farther from the Meridian than their corresponding points at g, h, i, k, and l, they must be later of coming to it: and as both Suns come at the same moment to the point ♎, they come to the Meridian at the moment of noon by the Clock.

In departing from Libra, through the third quadrant, the real Sun going through MNOPQ towards ♑ at R, and the fictitious Sun through mnopq towards r, the former comes to the Meridian every day sooner than the latter, until the real Sun comes to ♑, and the fictitious to r, and then they both come to the Meridian at the same time.

Lastly, as the real Sun moves equably through STUVW, from ♑ towards ♈; and the fictitious Sun through stuvw, from r towards ♈, the former comes later every day to the Meridian than the latter, until they both arrive at the point ♈, and then they make noon at the same time with the clock.

A Table of the Equation of Time depending on the Sun’s place
in the Ecliptic.
[PLATE VI].