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.
235. If the Sun’s motion were equable in the Ecliptic, the whole
difference between the equal time as shewn by a Clock, and the unequal
time as shewn by the Sun, would arise from the obliquity of the
Ecliptic. But the Sun’s motion sometimes exceeds a degree in 24 hours,
though generally it is less: and when his motion is slowest any
particular Meridian will revolve sooner to him than when his motion is
quickest; for it will overtake him in less time when he advances a less
space than when he moves through a larger.
236. Now, if there were two Suns moving in the plane of the Ecliptic, so
as to go round it in a year; the one describing an equal arc every 24
hours, and the other describing sometimes a less arc in 24 hours, and at
other times a larger; gaining at one time of the year what it lost at
the opposite; ’tis evident that either of these Suns would come sooner
or later to the Meridian than the other as it happened to be behind or
before the other: and when they were both in conjunction they would come
to the Meridian at the same moment.
[Sidenote: Fig. IV.]
237. As the real Sun moves unequably in the Ecliptic, let us suppose a
fictitious Sun to move equably in it. Let _ABCD_ be the Ecliptic or
Orbit in which the real Sun moves, and the dotted Circle _abcd_ the
imaginary Orbit of the fictitious Sun; each going round in a year
according to the order of letters, or from west to east. Let _HIKL_ be
the Earth turning round it’s Axis the same way every 24 hours; and
suppose both Suns to start from _A_ and _a_, in a right line with the
plane of the Meridian _EH_, at the same moment: the real Sun at _A_,
being then at his greatest distance from the Earth, at which time his
motion is slowest; and the fictitious Sun at _a_, whose motion is always
equable because his distance from the Earth is supposed to be always the
same. In the time that the Meridian revolves from _H_ to _H_ again,
according to the order of the letters _HIKL_, the real Sun has moved
from _A_ to _F_; and the fictitious with a quicker motion from _a_ to
_f_, through a larger arc: therefore, the Meridian _EH_ will revolve
sooner from _H_ to _h_ under the real Sun at _F_, than from _H_ to _k_
under the fictitious Sun at _f_; and consequently it will be noon by the
Sun-dial sooner than by the Clock.
[Sidenote: PLATE VI.]
As the real Sun moves from _A_ towards _C_, the swiftness of his motion
increases all the way to _C_, where it is at the quickest. But
notwithstanding this, the fictitious Sun gains so much upon the real,
soon after his departing from _A_, that the increasing velocity of the
real Sun does not bring him up with the equally moving fictitious Sun
till the former comes to _C_, and the latter to _c_, when each has gone
half round it’s respective orbit; and then being in conjunction, the
Meridian _EH_ revolving to _EK_ comes to both Suns at the same time, and
therefore it is noon by them both at the same moment.
But the increased velocity of the real Sun, now being at the quickest,
carries him before the fictitious; and therefore, the same Meridian will
come to the fictitious Sun sooner than to the real: for whilst the
fictitious Sun moves from _c_ to _g_, the real Sun moves through a
greater arc from _C_ to _G_: consequently the point _K_ has it’s
fictitious noon when it comes to _k_, but not it’s real noon till it
comes to _l_. And although the velocity of the real Sun diminishes all
the way from _C_ to _A_, and the fictitious Sun by an equable motion is
still coming nearer to the real Sun, yet they are not in conjunction
till the one comes to _A_ and the other to _a_; and then it is noon by
them both at the same moment.
And thus it appears, that the real noon by the Sun is always later than
the fictitious noon by the clock whilst the Sun goes from _C_ to _A_,
sooner whilst he goes from _A_ to _C_, and at these two points the Sun
and Clock being equal, it is noon by them both at the same moment.
[Sidenote: Apogee, Perigee, and Apsides, what.