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.
[Sidenote: 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.
[Sidenote: A Table of the Equation of Time depending on the Sun’s place
in the Ecliptic.