To illustrate this, let _ABCD_ be the _Ecliptic_, _RSTU_ a Circle lying
in the same Plane with the Ecliptic, and _VWXY_ the _Moon’s Orbit_, all
thrown into an oblique view, which gives them an elliptical shape to the
eye. One half of the Moon’s Orbit, as _VWX_, is always below the
Ecliptic, and the other half _XYV_ above it. The points _V_ and _X_,
where the Moon’s Orbit intersects the Circle _RSTU_, which lies even
with the Ecliptic, are the _Moon’s Nodes_; and a right line as _XEV_
drawn from one to the other, through the Earth’s center, is the _Line of
the Nodes_, which is carried almost parallel to itself round the Sun in
a year.
If the Moon moved round the Earth in the Orbit _RSTU_, which is
coincident with the Plane of the Ecliptic, her shadow would fall upon
the Earth every time she is in conjunction with the Sun; and at every
opposition she would go through the Earth’s shadow. Were this the case,
the Sun would be eclipsed at every Change, and the Moon at every Full,
as already mentioned.
But although the Moon’s shadow _N_ must fall upon the Earth at _a_, when
the Earth is at _E_, and the Moon in conjunction with the Sun at _i_,
because she is then very near one of her Nodes; and at her opposition
_n_ she must go through the Earth’s shadow _I_, because she is then near
the other Node; yet, in the time that she goes round the Earth to her
next Change, according to the order of the letters _XYVW_, the Earth
advances from _E_ to _e_, according to the order of the letters _EFGH_,
and the line of the Nodes _VEX_ being carried nearly parallel to itself,
brings the point _f_ of the Moon’s Orbit in conjunction with the Sun at
that next Change; and then the Moon being at _f_ is too high above the
Ecliptic to cast her shadow on the Earth: and as the Earth is still
moving forward, the Moon at her next opposition will be at _g_, too far
below the Ecliptic to go through any part of the Earth’s shadow; for by
that time the point _g_ will be at a considerable distance from the
Earth as seen from the Sun.
[Sidenote: Fig. I and II.]
When the Earth comes to _F_, the Moon in conjunction with the Sun _Z_ is
not at _k_, in a Plane coincident with the Ecliptic, but above it at _Y_
in the highest part of her Orbit: and then the point _b_ of her shadow
_O_ goes far above the Earth (as in Fig. II, which is an edge view of
Fig. I.) The Moon at her next opposition is not at _o_ (Fig I) but at
_W_ where the Earth’s shadow goes far above her, (as in Fig. II.) In
both these cases the line of the Nodes _VFX_ (Fig. I.) is about 90
degrees from the Sun, and both Luminaries as far as possible from the
limits of Eclipses.
[Sidenote: PLATE X.]
When the Earth has gone half round the Ecliptic from _E_ to _G_, the
line of the Nodes _VGX_ is nearly, if not exactly, directed towards the
Sun at _Z_; and then the New Moon _l_ casts her shadow _P_ on the Earth
_G_; and the Full Moon _p_ goes through the Earth’s shadow _L_; which
brings on Eclipses again, as when the Earth was at _E_.
When the Earth comes to _H_ the New Moon falls not at _m_ in a plane
coincident with the Ecliptic _CD_, but at _W_ in her Orbit below it: and
then her shadow _Q_ (see Fig. II) goes far below the Earth. At the next
Full she is not at _q_ (Fig. I) but at _Y_ in her orbit 5-1/3 degrees
above _q_, and at her greatest height above the Ecliptic _CD_; being
then as far as possible, at any opposition, from the Earth’s shadow _M_
(as in Fig. II.)
So, when the Earth is at _E_ and _G_, the Moon is about her Nodes at New
and Full; and in her greatest _North_ and _South Declination_, (or
Latitude as it is generally called) from the Ecliptic at her Quarters:
but when the Earth is at _F_ or _H_, the Moon is in her greatest _North_
and _South Declination_ from the Ecliptic at New and Full, and in the
_Nodes_ about her Quarters.
[Sidenote: The Moon’s ascending and descending Node.