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.)