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upon it. But this difference being always very small, ther,wo keep in near proximity to each other while they pursuetheir respective paths around the Sun. Even if the Earth ceased to exist, the Moon ’s orbit round the Sun would continueto be very little different from what it now is; nor wmuld theMoon , in that respect, much feel the absence of its largercompanion.
We must now pass on from the theory of the Moon ’smovements to that of its Phases and Lihratiom. We areall accustomed to the regular course of the former as, monthby month, we watch the alternate waxing and waning of thefull circular disc from the narrow crescent, seen two or threedays after the Moon is New, whose delicate beauty almosttempts us to exclaim :—
“ I would that aspect never might be changed.
Nor that fine form, so spirit-like, be spoiledWith fuller light.
Keep the delicious honour of thy youth,
Sweet sister of the Sun,.more beauteous thouThan he sublime I ”
But the explanation of these Phases is not a very simplematter, unless certain mathematical propositions can beassumed or certain experimental demonstrations be given.It is easy enough to understand that one-half of the Moon ’ssurface is always illuminated by the Sun, and that the whole ofthat illuminated half is seen at the time of Full Moon , whilethe dark half is turned towards us at the time of New Moon .The next point to be realized involves, however, slightly moredifficulty, viz., that when we look at the illuminated hemisphereof the Full Moon , the appearance presented, owing to itsdistance from us, is not that of a hemisphere, but that of aflat, circular disc, which is, in mathematical language, theprojection of the hemisphere upon a plane perpendicular tothe line of sight.
But to come to something still less easy, let us supposethat just one-half of the hemisphere, which we see, isilluminated. The boundary between the light and dark partsseen will in this case be a circle passing half-way round thespherical surface of the Moon . But, as the whole hemisphere