264. The Moon’s periodical and synodical revolution may be familiarly
represented by the motions of the hour and minute hands of a watch round
it’s dial-plate, which is divided into 12 equal parts or hours, as the
Ecliptic is divided into 12 Signs, and the year into 12 months. Let us
suppose these 12 hours to be 12 months, the hour hand the Sun, and the
minute hand the Moon; then will the former go round once in a year, and
the latter once in a month; but the Moon, or minute hand must go more
than round from any point of the Circle where it was last conjoined with
the Sun, or hour hand, to overtake it again: for the hour hand being in
motion, can never be overtaken by the minute hand at that point from
which they started at their last conjunction. The first column of the
annexed Table shews the number of conjunctions which the hour and minute
hand make whilst the hour hand goes once round the dial-plate; and the
other columns shew the times when the two hands meet at every
conjunction. Thus, suppose the two hands to be in conjunction at XII, as
they always are; then, at the first following conjunction it is 5
minutes 27 seconds 16 thirds 21 fourths 49-1/11 fifths past I where they
meet; at the second conjunction it is 10 minutes 54 seconds 32 thirds 43
fourths 38-1/2 fifths past II; and so on. This, though an easy
illustration of the motions of the Sun and Moon, is not precise as to
the times of their conjunctions; because, while the Sun goes round the
Ecliptic, the Moon makes 12-1/3 conjunctions with him; but the minute
hand of a watch or clock makes only 11 conjunctions with the hour hand
in one period round the dial-plate. But if, instead of the common
wheel-work at the back of the dial-plate, the Axis of the minute hand
had a pinion of 6 leaves turning a wheel of 40, and this last turning
the hour hand, in every revolution it makes round the dial-plate the
minute hand would make 12-1/3 conjunctions with it; and so would be a
pretty device for shewing the motions of the Sun and Moon; especially,
as the slowest moving hand might have a little Sun fixed on it’s point,
and the quickest a little Moon. Besides, the plate, instead of hours and
quarters, might have a Circle of months, with the 12 Signs and their
Degrees; and if a plate of 29-1/2 equal parts for the days of the Moon’s
age were fixed to the Axis of the Sun-hand, and below it, so as the Sun
always kept at the 1/2 day of that plate, the Moon-hand would shew the
Moon’s age upon that plate for every day pointed out by the Sun-hand in
the Circle of months; and both Sun and Moon would shew their places in
the Ecliptic: for the Sun would go round the Ecliptic in 365 Days and
the Moon in 27-1/3 days, which is her periodical revolution; but from
the Sun to the Sun again, or from Change to Change, in 29-1/2 days,
which is her synodical revolution.
+-----+-------------------------------+
|Conj.| H. M. S. ʺʹ ʺʺ v p^{ts}. |
+-----+-------------------------------+
| 1 | I 5 27 16 21 49-1/11 |
| 2 | II 10 54 32 43 38-2/11 |
| 3 | III 16 21 49 5 27-3/11 |
| 4 | IIII 21 49 5 27 16-4/11 |
| 5 | V 27 16 21 49 5-5/11 |
| 6 | VI 32 43 38 10 54-6/11 |
| 7 | VII 38 10 54 32 43-7/11 |
| 8 | VIII 43 38 10 54 32-8/11 |
| 9 | IX 49 5 27 16 21-9/11 |
| 10 | X 54 32 43 38 10-10/11|
| 11 | XII 0 0 0 0 0 |
+-----+-------------------------------+
[Sidenote: The Moon’s motion thro’ open space described.]
265. If the Earth had no annual motion, the Moon’s motion round the
Earth, and her track in absolute space, would be always the same[58].
But as the Earth and Moon move round the Sun, the Moon’s real path in
the Heavens is very different from her path round the Earth: the latter
being in a progressive Circle, and the former in a curve of different
degrees of concavity, which would always be the same in the same parts
of the Heavens, if the Moon performed a compleat number of Lunations in
a year.
[Sidenote: An idea of the Earth’s path and the Moon’s.]
266. Let a nail in the end of the axle of a chariot-wheel represent the
Earth, and a pin in the nave the Moon; if the body of the chariot be
propped up so as to keep that wheel from touching the ground, and the
wheel be then turned round by hand, the pin will describe a Circle both
round the nail and in the space it moves through. But if the props be
taken away, the horses put to, and the chariot driven over a piece of
ground which is circularly convex; the nail in the axle will describe a
circular curve, and the pin in the nave will still describe a circle
round the progressive nail in the axle, but not in the space through
which it moves. In this case, the curve described by the nail will
resemble in miniature as much of the Earth’s annual path round the Sun,
as it describes whilst the Moon goes as often round the Earth as the pin
does round the nail: and the curve described by the nail will have some
resemblance of the Moon’s path during so many Lunations.
[Sidenote: Fig. II.