enlightened side she appears gibbous, as at d. At E her whole enlightened side is toward the Earth, and therefore she appears round as at e; when we say it is full Moon. In her third octant at F, part of her dark side being toward the Earth, she again appears gibbous, and is on the decrease, as at ƒ. At G we see just one half of her enlightened side, and she appears half-decreased, or in her third quarter, as at g. At H we only see a quarter of her enlightened side, being in her fourth octant, where she appears horned, as at h. And at A, having completed her course from the Sun to the Sun again, she disappears; and we say, it is new Moon. Thus, in going from A to E, the Moon seems continually to increase; and in going from E to A, to decrease in the same proportion; having like phases at equal distances from A to E; but as seen from the Sun S, she is always full.

Moon's

256. The Moon appears not perfectly round when The she is full in the highest or lowest part of her orbit, disc not because we have not a full view of her enlightened always side at that time. When full in the highest part of quite her orbit a small deficiency appears on her lower when full. edge; and the contrary, when full in the lowest part of her orbit.

round

ses of the

257. It is plain by the figure, that when the Moon The phachanges to the Earth, the Earth appears full to the Earth and Moon; and vice versa. For when the Moon is at Moon conA, new to the Earth, the whole enlightened side oftrary. the Earth is toward the Moon; and when the Moon is at E, full to the Earth, its dark side is toward her. Hence a new Moon answers to a full Earth, and a full Moon to a new Earth. The quarters are also

reversed to each other.

nomenon.

258. Between the third quarter and change, the An agreeMoon is frequently visible in the forenoon, even when able phethe Sun shines; and then she affords us an opportunity of seeing a very agreeable appearance, wherever we find a globular stone above the level of the eye,

The nona

degree

what.

as suppose on the top of a gate. For, if the Sun shines on the stone, and we place ourselves so as the upper part of the stone may just seem to touch the point of the Moon's lowermost horn, we shall then see the enlightened part of the stone exactly of the same shape with the Moon; horned as she is, and inclined in the same way to the horizon. The reason is plain; for the Sun enlightens the stone the same way as he does the Moon: and both being globes, when we put ourselves into the above situation, the Moon and stone have the same position to our eye; and therefore we must see as much of the illuminated part of the one as of the other.

259. The position of the Moon's cusps, or a right gesimal line touching the points of her horns, is very differently inclined to the horizon at different hours of the same days of her age. Sometimes she stands, as it were, upright on her lower horn, and then such a line is perpendicular to the horizon; when this happens, she is in what the astronomers call the nonage simal degree; which is the highest point of the ecliptic above the horizon at that time, and is 90 degrees from both sides of the horizon, where it is then cut by the ecliptic. But this never happens when the Moon is on the meridian, except when she is at the very beginning of Cancer or Capricorn.

How the

of the ecliptic may be

Moon's

260. The inclination of that part of the ecliptic to inclination the horizon in which the Moon is at any time when horned, may be known by the position of her horns; for a right line touching their points is perpendicufound by lar to the ecliptic. And as the angle which the Moon's the posi tion of the orbit makes with the ecliptic can never raise her above, nor depress her below the ecliptic, more than two minutes of a degree, as seen from the Sun; it can have no sensible effect upon the position of her horns. Therefore, if a quadrant be held up, so as that one of its edges may seem to touch the Moon's horns, the graduated side being kept toward the eye, and as far from the eye as it can be conveniently held, the

horns.

VIL.

arc between the plumb-line and that edge of the PLATE quadrant which seems to touch the Moon's horns, will shew the inclination of that part of the ecliptic to the horizon. And the arc between the other edge of the quadrant and plumb-line, will shew the inclination of a line, touching the Moon's horns, to the horizon.

Moon ap.

pears as

261. The Moon generally appears as large as the Fig. I. Sun; for the angle v k A, under which the Moon is Why the seen from the Earth, is nearly the same with the angle LkM, under which the Sun is seen from it. And big as the therefore the Moon may hide the Sun's whole disc Sun. from us, as she sometimes does in solar eclipses. The reason why she does not eclipse the Sun at every change, shall be explained hereafter. If the Moon were farther from the Earth, as at a, she would never hide the whole of the Sun from us; for then she would appear under the angle Nk O, eclipsing only that part of the Sun which lies between Ñ and 0; were she still farther from the Earth, as at X, she would appear under the small angle Tk W, like a spot on the Sun, hiding only the part TW from our sight.

Moon's

axis.

262. That the Moon turns round her axis in the A proof time that she goes round her orbit, is quite demon- of the strable; for a spectator at rest, without the periphery turning of the Moon's orbit, would see all her sides turned round her regularly toward him in that time. She turns round her axis from any star to the same star again in 27 days 8 hours; from the Sun to the Sun again, in 291 days the former is the length of her sidereal day, and the latter the length of her solar day. A body moving round the Sun would have a solar day in eve ry revolution, without turning on its axis; the same as if it had kept all the while at rest, and the Sun moved round it: but without turning round its axis it could never have one sidereal day, because it would always keep the same side toward any given star.

Her periodical and

revolution.

263. If the Earth had no annual motion, the Moon synodical would go round it so as to complete a lunation, a sidereal, and a solar day, all in the same time. But because the Earth goes forward in its orbit while the Moon goes round the Earth in her orbit, the Moon must go as much more than round her orbit from change to change in completing a solar day, as the Earth has gone forward in its orbit during that time, i. e. almost a twelfth part of a circle.

Familiarly 264. The Moon's periodical and synodical revorepresent-lution may be familiarly represented by the motions

ed.

A Table shewing the times that the

of the hour and minute-hands of a watch round its 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 signs, the hour-hand, the Sun, and the minute-hand, the Moon; then the former will 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

hour and

minute

hands of a

in con

TT

junction.

6

VI 32

43

38 10

32 8

11

VII.

column of the preceding table shews the number of PLATE conjunctions which the hour and minute-hand make while the hour-hand goes once round the dial-plate; and the other columns shew the times when the two hands meet at each 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 fifths past I, where they meet: at the second conjunction it is 10 minutes 54 seconds 32 thirds 43 fourths 38 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 123 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 74, and this last turning the hourhand, in every revolution it makes round the dialplate, the minute-hand would make 123 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 its point, and the quickest, a little

moon.

motion

265. If the Earth had no annual motion, the The Moon's motion, round the Earth, and her track in Moon's open space, would be always the same. But as through the Earth and Moon move round the Sun, the open space Moon's real path in the heavens is very different from her visible path round the Earth: the latter be

*In this place, we may consider the orbits of all the satellites as circular, with respect to their primary planets; because the eccentricities of their orbits are too small to affect the phenomena here described.

Ff

describ

ed.