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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

differ. ently 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 nonagesimal 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.

260. The inclination of that part of the ecliptic to inclination the horizon in which the Moon is at any time when ecliptic 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 tion of the orbit makes with the ecliptic can never raise her Moon's 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

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arc between the plumb-line and that edge of the PLATZ 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.

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 an

pears as gle 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 0, eclipsing only that part of the Sun which lies between N and 0; were she still farther from the Earth, as at X, she would appear under the small angle T k W, like a spot on the Sun, hiding only the part T W from our sight.

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

axis. her axis from any star to the same star again in 27 days 8 hours; from the Sun to the Sun again, in 294 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.

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Her perio. 263. If the Earth had no annual motion, the Moon dical and synodical would go round it so as to complete a lunation, a sirevolu- dereal, 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

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 overtakenby the minute-handat that point from which they started at their last conjunction. The first

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II 10
III 16
IV 21
V 27
VI 32
VII 38
VIII 43
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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 384 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 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 124 conjunctions with it; and so would be a pretty device for shewing the motions of the Sun and Moon; espe. cially, as the slowest moving hand might have a little sun fixed on its point, and the quickest, a little moon.

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. * the Earth and Moon move round the Sun, the open space

describ. Moon's real path in the heavens is very different ed. 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 eccen. tricities of their orbits are too small to affect the phenomena here described.

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ing 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 complete number of luna

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fraction. 266. Let a nail in the end of the axle of a cha

riot-wheel represent the Earth, and a pin in the nave path, and the Moon; if the body of the chariot be propped up the

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 while 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 to the Moon's path during so many lunations.

Let us now suppose that the radius of the circular curve described by the nail in the axle is to the radius of the circle which the pin in the nave describes round the axle as 337 to 1; which is the proportion of the radius or semi-diameter of the Earth's orbit to that of the Moon's; or of the circular curve 4 1 2 3 4 5 6 7 B, &c. to the little circle a; and then while the progressive nail describes the said curve from A to E, the pin will go once round the nail with regard to the centre of its path, and in so doing, will describe the curve a b c d e. The former will be a true representation of the Earth's path for one lunation, and the latter of the Moon's for that time. Here we may set aside the inequalities of the Moon's motion, and also those of the

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