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each loop next the Earth, retrograde; and in all the Plate III. rest of their paths, direct.

If Cassini's figures of the paths of the Sun, Mercury, and Venus, were put together, the figure, as above traced out, would be exactly like them. It represents the Sun's apparent motion round the ecliptic, which is the same every year; Mercury's motion for seven years; and Venus's for eight; in which time Mercury's path makes 23 loops, crossing itself so many times, and Venus's only five. In eight years Venus falls so nearly into the same apparent path again, as to deviate very little from it in some ages; but in what number of years Mercury and the rest of the planets would describe the same visible paths over again, I cannot at present determine. Having finished the above figure of the paths of Mercury and Venus, I put the ecliptic round them as in the doctor's book; and added the dotted lines from the Earth to the ecliptic, for shewing Mercury's apparent or geocentric motion therein for one year; in which time his path makes three loops, and goes on a little farther. This shews that he has three inferior, and as many superior conjunctions with the Sun in that time; and also that he is six times stationary, and thrice retrograde. Let us now trace his motion for one year in the figure.

Suppose Mercury to be setting out from A toward B (between the Earth and left-hand corner of the plate) and as seen from the Earth, his mo- Fig. I. tion will then be direct, or according to the order of the signs. But when he comes to B, he appears to stand still in the 23d degree of m at F, as shewn by the line B F. While he goes from B to C, the line B F, supposed to move with him, goes backward from F to E, or contrary to the order of signs : and when he is at C, he appears stationary at E; having gone back 114 degrees. Now, suppose him stationary on the first of January at C, on the tenth of that month he will appear in the heavens

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as at 20, near F; on the 20th he will be seen as at G; on the 31st at H; on the 10th of February at F; on the 20th at K; and on the 28th at L; as the dotted lines shew, which are drawn through every tenth days' motion in his looped path, and continued to the ecliptic. On the 10th of March he appears at M; on the 20th at .N'; and on the 31st ato. On the tenth of April he appears stationary at P; on the 20th he seems to have gone back again to 0); and on the 30th he appears stationary at Q, having gone back 11 degrees. Thus Mercury seems to go forward 4 signs 11 degrees, or 131 degrees; and to go back only 11 or 12 degrees, at a mean rate, From the 30th of April to the 10th of May, he seems to move from Q to R; and on the 20th he is seen at S, going forward in the same manner again, according to the order of letters; and backward when they go back; which it is needless to explain any farther, as the reader can trace him out so easily, through the rest of the year. The same appearances happen in Venus's motion; but as she moves slower than Mercury, there are longer intervals of time between them.

Having already, § 120, given some account of the apparent diurnal motions of the heavens as seen from the different planets, we shall not trouble the reader any more with that subject.

CHAP. VI.

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The Ptolemean System refuted. The Motions and

Phases of Mercury and Venus explained. 139.

'HE Tychonic System, $ 97, being suffi

ciently refuted in the 109th article, we shall say nothing more about it.

140. The Ptolemean System, ( 96, which asserts the Earth to be at rest in the centre of the universe, and all the planets with the Sun and stars to move round it, is evidently false and absurd.

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For if this hypothesis were true, Mercury and Ve-
nus could never be hid behind the Sun, as their or-
bits are included within the Sun's; and again, these
two planets would always move direct, and be as
often in opposition to the Sun as in conjunction with
him. But the contrary of all this is true : for they
are just as often behind the Sun as before him, ap-
pear as often to move backward as forward, and are
so far from being seen at any time in the side of the
heavens opposite to the Sun, that they are never seen
a quarter of a circle in the heavens distant from himn.

141. These two planets, when viewed at different Appear.
times with a good telescope, appear in all the various anees of
shapes of the Moon; which is a plain proof that they and Ve
ate enlightened by the Sun, and shine not by any
light of their own; for if they did, they would con.
stantly appear round as the Sun does; and could
never be seen like dark spots upon the Sun when
they pass directly between him and us.

Their regular phases demonstrate them to be spherical bodies; as may be shewn by the following experiment:

Hang an ivory ball by a thread, and let any per-Experison move it round the flame of a candle, at two or prove they three yards distance from your eye; when the ball are round. is beyond the candle, so as to be almost hid by the flame, its enlightened side will be toward you, and appear round like the full Moon: When the ball is between you and the candle, its enlightened side will disappear as the Moon does at the change : When it is half-way between these two positions, it will appear half illuminated, like the Moon in her quarters : but in every other place between these positions, it will appear more or less horned or gibbous. If this experiment be made with a flat circular plate, you may make it appear fully enlightened, or not enlightened at all; but can never make it appear either horned or gibbous.

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Plate II. Experiment to represent the motions of Mercury nus.

142. If you remove about six or seven yards from the candle, and place yourself so that its fame may be just about the height of your eye, and then desire the other person to move the ball slowly round

the candle as before, keeping it as nearly of an equal and Ve height with the fame as he possibly can, the ball

will

appear to you not to move in a circle, but to vibrate backward and forward like a pendulum; moving quickest when it is directly between you and the candle, and when directly beyond it; and gradually slower as it goes farther to the right or left side of the flame, until it appears at the greatest distance from the flame; and then, though it continues to move with the same velocity, it will seem for a moment to stand still. In every revolution it will shew all the above phases, À 141; and if two balls, a smaller and a greater, be moved in this manner round the candle, the smaller ball beng kept nearest the flame, and carried round almost three times as often as the greater, you will have a tolerable good repre. sentation of the apparent motions of Mercury and Venus; especially if the greater ball describe a circle almost twice as large in diameter as that describ

ed by the lesser. Fig. III.

.143. Let ABCDE be a part or segment of the

visible heavens, in which the Sun, Moon, planets, like ll and stars, appear to move at the same distance from

the Earth E. For there are certain limits, beyond which the eye cannot judge of different distances; as is plain from the Moon's appearing to be as far from us as the Sun and stars are Let the circle fg hiklmno be the orbit in which Mercury m moves round the Sun S, according to the order of the letters. When Mercury is at f, he disap

pears to the Earth at E, because his enlightened The elon-side is turned from it; unless he be then in one of unities or his nodes, $ 20, 25; in which case he will appear sions of like a dark spot upon the Sun. When he is at g Mercury in his orbit, he appears at B in the heavens, west

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ward of the Sun S, which is seen at C: when at h, Plate 11.
he appears at A, at his greatest western elongation
or distance from the Sun; and then seems to stand
still. But, as 'he moves from h to i, he appears to
go from A to B ; and seems to be in the same place
when at i, as when he was at g, but not near so
large : at k he is hid from the Earth E, by the Sun

S; being then in his superior conjunction. In go-
ing from k to 1, he appears to move from C to D;
and when he is at n, he appears stationary at E;
being seen as far east from the Sun then, as he was
west from it at A. In going from n to o, in his
orbit, he seems to go back again in the heavens,
from E to D; and is seen in the same place (with
respect to the Sun) at 0, as when he was at l; but
of a larger diameter at o, because he is then nearer
the Earth E: and when he comes to f, he again
passes by the Sun, and disappears as before. In go-
ing from n to h, in his orbit, he seems to go back-
ward in the heavens from E to A; and in going
from h to n, he seems to go forward from A to E:
as he goes on from f, a little of his enlightened side
at g is seen from E ; at h he appears half full, be-
cause half of his enlightened side is seen; at i,
gibbous, or more than half full; and at k he would
appear quite full, were he not hid from the Earth

E by the Sun S. At l he appears gibbous again, at n half decreased, at o horned, and at f new, like the Moon at her change. He goes sooner from his eastern station at n to his western station at h, than again from h to n; because he goes through less than half his orbit in the former case, and through more in the latter.

144. In the same figure, let FGHIKLMN be fig. 111. the orbit in which Venus v goes round the Sun S, according to the order of the letters: and let E be the Earth, as before. When Venus is at F, she is the elon. in her inferior conjunction ; and disappears like the gations

and phanew Moon, because her dark side is toward the Earth. At G, she appears half enlightened to the Venus.

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