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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, Mer. cury, 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 11f degrees. Now, suppose him stationary on the first of January at C, on the tenth of that month he will appear in the heavens
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
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 de grees; and to go back only li 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.
The Ptolemean System refuted. The Motions and
Phases of Mercury and Venus explained. 139.
HE Tychonic System, $ 97, being suff
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.
For if this hypothesis were true, Mercury and Venus could never be hid behind the Sun, as their orbits 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, appear 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 ances of shapes of the Moon; which is a plain proof that they and Ve are enlightened by the Sun, and shine not by any light of their own; for if they did, they would constantly 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
Experi. son 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.
142. If you remove about six or seven yards from Experi- the candle, and place yourself so that its flame may
be just about the height of your eye, and then derepresent
sire the other person to move the ball slowly round tions of
the candle as before, keeping it as nearly of an equal Mercury and Ved 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, s 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 representation 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, and stars, appear to move at the same distance from the Earth Ê. 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 gations of his nodes, 20, 25; in which case he will appear digres. sions of like a dark spot upon the Sun. When he is at g Mercur in his orbit, he appears at B in the heavens, westfrom the
ward of the Sun S, which is seen at C: when at h, Plare 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 going from k to l, 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 going from n to h, in his orbit, he seems to go backward 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
a at g is seen from É; at h he appears half full, because half of his enlightened side is seen; at in gibbous, or more than half full; and at k he would appear quite full, were he not hid from the Earth È 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. Iii. 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 elonin 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.