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and Ve. nus.
Earth, like the moon in her first quarter : at H, she appears gibbous; at I, almost full; her enlightened side being then nearly towards the Earth ; at K, she would appear quite full to the Earth E ; but is bid from it by the Sun S; at L, she appears upon the
decrease, or gibbous; at M, more so; at N, only half The great- enlightened ; and at F, she again disappears. In mov. est eloni ing from N to G, she seems to go backward in the Mercury heavens; and from G to N, forward ; but as she de.
scribes a much greater portion of her orbit in going from G to N, than from N to G, she appears much longer direct than retrograde in her motion. At N and G she appears stationary; as Mercury does at n and h. Mercury, when stationary, seems to be only 28 degrees from the Sun; and Venus, when so, 47; which is a demonstration that Mercury's orbit is included within Venus's, and Venus's within the Earth's.
145. Venus, from her superior conjunction at K, to her inferior conjunction at F, is seen on the east side of the Sun S, from the Earth E; and therefore
she shines in the evening after the Sun sets, and is Morning
called the evening star; for, the Sun being then to and even the westward of Venus, must set first. From her ing star, inferior conjunction to her superior, she appears on
the west side of the Sun; and therefore rises before him ; for which reason she is called the morning star. When she is about Nor G, she shines so bright, that bodies by her light cast shadows in the nighttime.
146. If the Earth kept always at E, it is evident that the stationary places of Mercury and Venus would always be in the same points of the heavens where they were before. For example: whilst
Mercury m goes from h to n, according to the order The sta. of the letters, he appears to describe the arc ABCDE tionary in the heavens, direct : and while he goes from n to the pla. h, he seems to describe the same arc back again, nets vari- from E to A, retrograde; always at n and h he
appears stationary at the same points E and A as before. But Mercury goes round his orbit, from f to f again, in 88 days; and yet there are 116 days from any one of his conjunctions, or apparent stations, to the same again: and the places of these conjunctions and stations are found to be about 114 degrees eastward from the points of the heavens where they were last before; which proves that the Earth has not kept all that time at E, but has had a progressive motion in its orbit from E to t. Venus also differs every time in the places of her conjunctions and stations; but much more than Mercury ; because, as Venus describes a much larger orbit than Mercury does, the Earth advances so much the farther in its annual path, before Venus comes round again.
147. As Mercury and Venus, seen from the The elon. Earth, have their respective elongations from the gations of Sun, and stationary places; so has the Earth, seen turn's in. from Mars; and Mars, seen from Jupiter; and ferior plaJupiter, seen from Saturn : that is, to every supe- seen from rior planet, all the inferior ones have their stations him. and elongations; as Venus and Mercury have to the Earth. As seen from Saturn, Mercury never goes more than 24 degrees from the Sun; Venus 4}; the Earth 6; Mars 9į; and Jupiter 331; so that Mercury, as seen from the Earth, has almost as great a digression or elongation from the Sun, as Jupiter, seen from Saturn.
148. Because the Earth's orbit is included with. A proof of in the orbits of Mars, Jupiter, and Saturn, they are annual
the Earth's seen on all sides of the heavens : and are as often in motion. opposition to the Sun as in conjunction with him. If the Earth stood still, they would always appear direct in their motions; never retrograde nor stationary. But they seem to go just as often backward as forward; which, if gravity be allowed to exist, affords a sufficient proof of the Earth's annual mo. tion: and without its existence, the planets could never fall from the tangents of their orbits towards
Plate II. the Sun, nor could a stone, which is once thrown
up from the Earth, ever fall to the earth again.
149. As Venus and the Earth are superior planets to Mercury, they exhibit much the same appearances to him, that Mars and Jupiter do to us. Let Mercury m be at f, Venus v at F, and the Earth
at E; in which situation Venus hides the Earth Fig. III.
from Mercury; but being in opposition to the Sun, phenome. she shines on Mercury with a full illumined orb; perior pla: though, with respect to the Earth, she is in connet to an junction with the Sun, and invisible. When Mer. ipferior.
cury is at f, and Venus at G, her enlightened side not being directly toward him, she appears a little gibbous; as Mars does in a like situation to us: but, when Venus is at 1, her enlightened side is so much toward Mercury at f, that she appears to him almost of a round figure. At K, Venus disappears to Mercury at f, being then hid by the Sun, as all our su. perior
, planets are to us, when in conjunction with the Sun. When Venus has, as it were, emerged out of the Sun-beams, as at L, she appears almost full to Mercury at f; at M and N, a little gibbous; quite full at F, and largest of all; being then in opposition to the Sun, and consequently nearest to Mercury at F; shining strongly on him in the night, because her distance from him then is somewhat less than a fifth part of her distance from the Earth, when she appears roundest to it between I and K, or be. tween K and L, as seen from the Earth E. Consequently, when Venus is opposite to the Sun as seen from Mercury, she appears more than 25 times as large to him as she does to us when at the fullest. Our case is almost similar with respect to Mars, when he is opposite to the Sun; because he is then so near the Earth, and has his whole enlightened side toward it. But, because the orbits of Jupiter and Saturn are very large in proportion to the Earth's orbit, these two planets appear much less magnified
at their oppositions, or diminished at their con- Plate II.
or pe ne
to F E21
The Physical Causes of the Motions of the Planets.
The Eccentricities of their Orbits. The Times in
ROM the uniform projectile motion of Gravita, 150. bodies in straight lines, and the universal
projeca power of attraction which draws them off from these tion. fines, the curvilineal motions of all the planets arise. Fig. IV. If the body A be projected along the right line ABX, in open space, where it meets with no resistance, and is not drawn aside by any other power,
it would for ever go on with the same velocity, and in the same direction. For, the force which inoves it from A to B in any given time, will carry it from B Circular to X in as much more time, and so on, there being orbits. nothing to obstruct or alter its motion. But if, when this projectile force has carried it, suppose to B, the body S begin to attract it, with a power duly adjusted, and perpendicular to its motion at B, it will then be drawn from the straight line ABX, and forced to revolve about S in the circle BYTU. When the Fig. IV. body A comes to U, or any other part of its orbit, if the small body u, within the sphere of U's attraction, be projected, as in the right line 2, with a force perpendicular to the attraction of U, then ù will
go round U in the orbit W, and accompany it in its whole course round the body S. Here S may represent the Sun, U the Earth, and u the Moon.
151. If a planet at B gravitate, or be attracted, toward the Sun, so as to fall from B to y in the
5 time ullest
Mars s the atenet
time that the projectile force would have carried it from B to X, it will describe the curve B Y by the combined action of these two forces, in the same time that the projectile force singly would have car. ried it from B to X, or the gravitating power singly have caused it to descend from B to y; and these two forces being duly proportioned, and perpendi. cular to each other, the planet, obeying them both, will move in the circle BYTU*.
152. But if, while the projectile force would carry the planet from B to b, the Sun's attraction (which constitutes the planet's gravitation) should bring it down from B to 1, the gravitating power would then be too strong for the projectile force; and would
cause the planet to describe the curve B C. When Elliptical the planet comes to C, the gravitating power (which orbits.
always increases as the square of the distance from the Sun S diminishes) will be yet stronger on account of the projectile force; and by conspiring in some degree therewith, will accelerate the planet's motion all the way from C to K; causing it to describe the arcs BC, CD, DE, EF, &c. all in equal times. Having its motion thus accelerated, it there. by gains so much centrifugal force or tendency to fly off at K in the line Kk, as overcomes the Sun's attraction: and the centrifugal force being too great to allow the planet to be brought nearer the Sun, or even to move round him in the circle Klmn, &c. it goes off, and ascends in the curve KLMN, &c. its motion decreasing as gradually from K to B, as it increases from B to K; because the Sun's attraction now acts against the planet's projectile motion just as much as it acted with it before. When the pla. net has got round to B, its projectile force is as much diminished from its mean state about Gor N,
To make the projectile force balance the gravitating power so exactly as that the body may move in a circle, the projectile velocity of the body must be such as it would have acquired by gravity alone, in falling through half the radius of the circle.