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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 infrom 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 vat F, and the Earth

at E; in which situation Venus hides the Earth Fig. III, General 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 Merīpferior.

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 I, 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 superior 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. junctions, than Mars does, in proportion to their mean apparent diameters.

CHAP. VII.

The Physical Causes of the Motions of the Planets.

The Eccentricities of their Orbits. The Times in which the Action of Gravity would bring them to the Sun. ARCHIMEDES's ideal Problem for moving the Earth. The World not eternal.

F

tion and

ROM the uniform projectile motion of Gravita, 150. bodies in straight lines, and the universal

projecpower of attraction which

draws them off from these tion. lines, 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 rig. 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 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

go

orbits.

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 carried 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 perpendicular 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

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 thereby gains so much centrifugal force or tendency to fily 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 planet 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.

as it was augmented at K; and so, the Sun's attrac- Plate II. tion being more than sufficient to keep the planet from going off at B, it describes the same orbit over again, by virtue of the same forces or powers.

153. A double projectile force will always balance a quadruple power of gravity. Let the planet at B have twice as great an impulse from thence toward X, as it had before; that is, in the same length of time that it was projected from B to b, as in the last example, let it now be projected from B to c; and it will require four times as much gravity to retain it in its orbit: that is, it must fall as far as from B to 4 in the time that the projectile force would carry it from B to c; otherwise it could not describe the curve BD; as is evident by the figure. But, in as much time as the planet moves from B to C in the higher Fig. IV. part of its orbit, it moves from I to K, or from K to The plaL, in the lower part thereof; because, from the joint scribe action of these two forces, it must always describe equal are, equal areas in equal times, throughout its annual as in equal course. These areas are represented by the triangles BSC, CSD, DSE, ESF, &c. whose contents are equal to one another quite round the figure.

154. As the planets approach nearer the Sun, and A difficulrecede farther from him, in every revolution; there ty removmay be some difficulty in conceiving the reason why the power of gravity, when it once gets the better of the projectile force, does not bring the planets nearer and nearer the Sun in every revolution, till they fall upon, and unite with him; or why the projectile force, when it once gets the better of gravity, does not carry the planets farther and farther from the Sun, till it removes them quite out of the sphere of his attraction, and causes them to go on in straight lines for ever afterward. But by considering the effects of these powers as described in the two last articles, this difficulty will be removed. Suppose a planet

.

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