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veral miles above the Earth, and there projected in a horizontal direction, with so great a velocity, that it would move more than a semidiameter of the Earth in the time it would take to fall to the Earth by gravity ; in that case, if there were no resisting medium in the way, the body would not fall to the Earth at all, but continue to circulate round the Earth, keeping always the same path, and returning to the point from whence it was projected, with the same velocity as at first.

102. We find that the Moon moves round the Earth Projectile in an orbit nearly circular. The Moon therefore force demust be acted on by two powers or forces; one, ble. which would cause her to move in a right line; another, bending her motion from that line into a curve. This attractive power must be seated in the Earth; for there is no other body within the Moon's orbit to draw her. The attractive power of the Earth therefore extends to the Moon; and, in combination with her projectile force, causes her to move round the Earth, in the same manner as the circulating body above supposed. 103. The moons of Jupiter and Saturn are ob- The Sun

and planserved to move round their primary planets: there

ets attract fore there is an attractive power in these planets. each All the planets move round the Sun, and respect it other. for their centre of motion: therefore the Sun must be endowed with an attracting power, as well as the Earth and planets. The like may be proved of the comets. So that all the bodies or matter of the solar system, are possessed of this power; and so perhaps is all matter universally.

104. As the Sun attracts the planets with their satellites, and the Earth the Moon; so the planets and satellites re-attract the Sun, and the Moon the Earth; action and re-action being always equal. This is also confirmed by observation for the Moon raises tides in the ocean, and the satellites and planets disturb one another's motions.

105. Every particle of matter being possessed of an attracting power, the effect of the whole must be in proportion to the number of attracting particles: that is, to the quantity of matter in the body. This is demonstrated from experiments on pendulums: for, when they are of equal lengths, whatever their weights be, they always vibrate in equal times. Now, if one be double the weight of another, the force of gravity or attraction must be double to make it oscillate with the same celerity; if one have thrice the weight or quantity of matter of another, it requires thrice the force of gravity to make it move with the same celerity. Hence it is certain, that the power of gravity is always proportional to the quantity of matter in bodies, whatever may be their magnitudes or figures.

106. Gravity also, like all other virtues or emanations, either drawing or impelling a body toward the centre, decreases as the square of the distance increases: that is, a body at twice the distance attracts another with only a fourth part of the force; at four times the distance, with a sixteenth part of the force, &c. This too is confirmed from observation, by comparing the distance which the Moon falls in a minute from a right line touching her orbit, with the space which bodies near the Earth fall in the same time: and also by comparing the forces which retain Jupiter's moons in their orbits: as will be more fully

explained in the seventh chapter. Gravita

107. The mutual attraction of bodies may be projection exemplified by a boat and a ship on the water, exempli- tied together by a rope. Let a man either in the fied.

ship or boat pull the rope (it is the same in effect at which end he pulls, for the rope will be equally stretched throughout) the ship and boat will be drawn toward one another; but with this difference, that the boat will move as much faster than the ship, as the ship is heavier than the boat. Suppose the boat as heavy as the ship, and they will draw one

tion and

another equally, (setting aside the greater resistance of the water on the larger body) and meet in the middle of the first distance between them. If the ship be a thousand or ten thousand times heavier than the boat, the boat will be drawn a thousand or ten thousand times faster than the ship; and meet proportionably nearer the place from which the ship set out. Now, while one man pulls the rope, endeavouring to bring the ship and boat together, let another man in the boat, endeavour to row it off sideways, or at right angles to the rope; and the former, instead of being able to draw the boat to the ship, will find it enough for him to keep the boat from going further off; while the latter endeavouring to row off the boat in a straight line, will, by means of the other's pulling it toward the ship, row the boat round the ship at the rope's length from her. Here the power employed to draw the ship and boat to one another represents the mutual attraction of the Sun and planets by which the planets would fall freely toward the Sun with a quick motion; and would also in falling attract the Sun toward them. And the power employed to row off the boat, represents the projectile force impressed on the planets, at right angles, or nearly so, to the Sun's attraction; by which means the planets move round the Sun, and are kept from falling to it. On the other hand, if it be attempted to make a heavy ship go round a light boat, they will meet sooner than the ship can get round; or the ship will drag the boat after it.

108. Let the above principles be applied to the Sun and Earth; and they will evince, beyond a possibility of doubt, that the Sun, not the Earth, is the centre of the system; and that the Earth moves round the Sun as the other planets do.

For, if the Sun move about the Earth, the Earth's attractive power must draw the Sun toward it, from the line of projection, so as to bend its motion into a curve. But the Sun being at least


at rest.

227 thousand times as heavy as the Earth, being so much heavier as its quantity of matter is greater, it must move 227 thousand times as slowly toward the Earth, as the Earth does toward the Sun; and consequently the Earth would fall to the Sun in a short time, if it had not a very strong projectile motion to carry it off. The Earth therefore, as well as every

other planet in the system, must have a rectilineal im. surdity of pulse, to prevent its falling to the Sun. To say, supposing that gravitation retains all the other planets in their the Earth orbits, without affecting the Earth, which is placed

between the orbits of Mars and Venus, is as absurd as to suppose that six cannon bullets might be projected upward to different heights in the air ; and that five of them should fall down to the ground, but the sixth, which is neither the highest nor the lowest should remain suspended in the air without falling, and the Earth move round about it.

109. There is no such thing in nature as a heavy body moving round a light one, as its centre of motion. A pebble fastened to a mill-stone, by a string, may, by an easy impulse, be made to circulate round the mill-stone ; but no impulse whatever can make a mill-stone circulate round a loose pebble ; for the mill-stone would go off, and carry the pebble along with it.

110. The Sun is so immensely greater and hea. vier than the Earth,* that if he were moved out of his place, not only the Earth, but all the other pla. nets, if they were united into one mass, would be carried along with the Sun, as the pebble would be, with the mill-stone.

111. By considering the law of gravitation which takes place throughout the solar system, in another light, it will be evident, that the Earth moves round the Sun in a year; and not the Sun round the Earth. It has been shewn (f 106) that the

* As will be demonstrated in the ninth chapter.

the celes.

power of gravity decreases as the square of the dis. The har. tance increases; and from this it follows, with mathe-mony of matical certainty, that when two or more bodies tial mo. move round another as their centre of motion, the tions. squares of their periodic times will be to one another in the same proportion as the cubes of their distances from the central body. This holds precisely with regard to the planets round the Sun, and the satellites round the planets; the relative distances of all

which are well known. But, if we suppose the Sun - to move round the Earth, and compare its period with the Moon's by the above rule, it will be found that the Sun would take no less than 173,510 days to move round the Earth; in which case our year would be 475 times as long as it now is. To this we may add, that the aspects of increase and decrease of the planets, the times of their seeming to stand still, and to move direct and retrograde, answer precisely to the Earth's motion; but not at all to the Sun's, without introducing the most absurd and monstrous suppositions, which would destroy all harmony, order, and simplicity in the system. More. over, if the Earth be supposed to stand still, and the stars to revolve in free space about the Earth in 24 hours, it is certain that the forces by which the stars revolve in their orbits are not directed to the Earth, but to the centres of the several orbits; that is, of the several parallel circles which the stars on different The absides of the equator describe every day; and the like surdity of inferences may be drawn from the supposed diurnal the stars motion of the planets, since they are never in the and plaequinoctial but twice in their courses with regard to the starry heavens. But, that forces should be di round the rected to no central body, on which they physically depend, but to innumerable imaginary points in the axis of the Earth produced to the poles of the hea. vens, is a hypothesis too absurd to be allowed of by any rational creature. And it is still more ab.


nets to move


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