nets de 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 ed. at B, to be carried by the projectile force as far as from B to b, in the time that gravity would have brought it down from B to 1: by these two forces it will describe the curve B C. When the planet comes down to K, it will be but half as far from the Sun S as it was at B; and therefore by gravitating four times as strongly towards him, it would fall from K’to V in the same length of time that it would have fallen from B 10 1 in the higher part of its orbit; that is through four times as much space; but its projectile force is then so much increased at K, as would carry it from K to k in the same time; being double of what it was at B; and is therefore too strong for the gravitating power, either to draw the planet to the Sun, or cause it to go round him in the circle Klmn, &c. which would require its falling from K to w, through a greater space than that through which gravity can draw it, while the projectile force is such as would carry it from K’to k: and therefore the planet ascends in its orbit KLMN; decreasing in its velocity, for the causes already as. signed in ġ 152. The pla 155. The orbits of all the planets are ellipses, very netary or- little different from circles: but the orbits of the bits elliptical. comets are very long ellipses; and the lower focus of them all is in the Sun. If we suppose the mean distance (or middle between the greatest and least) of every planet and comet from the Sun to be divid. Their ec. ed into 1000 equal parts, the eccentricities of their centrici- orbits, both in such parts and in English miles, will be as follow: Mercury's, 210 parts, or 6,720,000 miles; Venus's, 7 parts, or 413,000 miles; the Earth’s, 17 parts, or 1,377,000 miles; Mars's, 93 parts, or 11,439,000 miles; Jupiter's, 48 parts, or 20,352,000 miles ; Saturn's, 55 parts, or 42,735, 000 miles. Of the nearest of the tree forementioned comets, 1,458,000 miles; of the middlemost, 2,025,000,000 miles; and of the outermost, 6,600, 000,000. ties. circular 156. By the above-mentioned law, $ 150 & seq. The above bodies will move in all kinds of ellipses, whether long laws sulti cient for or short, if the spaces they move in be void of resist-motions ance. Only those which move in the longer ellipses both in have so much the less projectile force impressed upon and ellipthem in the higher parts of their orbits; and their ve- tic orbits. locities, in coming down towards the Sun, are so prodigiously increased by his attraction, that their centrifugal forces in the lower parts of their orbits are so great, as to overcome the Sun's attrac.ion there, and cause them to ascend again towards the higher parts of their orbit; during which time the Sun's attraction, acting so contrary to the motions of those bodies, causes them to move slower and slower, until their projectile forces are diminished almost to nothing; and then they are brought back again by the Sun's attraction as before. 157. If the projectile forces of all the planets and In what comets were destroyed at their mean distances from times the the Sun, their gravities would bring them down so, would fall planets as that Mercury would fall to the Sun in 15 days 13 to the Sun hours; Venus, in 39 days 17 hours; the Earth or by the Moon, in 64 days 10 hours; Mars, in 121 days; Ju- gravity. piter, in 290; and Saturn, in 767. The nearest comet, in 13 thousand days; the middlemost, in 23 thousand days; and the outermost, in 66 thousand days. The Moon would fall to the Earth in 4 days 20 hours; Jupiter's first moon would fall to him in 7 hours, his second in 15, his third in 30, and his fourth in 71 hours. Saturn's first moon would fall to him in 8 hours, his second in 12, his third in 19, his fourth in 68, and his fifth in 336 hours. A stone would fall to the Earth's centre, if there were a hollow passage, in 21 minutes 9 seconds. Mr. WHISTON gives the following rule for such computations. “* It is demonstrable, that half the period of any planet, when it is diminished in the sesquialteral proportion power of Astronomical Principles of Religion, p. 66. P P The pro nets, of the number 1 to the number 2, or nearly in the proportion of 1000 to 2828, is the time in which it would fall to the centre of its orbit. 158. The quick motions of the moons of Jupiter digious at: and Saturn round their primaries, demonstrate that traction of the Sun these two planets have stronger attractive powers and Pla- than the Earth has. For the stronger that one body attracts another, the greater must be the projectile force, and consequently the quicker must be the mo , tion of that other body to keep it from falling to its primary or central planet. Jupiter's second moon is 124 thousand miles farther from Jupiter than our Moon is from us; and yet this second moon goes almost eight times round Jupiter whilst our moon goes only once round the Earth. What a prodigious attractive power must the Sun then have, to draw all the planets and satellites of the system towards him! and what an amazing power must it have required to put all these planets and moons into such rapid motions at first! Amazing indeed to us, because impossible to be effected by the strength of all the living creatures in an unlimited number of worlds; but no ways hard for the Almighty, whose planetarium takes in the whole universe. ARCHI- 159. The celebrated ARCHIMEDES affirmed he MEDES's. could move the Earth, if he had a place at a disfor raising tance from it to stand upon to manage his machinethe Earth. ry.*. This assertion is true in theory, but, upon examination, will be found absolutely impossible in fact, even though a proper place, and materials of sufficient strength could be had. The simplest and easiest method of moving a heavy body a little way, is by a lever or crow; where a small weight or power applied to the long arm will raise a great weight on the short one. But then the small weight must move as much quicker than the great weight, as the latter is heavier than Δος σε σώ, και τον κοσμον κινήση, ι. c. Give me a place to stand on, and I shall move the Earth. the former; and the length of the long arm of the lever must be in the same proportion to the length of the short one. Now, suppose a man to pull, or press the end of the long arm with the force of 200 pounds weight, and that the Earth contains in round numbers, 4,000,000,000,000,000,000,000, or 4000 trillions of cubit feet, each at a mean rate weighing 100 pound; and that the prop or centre of motion of the lever is 6000 miles from the Earth's centre : in this case, the length of the lever from the fulcrum or centre of motion to the moving power or weight ought to bel2,000,000,000,000,000,000,000, 000, orl2quadrillions of miles; and so many miles must the power move, in order to raise the Earth but one mile; whence it is easy to compute, that if ARCHIMEDES, or the power applied, could move as swift as a cannon bullet, it would take 27,000,000,000, 000, or 27 billions of years to raise the Earth one inch, If any other machine, such as a combination of wheels and screws, were proposed to move the Earth, the time it would require, and the space gone through by the hand that turned the machine, would be the same as before. Hence we may learn, that however boundless our imagination and theory may be, the actual operations of man are confined within narrow bounds; and more suited to our real wants than to our desires. 160. The Sun and planets mutually attract each Hard to other: the power by which they do so we call determine gravity. But whether this power be mechanical or wity is. not, is very much disputed. Observation proves that by it the planets disturb one another's motions, and that it decreases, according to the squares of the distances of the Sun and planets inversely; as light, which is known to be material, likewise does. Hence, gravity should seem to arise from the agency of some subtle matter pressing toward the Sun and planets, and acting, like all mechanical causes, by contact. what gra |