150. From the uniform projectile motion of bodies in straight lines, and the universal power of attraction, arises the curvilineal motions of all the Heavenly bodies. 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 will for ever go on with the same velocity, and in the same direction. For, the force which moves it from A to B in any given time, will carry it from B to X in as much more time; and so on, there being nothing to obstruct or alter it’s motion. But if, when this projectile force has carried it, suppose to B, the body S begins to attract it, with a power duly adjusted, and perpendicular to it’s 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 body A comes to U, or any other part of it’s Orbit, if the small body u, within the sphere of U’s attraction, be projected as in the right line Z, with a force perpendicular to the attraction of U, then u will go round U in the Orbit W, and accompany it in it’s 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 gravitates, or is attracted, toward the Sun, so as to fall from B to y in the time that the projectile force would have carried it from B to X, it will describe the curve BY 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 one another, the Planet obeying them both, will move in the circle BYTU[30].
152. But if, whilst the projectile force carries the Planet from B to b, the Sun’s attraction (which constitutes the Planet’s gravitation) should bring it down from B to I, the gravitating power would then be too strong for the projectile force; and would cause the Planet to describe the curve BC. When 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 for 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 it’s motion thus accelerated, it 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. it’s motion decreasing as gradually from K to B as it increased from B to K, because the Sun’s attraction acts now against the Planet’s projectile motion just as much as it acted with it before. When the Planet has got round to B, it’s projectile force is as much diminished from it’s mean state about G or N, as it was augmented at K; and so, the Sun’s attraction 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 laws.
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 towards 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 it’s 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 part of it’s Orbit, it moves from I to K or from K to L in the lower part thereof; because, from the joint action of these two forces, it must always describe equal areas in equal times, throughout it’s annual 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 recede farther from him, in every Revolution; there may 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 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 BC. 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 to 1 in the higher part of it’s Orbit, that is, through four times as much space; but it’s 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 tendency of 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 it’s falling from K to w, through a greater space than gravity can draw it whilst the projectile force is such as would carry it from K to k: and therefore the Planet ascends in it’s Orbit KLMN, decreasing in it’s velocity for the cause already assigned in § 152.
155. The Orbits of all the Planets are Ellipses, very little different from Circles: but the Orbits of the Comets are very long Ellipses; the lower focus of them all being 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 divided into 1000 equal parts, the Excentricities of their Orbits, both in such parts and in English miles, will be as follows. 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 three forementioned Comets, 1,458,000 miles; of the middlemost, 2,025,000,000 miles; and of the outermost, 6,600,000,000.
156. By the above-mentioned laws § 150 & seq. bodies will move in all kinds of Ellipses, whether long or short, if the spaces they move in be void of resistance. Only, those which move in the longer Ellipses, have so much the less projectile force impressed upon them in the higher parts of their Orbits; and their velocities, 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 attraction there, and cause them to ascend again towards the higher parts of their Orbits; 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 Comets were destroyed at their mean distances from the Sun, their gravities would bring them down so, as that Mercury would fall to the Sun in 15 days 13 hours; Venus in 39 days 17 hours; the Earth or Moon in 64 days 10 hours; Mars in 121 days; Jupiter 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 hours, and the fifth in 336. A stone would fall to the Earth’s center, if there were an hollow passage, in 21 minutes 9 seconds. Mr. Whiston gives the following Rule for such Computations. “[31]It is demonstrable, that half the Period of any Planet, when it is diminished in the sesquialteral proportion of the number 1 to the number 2, or nearly in the proportion of 1000 to 2828, is the time that it would fall to the Center of it’s Orbit.” This proportion is, when a quantity or number contains another once and a half as much more.
158. The quick motions of the Moons of Jupiter and Saturn round their Primaries, demonstrate that these two Planets have stronger attractive powers 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 motion of that other body, to keep it from falling to it’s 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!
159. The celebrated Archimedes affirmed he could move the Earth if he had a place to stand on to manage his machinery[32]. 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 the former; and the length of the long arm of the lever to the length of the short arm must be in the same proportion. Now, suppose a man pulls or presses the end of the long arm with the force of 200 pound weight, and that the Earth contains in round Numbers 4,000,000,000,000,000,000,000 or 4000 Trillions of cubic feet, each at a mean rate weighing 100 pound; and that the prop or center of motion of the lever is 6000 miles from the Earth’s center: in this case, the length of the lever from the Fulcrum or center of motion to the moving power or weight ought to be 12,000,000,000,000,000,000,000,000 or 12 Quadrillions of miles; and so many miles must the power move, in order to raise the Earth but one mile, whence ’tis 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, was 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 other: the power by which they do so we call Gravity. But whether this power be mechanical or no, is very much disputed. We are certain that the Planets disturb one another’s motions by it, and that it decreases according to the squares of the distances of the Sun and Planets; as light, which is known to be material, likewise does. Hence Gravity should seem to arise from the agency of some subtile matter pressing towards the Sun and Planets, and acting, like all mechanical causes, by contact. But on the other hand, when we consider that the degree or force of Gravity is exactly in proportion to the quantities of matter in those bodies, without any regard to their bulks or quantity of surface, acting as freely on their internal as external parts, it seems to surpass the power of mechanism; and to be either the immediate agency of the Deity, or effected by a law originally established and imprest on all matter by him. But some affirm that matter, being altogether inert, cannot be impressed with any Law, even by almighty Power: and that the Deity must therefore be constantly impelling the Planets toward the Sun, and moving them with the same irregularities and disturbances which Gravity would cause, if it could be supposed to exist. But, if a man may venture to publish his own thoughts, (and why should not one as well as another?) it seems to me no greater absurdity, to suppose the Deity capable of superadding a Law, or what Laws he pleases, to matter, than to suppose him capable of giving it existence at first. The manner of both is equally inconceivable to us; but neither of them imply a contradiction in our ideas: and what implies no contradiction is within the power of Omnipotence. Do we not see that a human creature can prepare a bar of steel so as to make it attract needles and filings of iron; and that he can put a stop to that power or virtue, and again call it forth again as often as he pleases? To say that the workman infuses any new power into the bar, is saying too much; since the needle and filings, to which he has done nothing, re-attract the bar. And from this it appears that the power was originally imprest on the matter of which the bar, needle, and filings are composed; but does not seem to act until the bar be properly prepared by the artificer: somewhat like a rope coiled up in a ship, which will never draw a boat or any other thing towards the ship, unless one end be tied to it, and the other end to that which is to be hauled up; and then it is no matter which end of the rope the sailors pull at, for the rope will be equally stretched throughout, and the ship and boat will move towards one another. To say that the Almighty has infused no such virtue or power into the materials which compose the bar, but that he waits till the operator be pleased to prepare it by due position and friction, and then, when the needle or filings are brought pretty near the bar, the Deity presses them towards it, and withdraws his hand whenever the workman either for use, curiosity or whim, does what appears to him to destroy the action of the bar, seems quite ridiculous and trifling; as it supposes God not only to be subservient to our inconstant wills, but also to do what would be below the dignity of any rational man to be employed about.
161. That the projectile force was at first given by the Deity is evident. For, since matter can never put itself into motion, and all bodies may be moved in any direction whatsoever; and yet all the Planets both primary and secondary move from west to east, in planes nearly coincident; whilst the Comets move in all directions, and in planes so different from one another; these motions can be owing to no mechanical cause of necessity, but to the free choice and power of an intelligent Being.
162. Whatever Gravity be, ’tis plain that it acts every moment of time: for should it’s action cease, the projectile force would instantly carry off the Planets in straight lines from those parts of their Orbits where Gravity left them. But, the Planets being once put into motion, there is no occasion for any new projectile force, unless they meet with some resistance in their Orbits; nor for any mending hand, unless they disturb one another too much by their mutual attractions.
163. It is found that there are disturbances among the Planets in their motions, arising from their mutual attractions when they are in the same quarter of the Heavens; and that our years are not always precisely of the same length[33]. Besides, there is reason to believe that the Moon is somewhat nearer the Earth now than she was formerly; her periodical month being shorter than it was in former ages. For, our Astronomical Tables, which in the present Age shew the times of Solar and Lunar Eclipses to great precision, do not answer so well for very ancient Eclipses. Hence it appears, that the Moon does not move in a medium void of all resistance, § 174; and therefore her projectile force being a little weakened, whilst there is nothing to diminish her gravity, she must be gradually approaching nearer the Earth, describing smaller and smaller Circles round it in every revolution, and finishing her Period sooner, although her absolute motion with regard to space be not so quick now as it was formerly: and therefore, she must come to the Earth at last; unless that Being, which gave her a sufficient projectile force at the beginning, adds a little more to it in due time. And, as all the Planets move in spaces full of æther and light, which are material substances, they too must meet with some resistance. And therefore, if their gravities are not diminished, nor their projectile forces increased, they must necessarily approach nearer and nearer the Sun, and at length fall upon and unite with him.
164. Here we have a strong philosophical argument against the eternity of the World. For, had it existed from eternity, and been left by the Deity to be governed by the combined actions of the above forces or powers, generally called Laws, it had been at an end long ago. And if it be left to them it must come to an end. But we may be certain that it will last as long as was intended by it’s Author, who ought no more to be found fault with for framing so perishable a work, than for making man mortal.