OUR author, after having discovered that the celestial motions are performed by a force extended from the sun and primary planets, follows this power into the deepest recesses of those bodies themselves, and proves the same to accompany the smallest particle, of which they are composed.
2. Preparative hereto he shews first, that each of the heavenly bodies attracts the rest, and all bodies, with such different degrees of force, as that the force of the same attracting body is exerted on others exactly in proportion to the quantity of matter in the body attracted[238].
3. Of this the first proof he brings is from experiments made here upon the earth. The power by which the moon is influenced was above shewn to be the same, with that power here on the surface of the earth, which we call gravity[239]. Now one of the effects of the principle of gravity is, that all bodies descend by this force from the same height in equal times. Which has been long taken notice of; particular methods having been invented to shew that the only cause, why some bodies were observed to fall from the same height sooner than others, was the resistance of the air. This we have above related[240]; and proved from hence, that since bodies resist to any change of their state from rest to motion, or from motion to rest, in proportion to the quantity of matter contained in them; the power that can move different quantities of matter equally, must be proportional to the quantity. The only objection here is, that it can hardly be made certain, whether this proportion in the effect of gravity on different bodies holds perfectly exact or not from these experiments; by reason that the great swiftness, with which bodies fall, prevents our being able to determine the times of their descent with all the exactness requisite. Therefore to remedy this inconvenience, our author substitutes another more certain experiment in the room of these made upon falling bodies. Pendulums are caused to vibrate by the same principle, as makes bodies descend; the power of gravity putting them in motion, as well as the other. But if the ball of any pendulum, of the same length with another, were more or less attracted in proportion to the quantity of solid matter in the ball, that pendulum must accordingly move faster or slower than the other. Now the vibrations of pendulums continue for a great length of time, and the number of vibrations they make may easily be determined without suspicion of error; so that this experiment may be extended to what exactness one pleases: and our author assures us, that he examined in this way several substances, as gold, silver, lead, glass, sand, common salt, wood, water, and wheat; in all which he found not the least deviation from the proportion mentioned, though he made the experiment in such a manner, that in bodies of the same weight a difference in the quantity of their matter less than a thousandth part of the whole would have discovered it self[241]. It appears therefore, that all bodies are made to descend by the power of gravity here, near the surface of the earth, with the same degree of swiftness. We have above observed this descent to be after the rate of 16⅛ feet in the first second of time from the beginning of their fall. Moreover it was also observed, that if any body, which fell here at the surface of the earth after this rate, were to be conveyed up to the height of the moon, it would descend from thence just with the same degree of velocity, as that with which the moon is attracted toward the earth; and therefore the power of the earth upon the moon bears the same proportion to the power it would have upon those bodies at the same distance, as the quantity of matter in the moon bears to the quantity in those bodies.
4. Thus the assertion laid down is proved in the earth, that the power of the earth on every body it attracts is, at the same distance from the earth, proportional to the quantity of solid matter in the body acted on. As to the sun, it has been shewn, that the power of the sun’s action upon the same primary planet is reciprocally in the duplicate proportion of the distance; and that the power of the sun decreases throughout in the same proportion, the motion of comets traversing the whole planetary region testifies. This proves, that if any planet were removed from the sun to any other distance whatever, the degree of its acceleration toward the sun would yet remain reciprocally in the duplicate proportion of its distance. But it has likewise been shewn, that the degree of acceleration, which the sun gives to every one of the planets, is reciprocally in the duplicate proportion of their respective distances. All which compared together puts it out of doubt, that the power of the sun upon any planet, removed into the place of any ether, would give it the same velocity of descent, as it gives that other; and consequently, that the sun’s action upon different planets at the same distance would be proportional to the quantity of matter in each. It has farther been shewn, that the sun attracts the primary planets, and their respective secondary, when at the same distance, so as to communicate to both the same degree of velocity; and therefore the force, wherewith the sun acts on the secondary planet, bears the same proportion to the force, wherewith at the same distance it attracts the primary, as the quantity of solid matter in the secondary planet bears to the quantity of matter in the primary.
5. This property therefore is proved of both kinds of planets, in respect of the sun. Therefore the sun possesses the quality found in the earth, of acting on bodies with a degree of force proportional to the quantity of matter in the body, which receives the influence.
6. That the power of attraction, with which the other planets are endued, should differ from that of the earth, can hardly be supposed, if we consider the similitude between those bodies; and that it does not in this respect, is farther proved from the satellites of Saturn and Jupiter, which are attracted by their respective primary according to the same law, that is, in the same proportion to their distances, as the primary are attracted by the sun: so that what has been concluded of the sun in relation to the primary planets, may be justly concluded of these primary in respect of their secondary, and in consequence of that, in regard likewise to all other bodies, viz. that they will attract every body in proportion to the quantity of solid matter it contains.
7. Hence it follows, that this attraction extends itself to every particle of matter in the attracted body: and that no portion of matter whatever is exempted from the influence of those bodies, to which we have proved this attractive power to belong.
8. Before we proceed farther, we may here remark, that this attractive power both of the sun and planets now appears to be quite of the same nature in all; for it acts in each in the same proportion to the distance, and in the same manner acts alike upon every particle of matter. This power therefore in the sun and other planets is not of a different nature from this power in the earth; which has been already shewn to be the same with that, which we call gravity[242].
9. And this lays open the way to prove, that the attracting power lodged in the sun and planets, belongs likewise to every part of them: and that their respective powers upon the same body are proportional to the quantity of matter, of which they are composed; for instance, that the force with which the earth attracts the moon, is to the force, with which the sun would attract it at the same distance, as the quantity of solid matter contained in the earth, to the quantity contained in the sun[243].
10. The first of these assertions is a very evident consequence from the latter. And before we proceed to the proof, it must first be shewn, that the third law of motion, which makes action and reaction equal, holds in these attractive powers. The most remarkable attractive force, next to the power of gravity, is that, by which the loadstone attracts iron. Now if a loadstone were laid upon water, and supported by some proper substance, as wood or cork, so that it might swim; and if a piece of iron were caused to swim upon the water in like manner: as soon as the loadstone begins to attract the iron, the iron shall move toward the stone, and the stone shall also move toward the iron; when they meet, they shall stop each other, and remain fixed together without any motion. This shews, that the velocities, wherewith they meet, are reciprocally proportional to the quantities of solid matter in each; and that by the stone’s attracting the iron, the stone itself receives as much motion, in the strict philosophic sense of that word[244], as it communicates to the iron: for it has been declared above to be an effect of the percussion of two bodies, that if they meet with velocities reciprocally proportional to the respective bodies, they shall be stopped by the concourse, unless their elasticity put them into fresh motion; but if they meet with any other velocities, they shall retain some motion after meeting[245]. Amber, glass, sealing-wax, and many other substances acquire by rubbing a power, which from its having been remarkable, particularly in amber, is called electrical. By this power they will for some time after rubbing attract light bodies, that shall be brought within the sphere of their activity. On the other hand Mr. Boyle found, that if a piece of amber be hung in a perpendicular position by a string, it shall be drawn itself toward the body whereon it was rubbed, if that body be brought near it. Both in the loadstone and in electrical bodies we usually ascribe the power to the particular body, whose presence we find necessary for producing the effect. The loadstone and any piece of iron will draw each other, but in two pieces of iron no such effect is ordinarily observed; therefore we call this attractive power the power of the loadstone: though near a loadstone two pieces of iron will also draw each other. In like manner the rubbing of amber, glass, or any such body, till it is grown warm, being necessary to cause any action between those bodies and other substances, we ascribe the electrical power to those bodies. But in all these cases if we would speak more correctly, and not extend the sense of our expressions beyond what we see; we can only say that the neighbourhood of a loadstone and a piece of iron is attended with a power, whereby the loadstone and the iron are drawn toward each other; and the rubbing of electrical bodies gives rise to a power, whereby those bodies and other substances are mutually attracted. Thus we must also understand in the power of gravity, that the two bodies are mutually made to approach by the action of that power. When the sun draws any planet, that planet also draws the sun; and the motion, which the planet receives from the sun, bears the same proportion to the motion, which the sun it self receives, as the quantity of solid matter in the sun bears to the quantity of solid matter in the planet. Hitherto, for brevity sake in speaking of these forces, we have generally ascribed them to the body, which is least moved; as when we called the power, which exerts itself between the sun and any planet, the attractive power of the sun; but to speak more correctly, we should rather call this power in any case the force, which acts between the sun and earth, between the sun and Jupiter, between the earth and moon, &c. for both the bodies are moved by the power acting between them, in the same manner, as when two bodies are tied together by a rope, if that rope shrink by being wet, or otherwise, and thereby cause the bodies to approach, by drawing both, it will communicate to both the same degree of motion, and cause them to approach with velocities reciprocally proportional to the respective bodies. From this mutual action between the sun and planet it follows, as has been observed above[246], that the sun and planet do each move about their common center of gravity. Let A (in fig. 108.) represent the sun, B a planet, C their common center of gravity. If these bodies were once at rest, by their mutual attraction they would directly approach each other with such velocities, that their common center of gravity would remain at rest, and the two bodies would at length meet in that point. If the planet B were to receive an impulse, as in the direction of the line D E, this would prevent the two bodies from falling together; but their common center of gravity would be put into motion in the direction of the line C F equidistant from B E. In this case Sir Isaac Newton proves[247], that the sun and planet would describe round their common center of gravity similar orbits, while that center would proceed with an uniform motion in the line C F; and so the system of the two bodies would move on with the center of gravity without end. In order to keep the system in the same place, it is necessary, that when the planet received its impulse in the direction B E, the sun should also receive such an impulse the contrary way, as might keep the center of gravity C without motion; for if these began once to move without giving any motion to their common center of gravity, that center would always remain fixed.
11. By this may be understood in what manner the action between the sun and planets is mutual. But farther, we have shewn above[248], that the power, which acts between the sun and primary planets, is altogether of the same nature with that, which acts between the earth and the bodies at its surface, or between the earth and its parts, and with that which acts between the primary planets and their secondary; therefore all these actions must be ascribed to the same cause[249]. Again, it has been already proved, that in different planets the force of the sun’s action upon each at the same distance would be proportional to the quantity of solid matter in the planet[250]; therefore the reaction of each planet on the sun at the same distance, or the motion, which the sun would receive from each planet, would also be proportional to the quantity of matter in the planet; that is, these planets at the same distance would act on the same body with degrees of strength proportional to the quantity of solid matter in each.
12. In the next place, from what has been now proved, our great author has deduced this farther consequence, no less surprizing than elegant; that each of the particles, out of which the bodies of the sun and planets are framed, exert their power of gravitation by the same law, and in the same proportion to the distance, as the great bodies which they compose. For this purpose he first demonstrates, that if a globe were compounded of particles, which will attract the particles of any other body reciprocally in the duplicate proportion of their distances, the whole globe will attract the same in the reciprocal duplicate proportion of their distances from the center of the globe; provided the globe be of uniform density throughout[251]. And from this our author deduces the reverse, that if a globe acts upon distant bodies by the law just now specified, and the power of the globe is derived from its being composed of attractive particles; each of those particles will attract after the same proportion[252]. The manner of deducing this is not set down at large by our author, but is as follows. The globe is supposed to act upon the particles of a body without it constantly in the reciprocal duplicate proportion of their distances from its center; and therefore at the same distance from the globe, on which side soever the body be placed, the globe will act equally upon it. Now because, if the particles, of which the globe is composed, acted upon those without in the reciprocal duplicate proportion of their distances, the whole globe would act upon them in the same manner as it does; therefore, if the particles of the globe have not all of them that property, some must act stronger than in that proportion, while others act weaker: and if this be the condition of the globe, it is plain, that when the body attracted is in such a situation in respect of the globe, that the greater number of the strongest particles are nearest to it, the body will be more forcibly attracted; than when by turning the globe about, the greater quantity of weak particles should be nearest, though the distance of the body should remain the same from the center of the globe. Which is contrary to what was at first remarked, that the globe on all sides of it acts with the same strength at the same distance. Whence it appears, that no other constitution of the globe can agree to it.
13. From these propositions it is farther collected, that if all the particles of one globe attract all the particles of another in the proportion so often mentioned, the attracting globe will act upon the other in the same proportion to the distance between the center of the globe which attracts, and the center of that which is attracted[253]: and farther, that this proportion holds true, though either or both the globes be composed of dissimilar parts, some rarer and some more dense; provided only, that all the parts in the same globe equally distant from the center be homogeneous[254]. And also, if both the globes attract each other[255]. All which place it beyond contradiction, that this proportion obtains with as much exactness near and contiguous to the surface of attracting globes, as at greater distances from them.
14. Thus our author, without the pompous pretence of explaining the cause of gravity, has made one very important step toward it, by shewing that this power in the great bodies of the universe, is derived from the same power being lodged in every particle of the matter which composes them: and consequently, that this property is no less than universal to all matter whatever, though the power be too minute to produce any visible effects on the small bodies, wherewith we converse, by their action on each other[256]. In the fixed stars indeed we have no particular proof that they have this power; for we find no apperance to demonstrate that they either act, or are acted upon by it. But since this power is found to belong to all bodies, whereon we can make observation; and we see that it is not to be altered by any change in the form of bodies, but always accompanies them in every shape without diminution, remaining ever proportional to the quantity of solid matter in each; such a power must without doubt belong universally to all matter.
15. This therefore is the universal law of matter; which recommends it self no less for its great plainness and simplicity, than for the surprizing discoveries it leads us to. By this principle we learn the different weight, which the same body will have upon the surfaces of the sun and of diverse planets; and by the same we can judge of the composition of those celestial bodies, and know the density of each; which is formed of the most compact, and which of the most rare substance. Let the adversaries of this philosophy reflect here, whether loading this principle with the appellation of an occult quality, or perpetual miracle, or any other reproachful name, be sufficient to dissuade us from cultivating it; since this quality, which they call occult, leads to the knowledge of such things, that it would have been reputed no less than madness for any one, before they had been discovered, even to have conjectured that our faculties should ever have reached so far.
16. See how all this naturally follows from the foregoing principles in those planets, which have satellites moving about them. By the times, in which these satellites perform their revolutions, compared with their distances from their respective primary, the proportion between the power, with which one primary attracts his satellites, and the force with which any other attracts his will be known; and the proportion of the power with which any planet attracts its secondary, to the power with which it attracts a body at its surface is found, by comparing the distance of the secondary planet from the center of the primary, to the distance of the primary planet’s surface from the same: and from hence is deduced the proportion between the power of gravity upon the surface of one planet, to the gravity upon the surface of another. By the like method of comparing the periodical time of a primary planet about the sun, with the revolution of a satellite about its primary, may be found the proportion of gravity, or of the weight of any body upon the surface of the sun, to the gravity, or to the weight of the same body upon the surface of the planet, which carries about the satellite.
17. By these kinds of computation it is found, that the weight of the same body upon the surface of the sun will be about 23 times as great, as here upon the surface of the earth; about 10⅗ times as great, as upon the surface of Jupiter; and near 19 times as great, as upon the surface of Saturn[257].
18. The quantity of matter, which composes each of these bodies, is proportional to the power it has upon a body at a given distance. By this means it is found, that the sun contains 1067 times as much matter as Jupiter; Jupiter 158⅔ times as much as the earth, and 2-5/6 times as much as Saturn[258]. The diameter of the sun is about 92 times, that of Jupiter about 9 times, and that of Saturn about 7 times the diameter of the earth.
19. By making a comparison between the quantity of matter in these bodies and their magnitudes, to be found from their diameters, their respective densities are readily deduced; the density of every body being measured by the quantity of matter contained under the same bulk, as has been above remarked[259]. Thus the earth is found 4¼ times more dense than Jupiter; Saturn has between ⅔ and ¾ of the density of Jupiter; but the sun has one fourth part only of the density of the earth[260]. From which this observation is drawn by our author; that the sun is rarified by its great heat, and that of the three planets named, the more dense is nearer the sun than the more rare; as was highly reasonable to expect, the densest bodies requiring the greatest heat to agitate and put their parts in motion; as on the contrary, the planets which are more rare, would be rendered unfit for their office, by the intense heat to which the denser are exposed. Thus the waters of our seas, if removed to the distance of Saturn from the sun, would remain perpetually frozen; and if as near the sun as Mercury, would constantly boil[261].
20. The densities of the three planets Mercury, Venus, and Mars, which have no satellites, cannot be expresly assigned; but from what is found in the others, it is very probable, that they also are of such different degrees of density, that universally the planet which is nearest to the sun, is formed of the most compact substance.