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.