1. In chapter XXI I have defined thick and thin, as that place required, so, as that by thick was signified a more resisting body, and by thin, a body less resisting; following the custom of those that have before me discoursed of refraction. Now if we consider the true and vulgar signification of those words, we shall find them to be names collective, that is to say, names of multitude; as thick to be that, which takes up more parts of a space given, and thin that, which contains fewer parts of the same magnitude in the same space, or in a space equal to it. Thick therefore is the same with frequent, as a thick troop; and thin the same with unfrequent, as a thin rank, thin of houses; not that there is more matter in one place than in another equal place, but a greater quantity of some named body. For there is not less matter or body, indefinitely taken, in a desert, than there is in a city; but fewer houses, or fewer men. Nor is there in a thick rank a greater quantity of body, but a greater number of soldiers, than in a thin. Wherefore the multitude and paucity of the parts contained within the same space do constitute density and rarity, whether those parts be separated by vacuum or by air. But the consideration of this is not of any great moment in philosophy; and therefore I let it alone, and pass on to the search of the causes of gravity.
That the descent of heavy bodies proceeds not from their own appetite, but from some power of the earth.
2. Now we call those bodies heavy, which, unless they be hindered by some force, are carried towards the centre of the earth, and that by their own accord, for aught we can by sense perceive to the contrary. Some philosophers therefore have been of opinion, that the descent of heavy bodies proceeded from some internal appetite, by which, when they were cast upwards, they descended again, as moved by themselves, to such place as was agreeable to their nature. Others thought they were attracted by the earth. To the former I cannot assent, because I think I have already clearly enough demonstrated that there can be no beginning of motion, but from an external and moved body; and consequently, that whatsoever hath motion or endeavour towards any place, will always move or endeavour towards that same place, unless it be hindered by the reaction of some external body. Heavy bodies, therefore, being once cast upwards, cannot be cast down again but by external motion. Besides, seeing inanimate bodies have no appetite at all, it is ridiculous to think that by their own innate appetite they should, to preserve themselves, not understanding what preserves them, forsake the place they are in, and transfer themselves to another place; whereas man, who hath both appetite and understanding, cannot, for the preservation of his own life, raise himself by leaping above three or four feet from the ground. Lastly, to attribute to created bodies the power to move themselves, what is it else than to say that there be creatures which have no dependance upon the Creator? To the latter, who attribute the descent of heavy bodies to the attraction of the earth, I assent. But by what motion this is done, hath not as yet been explained by any man. I shall therefore in this place say somewhat of the manner and of the way by which the earth by its action attracteth heavy bodies.
The difference of gravities proceedeth from the difference of the impetus with which the elements, whereof heavy bodies are made, do fall upon the earth.
3. That by the supposition of simple motion in the sun, homogeneous bodies are congregated and heterogeneous dissipated, has already been demonstrated in the [5th article] of chapter XXI. I have also supposed, that there are intermingled with the pure air certain little bodies, or, as others call them, atoms; which by reason of their extreme smallness are invisible, and differing from one another in consistence, figure, motion, and magnitude; from whence it comes to pass that some of them are congregated to the earth, others to other planets, and others are carried up and down in the spaces between. And seeing those, which are carried to the earth, differ from one another in figure, motion, and magnitude, they will fall upon the earth, some with greater, others with less impetus. And seeing also that we compute the several degrees of gravity no otherwise than by this their falling upon the earth with greater or less impetus; it follows, that we conclude those to be the more heavy that have the greater impetus, and those to be less heavy that have the less impetus. Our inquiry therefore must be, by what means it may come to pass, that of bodies, which descend from above to the earth, some are carried with greater, others with less impetus; that is to say, some are more heavy than others. We must also inquire, by what means such bodies, as settle upon the earth, may by the earth itself be forced to ascend.
The cause of the descent of heavy bodies.
4. Let the circle made upon the centre C (in [fig. 2]) be a great circle in the superficies of the earth, passing through the points A and B. Also let any heavy body, as the stone A D, be placed anywhere in the plane of the equator; and let it be conceived to be cast up from A D perpendicularly, or to be carried in any other line to E, and supposed to rest there. Therefore, how much space soever the stone took up in A D, so much space it takes up now in E. And because all place is supposed to be full, the space A D will be filled by the air which flows into it first from the nearest places of the earth, and afterwards successively from more remote places. Upon the centre C let a circle be understood to be drawn through E; and let the plane space, which is between the superficies of the earth and that circle, be divided into plane orbs equal and concentric; of which let that be the first, which is contained by the two perimeters that pass through A and D. Whilst therefore the air, which is in the first orb, filleth the place A D, the orb itself is made so much less, and consequently its latitude is less than the strait line A D. Wherefore there will necessarily descend so much air from the orb next above. In like manner, for the same cause, there will also be a descent of air from the orb next above that; and so by succession from the orb in which the stone is at rest in E. Either therefore the stone itself, or so much air, will descend. And seeing air is by the diurnal revolution of the earth more easily thrust away than the stone, the air, which is in the orb that contains the stone, will be forced further upwards than the stone. But this, without the admission of vacuum, cannot be, unless so much air descend to E from the place next above; which being done, the stone will be thrust downwards. By this means therefore the stone now receives the beginning of its descent, that is to say, of its gravity. Furthermore, whatsoever is once moved, will be moved continually (as hath been shown in the [19th article] of chapter VIII) in the same way, and with the same celerity, except it be retarded or accelerated by some external movent. Now the air, which is the only body that is interposed between the earth A and the stone above it E, will have the same action in every point of the strait line E A, which it hath in E. But it depressed the stone in E; and therefore also it will depress it equally in every point of the strait line E A. Wherefore the stone will descend from E to A with accelerated motion. The possible cause therefore of the descent of heavy bodies under the equator, is the diurnal motion of the earth. And the same demonstration will serve, if the stone be placed in the plane of any other circle parallel to the equator. But because this motion hath, by reason of its greater slowness, less force to thrust off the air in the parallel circles than in the equator, and no force at all at the poles, it may well be thought (for it is a certain consequent) that heavy bodies descend with less and less velocity, as they are more and more remote from the equator; and that at the poles themselves, they will either not descend at all, or not descend by the axis; which whether it be true or false, experience must determine. But it is hard to make the experiment, both because the times of their descents cannot be easily measured with sufficient exactness, and also because the places near the poles are inaccessible. Nevertheless, this we know, that by how much the nearer we come to the poles, by so much the greater are the flakes of the snow that falls; and by how much the more swiftly such bodies descend as are fluid and dissipable, by so much the smaller are the particles into which they are dissipated.
In what proportion the descent of heavy bodies is accelerated.
5. Supposing, therefore, this to be the cause of the descent of heavy bodies, it will follow that their motion will be accelerated in such manner, as that the spaces, which are transmitted by them in the several times, will have to one another the same proportion which the odd numbers have in succession from unity. For if the strait line E A be divided into any number of equal parts, the heavy body descending will, by reason of the perpetual action of the diurnal motion, receive from the air in every one of those times, in every several point of the strait line E A, a several new and equal impulsion; and therefore also in every one of those times, it will acquire a several and equal degree of celerity. And from hence it follows, by that which Galileus hath in his Dialogues of Motion demonstrated, that heavy bodies descend in the several times with such differences of transmitted spaces, as are equal to the differences of the square numbers that succeed one another from unity; which square numbers being 1, 4, 9, 16, &c. their differences are 3, 5, 7, &c.; that is to say, the odd numbers which succeed one another from unity. Against this cause of gravity which I have given, it will perhaps be objected, that if a heavy body be placed in the bottom of some hollow cylinder of iron or adamant, and the bottom be turned upwards, the body will descend, though the air above cannot depress it, much less accelerate its motion. But it is to be considered that there can be no cylinder or cavern, but such as is supported by the earth, and being so supported is, together with the earth, carried about by its diurnal motion. For by this means the bottom of the cylinder will be as the superficies of the earth; and by thrusting off the next and lowest air, will make the uppermost air depress the heavy body, which is at the top of the cylinder, in such manner as is above explicated.
Why those that dive, do not, when they are under water, feel the weight of the water above them.