Delphi Collected Works of René Descartes

by René Descartes

  Now, from this follow two things that seem to me very worth considering. The first is that the matter of the heaven must make the planets turn not only about the sun, but also about their own center (except when there is some particular cause that hinders them from doing so), and consequently that the matter must compose around the planets small heavens that move in the same direction as the greater heaven. The second is that, if there should meet two planets unequal in size but disposed to take their course in the heaven at the same distance from the sun, and the planets are such that the one is exactly as much more massive as the other is larger, then the smaller of the two, having a faster motion than that of the larger, will have to link itself to the small heaven around that larger planet and turn continually about it.

  For, since the parts of the heaven that are, say, at A move faster than the planet marked T, which they push toward Z, it is evident that they must be diverted by it and constrained to take their course toward B. I say toward B rather than toward D; for, having inclination to continue their motion in a straight line, they must go toward the outside of the circle ACZN they are describing, rather than toward the center S. Now, passing thus from A to B, they force the planet T to turn with them about its center. In turn, this planet in so turning gives them occasion to take their course from B to C, then to D and to A, and thus to form about the planet a particular heaven, with which it must thereafter continue to move from the direction one calls the “occident” toward that which one calls the “orient,” not only about the sun but also about its own center.

  Moreover, knowing that the planet marked ~ [Moon] is disposed to take its course along the circle NACZ (just as is the planet marked T) and that it must move faster because it is smaller, it is easy to understand that, wherever it might have been in the heavens at the beginning, it shortly had to tend toward the exterior surface of the small heaven ABCD, and that, once having joined that heaven, it must thereafter always follow its course about T along with the parts of the second element that are at that surface.

  For, since we suppose that it would have exactly as much force as the matter of that heaven to turn along circle NACZ, if the other planet were not there, then we must imagine that it has a bit more force to turn along circle ABCD, because it is smaller and consequently always moves as far away as possible from the center T. In the same way, a stone being moved in a sling always tends to move away from the center of the circle it is describing. This planet, however, being at A, will not thereby act to move off toward L, in as much as it would then enter a place in the heaven of which the matter had the force to push it back toward circle NACZ. By the same token, being at C, it will not act to descend toward K, in as much as it would there be surrounded by a matter that would give it the force to ascend again toward that same circle NACZ. Nor will it go from B toward Z — much less from D toward N — in as much as it could not go as easily nor as fast as it could toward C and toward A.49 Thus, it must remain as if attached to the surface of the small heaven ABCD and turn continually with it about T. That is what impedes its forming another small heaven about it, which would make it turn again about its own center.

  I shall not add here how one can find a greater number of planets joined together and taking their course about one another, such as those that the new astronomers have observed about Jupiter and Saturn.50 For I have not undertaken to say everything, and I have spoken in particular about the two planets discussed above only in order to represent to you (by the planet marked T) the earth we inhabit and (by that marked ¢ [Moon]) the moon that turns about it.

  CHAPTER ELEVEN On Weight

  Now, however, I would like you to consider what the weight of this earth is; that is to say, what the force is that unites all its parts and that makes them all tend toward its center, each more or less according as it is more or less large and solid. That force is nothing other than, and consists in nothing other than, the fact that, since the parts of the small heaven surrounding it turn much faster than its parts about its center, they also tend to move away with more force from its center and consequently to push the parts of the earth back toward its center. You may find some difficulty in this, in light of my just saying that the most massive and most solid bodies — such as I have supposed those of the comets to be — tend to move outward toward the circumferences of the heavens and that only those that are less massive and solid are pushed back toward their centers. For it should follow therefrom that only the less solid parts of the earth could be pushed back toward its center and that the others should move away from it. But note that, when I said that the most solid and most massive bodies tended to move away from the center of any heaven, I supposed that they were already previously moving with the same agitation as the matter of that heaven. For it is certain that, if they have not yet begun to move, or if they are moving less fast than is required to follow the course of this matter, they must at first be pushed by it toward the center about which it is turning. Indeed, it is certain that, to the extent that they are larger and more solid, they will be pushed with more force and speed. Nevertheless, if they are solid and massive enough to compose comets, this does not hinder them from tending to move shortly thereafter toward the exterior circumferences of the heavens, in as much as the agitation they have acquired in descending toward any one of the heavens’ centers will most certainly give them the force to pass beyond and to ascend again toward its circumference.

  But, in order to understand this more clearly, consider the earth EFGH with water 1234 and air 5678, which (as I shall tell you below) are composed simply of some of the less solid of the earth’s parts and constitute a single mass with it. Then consider also the matter of the heaven, which fills not only all the space between the circles ABCD and 5678 but also all the small intervals below it among the parts of the air, the water, and the earth. And imagine that, as that heaven and this earth turn together about center T, all their parts tend to move away from it, but those of the heaven much more quickly than those of the earth, because the former are much more agitated. Or, indeed, imagine that, among the parts of the earth, those more agitated in the same direction as those of the heaven tend more to move away from the center than do the others. Thus, if the whole space beyond circle ABCD were void, i.e., were filled only with a matter that could not resist the actions of other bodies nor produce any considerable effect (for it is thus that we must construe the name “void”), then all the parts of the heaven in the circle ABCD would be the first to leave it; then those of the air and of the water would follow them, and finally also those of the earth, each that much sooner as it were less attached to the rest of its mass.51 In the same way, a stone leaves a sling in which it is being moved as soon as one releases the cord, and the dust one throws on a top while it is turning immediately flies off from it in all directions.

  Then consider that since there is no such space beyond circle ABCD that is void and where the parts of the heaven contained within that circle can go, unless at the same instant others completely like them enter in their place, the parts of the earth also cannot move away any farther than they do from center T, unless there descend in their place just as many parts of the heaven or other terrestrial parts as are needed to fill it. Nor, in turn, can they move closer to the center unless just as many others rise in their stead. Thus they are all opposed to one another, each to those that must enter in its place in the case that it should rise, and similarly to those that must enter therein in the case that it should descend, just as the two sides of a balance are opposed to one another. That is to say, just as one side of a balance can be raised or lowered only if the other side does exactly the contrary at the same instant and just as the heavier always raises the lighter, so too the stone R, for example, is so opposed to the quantity (exactly equal in size) of air above it, whose place it should occupy in the case that it were to move farther away from center T, that that air would necessarily have to descend to the extent that the stone rose. And, in the same way, it is also so
opposed to another, like quantity of air below it, whose place it should occupy in the case that it were to move closer to that center, that the stone must descend when this air rises.

  Now, it is evident that, since this stone contains in it much more of the matter of the earth than a quantity of air of equal extent — and in recompense contains that much less of the matter of the heaven — and since also its terrestrial parts are less agitated by the matter of the heaven than those of that air, the stone should not have the force to rise above that quantity of air, but on the contrary the quantity of air should have the force to make the stone fall downward. Thus, that quantity of air is light when compared with the stone but is heavy when instead it is compared with the wholly pure matter of the heaven. And so you see that each part of terrestrial bodies is pressed toward T, not indifferently by the whole matter surrounding it, but only by a quantity of this matter exactly equal to the size of the part; that quantity, being underneath the part, can take its place in the case that the part falls. That is the reason why, among the parts of any single body designated “homogeneous” (such as among those of air or water), the lowest are not notably more pressed than the highest, and why a man down below in very deep water does not feel it weigh on his back any more than if he were swimming right on top.52

  But it may seem to you that the matter of the heaven, in thus causing the stone R to fall toward T and below the air surrounding it, should also cause it to go toward 6 or toward 7 (i.e. toward the occident or toward the orient) faster than this air, so that the stone does not fall in a straight, plumb line as heavy bodies do on the real earth. If so, consider first that all the terrestrial parts contained in the circle 5678, in being pressed toward T by the matter of the heaven in the way I have just explained, and having in addition very irregular and diverse shapes, must join together and approach one another and thus compose only one mass, which is borne as a whole by the course of the heaven ABCD. Thus, while the mass turns, those of its parts that are, say, at 6 always remain opposite those that are at 2 and at F, without notably moving aside one way or the other except insofar as winds or other particular causes constrain them to do so.

  Note moreover that the little heaven ABCD turns much faster than the earth, but that those of its parts that are caught in the pores of terrestrial bodies cannot turn notably faster than those bodies about the center T, even though those parts move much faster in diverse other directions, according to the disposition of these pores.

  Then you should know that, even though the matter of the heaven makes the stone R move closer to that center (because the matter tends to move away from it with more force than the stone), the matter nevertheless cannot force the stone to back up toward the occident, even though the matter also tends with more force than the stone to go toward the orient. To see this, consider that this matter of the heaven tends to move away from the center T because it tends to continue its motion in a straight line; but it tends to move from the occident toward the orient only because it tends to continue its motion at the same speed and because it is moreover indifferent toward being at 6 or at 7.

  Now it is evident that the matter moves a bit more in a straight line while causing the stone R to fall toward T than it does in leaving the stone at R; but it could not move as fast toward the orient if it caused the stone to move back toward the occident as it could if it left the stone in its place or even if it pushed the stone before it.

  You should also know, however, that, even though this matter of the heaven has more force to cause this stone R to descend toward T than to cause the air surrounding the stone to descend there, it should nevertheless not have more force to push the stone before it from the occident toward the orient, nor consequently to cause the stone to move faster in that direction than the air. To see this, consider that there is exactly as much of this matter of the heaven acting on the stone to cause it to fall toward T (and using its full force to that end) as there is matter of the earth in the composition of the stone’s body and that, in as much as there is much more matter of the earth in the stone than in a quantity of air of equal extent, the stone must be pressed much more strongly toward T than is that air. By contrast, to cause the stone to turn toward the orient, all the matter of the heaven contained in circle R acts on it and conjointly on all the terrestrial parts of the air that is contained in that same circle. Thus, there being no more acting on the stone than on this air, the stone should not turn faster than the air in that direction.

  You can understand from this that the arguments that many philosophers use to refute the motion of the real earth have no force against the motion of the earth I am describing to you. For example, when they say that, if the earth moved, heavy bodies could not descend in a plumb line toward its center, but rather would have to depart from it every which way toward the heaven; and that cannons pointed toward the occident should carry much farther than if pointed toward the orient; and that one should always feel great winds in the air and hear great noises: these and like things do not take place except in the case that one supposes that the earth is not carried by the course of the heaven surrounding it, but that it is moved by some other force and in some other direction than that heaven.53

  CHAPTER TWELVE On the Ebb and Flow of the Sea

  Now, after having thus explained the weight of the parts of this earth, which is caused by the action of the matter of the heaven in their pores, I must now speak to you about a certain motion of its whole mass, which is caused by the presence of the moon, and also about some particular things that depend on that motion.

  To that end, consider the moon at, say, B (where you can suppose it to be immobile in comparison with the speed at which the matter of the heaven below it moves), and consider that this matter of the heaven, having less space to pass through between O and 6 than between B and 6 (if the moon does not occupy the space between O and B), and consequently having to move a bit faster there, cannot fail to have the force to push the whole earth a little bit toward D, so that its center T moves away (as you can see) a little bit from the point M, which is the center of the small heaven ABCD. For nothing but the course alone of the matter of that heaven maintains the earth in the place where it is. And, because the air 5678 and the water 1234 surrounding this earth are liquid bodies, it is evident that the same force that presses the earth in this way must also make them sink toward T, not only from the side 6,2 but also from its opposite 8,4, and in recompense cause them to rise in the places 5,1 and 7,3. Thus, the surface EFGH of the earth remaining round (because it is hard), that of the water 1234 and that of the air 5678 (which are liquids) must form an oval.

  Then consider that, since the earth is meanwhile turning about its center and by this means making the days that one divides up into 24 hours (like ours), the side F, which is now directly opposite the moon and on which the water is for that reason less high, must in six hours be directly opposite the heaven marked C, in which position this water will be higher; in twelve hours it should be directly opposite the place of the heaven marked D, where again the water will be lower. Thus the sea, which is represented by this water 1234, should have its ebb and flow about this earth once every six hours, just as it has about the earth we inhabit.

  Consider also that, while this earth turns from E through F to G (i.e. from the occident through the meridian toward the orient), the flood of the water and the air that remains at 1 and 5 and at 3 and 7 passes from its oriental side toward the occidental, there causing a flow without ebb very much like that which, according to the report of our pilots, makes navigation on our seas much easier going from the orient to the occident than from the occident to the orient.

  In order to forget nothing at this point, let us add that the moon each month makes the same circuit as the earth does each day, and thus that it cause to advance little by little toward the orient the points 1, 2, 3, 4 that mark high and low water. Hence, these waters do not change precisely every six hours, but rather lag behind by approximately the fifth p
art of an hour each time, as do those of our seas also.

  Consider in addition that the small heaven ABCD is not exactly round, but that it extends a bit more freely at A and at C and there moves proportionately more slowly than at B and at D, where it cannot so easily break the course of the matter of the other heaven containing it. Thus the moon, which always remains as if attached to its exterior surface, must move a bit faster and remove itself less from its path, and consequently be the reason why the ebb and flow of the sea are much greater when the moon is at B (where it is full) and at D (where it is new) than when it is at A or at C (where it is only half full). These are peculiarities also wholly like those that the astronomers observe in the real moon, although they perhaps cannot explain them as easily by the hypotheses they use.

  As for the other effects of this moon, which are different when it is full from when it is new, they manifestly depend on its light. And as for the other special properties of the ebb and flow of the sea, they depend in part on the diverse situation of the seacoasts and in part on the winds prevailing at the time and at the place they are observed. Finally, as for the other general motions, both of the earth and moon and of the other stars and heavens, either you can understand them well enough from what I have said, or they do not serve my purpose here; not falling under the same heading as those of which I have spoken, they would take me too long to describe. Thus, there remains for me here only to explain this action of the heavens and the stars that I have just said should be taken to be their light.