Delphi Collected Works of René Descartes

by René Descartes

  Imagine, for example, that the points S, E, ε, and A are the centers of which I speak, that all the matter contained in the space FGGF is a heaven turning about the sun marked S, that all the matter of the space HGGH is another heaven turning about the star marked ε, and so on for the others. Thus, there are as many different heavens as there are stars, and, since the number of stars is indefinite, so too is the number of heavens. Thus also the firmament is nothing other than the breadthless surface separating all the heavens from one another.

  Imagine also that the parts of the second element toward F, or toward G, are more agitated than those toward K, or toward L, so that their speed decreases little by little from the outside circumference of each heaven to a certain place (such as, for example, to the sphere KK about the sun, and to the sphere LL about the star ε) and then increases little by little from there to the centers of the heavens because of the agitation of the stars that are found there. Thus, while the parts of the second element toward K have the chance to describe there a complete circle about the sun, those toward T, which I suppose to be ten times closer, have not only the chance to describe ten circles (as they would do if they moved only equally fast), but perhaps more than thirty.42 Again, those parts toward F, or toward G, which I suppose to be two or three thousand times more distant, can perhaps describe more than sixty circles. Whence you will be able to understand immediately that the highest planets must move more slowly than the lowest (i.e. those closest to the sun), and that all the planets together move more slowly than the comets, which are nonetheless more distant.

  As for the size of each of the parts of the second element, one can imagine that it is equal among all those between the outside circumference FGGF of the heaven and the circle KK, or even that the highest among them are a bit smaller than the lowest (provided that one does not suppose the difference of their sizes to be proportionately greater than that of their speeds). By contrast, however, one must imagine that, from circle K to the sun, it is the lowest parts that are the smallest, and even that the difference of their sizes is proportionately greater than (or at least proportionately as great as) that of their speeds. Otherwise, since those lowest parts are the strongest (due to their agitation), they would go out to occupy the place of the highest.

  Note finally that, given the manner in which I have said the sun and the other fixed stars were formed, their bodies can be so small with respect to the heavens containing them that even all the circles KK, LL, etc., which mark the point to which the agitation of those bodies advances the course of the matter of the second element, can be considered merely as the points that mark the heavens’ center. In the same way, the new astronomers consider the whole sphere of Saturn as but a point in comparison with the firmament.

  CHAPTER NINE On the Origin and the Course of the Planets and Comets in General; and of Comets in Particular

  Now, for me to begin to tell you about the planets and comets, consider that, given the diversity of the parts of the matter I have supposed, even though most of them in breaking and dividing by collision with one another have taken the form of the first or second element, there nevertheless does not cease still to be found among them two sorts that had to retain the form of the third element, to wit, those of which the shapes were so extended and so impeding that, when they collided with one another, it was easier for several to join together, and by this means to become larger than to break up and become smaller; and those which, having been from the beginning the largest and most massive of all, could well break and shatter the others in striking them but not in turn be broken or shattered themselves.

  Now, whether you imagine that these two sorts of parts were at first very agitated or very little agitated, or not at all, it is certain that afterward they had to move with the same agitation as the matter of the heaven that contained them. For, if at first they were moving more quickly than that matter, then, not having been able to avoid pushing it upon colliding with it in their path, in a short time they had to transfer to it a part of their agitation. And if, on the contrary, they had in themselves no inclination to move, nevertheless, being surrounded on all sides by that matter of the heaven, they necessarily had to follow its course, just as we see all the time that boats and diverse other bodies floating on water (both the largest and most massive and those that are less so) follow the course of the water they are in when there is nothing else to impede them from doing so.43

  And note that, among the diverse bodies that thus float on water, those that are rather solid and rather massive (as boats ordinarily are, principally the largest and most heavily laden boats) always have much more force than the water to continue their motion, even though it is from the water alone that they have received their motion. By contrast, those floating bodies that are very light, like those lumps of white scum that one sees floating along the shores during storms, have less force to continue moving. Thus, if you imagine two rivers that join with one another at some point and then separate again shortly thereafter before their waters (which one must suppose to be very calm and to have a rather equal force, but also to be very rapid) have a chance to mix, then boats or other rather massive and heavy bodies that are borne by the course of the one river will be easily able to pass into the other river, while the lightest bodies will turn away from it and will be thrown back by the force of the water toward the places where it is the least rapid.

  For example, if ABF and CDG are two rivers which, coming from two different directions, meet at E and then turn away from there, AB going toward F and CD toward G, it is certain that boat H following the course of river AB must pass through E toward G, and reciprocally boat I toward F, unless both meet at the passage at the same time, in which case the larger and stronger will break the other. By contrast, scum, leaves of trees, feathers, straw, and other such light bodies that can be floating at A must be pushed by the course of the water containing them, not toward E and toward G, but toward B, where one must imagine that the water is less strong and less rapid than at E, since at B it takes its course along a line that less approaches a straight line.

  Moreover, one must consider that not only these light bodies, but also others heavier and more massive can join upon meeting and that, turning then with the water that bears them, several together can compose large balls such as you see at K and L, of which some, such as L go toward E and others, such as K, go toward B, according as each is more or less solid and composed of more or less large and massive parts.

  By this example, it is easy to understand that, wherever the parts of matter that could not take the form of the second or of the first element may have been at the beginning, all the larger and more massive among them shortly had to take their course toward the outside circumference of the heavens that contained them and thereafter pass continually from one of these heavens into another without ever stopping for a very long period of time in the same heaven. By contrast, all the less massive had to be pushed, each toward the center of the heaven containing it, by the course of the matter of that heaven. And (given the shapes that I have attributed to them) upon colliding with one another, they had to join together severally and compose large balls which, turning in the heavens, have there a motion tempered by all the motions the separate parts could have if they were in fact separate. Thus, some tend to move toward the circumferences of those heavens, and others toward their centers.

  Know also that we should take those that thus tend to range toward the center of any heaven to be the planets, and we should take those that pass across different heavens to be comets.

  Now, concerning these comets, one must note first that there must be few of them in this new world in comparison to the number of heavens. For, even if there were many at the beginning, over the course of time in passing across different heavens almost all of them would have to have collided with one another and broken one another up (just as I have said two boats do when they meet), so that now only the largest could remain.

  One must also note
that, when they pass thus from one heaven into another, they always push before them some small bit of the matter of the heaven they are leaving and remain enveloped by it for some time until they have entered far enough within the limits of the other heaven. Once there, they finally loose themselves from it almost all at once and without taking perhaps more time to do so than does the sun in rising at morning on our horizon. In this way, they move much more slowly when they thus tend to leave some heaven than they do shortly after having entered it.

  For example, you see here that the comet that takes its course along the line CDQR, having already entered rather far within the limits of the heaven FG, nevertheless when it is at point C still remains enveloped by matter from the heaven FI, from which it comes, and cannot be entirely freed of that matter before it is around point D. But, as soon as it has arrived there, it begins to follow the course of the heaven FG and thus to move much faster than it did before. Then, continuing its course from there toward R, its motion must again slow down little by little in proportion as it approaches point Q, both because of the resistance of the heaven FGH, within the limits of which it is beginning to enter, and because, there being less distance between S and D than between S and Q, all the matter of the heaven between S and D (where the distance is smaller) moves faster there, just as we see that rivers always flow more swiftly in the places where their bed is narrower and more confined than in those where it is wider and more extended.44

  Moreover, one should note that this comet should be visible to those who live at the center of the heaven FG only during the time it takes to pass from D to Q, as you will soon understand more clearly when I have told you what light is. In the same way, you will see that its motion should appear to viewers to be much faster, its body much greater, and its light much brighter, at the beginning of the time they see it than at the end.

  Beyond that, if you consider with some care the way in which the light that can come from the comet must spread out and be distributed in all directions in the heaven, you will also be well able to understand that, being very large (as we must suppose it to be), there can appear around it certain rays that sometimes extend in the form of a halo on all sides and sometimes gather together in the form of a tail on one side only, according to the different places from which it is viewed. m us, this comet lacks none of all the properties that have been observed up to now in those that have been seen in the real world, at least none of those properties that should be taken as true. For, if some historians, in order to construct a miracle that warns of the crescent of the Turks, tell us that in the year 1450 the moon was eclipsed by a comet which passed below it, or something similar, and if the astronomers, calculating badly the amount of refraction (which they do not know) of the heavens and the speed of motion of comets (which is uncertain), attribute to them enough parallax to be placed among the planets, or even below them (where some wish to pull them as by force), then we are not obliged to believe them.45

  CHAPTER TEN On the Planets in General, and in Particular on the Earth and Moon

  Similarly, there are several things to note concerning the planets. First, even though they all tend toward the center of the heavens containing them, that is not to say thereby that they could ever arrive at those centers. For, as I have already said above, the sun and the other fixed stars occupy them. But, in order to make you understand distinctly in what places the planets should stop, look for example at the one marked ~ [Saturn], which I suppose to follow the course of the matter of the heaven toward the circle K, and consider that, if this planet had the slightest bit more force to continue its motion in a straight line than do the parts of the second element surrounding it, then, instead of always following that circle K, it would go toward Y, and thus it would be more distant than it is from center S. Then, in as much as the parts of the second element that would surround it at Y move faster and even are a bit smaller (or at least are not larger) than those at K, they would give it still more force to pass beyond toward F, so that it would go out to the circumference of that heaven, without being able to stop anywhere in between. Then from there it would easily pass into another heaven and thus, instead of being a planet, would become a comet.

  Whence you see that no star can stop anywhere in all that vast space between the circle K and the circumference of the heaven FGGF, through which the comets take their course. In addition, the planets of necessity cannot have more force to continue their motion in a straight line than have the parts of the second element at K, when those planets move with the same agitation along with these parts; and all bodies that have more are comets.

  Therefore, let us now imagine that this planet ~ [Saturn] has less force than the parts of the second element surrounding it, so that those parts that follow it and that are placed a bit lower than it can divert it with the result that, instead of following circle K, it descends toward the planet marked ~ [Jupiter]. The planet ~ [Saturn] being there, it can happen that it is exactly as strong as the parts of the second element that will then surround it. The reason for this is that, these parts of the second element being more agitated than those at K, they will also agitate the planet more; being in addition smaller, they will not be able to resist it as much. In this case, the planet will remain perfectly balanced in the middle of them and will there take its course in the same direction as they about the sun, without being at one time or another more or less distant from the sun, except insofar as they can also be more or less distant from it.

  But, if this planet~ [Saturn], being at ~ [Jupiter], still has less force to continue its motion in a straight line than has the matter of the heaven found there, it will again be pushed lower by the matter, toward the planet marked [Mars], and so on, until finally it is surrounded by a matter that has neither more nor less force than it.

  Thus you see that there can be diverse planets, some more and others less distant from the sun, such as here ~[Saturn], [Jupiter], [Mars], T, [Venus], .[Mercury]46 Of these the lowest and least massive can reach to the sun’s surface, but the highest never pass beyond circle K which, although very large in comparison with each planet in particular, is nevertheless so extremely small in comparison with the whole of heaven FGGF that, as I have already said above, it can be considered as its center.

  But, if I still have not made you understand well enough why it can happen that the parts of the heaven beyond circle K, being incomparably smaller than the planets, do not cease to have more force than they to continue their motion in a straight line, consider that this force does not depend solely on the quantity of the matter that is in each body, but also on the extent of its surface. For, even though when two bodies move equally fast it is correct to say that, if one contains twice as much matter as the other, it also has twice as much agitation, that is not to say thereby that it has twice as much force to continue to move in a straight line; rather, it will have exactly twice as much if, in addition, its surface is exactly twice as extended, because it will always meet twice as many other bodies resisting it, and it will have much less force to continue if its surface is extended much more than twice.47

  Now, you know that parts of the heaven are just about all round and thus that, of all shapes, they have the one that includes the most matter within the least surface, whereas the planets, being composed of small parts having very irregular and extended shapes, have large surfaces in proportion to the quantity of their matter. Thus, the planets can have [a greater ratio of surface to volume] than most of those parts of the heaven and nevertheless also have a smaller one than some of the smallest parts that are closest to the centers. For one must know that, among two wholly massive balls such as are those parts of the heavens, the smaller always has more surface in proportion to its quantity than has the larger.48

  One can easily confirm all this by experience. For, if one pushes a large ball composed of many tree branches confusedly joined and piled on top of one another (as one must imagine are the parts of matter of which the planets are composed), it is cert
ain that, even if it be pushed by a force entirely proportional to its size, it will not be able to continue its motion as far as would another ball, very much smaller and composed of the same wood, but wholly massive. By contrast, it is also certain that one could make another ball of the same wood and wholly massive, but so extremely small that it would have much less force to continue its motion than had the first. Finally it is certain that this first ball can have more or less force to continue its motion according as the branches composing it are more or less large and compressed.

  Whence you see how diverse planets can be suspended within circle K at diverse distances from the sun, and how it is not simply those that outwardly appear the largest, but those that are the most solid and the most massive in their interior, that should be the most distant.

  Thereafter, one must note that, just as we experience that boats following the course of a river never move as fast as the water that bears them, nor indeed the larger among them as fast as the smaller, so too, even though the planets follow the course of the matter of the heaven without resistance and move with the same agitation as it, that is not to say thereby that the planets ever move entirely as fast as the matter. Indeed, the inequality of their motion must bear some relation to the inequality between the size of their mass and the smallness of the parts of the heaven that surround them. The reason for this is that, generally speaking, the larger a body is, the easier it is for it to communicate a part of its motion to other bodies, and the more difficult it is for the others to communicate to it something of their own motion. For, even though many small bodies all working together to act upon a larger one may have as much force as it, nevertheless they can never make it move as fast as they in all directions because, if they agree in some of their motions which they communicate to it, at the same time they most certainly differ in others which they cannot communicate to it.