(5-6) You can also easily conceive how several of these rays, coming from diverse points, come together at the same point (or, coming from the same point, go out toward different points) without impeding or depending on one another. As you see in Figure 6, several of them come from the points A, B, C, D and come together at point L, and several come from the single point D and extend, one toward E, another toward K, and thus toward an infinity of other places. In just the same way, the diverse forces with which one pulls the cords 1, 2, 3, 4, 5 all come together in the pulley, and the resistance of this pulley extends to all the diverse hands that are pulling those cords.
(7) But to conceive how several of those rays, coming from diverse points and going toward diverse points, can pass through the same point without impeding one another, just as in Figure 6 the two rays AN and DL pass through point E, one must consider that each of the parts of the second element is capable of receiving several diverse motions at the same time. Thus, the part at, say, point E can be pushed as a whole toward L by the action coming from the place on the sun marked D and, at the same time, toward N by that coming from the place marked A. You will understand this still better if you consider that one can push the air at the same time from F toward G, from H toward I, and from K toward L, through the three tubes FG, HI, and KL, even if those tubes are so joined at point N that all the air that passes through the middle of each of them must necessarily also pass through the middle of the other two.
(8) And this same comparison can serve to explain how a strong light impedes the effect of those that are weaker. For, if one pushes the air much more strongly F through than through H or through K, it will not tend at all toward I or toward L, but only toward G.
(9-10) As for reflection and refraction, I have already explained them sufficiently elsewhere.60 Nevertheless, because I then used the example of the motion of a ball instead of speaking of rays of light, in order by this means to render my discourse more intelligible, it still remains for me here to have you consider that the action, or the inclination to move, that is transmitted from one place to another by means of several bodies that touch one another and that continuously fill all the space between the places follows exactly the same path along which this same action could cause the first of those bodies to move if the others were not in its way.61 The only difference is that it requires time for that body to move, whereas the action that is in it can, through the intermediary of those touching it, extend to all sorts of distances in an instant. Whence it follows that, just as a ball is reflected when it strikes against the wall of a tennis court and undergoes refraction when it enters or leaves a body of water obliquely, so too, when the rays of light meet a body that does not permit them to pass beyond, they must be reflected, and when they enter obliquely some place through which they can extend more or less easily than they can through that from which they are coming, they must also be diverted and undergo refraction at the point of that change.
(11-12) Finally, the force of light is not only more or less great in each place according to the quantity of the rays that come together there, but it can also be increased or diminished by the diverse dispositions of the bodies in the places through which it passes. In the same way, the speed of a ball or a stone one is pushing in the air can be increased by winds blowing in the same direction that it is moving and diminished by their contraries.
CHAPTER FIFTEEN That the Face of the Heaven of that New World Must Appear to Its Inhabitants Completely Like That of Our World
Having thus explained the nature and the properties of the action I have taken to be light, I must also explain how, by its means, the inhabitants of the planet I have supposed to be the earth can see the face of their heaven as wholly like that of ours.
First, there is no doubt that they must see the body marked S as completely full of light and like our sun, given that that body sends rays from all points of its surface toward their eyes. And, because it is much closer to them than the stars, it must appear much greater to them. It is true that the parts of the small heaven ABCD that turns about the earth offer some resistance to those rays; but, because all the parts of the great heaven that are between S and D strengthen the rays, those that are between D and T, being comparatively small in number, can take away only very little of their force from them. And even all the action of the parts of the large heaven FGGF does not suffice to impede the rays of many fixed stars from reaching to the earth from the side on which it is not illuminated by the sun.
For one must know that, although the large heavens (i.e. those that have a fixed star or the sun for their center) may perhaps be rather unequal in size, they must always be exactly of the same force, so that all the matter that is, say, in the line SB must tend as strongly toward ε as that which is in the line εB tends toward S. For, if they do not have that equality among them, they will most certainly be destroyed in a short time, or at least they will change until they have acquired it.
Now, since the whole force of the ray SB, for example, is just exactly equal to that of the ray εB, it is manifest that that of the ray TB (which is less) cannot impede the force of the ray εB to extend to T. And in the same way, it is evident that the star A can extend its rays to the earth T, in as much as the matter of the heaven between A and 2 aids them more than that between 4 and T resists them, and in addition in as much as that between 3 and 4 aids them no less than that between 3 and 2 resists them. And thus, judging others proportionately, you can understand that those stars must appear no less confusedly arranged, nor less in number, nor less unequal to one another, than do those we see in the real world.
But you must still consider in regard to their arrangement that they can just about never appear in the true place where they are. For example, that marked e appears as if it were in the straight line TB, and the other marked A as if it were in the straight line T4.
The reason for this is that, since the heavens are unequal in size, the surfaces that separate them are just about never so disposed that the rays that pass through them to go from the stars toward the earth meet them at right angles. And when the rays meet them obliquely, it is certain, according to what has been demonstrated in the Dioptrics,62 that there they must bend and undergo a great deal of refraction, in as much as they pass much more easily through one side of this surface than through the other. And one must suppose those lines TB, T4, and ones like them to be so extremely long in comparison with the diameter of the circle the earth describes about the sun that, wherever the earth is on that circle, the men on it always see the stars as fixed and attached to the same places in the firmament; that is, to use the terms of the astronomers, they cannot observe parallax in the stars.63
Regarding the number of those stars, consider also that the same star can often appear in different places because of the different surfaces that divert its rays toward the earth. Here, for example, that marked A appears in the line T4 by means of the ray A24T and simultaneously in the line Tf by means of the ray A6fT. In the same way are the objects multiplied that one looks at through glasses or other transparent bodies cut along several faces.
Moreover, regarding their size, consider that they must appear much smaller than they are, because of their extreme distance; for this reason the greater part of them must not appear at all, and others appear only insofar as the rays of several joined together render the parts of the firmament through which they pass a bit whiter and similar to certain stars the astronomers call “nebulous,” or to that great belt of our heaven that the poets pretend to be whitened by the milk of Juno.64 Despite this, it nevertheless suffices to suppose the less distant stars to be about equal to our sun, in order to judge that they can appear as large as the largest of our world.
For, generally, all the bodies that send out stronger rays against the eyes of onlookers than do the bodies surrounding them appear proportionately that much greater than they, and consequently those stars must always seem larger than the parts of their heavens that are equal to them and t
hat neighbor them, as I will explain below. In addition to this, however, the surfaces FG, GG, GF and ones like them, where the refractions of [the stars’] rays take place, can be curved in such a way that they greatly increase [the stars’] size; indeed, even when completely flat, they increase it.
Moreover, it is very probable that those surfaces, being in a matter that is very fluid and that never ceases to move, should always shake and quiver somewhat, and consequently that the stars one sees through them should appear to scintillate and vibrate, just as ours do, and even, because of their vibration, appear a bit larger. In this way, the image of the moon appears larger when viewed from the bottom of a lake of which the surface is not very stirred up or agitated, but merely a bit rippled by the breath of some wind.
And, finally, it can happen that, over the course of time, those surfaces change a bit, or indeed even that some of them bend rather noticeably in a short time, even if this is only on the occasion of a comet’s approaching them. By this means, several stars seem after a long time to change a bit in place without changing in size, or to change a bit in size without changing in place. Indeed, some even begin rather suddenly to appear or to disappear, just as one has seen happen in the real world.65
As for the planets and the comets that are in the same heaven as the sun, knowing that the parts of the third element of which they are composed are so large or so joined severally together that they can resist the action of light, it is easy to understand that they must appear by means of the rays that the sun sends toward them and that are reflected from there toward the earth, just as the opaque or obscure objects that are in a room can be seen there by means of the rays that the lamp shining there sends toward them and that return from them toward the eyes of the onlookers. In addition, the rays of the sun have a quite noteworthy advantage over those of a lamp. It consists in their force’s being conserved, or even being increasingly strengthened to the degree that they move away from the sun, until they have reached the exterior surface of its heaven, because all the matter of that heaven tends there. By contrast, the rays of a lamp are weakened as they move away, in proportion to the size of the spherical surfaces they illuminate and, indeed, still somewhat more because of the resistance of the air through which they pass. Whence it is that the objects close to that lamp are noticeably more lighted by it than those far from it, and that the lowest planets are not, in the same proportion, more lighted by the sun than the highest, nor even more than the comets, which are incomparably more distant.
Now, experience shows us that the same thing also happens in the real world. I do not believe, however, that it is possible to give a reason for it if one supposes that light is anything in the objects other than an action or disposition such as I have set forth. I say an action or disposition; for, if you have attended well to what I have just demonstrated, to wit, that, if the space where the sun is were totally void, the parts of its heaven would not cease to tend toward the eyes of onlookers in the same way as when they are pushed by its matter (and even with almost as much force), you can well judge that there is just about no need to have any action in the sun itself nor just about even for it to be anything other than pure space in order to appear as we see it. This is something you would perhaps earlier have taken to be a quite paradoxical proposition. Furthermore, the motion those planets have about their center is the reason why they twinkle, though much less strongly and in another way than do the fixed stars; because the moon is deprived of that motion, it does not twinkle at all.
As for the comets that are not in the same heaven as the sun, they are far from being able to send out as many rays toward the earth as they could if they were in the same heaven, not even when they are all ready to enter it. Consequently, they cannot be seen by men, unless perhaps when their size is extraordinary. The reason for this is that most of the rays that the sun sends out toward them are borne away here and there and effectively dissipated by the refraction they undergo in the part of the firmament through which they pass. For example, whereas the comet CD receives from the sun, marked S, all the rays between the lines SC and SD and sends back toward the earth all those between the lines CT and DT,66 one must imagine that the comet EF receives from the same sun only the rays between the lines SGE and SHF because, since they pass much more easily from S to the surface GH (which I take to be a part of the firmament that they cannot pass beyond), their refraction there must be very great and very much outward. This diverts many of them from going toward the comet EF, given first of all that this surface is curved inward toward the sun, just as you know it should curve when a comet approaches it. But, even if it were completely flat, or even curved in the other direction, most of the rays that the sun sent out to it would not cease to be impeded by the refraction, if not from going up to it, at least from returning from there to the earth. For example, if one supposes the part IK of the firmament to be a portion of a sphere of which the center is at S, the rays SIL and SKM should not bend there at all in going toward the comet LM; by the same token, however, they should bend greatly in returning from the comet toward the earth, so that they can reach the earth only very feebly and in very small quantity. Beyond that, since this can happen when the comet is still rather far from the heaven that contains the sun (for otherwise, if it were close to that heaven, it would cause the heaven’s surface to curve inward), its distance also impedes it from receiving as many rays as when it is ready to enter the heaven. As for the rays it receives from the fixed star at the center of the heaven containing it, it cannot send them back toward the earth any more than the moon, being new, can send back those of the sun.
But, what is even more noteworthy regarding those comets is a certain refraction of their rays, which is ordinarily the reason why some of them appear about [the comets] in the form of a tail or of a curl.67 You will easily understand this if you cast your eyes on this figure, where S is the sun, C a comet, EBG the sphere that (according to what has been said above) is composed of those parts of the second element that are the largest and least agitated of all, and DA the circle described by the annual motion of the earth. Imagine further that the ray coming from C toward B passes straightaway to point A, but that in addition it begins at point B to grow larger and to be divided into many other rays, which extend every which way in all directions. Thus, each of them is that much weaker as it is carried farther away from the one in the middle, BA, which is the principal ray of all and the strongest. Then, too, when the ray CE is at point E, it begins to grow larger and also to be divided into many others, such as EH, EY, ES; the principal and strongest of these, however, is EH, and the feeblest is ES. In the same way, CG passes principally from G toward I, but in addition it is also carried away from S and toward all the spaces between GI and GS. Finally, all the other rays that can be imagined between those three rays CE, CB, and CG hold more or less to the nature of each of them, according as they are more or less close. To this I might add that they should be a bit bent toward the sun; but that is in fact not necessary for my purposes, and I often omit many things in order to render those I do explain that much simpler and easier.
Now, this refraction having been supposed, it is manifest that, when the earth is at A, not only should the ray BA cause men on it to see the body of comet C, but also the rays LA, KA, and others like them, which come to their eyes more feebly than BA, should cause to appear to them a crown or curl of light uniformly spread out in all directions around the comet (as you see at the place marked 11), at least if they are strong enough to be perceived. They can often be strong enough coming from comets, which we suppose to be very large, but not coming from planets, or even from fixed stars, which one must imagine to be smaller. It is also manifest that, when the earth is at M and the comet appears by means of the ray CKM, its curl should appear by means of QM and all the other rays tending toward M, so that it extends farther than before in the direction opposite to the sun, and less far or not at all toward the person looking at it, as you can see here at 22. And th
us appearing longer and longer on the side opposite the sun, to the degree that the earth is farther away from point A, it little by little loses the shape of a curl and is transformed into a long tail, which the comet trails behind it. For example, when the earth is at D, the rays QD and VD make it appear like 33. And, when the earth is at O, the rays VO, EO, and others like them make it appear still longer. And, finally, when the earth is at Y, one can no longer see the comet because of the interposition of the sun; however, the rays VY, EY, and others like them do not cease to cause its tail still to appear in the shape of a chevron or of a torch, such as here at 44. And one should note that, since the sphere EBG is not always exactly round, nor also any of the others it contains (as is easy to judge from what we have set out), those tails or torches should not always appear exactly straight, nor in fact in the same plane as the sun.
As for the refraction that is the cause of all this, I confess that it is of a nature very special and very different from all those commonly observed elsewhere. But you will not fail to see clearly that it should take place in the manner I have just described to you if you consider that the ball H, being pushed toward I, also pushes toward I all those below it down to K, but that the latter, K, being surrounded by many other smaller balls, such as 4, 5, and 6, only pushes 5 toward I, and meanwhile pushes 4 toward L and 6 toward M, and so on. Nevertheless, it does so in such a way that it pushes the middle one, 5, much more strongly than the others, 4, 6, and those like them which are on the sides. In the same way, the ball N, being pushed toward L, pushes the small balls 1, 2, and 3, one toward L, the other toward I, and the other toward M; but with this difference, that it pushes 1 the most strongly of all, and not the middle one, 2. Moreover, the small balls 1, 2, 3, 4, etc., being thus all pushed at the same time by the other balls N, P, H, P, impede one another from being able to go in the directions L and M as easily as toward the middle, I. Thus, if the whole space LIM were full of similar small balls, the rays of their action would be distributed there in the same manner as I have said are those of the comets within the sphere EBG.
Delphi Collected Works of René Descartes Page 14