RENE DESCARTES

THE WORLD

or

TREATISE ON LIGHT

Translated by Michael S. Mahoney

 

CHAPTER ONE On the Difference Between Our Sensations and the Things That Produce Them

In proposing to treat here of light, the first thing I want to make clear to you is that there can be a difference between our sensation[1] of light (i.e. the idea that is formed in our imagination through the intermediary of our eyes) and what is in the objects that produces that sensation in us (i.e. what is in the flame or in the sun that is called by the name of "light"). For, even though everyone is commonly persuaded that the ideas that are the objects of our thought are wholly like the objects from which they proceed, nevertheless I can see no reasoning that assures us that this is the case. On the contrary, I note many experiences that should cause us to doubt it.

You well know that words bear no resemblance to the things they signify, and yet they do not cease for that reason to cause us to conceive of those things, indeed often without our paying attention to the sound of the words or to their syllables. Thus it can happen that, after having heard a discourse, the sense of which we have very well understood, we might not be able to say in what language it was uttered.[2] Now, if words, which signify nothing except by human convention, suffice to cause us to conceive of things to which they bear no resemblance, why could not nature also have established a certain sign that would cause us to have the sensation of light, even though that sign in itself bore no similarity to that sensation? Is it not thus that she has established laughter and tears, to cause us to read joy and sorrow on the faces of men?

But perhaps you will say that our ears in fact cause us to hear only the sound of the words, or our eyes to see only the countenance of him who laughs or cries, and that it is our mind that, having remembered what those sounds and that countenance signify, represents their meaning to us at the same time.[3] To that I could respond that it is nonetheless our mind that represents to us the idea of light each time the action that signifies it touches our eye. But, rather than lose time in disputation, I would do better to adduce another example.

Do you think that, even when we do not pay attention to the meaning of words and hear only their sound, the idea of that sound, which forms in our thought, is anything like the object that is the cause of it? A man opens his mouth, moves his tongue, forces out his breath: in all these actions I see nothing that is not very different from the idea of the sound that they cause us to imagine. Also, most philosophers assure us that sound is nothing other than a certain vibration of air that strikes against our ears. Thus, if our sense of hearing were to report to our mind the true image of its object, then, instead of causing us to conceive of sound, it would have to cause us to conceive of the motion of the parts of air that then vibrate against our ears. But, because not everyone will perhaps want to believe what the philosophers say, I will adduce another example.

Of all our senses, touch is the one thought least misleading and most certain, so that, if I show you that even touch causes us to conceive many ideas that in no way resemble the objects that produce them, I do not think you will find it strange if I say that sight can do the same. Now, there is no one who does not know that the ideas of tickling and of pain, which are formed in our thought when bodies from without touch us, bear no resemblance whatever to those bodies. One passes a feather lightly over the lips of a child who is falling asleep, and he perceives that someone is tickling him.[4] Do you think the idea of tickling that he conceives resembles anything in this feather? A soldier returns from battle; during the heat of combat he could have been wounded without being aware of it. But now that he begins to cool off, he feels pain and believes he has been wounded. A surgeon is called, the soldier's armor is removed, and he is examined. In the end, one finds that what he felt was nothing but a buckler or a strap, which was caught under his armor and was pressing on him and making him uncomfortable. If, in causing him to feel this strap, his sense of touch had impressed its image on his thought, there would have been no need of a surgeon to show him what he was feeling.

Now, I see no reason that forces us to believe that what is in the objects from which the sensation of light comes to us is any more like that sensation than the actions of a feather and of a strap are like tickling and pain. Nevertheless, I have not adduced these examples to make you believe absolutely that this light is something different in the objects from what it is in our eyes, but only so that you will doubt it and so that, forbearing from being preoccupied by the contrary, you can now better examine with me what light is.

CHAPTER TWO In What the Heat and Light of Fire Consists

I know of only two sorts of bodies in the world in which light is found, to wit, the stars and flame, or fire.[5] And, because the stars are without a doubt farther from human knowledge than is fire or flame, I shall try first to explicate what I observe regarding flame.

When flame burns wood or some other similar material, we can see with our eyes that it moves the small parts of the wood and separates them from one another, thus transforming the subtler parts into fire, air, and smoke, and leaving the grosser parts as ashes. Hence, someone else may, if he wishes, imagine the form of "fire," the quality of "heat," and the action that "burns" it to be completely different things in this wood.[6] For my part, afraid of misleading myself if I suppose anything more than what I see must of necessity be there, I am content to conceive there the motion of its parts. For, posit "fire" in the wood, posit "heat" in the wood, and make the wood "burn" as much as you please. If you do not suppose in addition that some of its parts are moved or detached from their neighbors, I cannot imagine that it would undergo any alteration or change. By contrast, remove the "fire," remove the "heat," prevent the wood from "burning:" provided only that you grant me that there is some power that violently moves the subtler of its parts and separates them from the grosser, I find that that alone will be able to cause in the wood all the same changes that one experiences when it burns.

Now, insofar as it does not seem to me possible to conceive that one body could move another unless it itself were also moving,[7] I conclude from this that the body of the flame that acts against the wood is composed of small parts, which move independently of one another with a very fast and very violent motion. Moving in this way, they push and move with them the parts of the body that they touch and that do not offer them too much resistance. I say that its parts move independently of one another because, even though several of them often act in accord and conspire together to bring about a single effect, we gee nonetheless that each of them acts on its own against the bodies they touch. I say also that their motion is very fast and very violent because, being so small that we cannot distinguish them by sight, they would not have the force they have to act against other bodies if the quickness of their motion did not compensate for their lack of size.[8]

I add nothing concerning the direction in which each moves. For, if you consider that the power to move and the power that determines in what direction the motion should take place are two completely different things and can exist one without the other (as I have set out in the Dioptrics),[9] you will easily judge that each part moves in the manner made least difficult for it by the disposition of the bodies surrounding it.[10] Moreover, in the same flame there can be some parts going upward, and others downward, some in straight lines, and others in circles; indeed, they can go in all directions, without changing anything of the flame's nature. Thus, if you see almost all of them tending upward, you need not think that this is for any other reason than that the other bodies touching them are almost always disposed to offer them greater resistance in any other direction.

But, having recognized that the parts of the flame move in this manner, and that it suffices to conceive of their motions in order to understand how the flame has the power to consume the wood and to burn, pray let us examine if the same will not also suffice to make us understand how the flame heats us and how it sheds light for us. For, if that is the case, it will not be necessary for the flame to possess any other quality, and we will be able to say that it is this motion alone that is called now "heat" and now "light" according to the different effects it produces.

Now, as regards heat, the sensation that we have of it can, it seems to me, be taken for a type of pain when it is violent, and sometimes for a type of tickling when it is moderate.[11] Since we have already said that there is nothing outside our thought that is similar to the ideas we conceive of tickling and pain, we can well believe also that there is nothing that is similar to that which we conceive of heat; rather, anything that can move the small parts of our hands, or of any other part of our body, can arouse this sensation in us. Indeed, many experiences favor this opinion. For merely by rubbing our hands together we heat them, and any other body can also be heated without being placed close to a fire, provided only that it is shaken and rubbed in such a way that many of its small parts are moved and can move with them those of our hands.

As regards light, one can also well imagine that the same motion that is in the flame suffices to cause us to sense light. But, because it is in this that the main part of my design consists, I want to try to explain it at some length and to take up my discourse from anew.

CHAPTER THREE On Hardness and Liquidity

I consider that there is an infinity of diverse motions that endure perpetually in the world. After having noted the greatest of these (i.e. those that bring about the days, months, and years), I take note that the vapors of the earth never cease to rise to the clouds and to descend from them, that the air is forever agitated by the winds, that the sea is never at rest, that springs and rivers flow ceaselessly, that the strongest buildings finally fall into decay, that plants and animals are always either growing or decaying; in short, that there is nothing anywhere that is not changing. Whence I know clearly that it is not in the flame alone that there are a number of small parts never ceasing to move, but that there are also such parts in every other body, even though their actions are not as violent and they cannot, due to their smallness, be perceived by any of our senses.

I do not stop to seek the cause of their motion, for it is enough for me to think that they began to move as soon as the world began to exist. And that being the case, I find by my reasoning that it is impossible that their motions should ever cease or even that those motions should change in any way other than with regard to the subject in which they are present. That is to say, the virtue or power in a body to move itself can well pass wholly or partially to another body and thus no longer be in the first; but it cannot no longer exist in the world. My arguments, I say, are enough to satisfy me above, but I have not yet had occasion to relate them to you. In the meantime, you can imagine if you choose, as do most of the learned, that there is some first mover which, rolling about the world at an incomprehensible speed, is the origin and source of all the other motions found therein.

Now, in consequence of this consideration, there is a way of explaining the cause of all the changes that take place in the world and of all the variety that appears on the earth. However, I shall be content here to speak of those that serve my purpose.

The difference between hard bodies and those that are liquids is the first thing I would like you to note. To that end, consider that every body can be divided into extremely small parts. I do not wish to determine whether their number is infinite or not; at least it is certain that, with respect to our knowledge, it is indefinite and that we can suppose that there are several millions in the smallest grain of sand our eyes can perceive.

Note also that, if two of these small parts are touching one another, without being in the act[12] of moving away from one another, some force is necessary to separate them, however small it may be. For, once so placed, they would never be inclined to dispose themselves otherwise. Note also that twice as much force is necessary to separate two of them than to separate one of them, and a thousand times as much to separate a thousand of them. Thus, if it is necessary to separate several millions of them all at once, as is perhaps necessary in order to break a single hair, it is not surprising that a rather sensible force is necessary.

By contrast, if two or more of these small parts touch one another only in passing and while they are in the act of moving, one in one direction and the other in another, certainly it will require less force to separate them than if they were in fact without motion. Indeed, no force at all will be required if the motion with which they are able to separate themselves is equal to or greater than that with which one wishes to separate them. Now, I find no difference between hard bodies and liquid bodies other than that the parts of the one can be separated from the whole much more easily than those of the other. Thus, to constitute the hardest body imaginable, I think it is enough if all the parts touch each other with no space remaining between any two and with none of them being in the act of moving. For what glue or cement can one imagine beyond that to hold them better one to the other?

I think also that to constitute the most liquid body one could find, it is enough if all its smallest parts are moving away from one another in the most diverse ways and as quickly as possible, even though in that state they do not cease to be able to touch one another on all sides and to arrange the~selves in as small a space as if they were without motion. Finally, I believe that every body more or less approaches these extremes, according as its parts are more or less in the act of moving away from one another. All the phenomena on which I cast my eye confirm me in this opinion.

Since, as I have already said, all the parts of flame are perpetually agitated, not only is it liquid, but it also renders most other bodies liquid. Note also that, when it melts metals, it acts with no different power than when it burns wood. Rather, because the parts of metals are just about all equal, the flame cannot move one part without moving the other, and hence it forms completely liquid bodies from them. By contrast, the parts of wood are unequal in such a way that the flame can separate the smaller of them and render them liquid (i.e. cause them to fly away in smoke) without agitating the larger parts.

After flame, there is nothing more liquid than air, and one can see with the eye that its parts move separately from one another. For, if you take the effort to watch those small bodies that are commonly called "atoms" and that appear in rays of sunlight, you will see them flutter about incessantly here and there in a myriad of different ways, even when there is no wind stirring them up. One can also experience the same sort of thing in all the grosser liquids if one mixes them together in different colors, in order better to distinguish their motions. Finally, the phenomenon appears very clearly in acids[13] when they move and separate the parts of some metal.

But you could ask me here at this point why, if it is only the motion of the parts of flame that cause it to burn and make it liquid, the motion of the parts of air, which also make it extremely liquid, do not at all give it the power to burn but, on the contrary, make it such that our hands can hardly feel it? To this I reply that one must take into account not only the speed of motion, but also the size of the parts. It is the smaller ones that make the more liquid bodies, but it is the larger ones that have more force to burn and in general to act on other bodies.

Note in passing that here, and always hereafter, I take a single part to be everything that is joined together and is not in the act of separation, even though the smallest parts could easily be divided into many other smaller ones. Thus, a grain of sand, a stone, a rock, indeed the whole earth itself, may hereafter be taken as a single part insofar as we are there considering only a completely simple and completely equal motion.[14]

Now if, among the parts of air, there are some that are very large in comparison with the others (as are the "atoms" that are seen there), they also move very slowly; and, if there are some that move more quickly, they are also smaller. If, however, among the parts of flame there are some smaller than in air, there are also larger ones, or at least there is a larger number of parts equal to the largest of those of air. In addition, these larger parts of flame move much more quickly, and hence it is they alone that have the power to burn.

As far as the smaller parts are concerned, one may guess that they penetrate many bodies of which the pores are so narrow that even air cannot enter. As far as the larger parts are concerned (or the equally large parts in greater number), one sees clearly how air alone does not suffice to nourish flame. The violence of their action is enough to show us that they move more quickly. Finally, that it is the largest of these parts that have the power to burn, and not the others, is apparent from the fact that the flame that issues from brandy, or from other very subtle bodies, hardly burns at all, while on the contrary that which is engendered in hard and heavy bodies is very hot.

CHAPTER FOUR On the Void, and How it Happens that Our Senses Are Not Aware of Certain Bodies

But we must examine in greater detail why air, although it is as much a body as the others, cannot be sensed as well as they. By doing so, we will free ourselves from an error with which we have been preoccupied since childhood, when we believed that there were no other bodies around us except those that could be sensed and thus that, if air were one of them, then, because we sensed it so faintly, it at least could not be as material nor as solid as those we sense more clearly.[15]

On this subject, I would first like you to note that all bodies, both hard and liquid, are made from the same matter, and that it is impossible to conceive of the parts of that matter ever composing a more solid body, or one occupying less space, than they do when each of them is touched on all sides by the others surrounding it. Whence it seems to me to follow that, if there can be a void anywhere, it ought to be in hard bodies rather than liquid ones; for it is evident that the parts of the latter can much more easily press and arrange themselves against one another (because they are moving) than can those of the former (which are without motion).

For example, if you are placing powder in a jar, you shake the jar and pound against it to make room for more powder. But, if you are pouring some liquid into it, the liquid spontaneously arranges itself in as small a place as one can put it. By the same token, if you consider in this regard some of the experiments the philosophers have been wont to use in showing that there is no void in nature,[16] you will easily recognize that all those spaces that people think to be empty, and where we feel only air, are at least as full, and as full of the same matter, as those where we sense other bodies.

For pray tell me what reason would there be to think that nature would cause the heaviest bodies to rise and the most solid to break--as one experiences her doing in certain machines, rather than to suffer that any of their parts should cease to touch one another or to touch some other bodies--and yet permit the parts of air--which are so easy to bend and to be arranged in all manners--to remain next to one another without being touched on all sides, or even without there being another body among them that they touch? Could one really believe that the water in a well should mount upward against its natural inclination merely in order that the pipe of a pump may be filled and [yet] think that the water in clouds should not fall in order that the spaces here below be filled, if there were even some little void among the parts of the bodies that they contain?[17]

But you could propose to me here a rather considerable problem, to wit, that the parts composing liquid bodies cannot, it seems, move incessantly, as I have said they do, unless there is some empty space among them, at least in the places from which they depart by virtue of their being in motion. I would have trouble responding to this, had I not recognized through various experiences that all the motions that take place in the world are in some way circular. That is to say, when a body leaves its place, it always enters into that of another, and the latter into that of still another, and so on down to the last which occupies in the same instant the place left open by the first.[18] Thus, there is no more of a void among them when they are moving than when they are stopped. And note here that it is not thereby necessary that all the parts of bodies that move together be exactly disposed in the round, as in a true circle, nor even that they be of equal size and shape; for these inequalities can easily be compensated for by other inequalities to be found in their speed.

Now, when bodies move in the air, we do not usually notice these circular motions, because we are accustomed to conceiving of the air only as an empty space. But look at fish swimming in the pool of a fountain: if they do not approach too near to the surface of the water, they cause great speed. Whence it clearly appears that the water they push before them does not push indifferently all the water of the pool, but only that which can best serve to perfect the circle of the fishes' motion and return to the place they leave behind.[19] This experience suffices to show how these circular motions are easy for nature and familiar to her.

Now, however, I want to adduce another experience to show that no motion ever takes place that is not circular. When the wine in a cask does not flow through an opening at the bottom because the top is completely closed, it is improper to say (as one ordinarily does) that this takes place owing to horror vacui. One well knows that the wine has no mind to fear anything; and, even if it had one, I do not know for what reason it might fear that void, which is in fact nothing but a chimera. Rather, one should say that the wine cannot leave the cask because outside everything is as full as it can be and that the part of the air, whose place the wine would occupy should it descend, cannot find another place to put itself anywhere in the rest of the universe unless one makes an opening in the top of the cask, through which this air can rise circularly to its place.

Nevertheless, I do not want to make certain that there is no void at all in nature. I fear my discourse would become too long if I undertook to unfold the whole story, and the experiences of which I have spoken are not sufficient to prove it, although they are enough to persuade us that the spaces where we sense nothing are filled with the same matter, and contain at least as much of that matter, as those occupied by the bodies that we sense. Thus, for example, when a vessel is full of gold or lead, it nonetheless contains no more matter than when we think it is empty. This may well seem strange to many whose [powers of] reasoning do not extend beyond their fingertips and who think there is nothing in the world except what they touch. But when you have considered for a bit what makes us sense a body or not sense it, I am sure you will find nothing incredible in the above. For you will know clearly that, far from all the things around us being sensible, it is on the contrary those that are there most of the time that can be sensed the least, and those that are always there that can never be sensed at all.

The heat of our heart is quite great, but we do not feel it because it is always there. The weight of our body is not small, but it does not discomfort us. We do not even feel the weight of our clothes because we are accustomed to wearing them. The reason for this is clear enough; for it is certain that we cannot sense any body unless it is the cause of some change in our sensory organs, i.e. unless it moves in some way the small parts of the matter of which those organs are composed. The objects that are not always present can well do this, provided only that they have force enough; for, if they corrupt something there while they act, that can be repaired afterward by nature, when they are no longer acting. But if those that continually touch us ever had the power to produce any change in our senses, and to move any parts of their matter, in order to move them they had perforce to separate them entirely from the others at the beginning of our life, and thus they can have left there only those that completely resist their action and by means of which they cannot be sensed in any way. Whence you see that it is no wonder that there are many spaces about us in which we sense no body, even though they contain bodies no less than those in which we sense them the most.

But one need not therefore think that the coarse air that we draw into our lungs while breathing, that is converted into wind when agitated, that appears solid when enclosed in a balloon, and that is composed only of exhalations and smoke is as solid as water or earth. Here one should follow the common opinion of the philosophers, who all assure us that it is rarer, as one also easily recognizes from experience. For the parts of a drop of water, separated from one another by the agitation of heat, can make up much more of this air than the space that held the water can contain. Whence it follows most certainly that there is a great quantity of small intervals among the parts of which the air is composed; for there is no other way to conceive of a rare body. But, because these intervals cannot be empty, as I have said above, I conclude from all this that of necessity there are mixed with the air some other bodies, either one or several, which fill as exactly as possible the small intervals left among its parts. Now there remains to consider only what these other bodies can be; thereafter I hope it will not be difficult to understand what the nature of light can be.

CHAPTER FIVE On the Number of Elements and on Their Qualities

The philosophers assure us that there is above the clouds a certain air much subtler than ours. That air is not composed of vapors of the earth as it is, but constitutes an element in itself. They say also that above this air there is still another, much subtler body, which they call the element of fire. They add, moreover, that these two elements are mixed with water and earth in the composition of all the inferior bodies. Thus~ I am only following their opinion if I say that this subtler air and this element of fire fill the intervals among the parts of the grosser air we breathe, so that these bodies, interlaced with one another, compose a mass as solid as any body can be.

But, in order better to make you understand my thought on this subject, and so that you will not think I want to force you to believe all the philosophers tell us about the elements, I should describe them to you in my fashion.

I conceive of the first, which one may call the element of fire, as the most subtle and penetrating fluid there is in the world. And in consequence of what has been said above concerning the nature of liquid bodies, I imagine its parts to be much smaller and to move much faster than any of those of other bodies. Or rather, in order not to be forced to admit any void in nature, I do not attribute to this first element parts having any determinate size or shape; but I am persuaded that the impetuosity of their motion is sufficient to cause it to be divided, in every way and in every sense, by collision with other bodies and that its parts change shape at every moment to accommodate themselves to the shape of the places they enter. Thus, there is never a passage so narrow, nor an angle so small, among the parts of other bodies, where the parts of this element do not penetrate without any difficulty and which they do not fill exactly.[20]

As for the second, which one may take to be the element of air, I conceive of it also as a very subtle fluid in comparison with the third; but in comparison with the first there is need to attribute some size and shape to each of its parts and to imagine them as just about all round and joined together like grains of sand or dust. Thus, they cannot arrange themselves so well, nor so press against one another that there do not always remain around them many small intervals into which it is much easier for the first element to slide than for the parts of the second to change shape expressly in order to fill them. And so I am persuaded that this second element cannot be so pure anywhere in the world that there is not always some little matter of the first with it.

Beyond these two elements, I accept only a third, to wit, that of earth. Its parts I judge to be as much larger and to move as much less swiftly in comparison with those of the second as those of the second in comparison with those of the first. Indeed, I believe it is enough to conceive of it as one or more large masses, of which the parts have very little or no motion that might cause them to change position with respect to one another.

If you find it strange that, in setting out these elements, I do not use the qualities called "heat," "cold," "moistness," and "dryness," as do the philosophers, I shall say to you that these qualities appear to me to be themselves in need of explanation.[21] Indeed, unless I am mistaken, not only these four qualities, but also all the others (indeed all the forms of inanimate bodies) can be explained without the need of supposing for that purpose any other thing in their matter than the motion, size, shape, and arrangement of its parts. In consequence whereof I shall easily be able to make you understand why I do not accept any other elements than the three I have described. For the difference that should exist between them and the other bodies that the philosophers call "mixed" or "composite" consists in the forms of these mixed bodies always containing in themselves some qualities that are contrary and that counteract one another, or at least do not tend to the conservation of one another, whereas the forms of the elements should be simple and not have any qualities that do not accord with one another so perfectly that each tends to the conservation of all the others.

Now I could not find any such forms in the world except the three I have described. For the form I have attributed to the first element consists in its parts moving so extremely fast and being so small that there are no other bodies capable of stopping them. Beyond that, they require no determinate size or shape or position. The form of the second consists in its parts having such a middling motion and size that, if there are in the world many causes that could increase their motion and decrease their size, there are just as many others that can do exactly the opposite. Thus, they always remain balanced as it were in that same middling condition. And the form of the third consists in its parts being so large or so joined together that they have the force always to resist the motions of the other bodies.

Examine as much as you please all the forms that the diverse motions, the diverse shapes and sizes, and the different arrangement of the parts of matter can lend to mixed bodies. I am sure you will find none that does not contain in itself qualities that tend to cause it to change and, in changing, to reduce to one of the forms of the elements.

Flame, for example, the form of which demands its having parts that move very fast and that in addition have some size (as has been said above), cannot last long without being corrupted. For either the size of its parts, in giving them the force to act against other bodies, will be the cause of the diminution of their motion, or the violence of their agitation, in causing them to break upon hurtling themselves against the bodies they encounter, will be the cause of their loss of size. Thus, little by little they will be able to reduce themselves to the form of the third element, or to that of the second, and even also some of them to that of the first.[22] Thereby you can see the difference between this flame, or the fire common among us, and the element of fire I have described. You should know also that the elements of air and of earth (i.e. the second and third elements) are none the more similar to that grosser air we breathe nor to this earth on which we walk, but that generally all the bodies that appear about us are mixed or composite and subject to corruption.

And nevertheless one need not think therefore that the elements have in the world no places that are particularly destined for them and where they can be perpetually conserved in their natural purity.[23] On the contrary, each part of matter always tends to be reduced to one of their forms and, once having been reduced, never tends to leave that form. Hence, even if God at the beginning had created only mixed bodies, nevertheless since the world began all these bodies could have had the chance to leave their forms and to take on those of the elements. Thus, there is now much reason to think that all the bodies that are large enough to be counted among the most notable parts of the universe each have the form of only one of these elements alone, and that there cannot be mixed bodies anywhere but on the surfaces of these large bodies. But there, of necessity, there must be some mixed bodies; for, the elements being of a very contrary nature, it cannot happen that two of them touch one another without acting against each other's surfaces and thus lending the matter there the diverse forms of these mixed bodies.

Apropos of this, if we consider in general all the bodies of which the universe is composed, we will find among them only three sorts that can be called large and be counted among the principal parts, to wit, the sun and the fixed stars as the first sort, the heavens as the second, and the earth with the planets and the comets as the third. That is why we have good reason to think that the sun and the fixed stars have no other form than that of the wholly pure first element, the heavens that of the second, and the earth with the planets and comets that of the third.

I link the planets and the comets with the earth because, seeing that they, like she, resist light and reflect its rays, I find no difference between them. I also link the sun with the fixed stars and attribute to them a nature totally contrary to that of the earth because the action alone of their light is enough to make me know that their bodies are of a very subtle and very agitated matter.

As for the heavens, in as much as they cannot be perceived by our senses, I think I am right in attributing to them a middle nature between that of the luminous bodies whose action we perceive and that of the solid and heavy bodies whose resistance we perceive.

Finally, we do not perceive mixed bodies in any other place than on the surface of the earth.[24] And, if we consider that the whole space that contains them (i.e. all that which stretches from the highest clouds to the deepest mines that the greed of man has ever dug out to draw metals from them) is extremely small in comparison with the earth and with the immense expanses of the heavens, we will easily be able to imagine to ourselves that these mixed bodies taken all together are but as a crust engendered on top of the earth by the agitation and mixing of the matter of the heavens surrounding it.

And thus we will have reason to think that it is not only in the air we breathe, but also in all the other composite bodies right down to the hardest rocks and the heaviest metals, that there are parts of the element of air mixed with those of earth and, consequently, also parts of the element of fire, because they are always found in the pores of the element of air.

But one should note that, even though there are parts of these three elements mixed with one another in all bodies, nonetheless, properly speaking, only those which (because of their size or the difficulty they have in moving) can be referred to the third element compose all the bodies we see about us. For the parts of the two other elements are so subtle that they cannot be perceived by our senses. One may picture all these bodies as sponges; even though a sponge has a quantity of pores, or small holes, which are always full of air or water or some other liquid, one nonetheless does not think that these liquids enter into its composition.

Many other things remain for me to explain here, and I would myself be happy to add here several arguments to make my opinions more plausible. In order, however, to make the length of this discourse less boring for you, I want to wrap part of it in the cloak of a fable, in the course of which I hope that the truth will not fail to appear sufficiently and that it will be no less agreeable to see than if I were to set it forth wholly naked.

CHAPTER SIX Description of a New World, and on the Qualities of the Matter of Which it is Composed

For a short time, then, allow your thought to wander beyond this world to view another, wholly new one, which I shall cause to unfold before it in imaginary spaces. The philosophers tell us that these spaces are infinite, and they should very well be believed, since it is they themselves who have made the spaces so.[25] Yet, in order that this infinity not impede us and not embarrass us, let us not try to go all the way to the end; let us enter in only so far that we can lose from view all the creatures that God made five or six thousand years ago and, after having stopped there in some fixed place, let us suppose that God creates from anew so much matter all about us that, in whatever direction our imagination can extend itself, it no longer perceives any place that is empty.

Although the sea is not infinite, those who are on some vessel in the middle of it can extend their view seemingly to infinity, and nevertheless there is still water beyond what they see.[26] Thus, even though our imagination seems to be able to extend itself to infinity, and this new matter is not assumed to be infinite, we can nonetheless well suppose that it fills spaces much greater than all those we shall have imagined. Indeed, in order that there be nothing in all this that you could find to blame, let us not permit our imagination to extend itself as far as it could, but let us purposely restrict it to a determinate space that is no greater, say, than the distance between the earth and the principal stars of the firmament, and let us suppose that the matter that God shall have created extends quite far beyond in all directions, out to an indefinite distance. For there is more reason, and we have much better the power, to prescribe limits to the action of our thought than to the works of God.

Now, since we are taking the liberty of imagining this matter to our fancy, let us attribute to it, if you will, a nature in which there is absolutely nothing that anyone cannot know as perfectly as possible. To that end, let us expressly assume that it does not have the form of earth, nor of fire, nor of air, nor any more particular form (such as wood, or a stone, or of a metal); nor does it have the qualities of being hot or cold, dry or moist, light or heavy, or of having some taste, or smell, or sound or color, or light, or suchlike, in the nature of which one could say that there is something that is not clearly known by everyone.[27]

Let us not also think, on the other hand, that our matter is that prime matter of the philosophers that has been so well stripped of all its forms and qualities that nothing more remains that can be clearly understood.[28] Let us rather conceive of it as a real, perfectly solid body, which uniformly fills the entire length, breadth, and depth of the great space at the center of which we have halted our thought. Thus, each of its parts always occupies a part of that space and is so proportioned to its size that it could not fill a larger one nor squeeze itself into a smaller one, nor (while it remains there) suffer another to find a place there.

Let us add further that this matter can be divided into any parts and according to any shapes that we can imagine, and that each of its parts is capable of receiving in itself any motions that we can also conceive. Let us suppose in addition that God truly divides it into many such parts, some larger and some smaller, some of one shape and some of another, as it pleases us to imagine them. It is not that He thereby separates them from one another, so that there is some void in between them; rather, let us think that the entire distinction that He makes there consists in the diversity of the motions He gives to them. From the first instant that they are created, He makes some begin to move in one direction and others in another, some faster and others slower (or indeed, if you wish, not at all); thereafter, He makes them continue their motion according to the ordinary laws of nature. For God has so wondrously established these laws that, even if we suppose that He creates nothing more than what I have said, and even if He does not impose any order or proportion on it but makes of it the most confused and most disordered chaos that the poets could describe, the laws are sufficient to make the parts of that chaos untangle themselves and arrange themselves in such right order[29] that they will have the form of a most perfect world, in which one will be able to see not only light, but also all the other things, both general and particular, that appear in this true world.

But, before I explain this at greater length, stop again for a bit to consider that chaos, and note that it contains nothing that is not so perfectly known to you that you could not even pretend not to know it. For, as regards the qualities that I have posited there, I have, if you have noticed, supposed them to be only such as you can imagine them. And, as regards the matter from which I have composed the chaos, there is nothing simpler nor easier to know among inanimate creatures. The idea of that matter is so included in all those that our imagination can form that you must necessarily conceive of it or you can never imagine anything.

Nonetheless, because the philosophers are so subtle that they can find difficulties in things that appear extremely clear to other men, and because the memory of their prime matter (which they know to be rather difficult to conceive of) could divert them from knowledge of the matter of which I speak, I should say to them at this point that, unless I am mistaken, the whole problem they face with their matter derives only from their wanting to distinguish it from its own proper quantity and from its outward extension, i.e. from the property it has of occupying space. In this, however, I am willing that they think themselves correct, for I have no intention of stopping to contradict them. But they should also not find it strange if I suppose that the quantity of the matter I have described does not differ from its substance any more than number differs from the things numbered. Nor should they find it strange if I conceive of its extension, or the property it has of occupying space, not as an accident, but as its true form and its essence. For they cannot deny that it is quite easy to conceive of it in that way. And my plan is not to set out (as they do) the things that are in fact in the true world, but only to make up as I please from [this matter] a [world] in which there is nothing that the densest minds are not capable of conceiving, and which nevertheless could be created exactly the way I have made it up.

Were I to posit in this new world the least thing that is obscure, it could happen that, within that obscurity, there might be some hidden contradiction I had not perceived, and thus that, without thinking, I might suppose something impossible. Instead, being able to imagine distinctly everything I am positing there, it is certain that, even if there be no such thing in the old world, God can nevertheless create it in a new one; for it is certain that He can create everything we can imagine.[30]

CHAPTER SEVEN On the Laws of Nature of this New World

But I do not want to defer any longer from telling you by what means nature alone could untangle the confusion of the chaos of which I have been speaking, and what the laws of nature are that God has imposed on her.

Know, then, first that by "nature" I do not here mean some deity or other sort of imaginary power. Rather, I use that word to signify matter itself, insofar as I consider it taken together with all the qualities that I have attributed to it, and under the condition that God continues to preserve it in the same way that He created it. For from that alone (i.e. that He continues thus to preserve it) it follows of necessity that there may be many changes in its parts that cannot, it seems to me, be properly attributed to the action of God (because that action does not change) and hence are to be attributed to nature. The rules according to which these changes take place I call the "laws of nature."

To understand this better, recall that, among the qualities of matter, we have supposed that its parts have had diverse motions since the beginning when they were created, and furthermore that they all touch one another on all sides, without there being any void in between. Whence it follows of necessity that from then on, in beginning to move, they also began to change and diversify their motions by colliding with one another. Thus, if God preserves them thereafter in the same way that He created them, He does not preserve them in the same state. That is to say, with God always acting in the same way and consequently always producing the same effect in substance, there occur, as by accident, many diversities in that effect. And it is easy to believe that God, who, as everyone must know, is immutable, always acts in the same way. Without, however, involving myself any further in these metaphysical considerations, I will set out here two or three of the principal rules according to which one must think God to cause the nature of this new world to act and which will suffice, I believe, for you to know all the others.[31]

The first is that each individual part of matter always continues to remain in the same state unless collision with others constrains it to change that state. That is to say, if the part has some size, it will never become smaller unless others divide it; if it is round or square, it will never change that shape without others forcing it to do so; if it is stopped in some place, it will never depart from that place unless others chase it away; and if it has once begun to move, it will always continue with an equal force until others stop or retard it.

There is no one who does not believe that this same rule is observed in the old world with respect to size, shape, rest, and a thousand other like things. But from it the philosophers have exempted motion, which is, however, the thing I most expressly desire to include in it. Do not think thereby that I intend to contradict them. The motion of which they speak is so very different from that which I conceive that it can easily happen that what is true of the one is not true of the other.

They themselves avow that the nature of their motion is very little known.[32] To render it in some way intelligible, they have still not been able to explain it more clearly than in these terms: motus est actus entis in potentia, prout in potentia est,[33] which terms are for me so obscure that I am constrained to leave them here in their language, because I cannot interpret them. (And, in fact, the words, "motion is the act of a being in potency, insofar as it is in potency," are no clearer for being in [English].) On the contrary, the nature of the motion of which I mean to speak here is so easy to know that mathematicians themselves, who among all men studied most to conceive very distinctly the things they were considering, judged it simpler and more intelligible than their surfaces and their lines. So it appears from the fact that they explained the line by the motion of a point, and the surface by that of a line.

The philosophers also suppose several motions that they think can be accomplished without any body's changing place, such as those they call motus ad formam, motus ad calorem, motus ad quantitatem ("motion to form," "motion to heat," "motion to quantity"), and myriad others. As for me, I conceive of none except that which is easier to conceive of than the lines of mathematicians: the motion by which bodies pass from one place to another and successively occupy all the spaces in between.

Beyond that, the philosophers attribute to the least of these motions a being much more solid and real than they do to rest, which they say is nothing but the privation of motion. As for me, I conceive of rest as being a quality also, which should be attributed to matter while it remains in one place, just as motion is a quality attributed to it while it is changing place.[34]

Finally, the motion of which they speak is of such a strange nature that, whereas all other things have as a goal their perfection and strive only to preserve themselves, it has no other end and no other goal than rest. Contrary to all the laws of nature, it strives on its own to destroy itself. By contrast, the motion I suppose follows the same laws of nature as do generally all the dispositions and all the qualities found in matter, as well those which the scholars call modos et entia rationis cum fundamento in re (modes and beings of thought with foundation in the thing) as qualitates reales (their real qualities), in which I frankly confess I can find no more reality than in the others.

I suppose as a second rule that, when one of these bodies pushes another, it cannot give the other any motion except by losing as much of its own at the same time; nor can it take away from the other body's motion unless its own is increased by as much. This rule, joined to the preceding, agrees quite well with all experiences in which we see one body begin or cease to move because it is pushed or stopped by some other. For, having supposed the preceding rule, we are free from the difficulty in which the scholars find themselves when they want to explain why a stone continues to move for some time after being out of the hand of him who threw it. For one should ask instead, why does it not continue to move always? Yet the reason is easy to give. For who is there who can deny that the air in which it is moving offers it some resistance? One hears it whistle when it divides the air; and, if one moves in the air a fan or some other very light and very extended body, one will even be able to feel by the weight of one's hand that the air is impeding its motion, far from continuing it, as some have wanted to say. If, however, one fails to explain the effect of the air's resistance according to our second rule, and if one thinks that the more a body can resist the more it is capable of stopping the motion of others (as one can perhaps be persuaded at first), one will in turn have a great deal of trouble explaining why the motion of this stone is weakened more in colliding with a soft body of middling resistance than it is when it collides with a harder one that resists it more. Or also why, as soon as it has made a little effort against the latter, it spontaneously turns on its heels rather than stopping or interrupting the motion it has. Whereas, supposing this rule, there is no difficulty at all in this. For it teaches us that the motion of a body is not retarded by collision with another in proportion to how much the latter resists it, but only in proportion to how much the latter's resistance is surmounted, and to the extent that, in obeying the law, it receives into itself the force of motion that the former surrenders.[35]

Now, even though in most of the motions we see in the true world we cannot perceive that the bodies that begin or cease to move are pushed or stopped by some others, we do not thereby have reason to judge that these two rules are not being observed exactly. For it is certain that those bodies can often receive their agitation from the two elements of air and fire, which are always found among them without being perceptible (as has just been said), or even from the grosser air, which also cannot be perceived. And they can transfer the agitation, sometimes to that grosser air and sometimes to the whole mass of the earth; dispersed therein, it also cannot be perceived.

But, even if all that our senses have ever experienced in the true world seemed manifestly contrary to what is contained in these two rules, the reasoning that has taught them to me seems to me so strong that I would not cease to believe myself obliged to suppose them in the new world I am describing to you. For what more firm and solid foundation could one find to establish a truth (even if one wanted to choose it at will) than to take the very firmity and immutability that is in God?[36]

Now it is the case that those two rules manifestly follow from this alone: that God is immutable and that, acting always in the same way, He always produces the same effect. For, supposing that He placed a certain quantity of motions in all matter in general at the first instant He created it, one must either avow that He always conserves as many of them there or not believe that He always acts in the same way. Supposing in addition that, from that first instant, the diverse parts of matter, in which these motions are found unequally dispersed began to retain them or to transfer them from one to another according as they had the force to do, one must of necessity think that He causes them always to continue the same thing. And that is what those two rules contain.

I will add as a third rule that, when a body is moving, even if its motion most often takes place along a curved line and (as has been said above) can never take place along any line that is not in some way circular, nevertheless each of its individual parts tends always to continue its motion along a straight line. And thus their action, i.e. the inclination they have to move, is different from their motion.

For example, if a wheel is made to turn on its axle, even though its parts go around (because, being linked to one another, they cannot do otherwise), nevertheless their inclination is to go straight ahead, as appears clearly if perchance one of them is detached from the others. For, as soon as it is free, its motion ceases to be circular and continues in a straight line.

By the same token, when one whirls a stone in a sling, not only does it go straight out as soon as it leaves the sling, but in addition, throughout the time it is in the sling, it presses against the middle of the sling and causes the cord to stretch. It clearly shows thereby that it always has an inclination to go in a straight line and that it goes around only under constraint.

This rule rests on the same foundation as the two others and depends only on God's conserving everything by a continuous action and, consequently, on His conserving it not as it may have been some time earlier but precisely as it is at the same instant that He conserves it. Now it is the case that, of all motions, only the straight is entirely simple; its whole nature is understood in an instant. For, to conceive of it, it suffices to think that a body is in the act of moving in a certain direction, and that is the case in each instant that might be determined during the time that it is moving. By contrast, to conceive of circular motion, or of any other possible motion, one must consider at least two of its instants, or rather two of its parts, and the relation between them.[37]

But, so that the philosophers (or rather the sophists) do not find occasion here to exercise their superfluous subtleties, note that I do not thereby say that rectilinear motion can take place in an instant; but only that all that is required to produce it is found in bodies in each instant that might be determined while they are moving, and not all that is required to produce circular motion.

For example, suppose a stone is moving in a sling along the circle marked AB and you consider it precisely as it is at the instant it arrives at point A: you will readily find that it is in the act of moving[38] (for it does not stop there) and of moving in a certain direction (that is, toward C), for it is in that direction that its action is directed in that instant. But you can find nothing there that makes its motion circular. Thus, supposing that the stone then begins to leave tile sling and that God continues to preserve it as it is at that moment, it is certain that He will not preserve it with the inclination to go circularly along the line AB, but with the inclination to go straight ahead toward point C.

According to this rule, then, one must say that God alone is the author of all the motions in the world, insofar as they exist and insofar as they are straight, but that it is the diverse dispositions of matter that render the motions irregular and curved. So the theologians teach us that God is also the author of all our actions, insofar as they exist and insofar as they have some goodness, but that it is the diverse dispositions of our wills that can render those actions evil.

I could set out here many additional rules for determining in detail when and how and by how much the motion of each body can be diverted and increased or decreased by colliding with others, something that comprises summarily all the effects of nature.[39] But I shall be content with showing you that, besides the three laws that I have explained, I wish to suppose no others but those that most certainly follow from the eternal truths on which the mathematicians are wont to support their most certain and most evident demonstrations; the truths, I say, according to which God Himself has taught us He disposed all things in number, weight, and measure.[40] The knowledge of those laws is so natural to our souls that we cannot but judge them infallible when we conceive them distinctly, nor doubt that, if God had created many worlds, the laws would be as true in all of them as in this one. Thus, those who can examine sufficiently the consequences of these truths and of our rules will be able to know effects by their causes and (to explain myself in the language of the School) will be able to have demonstrations a priori of everything that can be produced in that new world.

And so there will be no exception that impedes this, we will add, if you wish, to our suppositions that God will never mark any miracle in the new world and that the intelligences, or the rational souls, which we might hereafter suppose to be there, will in no way disturb the ordinary course of nature.

Nonetheless, in consequence of this, I do not promise you to set out here exact demonstrations of all the things I will say. It will be enough for me to open to you the path by which you will be able to find them yourselves, whenever you take the trouble to look for them. Most minds lose interest when one makes things too easy for them. And to compose here a setting that pleases you, I must employ shadow as well as bright colors. Thus I will be content to pursue the description I have begun, as if having no other design than to tell you a fable.

CHAPTER EIGHT On the Formation of the Sun and the Stars of the New World

Whatever inequality and confusion we might suppose God put among the parts of matter at the beginning, the parts must, according to the laws He imposed on nature, thereafter almost all have been reduced to one size and to one middling motion and thus have taken the form of the second element as I described it above. For to consider this matter in the state in which it could have been before God began to move it, one should imagine it as the hardest and most solid body in the world. And, since one could not push any part of such a body without pushing or pulling all the other parts by the same means, so one must imagine that the action or the force of moving or dividing, which had first been placed in some of the parts of matter, spread out and distributed itself in all the others in the same instant, as equally as it could.

It is true that this equality could not be totally perfect. First, because there is no void at all in the new world, it was impossible for all the parts of matter to move in a straight line. Rather, all of them being just about equal and as easily divertible, they all had to unite in some circular motions. And yet, because we suppose that God first moved them diversely, we should not imagine that they all came together to turn about a single center, but about many different ones, which we may imagine to be diversely situated with respect to one another.

Consequently, one can conclude that they had to be naturally less agitated or smaller, or both, toward the places nearest to these centers than toward those farthest away. For, all of them having an inclination to continue their motion in a straight line, it is certain that the strongest (i.e. the largest among those equally agitated and the most agitated among those equally large) had to describe the greatest circles, i.e. the circles most approaching a straight line. As for the matter contained in between three or more of these circles, it could have been at first much less divided and less agitated than all the other. What is more, in as much as we suppose that at the beginning God placed every sort of inequality among the parts of this matter, we must imagine that there were then all sorts of sizes and shapes, and dispositions to move or not to move, in all ways and in all directions.

But that does not prevent them from having afterwards been rendered almost all fairly equal, principally those that remained an equal distance from the centers about which they were turning. For, since some could not move without the others' moving, the more agitated had to communicate some of their motion to those that were less so, and the larger had to break and divide in order to be able to pass through the same places as those that preceded them, or in order to rise higher. Thus, in a short time all the parts were arranged in order, so that each was more or less distant from the center about which it had taken its course, according as it was more or less large and agitated in comparison with the others. Indeed, in as much as size always resists speed of motion, one must imagine that the parts more distant from each center were those which, being a bit smaller than the ones nearer the center, were thereby much more agitated.[41]

Exactly the same holds for their shapes. Even if we were to suppose that there were at the beginning all sorts of shapes and that they had for the most part many angles and many sides, like the pieces that fly off from a stone when it is broken, it is certain that afterward, in moving and hurtling themselves against one another, they little by little had to break the small points of their angles and dull the square edges of their sides, until they had almost all been rendered round, just as grains of sand and pebbles do when they roll with the water of a river. Thus there cannot now be any notable difference among those parts that are rather close, nor indeed even among those that are quite distant, except that they can move a bit more quickly one than another and be a bit larger or a bit smaller, and that does not prevent one's attributing the same form to all of them.

Only one must except some which, having been from the beginning much larger than the others, could not be so easily divided or which, having had very irregular and impeding shapes, joined together severally rather than breaking up and rounding off. Thus, they have retained the form of the third element and have served to compose the planets and the comets, as I shall tell you below.

It is necessary to note in addition that the matter that came out from around the parts of the second element, to the extent that they broke and dulled the small points of their angles in rounding off, necessarily had to acquire a much faster motion than theirs and along with it a facility for dividing and changing shape at every moment to accommodate itself to the shape of the places where it is. Thus, it took the form of the first element.

I say that it had to acquire a much faster motion than theirs, and the reason is clear. For, having to go off to the side through very narrow passages and out of the small spaces left between the parts of the second element as they proceeded to collide head-on with one another, it had much more of a path than they to traverse in the same time.

It is also necessary to note that what there is of that first element beyond what is needed to fill the small intervals that the parts of the second (which are round) necessarily leave around them must draw back toward the centers about which those parts turn, because [the parts of the second] occupy all the other, more distant places. At those centers, the remaining first element must compose perfectly liquid and subtle round bodies which, incessantly turning much faster than, and in the same direction as, the parts of the second element surrounding them, have the force to increase the agitation of those parts to which they are closest and even (in moving from the center toward the circumference) to push the parts in all directions, just as they push one another. This takes place by an action that I must soon explain as exactly as I can. For I tell you here in advance that it is this action that we shall take to be light, as also we shall take one of those round bodies composed purely of the matter of the first element to be the sun, and the others to be the fixed stars, of the new world I am describing to you; and we shall take the matter of the second element turning about them to be the heavens.

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 certain 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.

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 part 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.

CHAPTER THIRTEEN On Light

I have already said several times that bodies that revolve always tend to move away from the centers of the circles they describe. Here, however, I must determine more specifically in what directions the parts of the matter of which the heavens and the stars are composed do tend.[54]

To that end, one must know that, when I say that a body tends in some direction, I do not thereby want anyone to imagine that there is in the body a thought or a desire carrying it there, but only that it is disposed to move there, whether it truly moves or, rather, some other body prevents it from doing so. It is principally in this last sense that I use the word "tend," because it seems to signify some effort and because every effort presupposes some resistance. Now, in as much as there are often diverse causes that, acting together on the same body, impede one another's effect, one can, according to various points of view, say that the same body tends in different directions at the same time. Thus it has just been said that the parts of the earth tend to move away from its center insofar as they are considered all alone, and that they tend on the contrary to move closer to it insofar as one considers the force of the parts of the heaven pushing them there, and again that they tend to move away from it if one considers them as opposed to other terrestrial parts that compose bodies more massive than they.

Thus, for example, the stone turning in a sling along circle AB tends toward C when it is at point A, if one considers nothing other than its agitation all alone; and it tends circularly from A to B, if one considers its motion as regulated and determined by the length of the cord retaining it; and finally the same stone tends toward E if, without considering the part of its agitation of which the effect is not impeded, one opposes the other part of it to the resistance that this sling continually makes to it.

But, to understand this last point distinctly, imagine the inclination this stone has to move from A toward C as if it were composed of two other inclinations, of which one were to turn along the circle AB and the other to rise straight up along the line VXY; and imagine the inclinations were in such a proportion that, if the stone were at the place of the sling marked V when the sling was at the place of the circle marked A, it should thereafter be at the place marked X when the sling is at B, and at the place marked Y when the sling is at F, and thus should always remain in the straight line ACG. Then, knowing that one of the parts of its inclination (to wit, that which carries it along the circle AB) is in no way impeded by the sling, you will easily see that the stone meets resistance only for the other part (to wit, for that which would cause it to move along the line DVXY if it were not impeded). Consequently, it tends (that is, it makes an effort) only to move directly away from the center D. And note that, from this point of view, when the stone is at point A, it tends so truly toward E that it is not at all more disposed to move toward H than toward I, although one could easily persuade oneself of the contrary if one failed to consider the difference between the motion it already has and the inclination to move that remains with it.

Now, you should think of each of the parts of the second element that compose the heavens in the same way that you think of this stone, to wit, that those which are, say, at E tend of their own inclination only toward P, but that the resistance of the other parts of the heaven which are above them cause them to tend (i.e. dispose them to move) along the circle ER. In turn, this resistance, opposed to the inclination they have to continue their motion in a straight line, causes them to tend (i.e. is the reason why they make an effort to move) toward M. And thus, judging all the others in the same way, you see in what sense one can say that they tend toward the places that are directly opposite the center of the heaven they compose.

But there is still more to consider in the parts of the heaven than in a stone turning in a sling: the parts are continually pushed, both by all those like them between them and the star that occupies the center of their heaven and by the matter of that star; and they are not pushed at all by the others. For example, those at E are not pushed by those at M, or at T, or at R, or at K or at H, but only by all those that are between the two lines AF and DG together with the matter of the sun. That is why they tend, not only toward M, but also toward L and toward N, and generally toward all the points which the rays or straight lines, coming from some part of the sun and passing through the place where the parts are, can reach.[55]

But, in order that the explanation of all this be easier, I want you to consider the parts of the second element all alone, as if all the spaces occupied by the matter of the first element, both [the space] where the sun is and the other [spaces], were void. Indeed, because there is no better means of knowing if a body is being pushed by some others than to see if these others actually advance toward the place where it is in order to fill the place in the case that it is void,[56] I also want you to imagine that the parts of the second element at E are removed from it and, having posited that, to note in the first place that none of those above the circle TER, say at M, is disposed to fill their place, in as much as each tends on the contrary to move away from it. Then note in the second place also that those in that circle, to wit, at T are no more disposed to do so; for, even though they really move from T toward G along the course of the whole heaven, nevertheless, because those at F also move with the same speed toward R, the space E (which one must imagine to be mobile like them) will not fail to remain void between G and F, provided others do not come from elsewhere to fill it. In the third place, those that are below that circle but that are not contained between the lines AF and DG (such as those at H and at K) also do not tend in any way to advance toward that space E to fill it, even though the inclination they have to move away from point S disposes them in some way to do so (as the weight of a stone disposes it, not only to descend along a straight line in the free air, but also to roll sideways on the slope of a mountain in the case that it cannot descend any other way).

Now the reason that impedes them from tending toward that space is that all motions continue, so far as is possible, in a straight line, and consequently, when nature has many ways of arriving at the same effect, she most certainly always follows the shortest.[57] For, if the parts of the second element which are, say, at K advanced toward E, all those closer to the sun than they would also advance at the same instant toward the place they were leaving; hence, the effect of their motion would be only that space E would be filled and there would be another of equal size in the circumference ABCD that would become void at the same time. But it is manifest that same effect can follow much better if those parts that are between the lines AF and DG advance straightaway toward E; and consequently, when there is nothing to impede the latter from doing so, the others do not tend at all toward E, no more than a stone ever tends to fall obliquely toward the center of the earth when it can fall in a straight line.

Finally, consider that all the parts of the second element that are between the lines AF and DG must advance together toward that space E in order to fill it at the same instant it is void. For, even though it is only the inclination they have to move away from point S that carries them toward E, and this inclination causes those between the lines BF and CG to tend more directly toward E than those that remain between the lines AF and BF and DG and CG, you will nevertheless see that these latter parts do not fail to be as disposed as the others to go there, if you take note of the effect that should follow from their motion. That effect is none other than, as I have just now said, that space E is filled and that there is another of equal size in the circumference ABCD that becomes void at the same time. For, as regards the change of position they undergo in the other places that they were previously filling and that still remain full of them afterwards, it is not at all considerable, in as much as they must be supposed to be so equal and so completely like one another that it does not matter by which parts each of these places is filled. Note, nevertheless, that one should not conclude from this that they are all equal, but merely that the motions of which their inequality can be the cause are not pertinent to the action of which we are speaking.

Now there is no shorter way of causing one part E of space to be filled while another, for example at D, becomes void than if all the parts of matter on the straight line DG, or DE, advance together toward E. For, if it were only those between the lines BF and CF that were to advance first toward that space E, they would leave another space below them at V, into which those which are at D had to come. Thus, the same effect that can be produced by the motion of the matter in the straight line DG, or DE, would be made by the motion of that in the curved line DVE:, and that is contrary to the laws of motion.

But you may find here some difficulty in understanding how the parts of the second element between the lines AF and DG can advance all together toward E, considering that, since the distance between A and D is greater than that between F and G, the space they must enter to advance thus is narrower than that they must leave. If so, consider that the action by which they tend to move away from the center of their heaven does not force them to touch those of their neighbors that are at the same distance as they from that center, But only to touch those that are to a degree more distant from it.[58] Thus the weight of the small balls 1, 2, 3, 4, 5 does not force those marked by the same numerals to touch one another, but only forces those marked 1 or 10 to rest on those marked 2 or 20, and the latter to rest on those marked 3 or 30, and so on. Thus, these small balls can well be arranged not only as you see them in Figure 7 but also as they are in Figures 8 and 9 and in myriad other diverse ways.
Then consider that those parts of the second element, moving separately from one another (as has been said above that they must do), cannot ever be arranged like the balls in Figure 7. Nonetheless, it is only in that mode [of arrangement] that the proposed difficulty can obtain. For one could not suppose between those of its parts that are the same distance from the center of their heaven an interval so small that it would not suffice to conceive that the inclination they have to move away from that center must cause those between the lines AF and DG to advance all together toward the space E when it is void. Thus you see in Figure 9, compared with Figure 10, that the weight of the small balls 40, 30, etc. must cause them to fall all together toward the space occupied by that marked 50 as soon as the latter can leave it.
And one can clearly perceive here how those of the balls that are marked with the same numeral are arranged in a space narrower than that which they leave, that is, by moving closer to one another. One can also perceive that the two balls marked 40 must fall a bit faster, and move proportionately a bit closer to one another, than the three marked 30, and these three must move faster and closer to one another than the four marked 20, and so on.

Hereupon you will perhaps say to me that, as it appears in Figure 10 that the two balls 40, 40, after having fallen the slightest bit, come to touch one another (which is why they stop without being able to fall lower). In the very same way, the parts of the second element that should advance toward E will stop before having succeeded in filling the whole space we have supposed there.

But I respond thereto that they cannot advance toward E the slightest bit without it being enough to prove perfectly what I have said, to wit, that since the whole space that is there is already filled by some body (whatever it might be), the parts press continually on that body and make an effort against it as if to chase it out of its place.[59]

Then, beyond that, I reply that, since their other motions, which continue in them while they are thus advancing toward E, do not permit them for a moment to remain arranged in the same way, those motions impede them from touching one another, or rather cause them, upon touching, immediately to separate again and thus not to cease for that reason to advance uninterruptedly toward the space E, until it is completely filled. Thus one cannot conclude from this anything other than that the force with which they tend toward E is perhaps vibratory in nature and redoubles and relaxes in diverse small tremors according as the parts change position. This seems to be a property quite suited to light.

Now, if you have understood all this sufficiently by supposing the spaces E and S and all the small angles between the parts of the heaven to be empty, you will understand it still better by supposing them filled with the matter of the first element. For the parts of that first element in the space E cannot impede those of the second between the lines AF and DG from advancing to fill it in just the same way as they would if it were void, because, being extremely subtle and extremely agitated, they are always as ready to leave the places where they are as any other body might be to enter them. And for this same reason, the parts of the first element that occupy the small angles between the parts of the heaven cede their place without resistance to those coming from that space E and tending to go toward the point S. I say toward S rather than toward any other place because the other bodies which, being more united and larger, have more force all tend to move away from it.

Indeed, one should note that they pass from E toward S among the parts of the second element that go from S toward E, without the ones in any way impeding the others. Thus, the air enclosed in the sand clock XYZ rises from Z toward X through the sand Y, which does not for that reason cease to fall in the meantime toward Z.

Finally, the parts of that first element that are in the space ABCD, where they compose the body of the sun and there turn very rapidly in a circle about point S, tend to move away from it in all directions in a straight line, in accordance with what I have just set out. By this means, all those in line SD together push the part of the second element that is at point D, and all those in line SA push that which is at point A, and so on. And they do so in such a way that this alone suffices to cause all those parts of the second element between the lines AF and DG to advance toward the space E, even though they might have no inclination themselves to do so.

Moreover, since they must thus advance toward that space E when it is occupied only by the matter of the first element, it is certain that they also tend to go there even though it is filled by some other body and, consequently, that they push and make an effort against that body as if to drive it out of its place. Thus, if it were the eye of a man that were at the point E, it would actually be pushed, both by the sun and by all the matter of the heaven between the lines AF and DG.

Now one must know that the men of this new world will be of such a nature that, when their eyes are pushed in this manner, they will have from it a sensation very much like that which we have of light, as I will say more fully below.

CHAPTER FOURTEEN On the Properties of Light

But I want to stop a while at this point to set out the properties of the action by which their eyes can be thus pushed. For they all agree so perfectly with those that we note in light that, when you have considered them, I am sure you will admit, like me, that there is no need to imagine in the stars or in the heavens any other quality but this action that is called by the name of "light."

The principal properties of light are: (1) that it extends around in all directions about bodies one calls "luminous," (2) to any distance, (3) and in an instant, (4) and ordinarily in straight lines, which must be taken to be the rays of light; (5) and that several of these rays coming from diverse points can come together at the same point, (6) or, coming from the same point, can go out toward different points, (7) or, coming from diverse points and going toward diverse points, can pass through the same point without impeding one another; (8) and that they can also sometimes impede one another, to wit, when their force is very unequal and that of some of the rays is much greater than that of the others; (9) and, finally, that they can be diverted by reflection, (10) or by refraction, (11) and that their force can be increased, (12) or diminished, by the diverse dispositions or qualities of the matter that receives them. There are the principal qualities that one observes in light and that all agree with this action, as you are about to see.

(l) The reason is evident why this action should extend in all directions around luminous bodies, because it proceeds from the circular motion of their parts.

(2) It is also evident that it can extend to any distance. For example, supposing that the parts of the heaven between AF and DG are already themselves disposed to advance toward E, as we have said they are, one can no longer doubt that the force with which the sun pushes those at ABCD should also extend out to E, even though there is a greater distance from the one to the other than there is from the highest stars of the firmament down to us.

(3) And knowing that the parts of the second element between AF and DG all touch and press one another as much as possible, one also cannot doubt that the action by which the first ones are pushed must pass in an instant out to the last, in just the same way that the force with which one pushes one end of a stick passes to the other end in the same instant; or rather (so you make no difficulty on the basis that the parts of the heaven are not attached to one another as are those of a stick) in just the same way that, as the small ball marked 50 falls toward 6, the others marked 10 also fall toward 6 at the same instant.

(4) Regarding the lines along which this action is communicated and which are properly the rays of light, one must note that they differ from the parts of the second element through the intermediary of which this same action is communicated, and that they are nothing material in the medium through which they pass, but they designate only in what direction and according to what determination the luminous body acts on the body it is illuminating. Thus, one should not cease to conceive of them as exactly straight even though the parts of the second element that serve to transmit this action, i.e. light, can almost never be placed so directly one on the other that they compose completely straight lines. In just the same way, you can easily conceive that the hand A pushes the body E along the straight line AE even though it pushes it only through the intermediary of the stick BCD, which is twisted. And in just the same way, you can conceive that the ball marked 1 pushes that marked 7 through the intermediary of the two marked 5 and 5 as directly as through the intermediary of the others, 2, 3, 4, 6.
(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 that 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 thus 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.

If to this you object that the inequality between the balls N, P, H, P and 1, 2, 3, 4, etc. is much greater than that which I have supposed between the parts of the second element that compose the sphere EBG and those that are immediately below them toward the sun, I respond that one can draw no other consequence from this than that there should not take place as much refraction in the sphere EBG as in that composed by the balls 1, 2, 3, 4, etc. However, since there is in turn some inequality between the parts of the second element that are immediately below this sphere EBG and those that are still lower toward the sun, this refraction increases more and more as the rays penetrate farther. Thus, when the rays reach to the sphere of the earth DAF, the refraction can well be as great as, or even greater than, that of the action by which the small balls 1, 2, 3, 4, etc. are pushed. For it is very likely that the parts of the second element toward this sphere of the earth DAF are no less small in comparison with those toward the sphere EBG than are those balls 1, 2, 3, 4, etc. in comparison with the other balls N, P, H, P . . .

[The extant text breaks off here.]