Book IV

1

THE physicist¹ must have a knowledge of Place, too, as well as of the infinite — namely, whether there is such a thing or not, and the manner of its existence and what it is — both because all suppose that things which exist are somewhere (the non-existent is nowhere — where is the goat-stag or the sphinx?), and because ‘motion’ in its most general and primary sense is change of place, which we call ‘locomotion²’.

The question, what is place? presents many difficulties. An examination of all the relevant facts seems to lead to divergent conclusions. Moreover, we have inherited nothing from previous thinkers, whether in the way of a statement of difficulties or of a solution.

The existence of place is held to be obvious from the fact of mutual³ replacement⁴. Where water now is, there in turn, when the water has gone out as from a vessel⁵, air is present. When therefore another body occupies this same place, the place is thought to be different from all the bodies which come to be in it and replace one another. What now contains air formerly⁶ contained water, so that clearly the place or space into which and out of which they passed was something different from both.

Further, the typical locomotions of the elementary natural bodies — namely, fire, earth, and the like — show not only that place is something, but also that it exerts a certain influence. Each is carried to its own place, if it is not hindered, the one up, the other down. Now these are regions or kinds of place — up and down and the rest of the six directions. Nor do such distinctions (up and down and right and left, &c.) hold only in relation to us. To us they are not always the same but change with the direction in which we are turned: that is why the same thing may be both right and left, up and down, before and behind. But in nature each is distinct, taken apart by itself. It is not every chance direction which is ‘up’, but where fire and what is light are carried; similarly, too, ‘down’ is not any chance direction but where what has weight and what is made of earth are carried — the implication being that these places do not differ merely in relative position, but also as possessing distinct potencies⁷. This is made plain also by the objects studied by mathematics. Though they have no real place, they nevertheless, in respect of their position relatively⁸ to us, have a right and left as attributes ascribed to them only in consequence of their relative position, not having by nature these various characteristics. Again, the theory that the void exists involves the existence of place: for one would define void as place bereft⁹ of body.

These considerations then would lead us to suppose that place is something distinct from bodies, and that every sensible body is in place. Hesiod too might be held to have given a correct account of it when he made chaos¹⁰ first. At least he says:

‘First of all things came chaos to being, then broad-breasted earth,’ implying that things need to have space first, because he thought, with most people, that everything is somewhere and in place. If this is its nature, the potency¹¹ of place must be a marvellous thing, and take precedence of all other things. For that without which nothing else can exist, while it can exist without the others, must needs be first; for place does not pass out of existence when the things in it are annihilated¹².

True, but even if we suppose its existence settled, the question of its nature presents difficulty — whether it is some sort of ‘bulk’ of body or some entity¹³ other than that, for we must first determine its genus.

(1) Now it has three dimensions, length, breadth, depth, the dimensions by which all body also is bounded. But the place cannot be body; for if it were there would be two bodies in the same place.

(2) Further, if body has a place and space, clearly so too have surface and the other limits of body; for the same statement will apply to them: where the bounding planes of the water were, there in turn will be those of the air. But when we come to a point we cannot make a distinction between it and its place. Hence if the place of a point is not different from the point, no more will that of any of the others be different, and place will not be something different from each of them.

(3) What in the world then are we to suppose place to be? If it has the sort of nature described, it cannot be an element or composed of elements, whether these be corporeal¹⁴ or incorporeal¹⁵: for while it has size, it has not body. But the elements of sensible bodies are bodies, while nothing that has size results from a combination of intelligible¹⁶ elements.

(4) Also we may ask: of what in things is space the cause? None of the four modes of causation can be ascribed to it. It is neither in the sense of the matter of existents (for nothing is composed of it), nor as the form and definition of things, nor as end, nor does it move existents.

(5) Further, too, if it is itself an existent, where will it be? Zeno’s difficulty demands an explanation: for if everything that exists has a place, place too will have a place, and so on ad infinitum.

(6) Again, just as every body is in place, so, too, every place has a body in it. What then shall we say about growing things? It follows from these premisses that their place must grow with them, if their place is neither less nor greater than they are.

By asking these questions, then, we must raise the whole problem about place — not only as to what it is, but even whether there is such a thing.
2

We may distinguish generally between predicating B of A because it (A) is itself, and because it is something else; and particularly between place which is common and in which all bodies are, and the special place occupied primarily by each. I mean, for instance, that you are now in the heavens because you are in the air and it is in the heavens; and you are in the air because you are on the earth; and similarly on the earth because you are in this place which contains no more than you.

Now if place is what primarily contains each body, it would be a limit, so that the place would be the form or shape of each body by which the magnitude or the matter of the magnitude is defined: for this is the limit of each body.

If, then, we look at the question in this way the place of a thing is its form. But, if we regard the place as the extension of the magnitude, it is the matter. For this is different from the magnitude: it is what is contained and defined by the form, as by a bounding plane. Matter or the indeterminate is of this nature; when the boundary and attributes of a sphere are taken away, nothing but the matter is left.

This is why Plato in the Timaeus says that matter and space are the same; for the ‘participant’ and space are identical. (It is true, indeed, that the account he gives there of the ‘participant’ is different from what he says in his so-called ‘unwritten teaching’. Nevertheless, he did identify place and space.) I mention Plato because, while all hold place to be something, he alone tried to say what it is.

In view of these facts we should naturally expect to find difficulty in determining what place is, if indeed it is one of these two things, matter or form. They demand a very close scrutiny¹⁷, especially as it is not easy to recognize them apart.

But it is at any rate not difficult to see that place cannot be either of them. The form and the matter are not separate from the thing, whereas the place can be separated. As we pointed¹⁸ out, where air was, water in turn comes to be, the one replacing the other; and similarly with other bodies. Hence the place of a thing is neither a part nor a state of it, but is separable from it. For place is supposed to be something like a vessel — the vessel being a transportable place. But the vessel is no part of the thing.

In so far then as it is separable from the thing, it is not the form: qua containing, it is different from the matter.

Also it is held that what is anywhere is both itself something and that there is a different thing outside it. (Plato of course, if we may digress, ought to tell us why the form and the numbers are not in place, if ‘what participates’ is place — whether what participates is the Great and the Small or the matter, as he called it in writing in the Timaeus.)

Further, how could a body be carried to its own place, if place was the matter or the form? It is impossible that what has no reference to motion or the distinction of up and down can be place. So place must be looked for among things which have these characteristics.

If the place is in the thing (it must be if it is either shape or matter) place will have a place: for both the form and the indeterminate undergo change and motion along with the thing, and are not always in the same place, but are where the thing is. Hence the place will have a place.

Further, when water is produced from air, the place has been destroyed, for the resulting body is not in the same place. What sort of destruction then is that?

This concludes my statement of the reasons why space must be something, and again of the difficulties that may be raised about its essential nature.
3

The next step we must take is to see in how many senses one thing is said to be ‘in’ another.

(1) As the finger is ‘in’ the hand and generally the part ‘in’ the whole.

(2) As the whole is ‘in’ the parts: for there is no whole over and above the parts.

(3) As man is ‘in’ animal and generally species ‘in’ genus.

(4) As the genus is ‘in’ the species and generally the part of the specific form ‘in’ the definition of the specific form.

(5) As health is ‘in’ the hot and the cold and generally the form ‘in’ the matter.

(6) As the affairs of Greece centre ‘in’ the king, and generally events centre ‘in’ their primary motive¹⁹ agent.

(7) As the existence of a thing centres ‘in its good and generally ‘in’ its end, i.e. in ‘that for the sake of which’ it exists.

(8) In the strictest sense of all, as a thing is ‘in’ a vessel, and generally ‘in’ place.

One might raise the question whether a thing can be in itself, or whether nothing can be in itself — everything being either nowhere or in something else.

The question is ambiguous; we may mean the thing qua itself or qua something else.

When there are parts of a whole — the one that in which a thing is, the other the thing which is in it — the whole will be described as being in itself. For a thing is described in terms of its parts, as well as in terms of the thing as a whole, e.g. a man is said to be white because the visible surface of him is white, or to be scientific because his thinking faculty²¹ has been trained. The jar then will not be in itself and the wine will not be in itself. But the jar of wine will: for the contents and the container are both parts of the same whole.

In this sense then, but not primarily, a thing can be in itself, namely, as ‘white’ is in body (for the visible surface is in body), and science is in the mind.

It is from these, which are ‘parts’ (in the sense at least of being ‘in’ the man), that the man is called white, &c. But the jar and the wine in separation are not parts of a whole, though together they are. So when there are parts, a thing will be in itself, as ‘white’ is in man because it is in body, and in body because it resides in the visible surface. We cannot go further and say that it is in surface in virtue²² of something other than itself. (Yet it is not in itself: though these are in a way the same thing,) they differ in essence, each having a special nature and capacity, ‘surface’ and ‘white’.

Thus if we look at the matter inductively we do not find anything to be ‘in’ itself in any of the senses that have been distinguished²³; and it can be seen by argument that it is impossible. For each of two things will have to be both, e.g. the jar will have to be both vessel and wine, and the wine both wine and jar, if it is possible for a thing to be in itself; so that, however true it might be that they were in each other, the jar will receive the wine in virtue not of its being wine but of the wine’s being wine, and the wine will be in the jar in virtue not of its being a jar but of the jar’s being a jar. Now that they are different in respect of their essence is evident; for ‘that in which something is’ and ‘that which is in it’ would be differently defined.

Nor is it possible for a thing to be in itself even incidentally: for two things would at the same time in the same thing. The jar would be in itself — if a thing whose nature it is to receive can be in itself; and that which it receives, namely (if wine) wine, will be in it.

Obviously then a thing cannot be in itself primarily.

Zeno’s problem — that if Place is something it must be in something — is not difficult to solve. There is nothing to prevent the first place from being ‘in’ something else — not indeed in that as ‘in’ place, but as health is ‘in’ the hot as a positive determination of it or as the hot is ‘in’ body as an affection. So we escape the infinite regress.

Another thing is plain: since the vessel is no part of what is in it (what contains in the strict sense is different from what is contained), place could not be either the matter or the form of the thing contained, but must different — for the latter, both the matter and the shape, are parts of what is contained.

This then may serve as a critical statement of the difficulties involved.
4

What then after all is place? The answer to this question may be elucidated²⁴ as follows.

Let us take for granted about it the various characteristics which are supposed correctly to belong to it essentially²⁵. We assume then —

(1) Place is what contains that of which it is the place.

(2) Place is no part of the thing.

(3) The immediate²⁶ place of a thing is neither less nor greater than the thing.

(4) Place can be left behind by the thing and is separable. In addition:

(5) All place admits of the distinction of up and down, and each of the bodies is naturally carried to its appropriate place and rests there, and this makes the place either up or down.

Having laid these foundations, we must complete the theory. We ought to try to make our investigation²⁷ such as will render an account of place, and will not only solve the difficulties connected with it, but will also show that the attributes supposed to belong to it do really belong to it, and further will make clear the cause of the trouble and of the difficulties about it. Such is the most satisfactory kind of exposition.

First then we must understand that place would not have been thought of, if there had not been a special kind of motion, namely that with respect to place. It is chiefly for this reason that we suppose the heaven also to be in place, because it is in constant movement. Of this kind of change there are two species — locomotion on the one hand and, on the other, increase and diminution²⁸. For these too involve variation of place: what was then in this place has now in turn changed to what is larger or smaller.

Again, when we say a thing is ‘moved’, the predicate either (1) belongs to it actually, in virtue of its own nature, or (2) in virtue of something conjoined with it. In the latter case it may be either (a) something which by its own nature is capable of being moved, e.g. the parts of the body or the nail in the ship, or (b) something which is not in itself capable of being moved, but is always moved through its conjunction with something else, as ‘whiteness’ or ‘science’. These have changed their place only because the subjects to which they belong do so.

We say that a thing is in the world, in the sense of in place, because it is in the air, and the air is in the world; and when we say it is in the air, we do not mean it is in every part of the air, but that it is in the air because of the outer surface of the air which surrounds it; for if all the air were its place, the place of a thing would not be equal to the thing — which it is supposed to be, and which the primary place in which a thing is actually is.

When what surrounds, then, is not separate from the thing, but is in continuity with it, the thing is said to be in what surrounds it, not in the sense of in place, but as a part in a whole. But when the thing is separate and in contact, it is immediately ‘in’ the inner surface of the surrounding body, and this surface is neither a part of what is in it nor yet greater than its extension, but equal to it; for the extremities²⁹ of things which touch are coincident.

Further, if one body is in continuity with another, it is not moved in that but with that. On the other hand it is moved in that if it is separate. It makes no difference whether what contains is moved or not.

Again, when it is not separate it is described as a part in a whole, as the pupil in the eye or the hand in the body: when it is separate, as the water in the cask or the wine in the jar. For the hand is moved with the body and the water in the cask.

It will now be plain from these considerations what place is. There are just four things of which place must be one — the shape, or the matter, or some sort of extension between the bounding surfaces of the containing body, or this boundary itself if it contains no extension over and above the bulk of the body which comes to be in it.

Three of these it obviously cannot be:

(1) The shape is supposed to be place because it surrounds, for the extremities of what contains and of what is contained are coincident. Both the shape and the place, it is true, are boundaries. But not of the same thing: the form is the boundary of the thing, the place is the boundary of the body which contains it.

(2) The extension between the extremities is thought to be something, because what is contained and separate may often be changed while the container remains³⁰ the same (as water may be poured from a vessel) — the assumption being that the extension is something over and above the body displaced. But there is no such extension. One of the bodies which change places and are naturally capable of being in contact with the container falls in whichever it may chance to be.

If there were an extension which were such as to exist independently and be permanent, there would be an infinity³¹ of places in the same thing. For when the water and the air change places, all the portions of the two together will play the same part in the whole which was previously³² played by all the water in the vessel; at the same time the place too will be undergoing change; so that there will be another place which is the place of the place, and many places will be coincident. There is not a different place of the part, in which it is moved, when the whole vessel changes its place: it is always the same: for it is in the (proximate) place where they are that the air and the water (or the parts of the water) succeed each other, not in that place in which they come to be, which is part of the place which is the place of the whole world.

(3) The matter, too, might seem to be place, at least if we consider it in what is at rest and is thus separate but in continuity. For just as in change of quality there is something which was formerly black and is now white, or formerly soft and now hard — this is just why we say that the matter exists — so place, because it presents a similar phenomenon, is thought to exist — only in the one case we say so because what was air is now water, in the other because where air formerly was there a is now water. But the matter, as we said before, is neither separable from the thing nor contains it, whereas place has both characteristics.

Well, then, if place is none of the three — neither the form nor the matter nor an extension which is always there, different from, and over and above, the extension of the thing which is displaced — place necessarily is the one of the four which is left, namely, the boundary of the containing body at which it is in contact with the contained body. (By the contained body is meant what can be moved by way of locomotion.)

Place is thought to be something important and hard to grasp, both because the matter and the shape present themselves along with it, and because the displacement³³ of the body that is moved takes place in a stationary³⁴ container, for it seems possible that there should be an interval³⁵ which is other than the bodies which are moved. The air, too, which is thought to be incorporeal, contributes something to the belief: it is not only the boundaries of the vessel which seem to be place, but also what is between them, regarded as empty. Just, in fact, as the vessel is transportable place, so place is a non-portable vessel. So when what is within a thing which is moved, is moved and changes its place, as a boat on a river, what contains plays the part of a vessel rather than that of place. Place on the other hand is rather what is motionless: so it is rather the whole river that is place, because as a whole it is motionless.

Hence we conclude that the innermost motionless boundary of what contains is place.

This explains why the middle of the heaven and the surface which faces us of the rotating system are held to be ‘up’ and ‘down’ in the strict and fullest sense for all men: for the one is always at rest, while the inner side of the rotating body remains always coincident with itself. Hence since the light is what is naturally carried up, and the heavy what is carried down, the boundary which contains in the direction of the middle of the universe, and the middle itself, are down, and that which contains in the direction of the outermost³⁶ part of the universe, and the outermost part itself, are up.

For this reason, too, place is thought to be a kind of surface, and as it were a vessel, i.e. a container of the thing.

Further, place is coincident with the thing, for boundaries are coincident with the bounded.
5

If then a body has another body outside it and containing it, it is in place, and if not, not. That is why, even if there were to be water which had not a container, the parts of it, on the one hand, will be moved (for one part is contained in another), while, on the other hand, the whole will be moved in one sense, but not in another. For as a whole it does not simultaneously³⁷ change its place, though it will be moved in a circle: for this place is the place of its parts. (Some things are moved, not up and down, but in a circle; others up and down, such things namely as admit of condensation³⁸ and rarefaction.)

As was explained, some things are potentially in place, others actually. So, when you have a homogeneous substance which is continuous, the parts are potentially in place: when the parts are separated, but in contact, like a heap, they are actually in place.

Again, (1) some things are per se in place, namely every body which is movable either by way of locomotion or by way of increase is per se somewhere, but the heaven, as has been said, is not anywhere as a whole, nor in any place, if at least, as we must suppose, no body contains it. On the line on which it is moved, its parts have place: for each is contiguous the next.

But (2) other things are in place indirectly³⁹, through something conjoined with them, as the soul and the heaven. The latter is, in a way, in place, for all its parts are: for on the orb⁴⁰ one part contains another. That is why the upper part is moved in a circle, while the All is not anywhere. For what is somewhere is itself something, and there must be alongside it some other thing wherein it is and which contains it. But alongside the All or the Whole there is nothing outside the All, and for this reason all things are in the heaven; for the heaven, we may say, is the All. Yet their place is not the same as the heaven. It is part of it, the innermost part of it, which is in contact with the movable body; and for this reason the earth is in water, and this in the air, and the air in the aether, and the aether in heaven, but we cannot go on and say that the heaven is in anything else.

It is clear, too, from these considerations that all the problems which were raised about place will be solved when it is explained in this way:

(1) There is no necessity that the place should grow with the body in it,

(2) Nor that a point should have a place,

(3) Nor that two bodies should be in the same place,

(4) Nor that place should be a corporeal interval: for what is between the boundaries of the place is any body which may chance to be there, not an interval in body.

Further, (5) place is also somewhere, not in the sense of being in a place, but as the limit is in the limited; for not everything that is is in place, but only movable body.

Also (6) it is reasonable that each kind of body should be carried to its own place. For a body which is next in the series and in contact (not by compulsion) is akin⁴¹, and bodies which are united do not affect each other, while those which are in contact interact on each other.

Nor (7) is it without reason that each should remain naturally in its proper place. For this part has the same relation to its place, as a separable part to its whole, as when one moves a part of water or air: so, too, air is related to water, for the one is like matter, the other form — water is the matter of air, air as it were the actuality of water, for water is potentially air, while air is potentially water, though in another way.

These distinctions will be drawn⁴² more carefully later. On the present occasion it was necessary to refer to them: what has now been stated obscurely will then be made more clear. If the matter and the fulfilment are the same thing (for water is both, the one potentially, the other completely), water will be related to air in a way as part to whole. That is why these have contact: it is organic union when both become actually one.

This concludes my account of place — both of its existence and of its nature.
6

The investigation of similar questions about the void, also, must be held to belong to the physicist — namely whether it exists or not, and how it exists or what it is — just as about place. The views taken of it involve arguments both for and against, in much the same sort of way. For those who hold that the void exists regard it as a sort of place or vessel which is supposed to be ‘full’ when it holds the bulk which it is capable of containing, ‘void’ when it is deprived of that — as if ‘void’ and ‘full’ and ‘place’ denoted the same thing, though the essence of the three is different.

We must begin the inquiry⁴³ by putting down the account given by those who say that it exists, then the account of those who say that it does not exist, and third the current view on these questions.

Those who try to show that the void does not exist do not disprove what people really mean by it, but only their erroneous way of speaking; this is true of Anaxagoras and of those who refute the existence of the void in this way. They merely give an ingenious demonstration⁴⁴ that air is something — by straining wine-skins and showing the resistance of the air, and by cutting it off in clepsydras. But people really mean that there is an empty interval in which there is no sensible body. They hold that everything which is in body is body and say that what has nothing in it at all is void (so what is full of air is void). It is not then the existence of air that needs to be proved, but the non-existence of an interval, different from the bodies, either separable or actual — an interval which divides the whole body so as to break its continuity, as Democritus and Leucippus hold, and many other physicists⁴⁵ — or even perhaps as something which is outside the whole body, which remains continuous.

These people, then, have not reached even the threshold of the problem, but rather those who say that the void exists.

(1) They argue, for one thing, that change in place (i.e. locomotion and increase) would not be. For it is maintained that motion would seem not to exist, if there were no void, since what is full cannot contain anything more. If it could, and there were two bodies in the same place, it would also be true that any number of bodies could be together; for it is impossible to draw a line of division beyond which the statement would become untrue. If this were possible, it would follow also that the smallest body would contain the greatest; for ‘many a little makes a mickle’: thus if many equal bodies can be together, so also can many unequal bodies.

Melissus, indeed, infers from these considerations that the All is immovable; for if it were moved there must, he says, be void, but void is not among the things that exist.

This argument, then, is one way in which they show that there is a void.

(2) They reason from the fact that some things are observed to contract and be compressed, as people say that a cask will hold the wine which formerly filled it, along with the skins into which the wine has been decanted⁴⁶, which implies that the compressed body contracts into the voids present in it.

Again (3) increase, too, is thought to take always by means of void, for nutriment is body, and it is impossible for two bodies to be together. A proof of this they find also in what happens to ashes, which absorb as much water as the empty vessel.

The Pythagoreans, too, (4) held that void exists and that it enters the heaven itself, which as it were inhales⁴⁷ it, from the infinite air. Further it is the void which distinguishes the natures of things, as if it were like what separates and distinguishes the terms of a series. This holds primarily in the numbers, for the void distinguishes their nature.

These, then, and so many, are the main grounds on which people have argued for and against the existence of the void.
7

As a step towards settling which view is true, we must determine the meaning of the name.

The void is thought to be place with nothing in it. The reason for this is that people take what exists to be body, and hold that while every body is in place, void is place in which there is no body, so that where there is no body, there must be void.

Every body, again, they suppose to be tangible⁴⁸; and of this nature is whatever has weight or lightness.

Hence, by a syllogism⁴⁹, what has nothing heavy or light in it, is void.

This result, then, as I have said, is reached by syllogism. It would be absurd to suppose that the point is void; for the void must be place which has in it an interval in tangible body.

But at all events we observe then that in one way the void is described as what is not full of body perceptible to touch; and what has heaviness and lightness is perceptible to touch. So we would raise the question: what would they say of an interval that has colour or sound — is it void or not? Clearly they would reply that if it could receive what is tangible it was void, and if not, not.

In another way void is that in which there is no ‘this’ or corporeal substance. So some say that the void is the matter of the body (they identify the place, too, with this), and in this they speak incorrectly; for the matter is not separable from the things, but they are inquiring about the void as about something separable.

Since we have determined⁵⁰ the nature of place, and void must, if it exists, be place deprived of body, and we have stated both in what sense place exists and in what sense it does not, it is plain that on this showing void does not exist, either unseparated or separated; the void is meant to be, not body but rather an interval in body. This is why the void is thought to be something, viz. because place is, and for the same reasons. For the fact of motion in respect of place comes to the aid both of those who maintain that place is something over and above the bodies that come to occupy it, and of those who maintain that the void is something. They state that the void is the condition of movement in the sense of that in which movement takes place; and this would be the kind of thing that some say place is.

But there is no necessity for there being a void if there is movement. It is not in the least needed as a condition of movement in general, for a reason which, incidentally, escaped Melissus; viz. that the full can suffer qualitative⁵¹ change.

But not even movement in respect of place involves a void; for bodies may simultaneously make room for one another, though there is no interval separate and apart from the bodies that are in movement. And this is plain even in the rotation⁵² of continuous things, as in that of liquids.

And things can also be compressed not into a void but because they squeeze out what is contained in them (as, for instance, when water is compressed the air within it is squeezed out); and things can increase in size not only by the entrance of something but also by qualitative change; e.g. if water were to be transformed into air.

In general, both the argument about increase of size and that about water poured on to the ashes get in their own way. For either not any and every part of the body is increased, or bodies may be increased otherwise than by the addition of body, or there may be two bodies in the same place (in which case they are claiming to solve a quite general difficulty, but are not proving the existence of void), or the whole body must be void, if it is increased in every part and is increased by means of void. The same argument applies to the ashes.

It is evident, then, that it is easy to refute the arguments by which they prove the existence of the void.
8

Let us explain again that there is no void existing separately, as some maintain. If each of the simple bodies has a natural locomotion, e.g. fire upward and earth downward and towards the middle of the universe, it is clear that it cannot be the void that is the condition of locomotion. What, then, will the void be the condition of? It is thought to be the condition of movement in respect of place, and it is not the condition of this.

Again, if void is a sort of place deprived of body, when there is a void where will a body placed in it move to? It certainly cannot move into the whole of the void. The same argument applies as against those who think that place is something separate, into which things are carried; viz. how will what is placed in it move, or rest? Much the same argument will apply to the void as to the ‘up’ and ‘down’ in place, as is natural enough since those who maintain the existence of the void make it a place.

And in what way will things be present either in place — or in the void? For the expected result does not take place when a body is placed as a whole in a place conceived of as separate and permanent; for a part of it, unless it be placed apart, will not be in a place but in the whole. Further, if separate place does not exist, neither will void.

If people say that the void must exist, as being necessary if there is to be movement, what rather turns out to be the case, if one the matter, is the opposite, that not a single thing can be moved if there is a void; for as with those who for a like reason say the earth is at rest, so, too, in the void things must be at rest; for there is no place to which things can move more or less than to another; since the void in so far as it is void admits no difference.

The second reason is this: all movement is either compulsory⁵³ or according to nature, and if there is compulsory movement there must also be natural (for compulsory movement is contrary to nature, and movement contrary to nature is posterior to that according to nature, so that if each of the natural bodies has not a natural movement, none of the other movements can exist); but how can there be natural movement if there is no difference throughout the void or the infinite? For in so far as it is infinite, there will be no up or down or middle, and in so far as it is a void, up differs no whit²⁰ from down; for as there is no difference in what is nothing, there is none in the void (for the void seems to be a non-existent and a privation of being), but natural locomotion seems to be differentiated⁵⁴, so that the things that exist by nature must be differentiated. Either, then, nothing has a natural locomotion, or else there is no void.

Further, in point of fact things that are thrown move though that which gave them their impulse is not touching⁵⁵ them, either by reason of mutual replacement, as some maintain, or because the air that has been pushed pushes them with a movement quicker than the natural locomotion of the projectile⁵⁶ wherewith it moves to its proper place. But in a void none of these things can take place, nor can anything be moved save as that which is carried is moved.

Further, no one could say why a thing once set in motion should stop anywhere; for why should it stop here rather than here? So that a thing will either be at rest or must be moved ad infinitum, unless something more powerful get in its way.

Further, things are now thought to move into the void because it yields; but in a void this quality is present equally everywhere, so that things should move in all directions.

Further, the truth of what we assert is plain from the following considerations. We see the same weight or body moving faster than another for two reasons, either because there is a difference in what it moves through, as between water, air, and earth, or because, other things being equal, the moving body differs from the other owing to excess of weight or of lightness.

Now the medium causes a difference because it impedes⁵⁷ the moving thing, most of all if it is moving in the opposite direction, but in a secondary degree even if it is at rest; and especially a medium that is not easily divided, i.e. a medium that is somewhat dense⁵⁸. A, then, will move through B in time G, and through D, which is thinner, in time E (if the length of B is egual to D), in proportion to the density⁵⁹ of the hindering body. For let B be water and D air; then by so much as air is thinner and more incorporeal than water, A will move through D faster than through B. Let the speed have the same ratio to the speed, then, that air has to water. Then if air is twice as thin, the body will traverse B in twice the time that it does D, and the time G will be twice the time E. And always, by so much as the medium is more incorporeal and less resistant⁶⁰ and more easily divided, the faster will be the movement.

Now there is no ratio in which the void is exceeded by body, as there is no ratio of 0 to a number. For if 4 exceeds 3 by 1, and 2 by more than 1, and 1 by still more than it exceeds 2, still there is no ratio by which it exceeds 0; for that which exceeds must be divisible into the excess + that which is exceeded, so that will be what it exceeds 0 by + 0. For this reason, too, a line does not exceed a point unless it is composed of points! Similarly the void can bear no ratio to the full, and therefore neither can movement through the one to movement through the other, but if a thing moves through the thickest medium such and such a distance in such and such a time, it moves through the void with a speed beyond any ratio. For let Z be void, equal in magnitude to B and to D. Then if A is to traverse and move through it in a certain time, H, a time less than E, however, the void will bear this ratio to the full. But in a time equal to H, A will traverse the part O of A. And it will surely also traverse in that time any substance Z which exceeds air in thickness in the ratio which the time E bears to the time H. For if the body Z be as much thinner than D as E exceeds H, A, if it moves through Z, will traverse it in a time inverse⁶¹ to the speed of the movement, i.e. in a time equal to H. If, then, there is no body in Z, A will traverse Z still more quickly. But we supposed that its traverse of Z when Z was void occupied the time H. So that it will traverse Z in an equal time whether Z be full or void. But this is impossible. It is plain, then, that if there is a time in which it will move through any part of the void, this impossible result will follow: it will be found to traverse a certain distance, whether this be full or void, in an equal time; for there will be some body which is in the same ratio to the other body as the time is to the time.

To sum the matter up, the cause of this result is obvious, viz. that between any two movements there is a ratio (for they occupy time, and there is a ratio between any two times, so long as both are finite), but there is no ratio of void to full.

These are the consequences that result from a difference in the media; the following depend upon an excess of one moving body over another. We see that bodies which have a greater impulse either of weight or of lightness, if they are alike in other respects, move faster over an equal space, and in the ratio which their magnitudes bear to each other. Therefore they will also move through the void with this ratio of speed. But that is impossible; for why should one move faster? (In moving through plena it must be so; for the greater divides them faster by its force. For a moving thing cleaves⁶² the medium either by its shape, or by the impulse which the body that is carried along or is projected possesses.) Therefore all will possess equal velocity⁶³. But this is impossible.

It is evident from what has been said, then, that, if there is a void, a result follows which is the very opposite of the reason for which those who believe in a void set it up. They think that if movement in respect of place is to exist, the void cannot exist, separated all by itself; but this is the same as to say that place is a separate cavity; and this has already been stated to be impossible.

But even if we consider it on its own merits the so-called vacuum will be found to be really vacuous⁶⁴. For as, if one puts a cube in water, an amount of water equal to the cube will be displaced; so too in air; but the effect is imperceptible to sense. And indeed always in the case of any body that can be displaced, must, if it is not compressed, be displaced in the direction in which it is its nature to be displaced — always either down, if its locomotion is downwards⁶⁵ as in the case of earth, or up, if it is fire, or in both directions — whatever be the nature of the inserted body. Now in the void this is impossible; for it is not body; the void must have penetrated⁶⁶ the cube to a distance equal to that which this portion of void formerly occupied in the void, just as if the water or air had not been displaced by the wooden cube, but had penetrated right through it.

But the cube also has a magnitude equal to that occupied by the void; a magnitude which, if it is also hot or cold, or heavy or light, is none the less different in essence from all its attributes, even if it is not separable from them; I mean the volume of the wooden cube. So that even if it were separated from everything else and were neither heavy nor light, it will occupy an equal amount of void, and fill the same place, as the part of place or of the void equal to itself. How then will the body of the cube differ from the void or place that is equal to it? And if there can be two such things, why cannot there be any number coinciding?

This, then, is one absurd and impossible implication of the theory. It is also evident that the cube will have this same volume even if it is displaced, which is an attribute possessed⁶⁷ by all other bodies also. Therefore if this differs in no respect from its place, why need we assume a place for bodies over and above the volume of each, if their volume be conceived of as free from attributes? It contributes nothing to the situation if there is an equal interval attached to it as well. [Further it ought to be clear by the study of moving things what sort of thing void is. But in fact it is found nowhere in the world. For air is something, though it does not seem to be so — nor, for that matter, would water, if fishes were made of iron; for the discrimination of the tangible is by touch.]

It is clear, then, from these considerations that there is no separate void.
9

There are some who think that the existence of rarity and density shows that there is a void. If rarity and density do not exist, they say, neither can things contract and be compressed. But if this were not to take place, either there would be no movement at all, or the universe would bulge⁶⁸, as Xuthus said, or air and water must always change into equal amounts (e.g. if air has been made out of a cupful of water, at the same time out of an equal amount of air a cupful of water must have been made), or void must necessarily exist; for compression and expansion cannot take place otherwise.

Now, if they mean by the rare that which has many voids existing separately, it is plain that if void cannot exist separate any more than a place can exist with an extension all to itself, neither can the rare exist in this sense. But if they mean that there is void, not separately existent, but still present in the rare, this is less impossible, yet, first, the void turns out not to be a condition of all movement, but only of movement upwards⁶⁹ (for the rare is light, which is the reason why they say fire is rare); second, the void turns out to be a condition of movement not as that in which it takes place, but in that the void carries things up as skins by being carried up themselves carry up what is continuous with them. Yet how can void have a local movement or a place? For thus that into which void moves is till then void of a void.

Again, how will they explain, in the case of what is heavy, its movement downwards? And it is plain that if the rarer and more void a thing is the quicker it will move upwards, if it were completely void it would move with a maximum speed! But perhaps even this is impossible, that it should move at all; the same reason which showed that in the void all things are incapable⁷⁰ of moving shows that the void cannot move, viz. the fact that the speeds are incomparable.

Since we deny that a void exists, but for the rest the problem has been truly stated, that either there will be no movement, if there is not to be condensation and rarefaction, or the universe will bulge, or a transformation⁷¹ of water into air will always be balanced by an equal transformation of air into water (for it is clear that the air produced from water is bulkier than the water): it is necessary therefore, if compression does not exist, either that the next portion will be pushed outwards⁷² and make the outermost part bulge, or that somewhere else there must be an equal amount of water produced out of air, so that the entire bulk of the whole may be equal, or that nothing moves. For when anything is displaced this will always happen, unless it comes round in a circle; but locomotion is not always circular, but sometimes in a straight line.

These then are the reasons for which they might say that there is a void; our statement is based on the assumption that there is a single matter for contraries, hot and cold and the other natural contrarieties, and that what exists actually is produced from a potential existent, and that matter is not separable from the contraries but its being is different, and that a single matter may serve for colour and heat and cold.

The same matter also serves for both a large and a small body. This is evident; for when air is produced from water, the same matter has become something different, not by acquiring an addition to it, but has become actually what it was potentially, and, again, water is produced from air in the same way, the change being sometimes from smallness to greatness, and sometimes from greatness to smallness. Similarly, therefore, if air which is large in extent comes to have a smaller volume, or becomes greater from being smaller, it is the matter which is potentially both that comes to be each of the two.

For as the same matter becomes hot from being cold, and cold from being hot, because it was potentially both, so too from hot it can become more hot, though nothing in the matter has become hot that was not hot when the thing was less hot; just as, if the arc or curve of a greater circle becomes that of a smaller, whether it remains the same or becomes a different curve, convexity has not come to exist in anything that was not convex but straight (for differences of degree do not depend on an intermission of the quality); nor can we get any portion of a flame, in which both heat and whiteness are not present. So too, then, is the earlier heat related to the later. So that the greatness and smallness, also, of the sensible volume are extended, not by the matter’s acquiring anything new, but because the matter is potentially matter for both states; so that the same thing is dense and rare, and the two qualities have one matter.

The dense is heavy, and the rare is light. [Again, as the arc of a circle when contracted into a smaller space does not acquire a new part which is convex, but what was there has been contracted; and as any part of fire that one takes will be hot; so, too, it is all a question of contraction⁷³ and expansion of the same matter.] There are two types in each case, both in the dense and in the rare; for both the heavy and the hard are thought to be dense, and contrariwise both the light and the soft are rare; and weight and hardness fail to coincide in the case of lead and iron.

From what has been said it is evident, then, that void does not exist either separate (either absolutely separate or as a separate element in the rare) or potentially, unless one is willing to call the condition of movement void, whatever it may be. At that rate the matter of the heavy and the light, qua matter of them, would be the void; for the dense and the rare are productive of locomotion in virtue of this contrariety, and in virtue of their hardness and softness productive of passivity and impassivity, i.e. not of locomotion but rather of qualitative change.

So much, then, for the discussion of the void, and of the sense in which it exists and the sense in which it does not exist.
10

Next for discussion after the subjects mentioned is Time. The best plan will be to begin by working out the difficulties connected with it, making use of the current arguments. First, does it belong to the class of things that exist or to that of things that do not exist? Then secondly⁷⁴, what is its nature? To start, then: the following considerations would make one suspect that it either does not exist at all or barely, and in an obscure way. One part of it has been and is not, while the other is going to be and is not yet. Yet time — both infinite time and any time you like to take — is made up of these. One would naturally suppose that what is made up of things which do not exist could have no share in reality.

Further, if a divisible thing is to exist, it is necessary that, when it exists, all or some of its parts must exist. But of time some parts have been, while others have to be, and no part of it is though it is divisible. For what is ‘now’ is not a part: a part is a measure of the whole, which must be made up of parts. Time, on the other hand, is not held to be made up of ‘nows’.

Again, the ‘now’ which seems to bound the past and the future — does it always remain one and the same or is it always other and other? It is hard to say.

(1) If it is always different and different, and if none of the parts in time which are other and other are simultaneous (unless the one contains and the other is contained, as the shorter time is by the longer), and if the ‘now’ which is not, but formerly was, must have ceased-to-be at some time, the ‘nows’ too cannot be simultaneous with one another, but the prior ‘now’ must always have ceased-to-be. But the prior ‘now’ cannot have ceased-to-be in itself (since it then existed); yet it cannot have ceased-to-be in another ‘now’. For we may lay it down that one ‘now’ cannot be next to another, any more than point to point. If then it did not cease-to-be in the next ‘now’ but in another, it would exist simultaneously with the innumerable ‘nows’ between the two — which is impossible.

Yes, but (2) neither is it possible for the ‘now’ to remain always the same. No determinate divisible thing has a single termination, whether it is continuously extended in one or in more than one dimension: but the ‘now’ is a termination, and it is possible to cut off a determinate time. Further, if coincidence in time (i.e. being neither prior nor posterior) means to be ‘in one and the same “now”’, then, if both what is before and what is after are in this same ‘now’, things which happened ten thousand years ago would be simultaneous with what has happened to-day, and nothing would be before or after anything else.

This may serve as a statement of the difficulties about the attributes of time.

As to what time is or what is its nature, the traditional accounts give us as little light as the preliminary problems which we have worked through.

Some assert that it is (1) the movement of the whole, others that it is (2) the sphere itself.

(1) Yet part, too, of the revolution is a time, but it certainly is not a revolution: for what is taken is part of a revolution, not a revolution. Besides, if there were more heavens than one, the movement of any of them equally would be time, so that there would be many times at the same time.

(2) Those who said that time is the sphere of the whole thought so, no doubt, on the ground that all things are in time and all things are in the sphere of the whole. The view is too naive⁷⁵ for it to be worth while to consider the impossibilities implied in it.

But as time is most usually supposed to be (3) motion and a kind of change, we must consider this view.

Now (a) the change or movement of each thing is only in the thing which changes or where the thing itself which moves or changes may chance to be. But time is present equally everywhere and with all things.

Again, (b) change is always faster or slower, whereas time is not: for ‘fast’ and ‘slow’ are defined by time — ‘fast’ is what moves much in a short time, ‘slow’ what moves little in a long time; but time is not defined by time, by being either a certain amount or a certain kind of it.

Clearly then it is not movement. (We need not distinguish at present between ‘movement’ and ‘change’.)
11

But neither does time exist without change; for when the state of our own minds does not change at all, or we have not noticed its changing, we do not realize that time has elapsed, any more than those who are fabled⁷⁷ to sleep among the heroes in Sardinia do when they are awakened⁷⁸; for they connect the earlier ‘now’ with the later and make them one, cutting out the interval because of their failure to notice it. So, just as, if the ‘now’ were not different but one and the same, there would not have been time, so too when its difference escapes our notice the interval does not seem to be time. If, then, the non-realization of the existence of time happens to us when we do not distinguish any change, but the soul seems to stay in one indivisible state, and when we perceive and distinguish we say time has elapsed, evidently time is not independent of movement and change. It is evident, then, that time is neither movement nor independent of movement.

We must take this as our starting-point and try to discover — since we wish to know what time is — what exactly it has to do with movement.

Now we perceive movement and time together: for even when it is dark and we are not being affected⁷⁹ through the body, if any movement takes place in the mind we at once suppose that some time also has elapsed; and not only that but also, when some time is thought to have passed, some movement also along with it seems to have taken place. Hence time is either movement or something that belongs to movement. Since then it is not movement, it must be the other.

But what is moved is moved from something to something, and all magnitude is continuous. Therefore the movement goes with the magnitude. Because the magnitude is continuous, the movement too must be continuous, and if the movement, then the time; for the time that has passed is always thought to be in proportion to the movement.

The distinction of ‘before’ and ‘after’ holds primarily, then, in place; and there in virtue of relative position. Since then ‘before’ and ‘after’ hold in magnitude, they must hold also in movement, these corresponding to those. But also in time the distinction of ‘before’ and ‘after’ must hold, for time and movement always correspond with each other. The ‘before’ and ‘after’ in motion is identical in substratum with motion yet differs from it in definition, and is not identical with motion.

But we apprehend⁸⁰ time only when we have marked motion, marking it by ‘before’ and ‘after’; and it is only when we have perceived ‘before’ and ‘after’ in motion that we say that time has elapsed. Now we mark them by judging that A and B are different, and that some third thing is intermediate to them. When we think of the extremes as different from the middle and the mind pronounces that the ‘nows’ are two, one before and one after, it is then that we say that there is time, and this that we say is time. For what is bounded by the ‘now’ is thought to be time — we may assume this.

When, therefore, we perceive the ‘now’ one, and neither as before and after in a motion nor as an identity but in relation to a ‘before’ and an ‘after’, no time is thought to have elapsed, because there has been no motion either. On the other hand, when we do perceive a ‘before’ and an ‘after’, then we say that there is time. For time is just this — number of motion in respect of ‘before’ and ‘after’.

Hence time is not movement, but only movement in so far as it admits of enumeration⁸¹. A proof of this: we discriminate⁸² the more or the less by number, but more or less movement by time. Time then is a kind of number. (Number, we must note, is used in two senses — both of what is counted or the countable⁸³ and also of that with which we count. Time obviously is what is counted, not that with which we count: there are different kinds of thing.) Just as motion is a perpetual succession, so also is time. But every simultaneous time is self-identical; for the ‘now’ as a subject is an identity, but it accepts different attributes. The ‘now’ measures time, in so far as time involves the ‘before and after’.

The ‘now’ in one sense is the same, in another it is not the same. In so far as it is in succession, it is different (which is just what its being was supposed to mean), but its substratum is an identity: for motion, as was said, goes with magnitude, and time, as we maintain, with motion. Similarly, then, there corresponds to the point the body which is carried along, and by which we are aware of the motion and of the ‘before and after’ involved in it. This is an identical substratum (whether a point or a stone or something else of the kind), but it has different attributes as the sophists assume that Coriscus’ being in the Lyceum is a different thing from Coriscus’ being in the market-place. And the body which is carried along is different, in so far as it is at one time here and at another there. But the ‘now’ corresponds to the body that is carried along, as time corresponds to the motion. For it is by means of the body that is carried along that we become aware of the ‘before and after’ the motion, and if we regard these as countable we get the ‘now’. Hence in these also the ‘now’ as substratum remains the same (for it is what is before and after in movement), but what is predicated of it is different; for it is in so far as the ‘before and after’ is numerable that we get the ‘now’. This is what is most knowable: for, similarly, motion is known because of that which is moved, locomotion because of that which is carried. what is carried is a real thing, the movement is not. Thus what is called ‘now’ in one sense is always the same; in another it is not the same: for this is true also of what is carried.

Clearly, too, if there were no time, there would be no ‘now’, and vice⁸⁴ versa. just as the moving body and its locomotion involve each other mutually, so too do the number of the moving body and the number of its locomotion. For the number of the locomotion is time, while the ‘now’ corresponds to the moving body, and is like the unit of number.

Time, then, also is both made continuous by the ‘now’ and divided at it. For here too there is a correspondence with the locomotion and the moving body. For the motion or locomotion is made one by the thing which is moved, because it is one — not because it is one in its own nature (for there might be pauses in the movement of such a thing) — but because it is one in definition: for this determines the movement as ‘before’ and ‘after’. Here, too there is a correspondence with the point; for the point also both connects and terminates the length — it is the beginning of one and the end of another. But when you take it in this way, using the one point as two, a pause is necessary, if the same point is to be the beginning and the end. The ‘now’ on the other hand, since the body carried is moving, is always different.

Hence time is not number in the sense in which there is ‘number’ of the same point because it is beginning and end, but rather as the extremities of a line form a number, and not as the parts of the line do so, both for the reason given (for we can use the middle point as two, so that on that analogy time might stand still), and further because obviously the ‘now’ is no part of time nor the section any part of the movement, any more than the points are parts of the line — for it is two lines that are parts of one line.

In so far then as the ‘now’ is a boundary, it is not time, but an attribute of it; in so far as it numbers, it is number; for boundaries belong only to that which they bound, but number (e.g. ten) is the number of these horses, and belongs also elsewhere.

It is clear, then, that time is ‘number of movement in respect of the before and after’, and is continuous since it is an attribute of what is continuous.
12

The smallest number, in the strict sense of the word ‘number’, is two. But of number as concrete, sometimes there is a minimum, sometimes not: e.g. of a ‘line’, the smallest in respect of multiplicity is two (or, if you like, one), but in respect of size there is no minimum; for every line is divided ad infinitum. Hence it is so with time. In respect of number the minimum is one (or two); in point of extent there is no minimum.

It is clear, too, that time is not described as fast or slow, but as many or few and as long or short. For as continuous it is long or short and as a number many or few, but it is not fast or slow — any more than any number with which we number is fast or slow.

Further, there is the same time everywhere at once, but not the same time before and after, for while the present change is one, the change which has happened and that which will happen are different. Time is not number with which we count, but the number of things which are counted, and this according as it occurs before or after is always different, for the ‘nows’ are different. And the number of a hundred horses and a hundred men is the same, but the things numbered are different — the horses from the men. Further, as a movement can be one and the same again and again, so too can time, e.g. a year or a spring or an autumn.

Not only do we measure the movement by the time, but also the time by the movement, because they define each other. The time marks the movement, since it is its number, and the movement the time. We describe the time as much or little, measuring it by the movement, just as we know the number by what is numbered, e.g. the number of the horses by one horse as the unit. For we know how many horses there are by the use of the number; and again by using the one horse as unit we know the number of the horses itself. So it is with the time and the movement; for we measure the movement by the time and vice versa. It is natural that this should happen; for the movement goes with the distance and the time with the movement, because they are quanta and continuous and divisible. The movement has these attributes because the distance is of this nature, and the time has them because of the movement. And we measure both the distance by the movement and the movement by the distance; for we say that the road is long, if the journey is long, and that this is long, if the road is long — the time, too, if the movement, and the movement, if the time.

Time is a measure of motion and of being moved, and it measures the motion by determining a motion which will measure exactly the whole motion, as the cubit does the length by determining an amount which will measure out the whole. Further ‘to be in time’ means for movement, that both it and its essence are measured by time (for simultaneously it measures both the movement and its essence, and this is what being in time means for it, that its essence should be measured).

Clearly then ‘to be in time’ has the same meaning for other things also, namely, that their being should be measured by time. ‘To be in time’ is one of two things: (1) to exist when time exists, (2) as we say of some things that they are ‘in number’. The latter means either what is a part or mode of number — in general, something which belongs to number — or that things have a number.

Now, since time is number, the ‘now’ and the ‘before’ and the like are in time, just as ‘unit’ and ‘odd’ and ‘even’ are in number, i.e. in the sense that the one set belongs to number, the other to time. But things are in time as they are in number. If this is so, they are contained by time as things in place are contained by place.

Plainly, too, to be in time does not mean to co-exist with time, any more than to be in motion or in place means to co-exist with motion or place. For if ‘to be in something’ is to mean this, then all things will be in anything, and the heaven will be in a grain; for when the grain is, then also is the heaven. But this is a merely incidental conjunction, whereas the other is necessarily involved: that which is in time necessarily involves that there is time when it is, and that which is in motion that there is motion when it is.

Since what is ‘in time’ is so in the same sense as what is in number is so, a time greater than everything in time can be found. So it is necessary that all the things in time should be contained by time, just like other things also which are ‘in anything’, e.g. the things ‘in place’ by place.

A thing, then, will be affected by time, just as we are accustomed to say that time wastes things away, and that all things grow old through time, and that there is oblivion owing to the lapse⁷⁶ of time, but we do not say the same of getting to know or of becoming young or fair. For time is by its nature the cause rather of decay, since it is the number of change, and change removes what is.

Hence, plainly, things which are always are not, as such, in time, for they are not contained time, nor is their being measured by time. A proof of this is that none of them is affected by time, which indicates that they are not in time.

Since time is the measure of motion, it will be the measure of rest too — indirectly. For all rest is in time. For it does not follow that what is in time is moved, though what is in motion is necessarily moved. For time is not motion, but ‘number of motion’: and what is at rest, also, can be in the number of motion. Not everything that is not in motion can be said to be ‘at rest’ — but only that which can be moved, though it actually is not moved, as was said above.

‘To be in number’ means that there is a number of the thing, and that its being is measured by the number in which it is. Hence if a thing is ‘in time’ it will be measured by time. But time will measure what is moved and what is at rest, the one qua moved, the other qua at rest; for it will measure their motion and rest respectively.

Hence what is moved will not be measurable by the time simply in so far as it has quantity, but in so far as its motion has quantity. Thus none of the things which are neither moved nor at rest are in time: for ‘to be in time’ is ‘to be measured by time’, while time is the measure of motion and rest.

Plainly, then, neither will everything that does not exist be in time, i.e. those non-existent things that cannot exist, as the diagonal cannot be commensurate with the side.

Generally, if time is directly the measure of motion and indirectly of other things, it is clear that a thing whose existence is measured by it will have its existence in rest or motion. Those things therefore which are subject to perishing and becoming — generally, those which at one time exist, at another do not — are necessarily in time: for there is a greater time which will extend both beyond their existence and beyond the time which measures their existence. Of things which do not exist but are contained by time some were, e.g. Homer once was, some will be, e.g. a future event; this depends on the direction in which time contains them; if on both, they have both modes of existence. As to such things as it does not contain in any way, they neither were nor are nor will be. These are those nonexistents whose opposites always are, as the incommensurability of the diagonal always is — and this will not be in time. Nor will the commensurability, therefore; hence this eternally is not, because it is contrary to what eternally is. A thing whose contrary is not eternal can be and not be, and it is of such things that there is coming to be and passing away.
13

The ‘now’ is the link of time, as has been said (for it connects past and future time), and it is a limit of time (for it is the beginning of the one and the end of the other). But this is not obvious as it is with the point, which is fixed⁸⁵. It divides potentially, and in so far as it is dividing the ‘now’ is always different, but in so far as it connects it is always the same, as it is with mathematical lines. For the intellect it is not always one and the same point, since it is other and other when one divides the line; but in so far as it is one, it is the same in every respect.

So the ‘now’ also is in one way a potential dividing of time, in another the termination of both parts, and their unity⁸⁶. And the dividing and the uniting are the same thing and in the same reference, but in essence they are not the same.

So one kind of ‘now’ is described in this way: another is when the time is near this kind of ‘now’. ‘He will come now’ because he will come to-day; ‘he has come now’ because he came to-day. But the things in the Iliad have not happened ‘now’, nor is the flood ‘now’ — not that the time from now to them is not continuous, but because they are not near.

‘At some time’ means a time determined in relation to the first of the two types of ‘now’, e.g. ‘at some time’ Troy was taken, and ‘at some time’ there will be a flood; for it must be determined with reference to the ‘now’. There will thus be a determinate time from this ‘now’ to that, and there was such in reference to the past event. But if there be no time which is not ‘sometime’, every time will be determined.

Will time then fail? Surely not, if motion always exists. Is time then always different or does the same time recur⁸⁷? Clearly time is, in the same way as motion is. For if one and the same motion sometimes recurs⁸⁸, it will be one and the same time, and if not, not.

Since the ‘now’ is an end and a beginning of time, not of the same time however, but the end of that which is past and the beginning of that which is to come, it follows that, as the circle has its convexity and its concavity, in a sense, in the same thing, so time is always at a beginning and at an end. And for this reason it seems to be always different; for the ‘now’ is not the beginning and the end of the same thing; if it were, it would be at the same time and in the same respect two opposites. And time will not fail; for it is always at a beginning.

‘Presently’ or ‘just’ refers to the part of future time which is near the indivisible present ‘now’ (‘When do you walk?’ ‘Presently’, because the time in which he is going to do so is near), and to the part of past time which is not far from the ‘now’ (‘When do you walk?’ ‘I have just been walking’). But to say that Troy has just been taken — we do not say that, because it is too far from the ‘now’. ‘Lately’, too, refers to the part of past time which is near the present ‘now’. ‘When did you go?’ ‘Lately’, if the time is near the existing now. ‘Long ago’ refers to the distant past.

‘Suddenly’ refers to what has departed from its former condition in a time imperceptible because of its smallness; but it is the nature of all change to alter things from their former condition. In time all things come into being and pass away; for which reason some called it the wisest of all things, but the Pythagorean Paron called it the most stupid, because in it we also forget; and his was the truer view. It is clear then that it must be in itself, as we said before, the condition of destruction rather than of coming into being (for change, in itself, makes things depart from their former condition), and only incidentally of coming into being, and of being. A sufficient evidence of this is that nothing comes into being without itself moving somehow and acting⁸⁹, but a thing can be destroyed even if it does not move at all. And this is what, as a rule, we chiefly mean by a thing’s being destroyed by time. Still, time does not work even this change; even this sort of change takes place incidentally in time.

We have stated, then, that time exists and what it is, and in how many senses we speak of the ‘now’, and what ‘at some time’, ‘lately’, ‘presently’ or ‘just’, ‘long ago’, and ‘suddenly’ mean.
14

These distinctions having been drawn, it is evident that every change and everything that moves is in time; for the distinction of faster and slower exists in reference to all change, since it is found in every instance. In the phrase ‘moving faster’ I refer to that which changes before another into the condition in question, when it moves over the same interval and with a regular movement; e.g. in the case of locomotion, if both things move along the circumference⁹⁰ of a circle, or both along a straight line; and similarly in all other cases. But what is before is in time; for we say ‘before’ and ‘after’ with reference to the distance from the ‘now’, and the ‘now’ is the boundary of the past and the future; so that since ‘nows’ are in time, the before and the after will be in time too; for in that in which the ‘now’ is, the distance from the ‘now’ will also be. But ‘before’ is used contrariwise with reference to past and to future time; for in the past we call ‘before’ what is farther from the ‘now’, and ‘after’ what is nearer, but in the future we call the nearer ‘before’ and the farther ‘after’. So that since the ‘before’ is in time, and every movement involves a ‘before’, evidently every change and every movement is in time.

It is also worth considering how time can be related to the soul; and why time is thought to be in everything, both in earth and in sea and in heaven. Is because it is an attribute, or state, or movement (since it is the number of movement) and all these things are movable (for they are all in place), and time and movement are together, both in respect of potentiality and in respect of actuality?

Whether if soul did not exist time would exist or not, is a question that may fairly be asked; for if there cannot be some one to count there cannot be anything that can be counted, so that evidently there cannot be number; for number is either what has been, or what can be, counted. But if nothing but soul, or in soul reason, is qualified⁹¹ to count, there would not be time unless there were soul, but only that of which time is an attribute, i.e. if movement can exist without soul, and the before and after are attributes of movement, and time is these qua numerable.

One might also raise the question what sort of movement time is the number of. Must we not say ‘of any kind’? For things both come into being in time and pass away, and grow, and are altered in time, and are moved locally; thus it is of each movement qua movement that time is the number. And so it is simply the number of continuous movement, not of any particular kind of it.

But other things as well may have been moved now, and there would be a number of each of the two movements. Is there another time, then, and will there be two equal times at once? Surely not. For a time that is both equal and simultaneous is one and the same time, and even those that are not simultaneous are one in kind; for if there were dogs, and horses, and seven of each, it would be the same number. So, too, movements that have simultaneous limits have the same time, yet the one may in fact be fast and the other not, and one may be locomotion and the other alteration⁹²; still the time of the two changes is the same if their number also is equal and simultaneous; and for this reason, while the movements are different and separate, the time is everywhere the same, because the number of equal and simultaneous movements is everywhere one and the same.

Now there is such a thing as locomotion, and in locomotion there is included circular movement, and everything is measured by some one thing homogeneous with it, units by a unit, horses by a horse, and similarly times by some definite time, and, as we said, time is measured by motion as well as motion by time (this being so because by a motion definite in time the quantity both of the motion and of the time is measured): if, then, what is first is the measure of everything homogeneous with it, regular circular motion is above all else the measure, because the number of this is the best known. Now neither alteration nor increase nor coming into being can be regular, but locomotion can be. This also is why time is thought to be the movement of the sphere, viz. because the other movements are measured by this, and time by this movement.

This also explains the common saying that human affairs form a circle, and that there is a circle in all other things that have a natural movement and coming into being and passing away. This is because all other things are discriminated⁹³ by time, and end and begin as though conforming to a cycle; for even time itself is thought to be a circle. And this opinion again is held because time is the measure of this kind of locomotion and is itself measured by such. So that to say that the things that come into being form a circle is to say that there is a circle of time; and this is to say that it is measured by the circular movement; for apart from the measure nothing else to be measured is observed; the whole is just a plurality of measures.

It is said rightly, too, that the number of the sheep and of the dogs is the same number if the two numbers are equal, but not the same decad or the same ten; just as the equilateral and the scalene are not the same triangle, yet they are the same figure, because they are both triangles. For things are called the same so-and-so if they do not differ by a differentia of that thing, but not if they do; e.g. triangle differs from triangle by a differentia of triangle, therefore they are different triangles; but they do not differ by a differentia of figure, but are in one and the same division of it. For a figure of the one kind is a circle and a figure of another kind of triangle, and a triangle of one kind is equilateral and a triangle of another kind scalene. They are the same figure, then, that, triangle, but not the same triangle. Therefore the number of two groups also — is the same number (for their number does not differ by a differentia of number), but it is not the same decad; for the things of which it is asserted differ; one group are dogs, and the other horses.

We have now discussed time — both time itself and the matters appropriate to the consideration of it.

1 physicist   

n.物理学家，研究物理学的人

参考例句：

• He is a physicist of the first rank.他是一流的物理学家。
• The successful physicist never puts on airs.这位卓有成就的物理学家从不摆架子。

2 locomotion   

n.运动，移动

参考例句：

• By land,air or sea,birds are masters of locomotion.无论是通过陆地，飞越空中还是穿过海洋，鸟应算是运动能手了。
• Food sources also elicit oriented locomotion and recognition behavior patterns in most insects.食物源也引诱大多数昆虫定向迁移和识别行为。

3 mutual   

adj.相互的，彼此的；共同的，共有的

参考例句：

• We must pull together for mutual interest.我们必须为相互的利益而通力合作。
• Mutual interests tied us together.相互的利害关系把我们联系在一起。

4 replacement   

n.取代，替换，交换；替代品，代用品

参考例句：

• We are hard put to find a replacement for our assistant.我们很难找到一个人来代替我们的助手。
• They put all the students through the replacement examination.他们让所有的学生参加分班考试。

5 vessel   

n.船舶；容器，器皿；管，导管，血管

参考例句：

• The vessel is fully loaded with cargo for Shanghai.这艘船满载货物驶往上海。
• You should put the water into a vessel.你应该把水装入容器中。

6 formerly   

adv.从前，以前

参考例句：

• We now enjoy these comforts of which formerly we had only heard.我们现在享受到了过去只是听说过的那些舒适条件。
• This boat was formerly used on the rivers of China.这船从前航行在中国内河里。

7 potencies   

n.威力( potency的名词复数 )；权力；效力；（男人的）性交能力

参考例句：

• The soft gelatin liquid filled capsule manufacturing process is the same for all proposed potencies. 软明胶液体填注胶囊的生产工艺对所有提出的效用是一样的。 来自互联网

8 relatively   

adv.比较...地，相对地

参考例句：

• The rabbit is a relatively recent introduction in Australia.兔子是相对较新引入澳大利亚的物种。
• The operation was relatively painless.手术相对来说不痛。

9 bereft   

adj.被剥夺的

参考例句：

• The place seemed to be utterly bereft of human life.这个地方似乎根本没有人烟。
• She was bereft of happiness.她失去了幸福。

10 chaos   

n.混乱，无秩序

参考例句：

• After the failure of electricity supply the city was in chaos.停电后，城市一片混乱。
• The typhoon left chaos behind it.台风后一片混乱。

11 potency   

n. 效力，潜能

参考例句：

• Alcohol increases the drug's potency.酒精能增加这种毒品的效力。
• Sunscreen can lose its potency if left over winter in the bathroom cabinet.如果把防晒霜在盥洗室的壁橱里放一个冬天，就有可能失效。

12 annihilated   

v.（彻底）消灭( annihilate的过去式和过去分词 )；使无效；废止；彻底击溃

参考例句：

• Our soldiers annihilated a force of three hundred enemy troops. 我军战士消灭了300名敌军。 来自《现代汉英综合大词典》
• We annihilated the enemy. 我们歼灭了敌人。 来自《简明英汉词典》

13 entity   

n.实体，独立存在体，实际存在物

参考例句：

• The country is no longer one political entity.这个国家不再是一个统一的政治实体了。
• As a separate legal entity,the corporation must pay taxes.作为一个独立的法律实体，公司必须纳税。

14 corporeal   

adj.肉体的，身体的；物质的

参考例句：

• The body is the corporeal habitation of the soul.身体为灵魂之有形寓所。
• He is very religious;corporeal world has little interest for him.他虔信宗教，对物质上的享受不感兴趣。

15 incorporeal   

adj.非物质的，精神的

参考例句：

• The real life is guided by our incorporeal intellection.我想，这表示我们无形的思想导引着真实的人生。
• They seemed to have the power to touch the incorporeal and see the invisible.他们似乎有一种力量能触摸到无形的和看到不可见的东西。

16 intelligible   

adj.可理解的，明白易懂的，清楚的

参考例句：

• This report would be intelligible only to an expert in computing.只有计算机运算专家才能看懂这份报告。
• His argument was barely intelligible.他的论点不易理解。

17 scrutiny   

n.详细检查，仔细观察

参考例句：

• His work looks all right,but it will not bear scrutiny.他的工作似乎很好，但是经不起仔细检查。
• Few wives in their forties can weather such a scrutiny.很少年过四十的妻子经得起这么仔细的观察。

18 pointed   

adj.尖的，直截了当的

参考例句：

• He gave me a very sharp pointed pencil.他给我一支削得非常尖的铅笔。
• She wished to show Mrs.John Dashwood by this pointed invitation to her brother.她想通过对达茨伍德夫人提出直截了当的邀请向她的哥哥表示出来。

19 motive   

n.动机，目的；adv.发动的，运动的

参考例句：

• The police could not find a motive for the murder.警察不能找到谋杀的动机。
• He had some motive in telling this fable.他讲这寓言故事是有用意的。

20 whit   

n.一点，丝毫

参考例句：

• There's not a whit of truth in the statement.这声明里没有丝毫的真实性。
• He did not seem a whit concerned.他看来毫不在乎。

21 faculty   

n.才能；学院，系；(学院或系的)全体教学人员

参考例句：

• He has a great faculty for learning foreign languages.他有学习外语的天赋。
• He has the faculty of saying the right thing at the right time.他有在恰当的时候说恰当的话的才智。

22 virtue   

n.德行，美德；贞操；优点；功效，效力

参考例句：

• He was considered to be a paragon of virtue.他被认为是品德尽善尽美的典范。
• You need to decorate your mind with virtue.你应该用德行美化心灵。

23 distinguished   

adj.卓越的，杰出的，著名的

参考例句：

• Elephants are distinguished from other animals by their long noses.大象以其长长的鼻子显示出与其他动物的不同。
• A banquet was given in honor of the distinguished guests.宴会是为了向贵宾们致敬而举行的。

24 elucidated   

v.阐明，解释( elucidate的过去式和过去分词 )

参考例句：

• He elucidated a point of grammar. 他解释了一个语法要点。
• The scientist elucidated his theory by three simple demonstrations. 这位科学家以三个简单的实例来说明他的理论。 来自《简明英汉词典》

25 essentially   

adv.本质上，实质上，基本上

参考例句：

• Really great men are essentially modest.真正的伟人大都很谦虚。
• She is an essentially selfish person.她本质上是个自私自利的人。

26 immediate   

adj.立即的；直接的，最接近的；紧靠的

参考例句：

• His immediate neighbours felt it their duty to call.他的近邻认为他们有责任去拜访。
• We declared ourselves for the immediate convocation of the meeting.我们主张立即召开这个会议。

27 investigation   

n.调查，调查研究

参考例句：

• In an investigation,a new fact became known, which told against him.在调查中新发现了一件对他不利的事实。
• He drew the conclusion by building on his own investigation.他根据自己的调查研究作出结论。

28 diminution   

n.减少；变小

参考例句：

• They hope for a small diminution in taxes.他们希望捐税能稍有减少。
• He experienced no diminution of his physical strength.他并未感觉体力衰落。

29 extremities   

n.端点( extremity的名词复数 )；尽头；手和足；极窘迫的境地

参考例句：

• She was most noticeable, I thought, in respect of her extremities. 我觉得她那副穷极可怜的样子实在太惹人注目。 来自辞典例句
• Winters may be quite cool at the northwestern extremities. 西北边区的冬天也可能会相当凉。 来自辞典例句

30 remains   

n.剩余物，残留物；遗体，遗迹

参考例句：

• He ate the remains of food hungrily.他狼吞虎咽地吃剩余的食物。
• The remains of the meal were fed to the dog.残羹剩饭喂狗了。

31 infinity   

n.无限，无穷，大量

参考例句：

• It is impossible to count up to infinity.不可能数到无穷大。
• Theoretically,a line can extend into infinity.从理论上来说直线可以无限地延伸。

32 previously   

adv.以前，先前（地）

参考例句：

• The bicycle tyre blew out at a previously damaged point.自行车胎在以前损坏过的地方又爆开了。
• Let me digress for a moment and explain what had happened previously.让我岔开一会儿，解释原先发生了什么。

33 displacement   

n.移置，取代，位移，排水量

参考例句：

• They said that time is the feeling of spatial displacement.他们说时间是空间位移的感觉。
• The displacement of all my energy into caring for the baby.我所有精力都放在了照顾宝宝上。

34 stationary   

adj.固定的，静止不动的

参考例句：

• A stationary object is easy to be aimed at.一个静止不动的物体是容易瞄准的。
• Wait until the bus is stationary before you get off.你要等公共汽车停稳了再下车。

35 interval   

n.间隔，间距；幕间休息，中场休息

参考例句：

• The interval between the two trees measures 40 feet.这两棵树的间隔是40英尺。
• There was a long interval before he anwsered the telephone.隔了好久他才回了电话。

36 outermost   

adj.最外面的，远离中心的

参考例句：

• He fired and hit the outermost ring of the target.他开枪射中了靶子的最外一环。
• The outermost electron is shielded from the nucleus.原子核对最外层电子的作用受到屏蔽。

37 simultaneously   

adv.同时发生地，同时进行地

参考例句：

• The radar beam can track a number of targets almost simultaneously.雷达波几乎可以同时追着多个目标。
• The Windows allow a computer user to execute multiple programs simultaneously.Windows允许计算机用户同时运行多个程序。

38 condensation   

n.压缩，浓缩；凝结的水珠

参考例句：

• A cloud is a condensation of water vapour in the atmosphere.云是由大气中的水蒸气凝结成的。
• He used his sleeve to wipe the condensation off the glass.他用袖子擦掉玻璃上凝结的水珠。

39 indirectly   

adv.间接地，不直接了当地

参考例句：

• I heard the news indirectly.这消息我是间接听来的。
• They were approached indirectly through an intermediary.通过一位中间人，他们进行了间接接触。

40 orb   

n.太阳；星球；v.弄圆；成球形

参考例句：

• The blue heaven,holding its one golden orb,poured down a crystal wash of warm light.蓝蓝的天空托着金色的太阳，洒下一片水晶般明亮温暖的光辉。
• It is an emanation from the distant orb of immortal light.它是从远处那个发出不灭之光的天体上放射出来的。

41 akin   

adj.同族的，类似的

参考例句：

• She painted flowers and birds pictures akin to those of earlier feminine painters.她画一些同早期女画家类似的花鸟画。
• Listening to his life story is akin to reading a good adventure novel.听他的人生故事犹如阅读一本精彩的冒险小说。

42 drawn   

v.拖，拉，拔出；adj.憔悴的，紧张的

参考例句：

• All the characters in the story are drawn from life.故事中的所有人物都取材于生活。
• Her gaze was drawn irresistibly to the scene outside.她的目光禁不住被外面的风景所吸引。

43 inquiry   

n.打听，询问，调查，查问

参考例句：

• Many parents have been pressing for an inquiry into the problem.许多家长迫切要求调查这个问题。
• The field of inquiry has narrowed down to five persons.调查的范围已经缩小到只剩5个人了。

44 demonstration   

n.表明，示范，论证，示威

参考例句：

• His new book is a demonstration of his patriotism.他写的新书是他的爱国精神的证明。
• He gave a demonstration of the new technique then and there.他当场表演了这种新的操作方法。

45 physicists   

物理学家( physicist的名词复数 )

参考例句：

• For many particle physicists, however, it was a year of frustration. 对于许多粒子物理学家来说，这是受挫折的一年。 来自英汉非文学 - 科技
• Physicists seek rules or patterns to provide a framework. 物理学家寻求用法则或图式来构成一个框架。

46 decanted   

v.将（酒等）自瓶中倒入另一容器( decant的过去式和过去分词 )

参考例句：

• Afterwards the aqueous solution from above the nitroglycerine was decanted. 然后倒出硝化甘油之上的水溶液。 来自辞典例句
• The coated particles are centrifuged and the liquid decanted. 将包覆的颗粒进行离心，除去液体。 来自辞典例句

47 inhales   

v.吸入( inhale的第三人称单数 )

参考例句：

• Long, slow, full breaths with exhales at least as long as the inhales. 深长、缓慢、充分的呼吸，呼气至少要同吸气一样长。 来自互联网
• An impressive pile forms. Heywood bends down and inhales deeply, smelling the aroma. Rapture. 一小排香烟。海沃德低下头使劲地闻着香烟的气味，高兴不已。 来自互联网

48 tangible   

adj.有形的，可触摸的，确凿的，实际的

参考例句：

• The policy has not yet brought any tangible benefits.这项政策还没有带来任何实质性的好处。
• There is no tangible proof.没有确凿的证据。

49 syllogism   

n.演绎法，三段论法

参考例句：

• The ramifications or the mystery of a syllogism can become a weariness and a bore.三段论证法的分歧或者神秘会变成一种无聊、一种麻烦。
• The unexpected bursts forth from the syllogism.三段论里常出岔子。

50 determined   

adj.坚定的；有决心的

参考例句：

• I have determined on going to Tibet after graduation.我已决定毕业后去西藏。
• He determined to view the rooms behind the office.他决定查看一下办公室后面的房间。

51 qualitative   

adj.性质上的，质的，定性的

参考例句：

• There are qualitative differences in the way children and adults think.孩子和成年人的思维方式有质的不同。
• Arms races have a quantitative and a qualitative aspects.军备竞赛具有数量和质量两个方面。

52 rotation   

n.旋转；循环，轮流

参考例句：

• Crop rotation helps prevent soil erosion.农作物轮作有助于防止水土流失。
• The workers in this workshop do day and night shifts in weekly rotation.这个车间的工人上白班和上夜班每周轮换一次。

53 compulsory   

n.强制的，必修的；规定的，义务的

参考例句：

• Is English a compulsory subject?英语是必修课吗？
• Compulsory schooling ends at sixteen.义务教育至16岁为止。

54 differentiated   

区分，区别，辨别( differentiate的过去式和过去分词 )； 区别对待； 表明…间的差别，构成…间差别的特征

参考例句：

• The development of mouse kidney tubules requires two kinds of differentiated cells. 小鼠肾小管的发育需要有两种分化的细胞。
• In this enlargement, barley, alfalfa, and sugar beets can be differentiated. 在这张放大的照片上，大麦，苜蓿和甜菜都能被区分开。

55 touching   

adj.动人的，使人感伤的

参考例句：

• It was a touching sight.这是一幅动人的景象。
• His letter was touching.他的信很感人。

56 projectile   

n.投射物，发射体；adj.向前开进的；推进的；抛掷的

参考例句：

• The vertical and horizontal motions of a projectile can be treated independently.抛射体的竖直方向和水平方向的运动能够分开来处理。
• Have you altered the plans of the projectile as the telegram suggests?你已经按照电报的要求修改炮弹图样了吗?

57 impedes   

阻碍，妨碍，阻止( impede的第三人称单数 )

参考例句：

• High packing density greatly impedes the cooling of the array. 高存贮密度很不利于阵列的散热。
• The inflexibility of the country's labor market seriously impedes its economic recovery. 该国劳工市场缺乏灵活性，这严重阻碍了它的经济恢复。

58 dense   

a.密集的，稠密的，浓密的；密度大的

参考例句：

• The general ambushed his troops in the dense woods. 将军把部队埋伏在浓密的树林里。
• The path was completely covered by the dense foliage. 小路被树叶厚厚地盖了一层。

59 density   

n.密集，密度，浓度

参考例句：

• The population density of that country is 685 per square mile.那个国家的人口密度为每平方英里685人。
• The region has a very high population density.该地区的人口密度很高。

60 resistant   

adj.(to)抵抗的，有抵抗力的

参考例句：

• Many pests are resistant to the insecticide.许多害虫对这种杀虫剂有抵抗力。
• They imposed their government by force on the resistant population.他们以武力把自己的统治强加在持反抗态度的人民头上。

61 inverse   

adj.相反的，倒转的，反转的；n.相反之物；v.倒转

参考例句：

• Evil is the inverse of good.恶是善的反面。
• When the direct approach failed he tried the inverse.当直接方法失败时，他尝试相反的做法。

62 cleaves   

v.劈开，剁开，割开( cleave的第三人称单数 )

参考例句：

• This wood cleaves easily. 这木材好劈。 来自《现代英汉综合大词典》
• The water cleaves the banks away like a knife. 河水象一把刀似的，把两岸削掉。 来自辞典例句

63 velocity   

n.速度，速率

参考例句：

• Einstein's theory links energy with mass and velocity of light.爱因斯坦的理论把能量同质量和光速联系起来。
• The velocity of light is about 300000 kilometres per second.光速约为每秒300000公里。

64 vacuous   

adj.空的，漫散的，无聊的，愚蠢的

参考例句：

• Male models are not always so vacuous as they are made out to be.男模特儿并不总像人们说的那样愚蠢。
• His eyes looked dull,almost vacuous.他看上去目光呆滞，茫然若失。

65 downwards   

adj./adv.向下的（地），下行的（地）

参考例句：

• He lay face downwards on his bed.他脸向下伏在床上。
• As the river flows downwards,it widens.这条河愈到下游愈宽。

66 penetrated   

adj. 击穿的，鞭辟入里的 动词penetrate的过去式和过去分词形式

参考例句：

• The knife had penetrated his chest. 刀子刺入了他的胸膛。
• They penetrated into territory where no man had ever gone before. 他们已进入先前没人去过的地区。

67 possessed   

adj.疯狂的；拥有的，占有的

参考例句：

• He flew out of the room like a man possessed.他像着了魔似地猛然冲出房门。
• He behaved like someone possessed.他行为举止像是魔怔了。

68 bulge   

n.突出，膨胀，激增；vt.突出，膨胀

参考例句：

• The apple made a bulge in his pocket.苹果把他口袋塞得鼓了起来。
• What's that awkward bulge in your pocket?你口袋里那块鼓鼓囊囊的东西是什么？

69 upwards   

adv.向上，在更高处...以上

参考例句：

• The trend of prices is still upwards.物价的趋向是仍在上涨。
• The smoke rose straight upwards.烟一直向上升。

70 incapable   

adj.无能力的，不能做某事的

参考例句：

• He would be incapable of committing such a cruel deed.他不会做出这么残忍的事。
• Computers are incapable of creative thought.计算机不会创造性地思维。

71 transformation   

n.变化；改造；转变

参考例句：

• Going to college brought about a dramatic transformation in her outlook.上大学使她的观念发生了巨大的变化。
• He was struggling to make the transformation from single man to responsible husband.他正在努力使自己由单身汉变为可靠的丈夫。

72 outwards   

adj.外面的，公开的，向外的；adv.向外；n.外形

参考例句：

• Does this door open inwards or outwards?这门朝里开还是朝外开？
• In lapping up a fur,they always put the inner side outwards.卷毛皮时，他们总是让内层朝外。

73 contraction   

n.缩略词，缩写式，害病

参考例句：

• The contraction of this muscle raises the lower arm.肌肉的收缩使前臂抬起。
• The forces of expansion are balanced by forces of contraction.扩张力和收缩力相互平衡。

74 secondly   

adv.第二，其次

参考例句：

• Secondly,use your own head and present your point of view.第二，动脑筋提出自己的见解。
• Secondly it is necessary to define the applied load.其次，需要确定所作用的载荷。

75 naive   

adj.幼稚的，轻信的；天真的

参考例句：

• It's naive of you to believe he'll do what he says.相信他会言行一致，你未免太单纯了。
• Don't be naive.The matter is not so simple.你别傻乎乎的。事情没有那么简单。

76 lapse   

n.过失，流逝，失效，抛弃信仰，间隔；vi.堕落，停止，失效，流逝；vt.使失效

参考例句：

• The incident was being seen as a serious security lapse.这一事故被看作是一次严重的安全疏忽。
• I had a lapse of memory.我记错了。

77 fabled   

adj.寓言中的，虚构的

参考例句：

• For the first week he never actually saw the fabled Jack. 第一周他实际上从没见到传说中的杰克。
• Aphrodite, the Greek goddness of love, is fabled to have been born of the foam of the sea. 希腊爱神阿美罗狄蒂据说是诞生于海浪泡沫之中。 来自《现代汉英综合大词典》

78 awakened   

v.（使）醒( awaken的过去式和过去分词 )；（使）觉醒；弄醒；（使）意识到

参考例句：

• She awakened to the sound of birds singing. 她醒来听到鸟的叫声。
• The public has been awakened to the full horror of the situation. 公众完全意识到了这一状况的可怕程度。 来自《简明英汉词典》

79 affected   

adj.不自然的，假装的

参考例句：

• She showed an affected interest in our subject.她假装对我们的课题感到兴趣。
• His manners are affected.他的态度不自然。

80 apprehend   

vt.理解，领悟，逮捕，拘捕，忧虑

参考例句：

• I apprehend no worsening of the situation.我不担心局势会恶化。
• Police have not apprehended her killer.警察还未抓获谋杀她的凶手。

81 enumeration   

n.计数，列举；细目；详表；点查

参考例句：

• Predictive Categoriesinclude six categories of prediction, namely Enumeration, Advance Labeling, Reporting,Recapitulation, Hypotheticality, and Question. 其中预设种类又包括列举(Enumeration)、提前标示(Advance Labeling)、转述(Reporting)、回顾(Recapitulation)、假设(Hypotheticality)和提问(Question)。 来自互联网
• Here we describe a systematic procedure which is basically "enumeration" in nature. 这里介绍一个本质上是属于“枚举法”的系统程序。 来自辞典例句

82 discriminate   

v.区别，辨别，区分；有区别地对待

参考例句：

• You must learn to discriminate between facts and opinions.你必须学会把事实和看法区分出来。
• They can discriminate hundreds of colours.他们能分辨上百种颜色。

83 countable   

adj.可数的，可以计算的

参考例句：

• The word "person" is a countable noun.person这个词是个可数名词。
• Countable nouns have singular and plural forms.可数名词有单数和复数之分。

84 vice   

n.坏事；恶习；[pl.]台钳，老虎钳；adj.副的

参考例句：

• He guarded himself against vice.他避免染上坏习惯。
• They are sunk in the depth of vice.他们堕入了罪恶的深渊。

85 fixed   

adj.固定的，不变的，准备好的；(计算机)固定的

参考例句：

• Have you two fixed on a date for the wedding yet?你们俩选定婚期了吗？
• Once the aim is fixed,we should not change it arbitrarily.目标一旦确定，我们就不应该随意改变。

86 unity   

n.团结，联合，统一；和睦，协调

参考例句：

• When we speak of unity,we do not mean unprincipled peace.所谓团结，并非一团和气。
• We must strengthen our unity in the face of powerful enemies.大敌当前，我们必须加强团结。

87 recur   

vi.复发，重现，再发生

参考例句：

• Economic crises recur periodically.经济危机周期性地发生。
• Of course,many problems recur at various periods.当然，有许多问题会在不同的时期反复提出。

88 recurs   

再发生，复发( recur的第三人称单数 )

参考例句：

• This theme recurs several times throughout the book. 这一主题在整部书里出现了好几次。
• Leap year recurs every four years. 每四年闰年一次。

89 acting   

n.演戏，行为，假装；adj.代理的，临时的，演出用的

参考例句：

• Ignore her,she's just acting.别理她，她只是假装的。
• During the seventies,her acting career was in eclipse.在七十年代，她的表演生涯黯然失色。

90 circumference   

n.圆周，周长，圆周线

参考例句：

• It's a mile round the circumference of the field.运动场周长一英里。
• The diameter and the circumference of a circle correlate.圆的直径与圆周有相互关系。

91 qualified   

adj.合格的，有资格的，胜任的，有限制的

参考例句：

• He is qualified as a complete man of letters.他有资格当真正的文学家。
• We must note that we still lack qualified specialists.我们必须看到我们还缺乏有资质的专家。

92 alteration   

n.变更，改变；蚀变

参考例句：

• The shirt needs alteration.这件衬衣需要改一改。
• He easily perceived there was an alteration in my countenance.他立刻看出我的脸色和往常有些不同。

93 discriminated   

分别，辨别，区分( discriminate的过去式和过去分词 )； 歧视，有差别地对待

参考例句：

• His great size discriminated him from his followers. 他的宽广身材使他不同于他的部下。
• Should be a person that has second liver virus discriminated against? 一个患有乙肝病毒的人是不是就应该被人歧视？