The Truth

Final example to demonstrate the utility of this work. In this example, we seek the physical cause of the hardness or the cohesion of the parts of bodies with one another.

Bodies are united together in 3 ways:

1. continuity
2. contiguity
3. union

By continuity, or by the cause of continuity, I mean that certain “je ne sais quoi” that I endeavor to discover, which causes the parts of a body to cling so tightly to one another that effort is required to separate them, and which makes them be regarded as forming a single whole.

By contiguity, I mean that certain “je ne sais quoi” which leads me to judge that two bodies touch immediately, so that there is nothing between them, but which I do not judge to be strictly united, because I can easily separate them.

By this third term, union, I mean yet another “je ne sais quoi” which causes two panes of glass or two pieces of marble, whose surfaces have been ground and polished by rubbing them against each other, to adhere in such a way that, although they can be very easily separated by sliding them, one nonetheless experiences some difficulty in doing so in another direction. Now this is not continuity, since these two panes of glass or these two pieces of marble, being united in this manner, are not conceived as forming a single whole, because they can be separated in one direction with great ease. Nor is it simply contiguity, although it comes very close to it, because these two parts of glass or marble are quite closely united, and indeed much more so than the parts of soft and liquid bodies, such as those of butter and water.

These terms being thus explained, we must now seek the cause that unites bodies and the differences found between the continuity, contiguity, and union of bodies, according to the sense I have determined. I shall first seek the cause of continuity, or what is that certain “je ne sais quoi” which causes the parts of a body to cling so tightly to one another that effort is required to separate them, and that they are regarded as forming a single whole. I hope that once this cause is found, there will be no great difficulty in discovering the rest.

That “je ne sais quoi” which binds even the smallest parts of this piece of iron I hold in my hands to be something very powerful, since I must make a very great effort to break off a small part of it.

But am I not mistaken? Could it not be that this difficulty I find in breaking the smallest piece of iron comes from my weakness and not from the resistance of this iron: for I remember that I once made more effort than I do now to break a piece of iron similar to the one I am holding; and if I were to fall ill, it might happen that even with very great efforts I could not succeed. I see clearly that I must not absolutely judge the firmness with which the parts of iron are joined together by the efforts I make to separate them. I must only judge that they cling very tightly to one another in relation to my own lack of strength; or that they cling more tightly than the parts of my flesh, since the feelings of pain I experience when making too much effort warn me that I will separate the parts of my body before those of the iron. I therefore recognize that, just as I am not absolutely strong or weak, iron or other bodies are not absolutely hard or flexible, but only in relation to the cause that acts against them; and that the efforts I make cannot serve as a rule to measure the magnitude of the force required to overcome the resistance and hardness of iron. For rules must be invariable, and these efforts vary according to the times, according to the abundance of animal spirits and the hardness of the flesh, since I cannot always produce the same effects by making the same efforts.

This reflection delivers me from a prejudice I had, which made me imagine strong bonds to unite the parts of bodies; which bonds perhaps do not exist; and I hope it will not be useless to me in the future, for I have a strange tendency to judge everything in relation to myself and to follow the impressions of my senses, to which I shall pay closer heed. But let us continue. After having thought for some time and sought with some application the cause of this close union without being able to discover anything, I feel myself carried by my negligence and by my nature to judge, like many others, that it is the form of bodies that preserves the union between their parts, or the friendship and inclination they have for their like, for there is nothing more convenient than to let oneself be seduced sometimes and thus become learned all at once at little cost.

But since I wish to believe nothing that I do not know, I must not let myself be thus overcome by my own laziness, nor yield to mere glimmers. Let us then abandon these forms and inclinations of which we have no distinct and particular ideas, but only confused and general ones which we seem to form only in relation to our nature, and of the very existence of which many people and perhaps entire nations do not agree. It seems to me that I see the cause of this close union of the parts that compose hard bodies without admitting anything other than what everyone agrees is there, or at least what the world distinctly conceives can be there. For everyone distinctly knows that all bodies are composed or can be composed of small parts. Thus, it may be that there are some that are hooked and branched, and like small bonds capable of firmly arresting the others, or that they all interlace in their branches, so that they cannot be easily separated.

I have a great inclination to yield to this thought, and all the greater because I see that the visible parts of gross bodies stop and unite with one another in this manner. But I cannot distrust too much the preconceptions and impressions of my senses. I must therefore examine the matter still more closely, and even seek the reason why the smallest and ultimate solid parts of bodies, in short, the very parts of each of these bonds, hold together, for they cannot be united by other even smaller bonds since I suppose them to be solid. Or if I say they are united in this way, I will rightly be asked who will unite these others, and so on to infinity.

So that now the crux of the question is to know how the parts of these small bonds or of these branched parts can be as closely united together as they are, A for example with B, which I suppose to be parts of a small bond.

Or, which is the same thing, bodies being all the harder as they are more solid and have fewer pores, the question now is to know how the parts of a column composed of a matter that would have no pores can be firmly joined together and compose a very hard body, for one cannot say that the parts of this column hold together by small bonds, since, being supposed without pores, they have no particular figure. I feel again extremely inclined to say that this column is hard by its nature, or that the small bonds of which hard bodies are composed are atoms whose parts cannot be divided as being the essential and ultimate parts of bodies, and which are essentially hooked or branched, or of an entangled figure.

But I frankly recognize that this is not explaining the difficulty and that, quitting the preconceptions and illusions of my senses, I would be wrong to resort to an abstract form and embrace a phantom of logic for the cause I seek; I mean that I would be wrong to conceive as something real and distinct the vague idea of nature or essence which expresses only what is known, and to thus take an abstract and universal form as a physical cause of a very real effect. For there are two things of which I cannot distrust too much. The first is the impression of my senses, and the other is the facility I have to take abstract natures and general ideas of logic for those that are real and particular, and I remember having been several times deceived by these two principles of error.

For, to return to the difficulty, it is not possible for me to conceive how these small bonds would be indivisible by their essence and by their nature, nor consequently how they would be inflexible, since on the contrary I conceive them to be very divisible and necessarily divisible by their essence and by their nature. For the part A is very certainly a substance as well as B, and consequently it is clear that A can exist without B or separated from B, since substances can exist without one another, because otherwise they would not be substances. To say that A is not a substance is impossible; for I can conceive it without thinking of B, and everything that can be conceived alone is not a mode, since only modes or manners of being cannot be conceived alone or without the beings of which they are the modes. Therefore A not being a mode, it is a substance, since every being is necessarily either a substance or a manner of being. For finally, everything that is can be conceived alone or cannot; there is no middle ground in contradictory propositions, and that is called being or substance which can be conceived and consequently created alone. The part A can therefore exist without the part B, and all the more reason it can exist separately from B. So that this bond is divisible into A and into B.

Moreover, if this bond were indivisible or hooked by its nature and by its essence, the exact opposite of what we see by experience would happen, for no body could be broken. Let us suppose, as before, that a piece of iron is composed of an infinity of small bonds which interlace with one another, of which A, a, and B, b, are two. I say that they could not be unhooked, and consequently that this iron could not be broken; for to break it, one would have to bend the bonds that compose it, which however are supposed to be inflexible by their essence and by their nature.

If they are not supposed inflexible, but only indivisible by their nature, the supposition will serve nothing to resolve the question; for then the difficulty will be to know whence it comes that these small bonds do not yield to the effort made to bend an iron bar.

However, if they are not supposed inflexible, they should not be supposed indivisible; for if the parts of these bonds could change their situation with respect to one another, it is visible that they could separate, since there is no reason why if one part can move away a little from the other, it could not do so entirely. So whether one supposes these small bonds inflexible, or whether one supposes them indivisible, one cannot by this means resolve the question; for if one only supposes them indivisible, one must easily break a piece of iron; and if one supposes them inflexible, it will be impossible to break it; since the small bonds that compose the iron being entangled with one another, it will be impossible to unhook them. Let us therefore try to resolve the difficulty by clear and incontestable principles and to find the reason why this small bond has these two parts, A, B, so firmly attached to one another.

I see well that it is necessary for me to divide the subject of my meditation into parts, so that I may examine it more exactly and with less strain of mind, since I could not at first, by a single glance and with all the attention of which I am capable, discover what I was seeking. And this is what I could have done from the beginning, for when the subjects one considers are somewhat hidden, it is always best to examine them only in parts, and not to tire oneself uselessly on false hopes of meeting with success.

What I seek is the cause of the close union found between the small parts that compose the small bond A, B. Now, there are only three things that I distinctly conceive can be the cause I seek, namely: the very parts of this small bond, or the will of the author of nature, or finally the invisible bodies that surround these small bonds. I could also bring forward as the cause of these things the form of bodies, the qualities of hardness, or some occult quality, the sympathy that would be between parts of the same kind, etc. But because I have no distinct idea of these fine things, I must not and cannot base my reasonings on them; so that, if I do not find the cause I seek in the things of which I have distinct ideas, I will not trouble myself uselessly with the contemplation of these vague and general ideas of logic, and I will cease to want to speak of what I do not understand. But let us examine the first of these things that can be the cause of the parts of this small bond being so firmly attached, namely the small parts of which it is composed. When I consider only the parts of which hard bodies are composed, I feel inclined to believe that one cannot imagine any cement that unites the parts of this bond, other than themselves and their own rest; for of what nature could it be? It will not be a thing that subsists of itself; for all these small parts being substances, for what reason would they be united by other substances rather than by themselves? Nor will it be a quality different from rest, because there is no quality more contrary to the motion that could separate these parts than the rest which is in them; but besides substances and their qualities, we do not know that there are any other genres of things.

It is true indeed that the parts of hard bodies remain united, as long as they are at rest next to one another; and that once they are at rest, they continue of themselves to remain so as much as possible. But this is not what I seek, I am on the wrong track. I am not seeking whence it comes that the parts of hard bodies are at rest next to one another: I am trying here to discover whence it comes that the parts of these bodies have force to remain at rest next to one another, and that they resist the effort made to move or separate them.

I could however answer myself that each body truly has force to continue to remain in the state in which it is, and that this force is equal for motion and for rest; but that what causes the parts of hard bodies to remain at rest next to one another, and that one has difficulty separating and agitating them, is that not enough motion is employed to overcome their rest. This is plausible, but I seek certainty, if it can be found, and not mere plausibility. And how can I know with certainty and with evidence that each body has this force to remain in the state it is in, and that this force is equal for motion and for rest, since matter appears on the contrary indifferent to motion and to rest, and absolutely without any force? Let us then come, as M. Descartes did, to the will of the Creator, which is perhaps the force that bodies seem to have within themselves. It is the second thing we said before could conserve the parts of this small bond of which we were speaking, so firmly attached to one another.

Certainly it may happen that God wills that each body remain in the state in which it is, and that His will is the force that unites its parts to one another; just as I know otherwise that it is His will that is the moving force, which puts bodies into motion. For, since matter cannot move itself, it seems to me that I must judge that it is a mind, and indeed that it is the author of nature who preserves it and puts it in motion, by conserving it successively in several places by His simple will, since an infinitely powerful being does not act with instruments, and effects necessarily follow from His will.

I therefore recognize that it may happen that God wills that each thing remain in the state in which it is, whether it is at rest or in motion; and that this will is the natural power that bodies have to remain in the state in which they have once been placed. If this is so, it will be necessary, as M. Descartes did, to measure this power, conclude what its effects must be, and thus give rules of the force and communication of motions in the encounter of different bodies, by the proportion of the magnitude found between these bodies; since we have no other means of entering into the knowledge of this general and immutable will of God, which makes the different power that bodies have to act and to resist one another, than their different magnitude and their different speed. However, I have no certain proof that God wills, by a positive will, that bodies remain at rest; and it seems to suffice that God wills that there be matter, so that not only does it exist, but also that it exists at rest.

It is not the same with motion, because the idea of moved matter certainly involves two powers or efficacies, to which it has reference, namely, the one that created it and moreover the one that agitated it. But the idea of matter at rest involves only the idea of the power that created it, without there being need for another power to put it at rest; since if one simply conceives matter without thinking of any power, one will necessarily conceive it at rest. This is how I conceive things, I must judge them according to my ideas; and, according to my ideas, rest is only the privation of motion: I mean that the supposed force that makes rest is only the privation of that which makes motion; for it suffices, it seems to me, that God ceases to will that a body be moved, in order for it to cease to be so, and to be at rest. Indeed, reason and a thousand thousand experiences teach me that if of two bodies equal in mass, one moves with a degree of speed and the other with half a degree, the force of the first will be double that of the second. If the speed of the second is only a quarter, a hundredth, a millionth of that of the first; the second will have only a quarter, a hundredth, a millionth part of the force of the first. Whence it is easy to conclude that if the speed of the second is infinitely small, or finally null, as in rest, the force of the second will be infinitely small, or finally null, if it is at rest. Thus, it appears evident to me that rest has no force to resist that of motion.

But I remember having heard several very enlightened persons say that it seemed to them that motion was just as much the privation of rest, as rest the privation of motion. Someone even assured, by reasons I could not understand, that it was more probable that motion was a privation than rest. I do not distinctly remember the reasons they brought forward, but this must make me fear that my ideas are false. For although most men say whatever pleases them, on matters that seem of little importance, nevertheless I have reason to believe that the persons of whom I speak took pleasure in saying what they conceived. I must therefore examine my ideas again with care.

It is a thing that appears to me indubitable, and these gentlemen of whom I speak agreed on it, namely that it is the will of God that moves bodies. The force therefore that this ball I see rolling has, is the will of God that makes it roll; what must God now do to stop it? Must He will by a positive will that it be at rest, or does it suffice that He ceases to will that it be agitated? It is evident that if God only ceases to will that this ball be agitated, the cessation of this will of God will cause the cessation of the motion of the ball, and consequently rest. For the will of God, which was the force that moved the ball, no longer being, this force will no longer be, the ball will therefore no longer be moved. Thus the cessation of the force of motion causes rest. Rest therefore has no force that causes it. It is therefore only a pure privation which supposes no positive will in God. Thus it would be admitting in God a positive will without reason and without necessity, to give bodies some force to remain at rest.

But let us overturn, if possible, this argument. Let us now suppose a ball at rest, whereas we supposed it in motion; what must God do to agitate it? Does it suffice that He ceases to will that it be at rest? If this is so, I have advanced nothing yet; for motion will be just as much the privation of rest, as rest the privation of motion. I suppose then that God ceases to will that it be at rest. But, this being supposed, I do not see that the ball moves; and, if there are some who conceive that it moves, I beg them to tell me in what direction, and according to what degree of motion it is moved. Certainly, it is impossible that it be moved and that it have no determination and no degree of motion; and from the very fact that one conceives that God ceases to will that it be at rest, it is impossible to conceive that it goes with some degree of motion, because it is not the same with motion as with rest. Motions are of an infinity of ways, they are capable of more and less; but rest being nothing, they cannot differ from one another. The same ball, which goes twice as fast in one time as in another, has twice as much force or motion in one time as in another; but one cannot say that the same ball has twice as much rest in one time as in another.

There must therefore be in God a positive will to put a ball in motion, or to make a ball have such force to move, and it suffices that He ceases to will that it be moved in order for it to move no more, that is to say, in order for it to be at rest. Just as in order for God to create a world, it does not suffice that He ceases to will that it not be, but it is necessary that He positively will the manner in which it must be. But to annihilate it, God does not need to will that it not be, because God cannot will nothingness by a positive will, it suffices only that God ceases to will that it be.

I do not consider here motion and rest according to their relative being; for it is visible that bodies at rest have as real relations to those that surround them as those that are in motion. I only conceive that bodies in motion have a moving force, and that those at rest have no force for their rest; because, the relation of moved bodies to those that surround them always changing, a continual force is required to produce these continual changes, for indeed it is these changes that cause everything new that happens in nature. But no force is needed to do nothing. When the relation of a body to those that surround it is always the same, nothing happens; and the conservation of this relation, I mean the action of the will of God that conserves this relation, is not different from that which conserves the body itself.

If it is true, as I conceive, that rest is only the privation of motion, the least motion, I mean that of the smallest body agitated, will contain more force and power than the rest of the greatest body. Thus the least effort or the smallest body that one will conceive agitated in the void against a very large and vast body, will be capable of moving it somewhat, since this large body being at rest will have no power to resist that of this small body, which will come to strike against it. So that the resistance that the parts of hard bodies make to prevent their separation, necessarily comes from something other than their rest. But we must demonstrate by sensible experiments what we have just proved by abstract reasonings, in order to see if our ideas agree with the sensations we receive from objects; for it often happens that such reasonings deceive us, or at least that they cannot convince others, and those principally who are preoccupied with the contrary. The authority of M. Descartes makes such a great impression on the reason of some people, that we must prove in all ways that this great man was mistaken, in order to be able to undeceive them. What I have just said enters well into the minds of those who have not filled them with the contrary opinion, and indeed I see well that they will find fault with my dwelling too much on proving things that seem to them incontestable. But the Cartesians well deserve that one make an effort to satisfy them. Others may pass over what is capable of boring them.

Here then are some experiments that sensibly prove that rest has no power to resist motion, and which consequently make known that the will of the author of nature, which makes the power and force that each body has to continue in the state in which it is, regards only motion and not rest; since bodies have no force by themselves. Experience teaches that very large ships, which float in water, can be agitated by very small bodies that come to strike against them. Whence I pretend, despite all the evasions of M. Descartes and the Cartesians, that if these large bodies were in the void they could still be agitated with even more facility. For the reason why there is some slight difficulty in moving a ship in water, is that the water resists the force of the motion that is imparted to it, which would not happen in the void. And what manifestly shows that the water resists the motion imparted to the ship, is that the ship ceases to be agitated some time after it has been moved; for this would not happen, if the ship did not lose its motion by communicating it to the water, or if the water yielded to it without resisting it, or finally if it gave it some of its motion. Thus, since a ship agitated in water gradually ceases to move, it is an indubitable sign that the water resists its motion instead of facilitating it as M. Descartes claims; and consequently it would be infinitely easier to agitate a large body in the void than in water, since there would be no resistance on the part of the surrounding bodies. It is therefore evident that rest has no force to resist motion, and that the least motion contains more power and more force than the greatest rest; and that thus one must not compare the force of motion and rest, by the proportion found between the magnitude of the bodies that are in motion and at rest, as M. Descartes did. It is true that there is some reason to believe that a ship is agitated as soon as it is in the water, because of the continual change that happens to the parts of the water that surround it, although it seems to us that it does not change place. And this is what makes M. Descartes and some others believe that it is not the sheer force of the one who pushes it that makes it advance in the water, but that having already received much motion from the small parts of the liquid body that surround it and push it equally on all sides, this motion is only determined by a new motion of the one who pushes it, so that what agitates a body in water could not do so in the void. This is how M. Descartes and those of his opinion defend the rules of motion he has given us.

Let us suppose, for example, a piece of wood a foot square in a liquid body, all the small parts of the liquid body act and move against it; and because they push it equally on all sides, as much towards A as towards B, it cannot advance towards any side. If I then push another piece of wood half a foot against the first on the side A, I see that it advances. And from this I conclude that it could be moved in the void with less force than that with which this piece of wood pushes it, for the reasons I have just given. But the persons of whom I speak deny it, and they answer that what causes the large piece of wood to advance as soon as it is pushed by the small one, is that the small one, which could not move it if it were alone, being joined with the parts of the liquid body that are agitated, determines them to push it and communicate a part of their motion to it. But it is visible that according to this answer, the piece of wood being once agitated should not diminish its motion, and that on the contrary it should increase it continually. For according to this answer the piece of wood is more pushed by the water on the side A than on the side B, therefore it must always advance. And because this impulsion is continual, its motion must always grow. But, as I have already said, far from the water facilitating its motion, it constantly resists it and its resistance continually diminishing it, finally renders it quite insensible.

It must now be proved that the piece of wood which is equally pushed by the small parts of the water that surround it, has no motion or force at all capable of moving it, although it continually changes its immediate place, or that the surface of the water that surrounds it is never the same at different times. For if it is thus, that a body equally pushed on all sides like this piece of wood, has no motion, it will be indubitable that it is only the foreign force that strikes against it that gives it one, since at the time this foreign force pushes it, the water resists it and even gradually dissipates the motion that is imparted to it, for it gradually ceases to move. Now this appears evident, for a body equally pushed on all sides can be compressed; but certainly it cannot be transported; since more and less of an equal force is equal to zero.

Those to whom I speak maintain that there is never in nature more motion at one time than at another, and that bodies at rest are moved only by the encounter of some agitated bodies that communicate their motion to them. Whence I conclude that a body that I suppose created perfectly at rest in the middle of water, will never receive any degree of motion or any degree of force to move, from the small parts of the water that surround it and come continually to strike against it, provided they push it equally on all sides, because all these small parts that come to strike against it equally on all sides, rebounding with all their motion, communicate none to it; and consequently this body must always be considered as at rest and without any moving force, although it continually changes its surface.

Now, the proof I have that these small parts rebound thus with all their motion, is that besides the fact that one cannot conceive the thing otherwise, the water that touches this body should cool down a great deal or even freeze, and become almost as hard as the wood on its surface, since the motion of the parts of the water should spread equally into the small parts of the body they surround.

But to accommodate those who defend the opinion of M. Descartes, I am willing to grant that one must not consider a boat in the water as at rest. I also want all the parts of the water that surround it to agree on the new motion that the boatman imparts to it, although it is only too visible, by the diminution of the motion of the boat, that they resist it more on the side where it goes than on the side from which it was pushed. This being supposed, however, I say that, of all the parts of the water that are in the river, there are, according to M. Descartes, only those that immediately touch the boat on the side from which it was pushed, that can aid its motion. For, according to this philosopher, the water being fluid, all the parts of which it is composed do not act together against the body we wish to move. There are only those which, touching it, lean conjointly upon it. Now, those which lean conjointly on the boat, and the boatman together, are a hundred times smaller than the whole boat. It is therefore visible, by the explanation M. Descartes gives in this article on the difficulty we have in breaking a nail between our hands, that a small body is capable of agitating a much larger one than itself. For finally our hands are not as fluid as water; and when we want to break a nail, there are more parts joined together that act conjointly in our hands than in the water that pushes a boat.

But here is a more sensible experiment. If one takes a very smooth board, or some other extremely hard plane, and drives a nail halfway into it, and gives this plane a slight inclination. I say that, if one places an iron bar a hundred thousand times thicker than this nail, an inch or two above it, and lets it slide, this nail will not break. And one must meanwhile remark that, according to M. Descartes, all the parts of the bar lean and act conjointly on this nail, for this bar is hard and solid. If therefore there were no other cement than rest to unite the parts that compose the nail, the iron bar being a hundred thousand times thicker than the nail, should, according to the fifth rule of M. Descartes and according to reason, communicate some of its motion to the part of the nail it strikes, that is to say, break it and pass through, even if this bar slid with a very slow motion. Thus, one must seek another cause than the rest of the parts to render bodies hard or capable of resisting the effort made when one wishes to break them, since rest has no force to resist motion, and I believe these experiments suffice to make known that the abstract proofs we have brought forward are not false.

We must therefore examine the third thing we said before could be the cause of the close union found between the parts of hard bodies; namely, an invisible matter that surrounds them, which being extremely agitated, pushes with much violence the exterior and interior parts of these bodies, and compresses them in such a way that to separate them one must have more force than this invisible matter has, which is extremely agitated. It seems that I can conclude that the union of the parts of which hard bodies are composed, depends on the subtle matter that surrounds them and compresses them, since the other two things that one can think to be the causes of this union, are truly not so as we have just seen. For, since I find resistance in breaking a piece of iron, and that this resistance comes neither from the iron nor from the will of God, as I believe I have proved, it must necessarily come from some invisible matter, which can be none other than that which immediately surrounds it and compresses it. I explain and prove this opinion.

When one takes a ball of some metal, hollow inside and cut into two hemispheres, and joins these two hemispheres by pasting a small strip of wax at the place of their union, and draws the air out of them; experience teaches that these two hemispheres join one to the other in such a way that several horses, which are harnessed to them by means of some buckles, some on one side and some on the other, cannot separate them, provided the hemispheres are large in proportion to the number of horses. However, if one lets the air back in, a single person separates them without any difficulty. It is easy to conclude from this experiment that what united these two hemispheres so strongly to one another, came from the fact that being compressed on their exterior and convex surface by the air that surrounded them, they were not at the same time compressed on their concave and interior surface. So that the action of the horses pulling the two hemispheres on both sides, could not overcome the effort of an infinity of small parts of air that resisted them by pressing these two hemispheres. But the slightest force is capable of separating them, when the air having re-entered the copper sphere, pushes the concave and interior surfaces, as much as the air outside presses the exterior and convex surfaces. If on the contrary one takes a carp’s bladder and puts it in a vessel from which the air is drawn, this bladder being full of air bursts and breaks, because then there is no air outside the bladder that resists that which is inside. It is also for this reason that two planes of glass or marble having been ground on one another, join, in such a way that one feels resistance in separating them in one direction, because these two parts of marble are pressed and compressed by the outside air that surrounds them, and are not so strongly pushed from the inside. I could bring an infinity of other experiments to prove that the gross air that presses on the bodies it surrounds strongly unites their parts; but what I have said suffices to explain clearly my thought on the present question.

I say therefore that what causes the parts of hard bodies, and of these small bonds of which I spoke before, to be so firmly united with one another, is that there are other small bodies outside infinitely more agitated than the gross air we breathe, which push and compress them, and that what causes us to have difficulty separating them is not their rest, but the agitation of these small bodies that surround and compress them. So that what resists motion is not rest, which is only its privation and has of itself no force, but some contrary motion that must be overcome.

This simple exposition of my opinion may perhaps seem reasonable; nevertheless I foresee well that many people will have much difficulty entering into it. Hard bodies make such a great impression on our senses when they strike us, or when we make an effort to break them, that we are inclined to believe that their parts are united much more closely than they actually are. And on the contrary the small bodies that I have said surround them, to which I have given the force to be able to cause this union, making no impression on our senses, seem to be too weak to produce such a sensible effect.

But, to destroy this prejudice which is founded only on the impressions of our senses and on the difficulty we have in imagining bodies smaller and more agitated than those we see every day, we must consider that the hardness of bodies must not be measured in relation to our hands or the efforts we are capable of making, which are different at various times. For finally, if the greatest force of men were almost nothing in comparison with that of subtle matter, we would be greatly wrong to believe that diamonds and the hardest stones cannot have for the cause of their hardness the compression of very agitated small bodies that surround them. Now, one will visibly recognize that the force of men is very little, if one considers that the power they have of moving their body in so many ways, comes only from a very small fermentation of their blood, which agitates somewhat its small parts and thus produces the animal spirits. For it is the agitation of these spirits that makes the force of our body, and gives us the power to make those efforts that we wrongly regard as something very great and very powerful.

But we must well remark that this fermentation of our blood is only a very small communication of the motion of this subtle matter of which we have just spoken; for all the fermentations of visible bodies are only communications of the motion of invisible bodies, since every body receives its agitation from some other. We must therefore not be surprised if our force is not as great as that of this same subtle matter from which we receive it. But if our blood fermented as strongly in our heart, as gunpowder ferments and agitates when fire is put to it, that is to say, if our blood received a communication of the motion of subtle matter as great as that which gunpowder receives, we could do extraordinary things with enough facility, such as breaking iron, overturning a house, etc., provided one supposes that there is a suitable proportion between our limbs and blood agitated in this way. We must therefore rid ourselves of our prejudice, and not imagine according to the impression of our senses, that the parts of hard bodies are so firmly united with one another, because we have much difficulty breaking them.

That, if we consider besides the effects of fire in mines, in the gravity of bodies, and in several other effects of nature, which have no other cause than the agitation of these invisible bodies, as M. Descartes has proved in several places, we will manifestly recognize that it is not beyond their force to unite and compress together the parts of hard bodies as strongly as they do. For finally, I do not fear to say that a cannonball, whose motion appears so extraordinary, does not even receive a thousandth part of the motion of the subtle matter that surrounds it.

One will not doubt what I advance if one considers first, that gunpowder does not all inflame, nor in the same instant; secondly, that even if it all caught fire in the same instant, it swims for a very short time in the subtle matter: now, bodies that swim for a very short time in others cannot receive much motion from them, as can be seen in boats abandoned to the course of the water, which receive their motion only gradually. Thirdly, and principally, because each part of the powder can only receive the motion to which the subtle matter agrees; for water communicates to the boat only the direct motion which is common to all the parts, and this motion is ordinarily very small in relation to the others.

I could still prove the greatness of the motion of subtle matter to those who receive the principles of M. Descartes, by the motion of the earth and the gravity of bodies, and I would even draw from there proofs quite certain and exact, but this is not necessary for my subject. It suffices, so that, without having seen the works of M. Descartes, one has sufficient proof of the agitation of subtle matter, which I give as the cause of the hardness of bodies, it suffices, I say, to read with some application what I have already said about it.

Being therefore now delivered from the prejudices that led us to believe that our efforts are very powerful, and that that of the subtle matter which surrounds hard bodies and compresses them is very weak, being moreover persuaded of the violent agitation of this matter by the things I have said about gunpowder; it will not be difficult to see that it is absolutely necessary that this matter, acting infinitely more on the surface of the hard bodies it surrounds and compresses, than inside the same bodies, must be the cause of their hardness or of this resistance we feel when we endeavor to break them.

Now, as there are always many parts of this invisible matter that pass through the pores of hard bodies, they not only render them hard as we have just explained, but moreover they are the cause that there are some that act as a spring and straighten themselves, others that remain bent, others that are fluid and liquid; and finally, they are the cause not only of the force that the parts of hard bodies have to remain next to one another, but also of that which the parts of fluid bodies have to separate from one another, that is to say, that it is she who renders some bodies hard, and others fluid; hard, when their parts touch immediately; fluid, when their parts do not touch.

But, because it is absolutely necessary to know distinctly the physics of M. Descartes, the figure of his elements and the parts that compose particular bodies, to account for why certain bodies are stiff, and why some others are pliant, I will not stop to explain it.

Those who have read the works of this philosopher will easily enough imagine what can be the cause of it, which I could only explain with great difficulty; and those who do not know the same author, would only confusedly understand the reasons I could bring forward.

Nor will I stop to resolve a very great number of difficulties that I foresee could be raised against what I have just established, because, if those who raise them have no knowledge of true physics, I would only bore and annoy them instead of satisfying them; but if they are enlightened persons, their objections being very strong, I could only answer them with a great number of figures and long discourses. So that I think I must beg those who find some difficulty in the things I have just said, to reread this chapter with more care; for I hope that if they read it and meditate on it as they should, all their objections will vanish; but finally, if they find my prayer inconvenient, let them rest, for there is not great danger in ignoring the cause of the hardness of bodies. I do not speak here of contiguity, for it is visible that contiguous things touch so little, that there is always much subtle matter passing between them, and which making an effort to continue its motion in a straight line prevents them from uniting. As for the union found between two marbles that have been polished on one another, I have explained it; and it is easy to see that, although subtle matter always passes between these two parts however united they are, air cannot pass, and that thus it is its weight that compresses and presses these two parts of marble one on the other, and which causes one to have some difficulty in separating them, if one does not slide them across.

It is visible from all this that continuity, contiguity, and the union of the two marbles would be only the same thing in the void, for we have no different ideas of them either, so that it is saying what one does not understand to make them differ absolutely, and not in relation to the bodies that surround them. Here now are some reflections on the opinion of M. Descartes, and on the origin of his error. I call his opinion an error, because I find no means to defend what he says of the rules of motion, and of the cause of the hardness of bodies towards the end of the second part of his Principles in several places, and that I seem to have proved enough the truth of the opinion contrary to his.

This great man conceiving very distinctly that matter cannot move itself, and that the natural moving force of all bodies is nothing else than the general will of the author of nature, and that thus the communication of motions of bodies in their mutual encounter can only come from this same will, he let himself go to this thought that one could only give the rules of the different communication of motions by the proportion found between the different magnitudes of the bodies that collide, since it is not possible to penetrate the designs and the will of God: and because he judged that each thing had force to remain in the state in which it was, whether it was in motion or at rest, because God, whose will makes this force, always acts in the same manner, he concluded that rest had as much force as motion; thus, he measured the effects of the force of rest by the magnitude of the body at rest, like those of the force of motion, which made him give the rules of the communication of motion that are in his Principles, and the cause of the hardness of bodies that I have tried to refute.

It is difficult enough not to yield to the opinion of M. Descartes, when one views it from the same side as he; for, once again, since the communication of motions comes only from the will of the author of nature, and that we see that all bodies remain in the state in which they have once been placed, whether in motion or at rest, it seems that we should seek the rules of the different communication of motions in the encounter of bodies, not in the will of God which is unknown to us, but in the proportion found between the magnitudes of these bodies.

I am therefore not surprised that M. Descartes had this thought, but I am only surprised that he did not correct it, when having pushed his knowledge further, he recognized the existence and some effects of the subtle matter that surrounds bodies.

I am surprised that, in article 132 of the fourth part, he attributes the force that certain bodies have to straighten themselves to this subtle matter, and that in articles 55 and 43 of the second part and elsewhere, he does not attribute their hardness to it, or the resistance they make when one tries to bend and break them, but only to the rest of their parts. It appears evident to me that the cause that straightens and renders certain bodies stiff, is the same as that which gives them the force to resist when one wants to break them, for finally the force one employs to break steel differs only insensibly from that by which one bends it.

I do not want to bring forward here many reasons that can be said to prove these things, nor to answer some difficulties that could be formed on the fact that there are hard bodies that do not sensibly act as a spring, and which one nevertheless has some difficulty bending; for it suffices, to make these difficulties vanish, to consider that subtle matter cannot easily make new paths in bodies that break when one bends them, as in glass and tempered steel, and that it can do so more easily in bodies that are composed of branched parts and are not brittle, as in gold and lead, and that finally there is no hard body that does not act somewhat as a spring.

It is difficult enough to persuade oneself that M. Descartes positively believed that the cause of hardness was different from that which makes the spring; and what appears more likely, is that he did not reflect enough on this matter.

When one has meditated for a long time on some subject and one is satisfied with the things one wanted to know, one often thinks of it no more. One believes that the thoughts one has had about it are incontestable truths that it is useless to examine further. But there are in man so many things that disgust him with application, that lead him to too hasty consents and render him subject to error, that although the mind remains apparently satisfied, it is not always well informed of the truth. M. Descartes was a man like us; one never saw more solidity, more exactness, more extent and more penetration of mind than that which appears in his works; I admit it, but he was not infallible.

Thus, there is reason to believe that he remained so strongly persuaded of his opinion, that he did not reflect that he was asserting in the sequel of his Principles something that was contrary to it. He had supported it on very specious and very plausible reasons; but such however that he was not as if forced by them to yield to them. He could still suspend his judgment, and consequently he should have. It was not enough to examine in a hard body what can be there that renders it such, he should also have thought of the invisible bodies that can render it hard, as he thought of them at the end of his Principles of philosophy, when he attributed to them the cause of the spring; he should have made an exact division that included everything that could contribute to the hardness of bodies. It was not enough yet to seek its cause in the will of God; he should also have thought of the subtle matter that surrounds them.

For although the existence of this extremely agitated matter was not yet proved in the place of his Principles, where he speaks of hardness; it was not rejected either: he should therefore have suspended his judgment and well remembered that what he wrote of the cause of the hardness and the rules of motion, should be reviewed all over again, which I believe he did not do with enough care. Or else he did not consider enough the true reason of a thing that is very easy to recognize, and which however is of the last consequence in physics; I explain it.

M. Descartes knew well that to support his system, the truth of which he could perhaps not doubt, it was absolutely necessary that large bodies always communicated their motion to the small ones they met and that the small ones rebound at the encounter of the larger ones, without an equal loss of theirs. For without this the first element would not have all the motion it is necessary that it have over the second, nor the second over the third; and his whole system would be absolutely false, as those who have meditated on it a little know well. But in supposing that rest has force to resist motion and that a large body at rest cannot be moved by another smaller than itself, although it strikes it with a furious agitation; it is visible that large bodies must have much less motion than an equal volume of smaller ones, since they can always, according to this supposition, communicate the one they have, and cannot always receive it from the smaller ones. Thus, this supposition not being contrary to all that M. Descartes had said in his principles from the beginning to the establishment of his rules of motion, and accommodating itself very well with the sequel of these same principles, he believed that the rules of motion he thought to have demonstrated in their cause were still sufficiently confirmed by their effects.

I agree with M. Descartes on the substance of the matter that large bodies communicate their motion much more easily than small ones, and that thus his first element is more agitated than the second, and the second than the third. But the cause of it is clear without having regard to his supposition.

Small bodies and fluid bodies, water, air, etc., can communicate to large bodies only their uniform motion and common to all their parts; the water of a river can communicate to a boat only the motion of the descent which is common to all the small parts of which the water is composed, and each of these small parts, besides this common motion, has also an infinity of other particular ones. Thus, it is visible by this reason that a boat, for example, can never have as much motion as an equal volume of water, since the boat can receive from the water only the direct motion common to all the parts that compose it. If twenty parts of a fluid body push some body on one side, there are as many that push it on the other; it therefore remains immobile and all the small parts of the fluid body in which it swims rebound without losing any of their motion. Thus, gross bodies and whose parts are united with one another can only receive the circular and uniform motion of the vortex of subtle matter that surrounds them.

Gross bodies are not as agile as small ones and that it is not necessary to explain these things to suppose that rest has some force to resist motion.

The certainty of the principles of Descartes’ philosophy can therefore not serve as proof to defend his rules of motion; and there is reason to believe that if M. Descartes himself had examined his Principles anew without prejudice and weighing reasons similar to those I have said, he would not have believed that the effects of nature had confirmed his rules and would not have fallen into the contradiction in attributing the hardness of hard bodies only to the rest of their parts, and their spring to the effort of subtle matter.