The force of inertia is the property common to all bodies that remain in their state, either at rest or in motion, unless some external cause is introduced to make them alter this state.

Bodies do not display this force except when one alters their state; at which point it is called resistance or action. It is called resistance when one speaks of the effort that a body makes against that which tends to change its state and one says action when one wishes to express the same effort that the same body makes to change the state of the obstacle which causes the resistance. See Action [Action, Action (Ethics)], Cosmology, and the rest of this article.

In the definition of inertial force , I used the word property rather than that of force; since the latter of these words appears to give rise to a vague metaphysical being which resides in the body for which we have no precise idea as for the former says nothing less than an effect constantly observed in bodies.

Proof of inertial force . One can see clearly that a body cannot provide itself with motion; it cannot be forced from rest except by some foreign action. From there it stands that if a body receives motion, irrespective of what that might be, it cannot on its own accord neither accelerate nor slow this movement. In general power or motivating causes is termed as everything which obligates a body to move. See Power.

Once a body has been put in motion by any reason whatsoever, it will always continue uniformly and in a straight line and insofar that a new reason, different from the one that placed it in motion, does not act onto this body, then it will move perpetually in a straight line and will cover equal space in equal time.

Furthermore, when the indivisible and instantaneous action of the initiating cause of motion is sufficient to allow the body to cover a certain distance when the body when requires the sustained action of the initiating cause to remain in motion.

In the first case, it is apparent that the distance covered can be nothing other than a straight line uniformly described by the moving body; since (hypothetically) after the first moment of action the initiating cause vanishes and the motion nonetheless still exists. It will necessarily be uniform since a body cannot accelerate or slow its movement by itself. Furthermore, there is no reason that a body should tend to the right rather than to the left. Therefore in the first case where one supposes that it is possible for the body to move on its own, even during a certain time, independent of the initiating cause, it will move in a uniform and rectilinear direction during this time.

Furthermore, a body which can initiate its own motion in a uniform and rectilinear way must continue perpetually in motion as long as there is nothing to prevent it. If we suppose that the body leaves from A (fig.32.Mechanics) and is capable of traveling the distance along a straight line AB uniformly, and that any two points that are taken along C, D, between A and B that the body at D is precisely in the same state when it was at C [page 111 illus.], nothing else has happened but it is now in a different place. Thus the same effect must happen to the body when it is at C. Since when it is at C, it can (hypothetically) move on its own uniformly to B. Thus by being at D it can move of its own to point G in such that DG = CB and so on.

Therefore if the action is primary and instantaneous and as the motivating cause is capable of setting a body in motion, it will move uniformly and in a straight line insofar as no new force will prevent it from doing so.

In the second case, since we do not suppose that any foreign or different action will cause any motivating reason to act on the body or that anything will cause the motivating factor to either increase or diminish, it follows that the continued action will be uniform and constant and that during that time that it will act, the body will move uniformly in a straight line. For the same reason that has made the motivating cause to be constant and uniform during a certain time, always in existence insofar as nothing opposes its action and it is clear that this action must remain continuously the same and have the same effect.

Therefore in general a body put into motion by whatever cause, will remain so uniformly and in a straight line, insofar as no new cause will occur to change it.

The straight line that a body describes or tends to describe is called its direction. See Direction.

We have somewhat extended ourselves concerning the proof of this second law, since there has been and there may very well be still some philosophers who pretend that the motion of a body must slow by itself little by little as it appear that experiments indicate. One must agree, that the proofs that are ordinarily given for inertial force , insofar as it is the principle of the conservation of motion, do not contain the necessary evidence to convince us. They are nearly all founded on what is imagined to be inherent in matter and which resists all changes of state or is indifferent to whether the matter is in motion or rest. The first of these two principles, besides the fact that it supposes something in matter for which there is no clear idea, cannot possibly be sufficient to prove the law which it is question; since when a body is in uniform motion, the motion which it possesses at any moment has the distinction of being isolated from motion which it has had or will have in the moments preceding or following. The body is therefore in some way in a new state at any given moment, it only does as can be said to continuously be in a state of starting to move and one might imagine that it tends without falling into a state of rest, which if the same cause which initiated its movement was not in some way responsible to continue.

All that this principle represents in regards to the indifference of matter concerning motion or rest, appears to me to very distinct from some evanescent qualities and that is to say that it is not essential for matter to be always in motion neither to be always at rest. However it simply does not follow from this law that a body cannot tend continuously towards rest not that rest is any more important than motion, but simply that it would appear that nothing else is required for a body to be at rest and that to be in motion would require something else and that it would necessarily have to always reproduced within itself.

The proof that I gave concerning the conservation of motion, has certain particularities, as it takes place irrespective of whether the motivating cause is applied to the body or not. It is not that I believe in the continued action of this fact to be necessary to move the body since if the continuous action were insufficient, what then would be the effect of this action? And if this action had no effect, what would the continuous action have? However since one must use as few principles as possible in the solution to a problem, I believe it necessary to limit the proof that the continuation of movement takes place within these two hypotheses: It is true that our proof supposes the existence of motion and with greater reason its possibility; however to deny that motion exists is to refuse a fact that no one is asking to place in doubt.

See Motion

Unless I am mistaken here is how one can prove the law of continuous motion in such a way that it is protected from any chicanery. Within motion it appears, as we have already observed, that there is a type of continuous alteration this is true in this unique sense that the motion of a body within any instant has nothing in common with its movement immediately preceding or following that instant. However we would be mistaken to understand by change of state, the change of place that the movement produces; since when we examine this presumed change of state with the philosopher’s eyes one sees nothing else but a change in the relationship, that is to say a change of distance of the body which moved to the surrounding bodies.

We are strongly inclined to believe that there is in a body in motion an effort or energy which is not in a body at rest. The reason for which we have such problems to detach ourselves from this idea is that we are always ready to transfer to inanimate bodies the things that we have observed within our own bodies. Thus we see that when our bodies move or strike some obstacle, the shock or the motion is accompanied by a sensation which provides us with an idea of a force of more or less strength, and by transporting this same force to other bodies we perceive, by paying attention that we are able to attach three different feelings: 1. That of the sensation that we feel and that cannot be suggested for inanimate matter: 2. That of a metaphysical being different to our senses, but one to which it is impossible to conceive and consequentially to define: 3. Finally, (and this is the only sensible one) is the effect itself or the property which manifests itself by this effect without examining or researching the cause. If we attach to the word force the latter meaning we will see nothing else in its motion as we will in its rest and we may regard the continuation of motion as a law as essential as that of the continuation of rest. However, we will say that a body at rest will never place a body into motion, whereas a body in motion moves a body at rest. To that I will answer that if a body in motion moves a body at rest, it is by losing a part of its motion and this loss comes as a result of the resistance that occurs to a body at rest when it alters its state. A body at rest is no less possessed of a real force to conserve its state than a body in motion irrespective of the definition that we give to the term force. See Communication of motion.

The principle of inertial force can also be shown by experimentation.

We see that 1. Those bodies at rest remain there insofar as nothing pulls them away from it. Should that happen and a body moves without us being aware of the reason why it moves, we are allow the right to judge and by analogy and the uniformity [p.112 illus.] of the laws of nature and by the incapacity of matter to move itself even though the reason may not be apparent it is still no less real. 2. There are no bodies that eternally preserve their motion, since there are always causes to slow it little by little such as friction and air resistance; however we have noticed that a body in motion persists all that much longer since the reasons which might slow this motion become less and less for which we may conclude that motion would not end if the slowing forces were nil.

The daily experience of gravity seems to undermine the first of these two principles. Humanity has difficulty in imagining that it is necessary that a body should be pushed towards the earth in order for it to be drawn to it; more accustomed to see a body in free fall when it is not supported, it believes that this reason alone is sufficient to make a body move. But a truly simple thought can dispel this opinion. A body is placed on a horizontal table; why doesn’t this body move horizontally along the length of the table, since nothing stops it from doing so? Why doesn’t the body travel upwards since nothing is preventing it from moving in that direction? Since the body travels from up to down in one direction rather than another and that of it own accord it is indifferent to its motion in one direction or the other, there happens to be some reason which determines it motion in one direction. It is therefore not without reason that philosophers are astonished to see a stone fall and that people laugh because of their astonishment and they too would do the same if they only spent a little time thinking.

There is more; most bodies that we see in motion are moved from rest by the impulse that we see occurring by other bodies. We are therefore naturally brought to the conclusion that the motion is always the effect of an impulse. Therefore, the first idea that passes through a philosopher’s mind when he sees a falling body is to believe that it has been pushed by some invisible fluid. If it so happen that after having deepened our knowledge of this matter we find that gravity cannot be explained by the impulse of a fluid and that the phenomenon refuses to support this hypothesis, then the philosopher must suspend his judgement and perhaps even begin to believe that there may well be some other cause that makes bodies move besides impulse; or at least (this is also contrary to the commonly understood principles) that the impulsion to bodies and especially to those of certain unknown fluids, can possess entirely different laws to those that experiments have revealed to us at this point. See Attraction.

A brilliant geometer of our times ( See Euleri opuscula , Berlin, 1746.) has suggested that gravity, if we look at it differently than a principle of impulsion, is contrary to the principle of inertial force and consequentially it cannot be part of bodies; since as this geometer says, a body cannot provide itself with and consequentially cannot bend towards another body without some determining reason. It suffices to respond to this thinking as 1. That the bending of one body towards another, irrespective of the reasons is a law of nature observed through phenomenon. See Gravitation. 2. That if this bending is not produced by impulse, which we are not deciding, then in this case the presence of another body is sufficient to alter the motion of that one which is in motion; and similarly as the action of the soul on the body does not inhibit the principle of inertial force to be true in the same way that one body acts upon another at a distance does not bother the truth of this principle in any way. Since in the title of this principle we have made abstractions of all the reasons (whichever they might be) which may alter the motion of a body now allows us to understand or not the way in which these forces act.

This same geometer goes even further; he has undertaken to prove that inertial force is incompatible with the faculty of thought. The latter faculty involves the ability to change ones own state from which he concludes that the inertial force, being recognized as a property of matter, the faculty of thought cannot be one. We applaud the zeal with which this author finds the new proof to a truth that we have no objection to; however to consider the thing uniquely as philosophers, we cannot see by this new step that he has made a great step in Metaphysics. Inertial force only occurs, as experience tells us in an unrefined state, that is to say a state which is not connected to an intelligent principle whose intelligence can move it. For either that matter has the faculty to think on its own (which is far from our thinking) or that it has an intelligent principle which is different from it but connected to it, and from which it will lose its inertial force or to say it more exactly, it will no longer appear to obey this force. Without a doubt it is no easier to conceive how this intelligent principle, connected to matter but different from it, can act on its own to make it move any more than it is to understand how inertial force can reconcile itself to the thought process which the Materialists attribute incorrectly to bodies. However we are certain through religion that matter cannot think and we are certain of this because our experience tells us that the soul acts on the body. We hold these two truths to be incontestable without undertaking any reconciliation.