The active force that sets motion in the universe

Whether there is always the same quantity of forces in the world. Examination of force. How to calculate force. Conclusion of both parties.

Matter cannot move by itself.

Therefore it must receive motion from elsewhere; but it cannot receive it from other matter, for that would be a contradiction; it must therefore be an immaterial cause that produces motion.

God is this immaterial cause, and we must be careful here to understand that the common axiom — that one must not invoke God in philosophy — is only valid for things that must be explained by immediate physical causes.

For example, if I want to explain why a weight of four pounds is counterbalanced by a weight of one pound: if I simply say that God arranged it that way, I am ignorant;

But I answer the question properly if I say that it is because the one‑pound weight is four times farther from the fulcrum than the four‑pound weight.

It is not the same with the first principles of things: in that case, not invoking God is the mark of ignorance, for either there is no God, or first principles can only exist in God.

It is He who has impressed upon the planets the force by which they move from west to east; it is He who causes these planets and the sun to rotate on their axes.

He has imprinted a law upon all bodies, by which they all tend equally toward their center. Finally, He has formed animals to which He has given an active force with which they generate motion.

The great question is whether this force given by God to initiate motion always remains the same in nature.

Descartes, without speaking of force, asserted without proof that there is always an equal quantity of motion; and his opinion was all the less well‑founded because the very laws of motion were completely unknown to him.

Leibniz, coming in a more enlightened time, was forced to admit — with Newton — that motion is lost; but he maintained that, although the same quantity of motion does not persist, force always remains the same.

Newton, on the contrary, was persuaded that it is a contradiction to think that motion would not be proportional to force.

Before entering into any mechanical discussion, we must consider things in their very nature: the metaphysician must always guide the geometer.

A man has a certain quantity of active force; but where was this force before his birth? If we say it was in the germ of the child, what is a force that cannot be exercised?

But when he has become a man, is he not free? Can he not employ more or less of his force?

Suppose he exerts a force of three hundred pounds to move a machine; suppose, as is possible, that he exerted this force by pressing down a lever, and that the machine attached to that lever is in a vacuum chamber: the machine may easily acquire a force of two thousand pounds.

Once the operation is done, the arm withdrawn, the lever removed, the weight stands immobile — I ask: has the little bit of matter in the vacuum chamber received from the machine a force of two thousand pounds?

Do not all these considerations show that active force is continually being restored and lost in nature?

Pay close attention to this argument:

There can be no movement without a vacuum; now, when a body A‑B‑C‑D receives an impulse in all its parts, I ask whether the parts B‑C‑D, behind which there is no other body, will not lose motion; and if the parts B‑C lose their motion, do they not obviously lose their force?

Let us now listen to Newton and experience to end this metaphysical dispute.

Motion, he says, is produced and lost. But because of the viscosity of fluids and the lack of elasticity of solids, much more motion is lost than is regenerated in nature.

Given this, if we consider the indubitable axiom that the effect is always proportional to the cause, then where motion diminishes, force must necessarily diminish also.

Therefore, for the same quantity of forces to remain forever in the universe, this principle — that the cause is proportional to the effect — would have to stop being true.

It was believed that, to maintain always this same force in nature, it was enough to change the usual way of measuring that force:

Thus, instead of Mersenne, Descartes, Newton, Mariotte, Varignon, etc., who had always, after Archimedes, measured the motion of a body by multiplying its mass by its velocity…

…the Leibnizians — Leibniz, Bernoulli, Herman, Poleni, s’Gravesande, Wolff, etc. — multiplied the mass by the square of the velocity.

This dispute divided Europe; but in the end it seems we recognize that, at bottom, it is a dispute about words.

It is impossible that these great philosophers, although diametrically opposed, could be wrong in their calculations.

They are equally correct; the mechanical effects correspond equally to one or the other way of counting.

There is, then, indisputably a sense in which they are all correct.

And this point where they are right is what should unite them — and here it is, as Dr. Clarke was the first to point out (though rather bluntly):

If you consider the time in which a moving body acts, its force at the end of that time is as the square of its velocity multiplied by its mass.

Why? Because the space traversed by its mass is as the square of the time in which it is traversed.

Now time is proportional to velocity: thus the body which has traversed this space in that time acts, at the end of that time, by its mass multiplied by the square of its velocity.

Thus, when mass 2 travels in two units of time any given space with two degrees of velocity, at the end of that time its force is 2 × (2²); the total is 8, and the body produces an impact equal to 8; in this case, the Leibnizians are not wrong.

But likewise, the Cartesians and Newtonians together are quite right when they consider the matter from another angle, for they say:

In equal times, a body weighing four pounds with one degree of velocity acts exactly like a body of one pound with four degrees of velocity,

and the elastic bodies that collide rebound always in reciprocal proportion to their velocity and mass; that is, a double‑weight ball with motion “1,” and a half‑weight ball with motion “2,” when launched at each other, arrive in equal time and rebound to equal heights.

Thus, we must not consider what happens to moving bodies in unequal times, but in equal times — and there lies the source of misunderstanding.

Therefore:

The new way of conceiving forces is true in one sense and false in another.

It serves only to complicate, to tangle up a simple idea.

It is better to stick to the old rule.

What to conclude from these two ways of looking at things?

Everyone must agree that the effect is always proportional to the cause:

Now, if motion perishes in the universe,

Then the force which is its cause also perishes.

This is what Newton thought on most questions that touch upon metaphysics: it is for you to judge between him and Leibniz.