The Law of Equilibrium

The simplest law of Nature is that of equilibrium.

This has been known for many centuries. But until now, it had no connection to the laws of motion, which were much more difficult to discover.

Research into motion was not to the liking (or perhaps not within the scope) of the ancients. And so we may consider it as a completely new science.

How could the ancients have discovered the laws of moiton, given that some philosophers reduced all their speculations about motion to sophistic disputes, whereas others denied that motion existed at all?*

The more industrious and sensible philosophers knew that that it is difficult to understand the principles of motion. So they invented reasons to despair of ever knowing them, as an excuse to get out of doing experiments.

A true philosopher does not engage in vain disputes about the nature of motion.

Rather, he wishes to know the laws by which it is distributed, conserved or destroyed, knowing that such laws are the basis for all natural philosophy.

The great Descartes, boldest of the philosophers, sought such laws, but was mistaken.

However, time brought the subject of mechanics to a kind of maturity.

Its laws, unknown for centuries, were developed suddenly in several places at once.

Huygens, Wallis and Wren discovered them at the same time.

Many mathematicians after them have confirmed these laws, although they arrived at these laws by different routes.

Mathematicians agree today on the more complicated case. But they do not agree on the simpler case.

Everyone agrees on the distribution of motion in the collision of perfectly elastic bodies, but not in the collision of perfectly inelastic bodies.

Some even believe that the distribution of motion cannot be calculated in the latter case.

This embarassing failure has caused some to deny the existence and possibility of perfectly inelastic bodies.

• They claim that perfectly inelastic are actually elastic bodies whose hardness prevents us from seeing the deformation and recovery of its shape.

These people point to experiments on bodies commonly called “hard” and “undeformable” showing that these bodies are actually deformable and elastic.

For example, when spheres made of ivory, or maple wood, or glass collide, they seem to have deformed during the collision, only to recover their shape immediately afterwards.

This may be seen by painting one of the spheres with a color that comes off and stains the other sphere.

The size of the stain after the collision shows that the spheres were flattened during the collision, although no trace of the deformation remains afterwards.

These people then add metaphysical arguments to these arguments.

They require that every process in Nature to:

• take a certain time, and
• obey a law of continuity

They object that when a perfectly inelastic body collides with an impassable barrier, its speed must instantly:

• go to zero without passing through any intermediate values or
• be transformed into its opposite, without passing through zero.*

I do not feel the force of this argument.

I do not think we know enough of the means by which motion can be produced or destroyed to say whether it must follow the law of continuity.

If you assume that speed must change by degrees, doesn’t it change discontinuously between degrees?

Even imperceptible discontinuous changes would violate the law of continuity as much as the sudden destruction of the universe.

The experiments suggest that it is easy to confuse hardness with elasticity, but they do not show that all hard bodies are elastic.

On the contrary, those who have considered the impenetrability of bodies suggest that perfect inelasticity is a necessary consequence of matter. Most bodies are deformable because they are made up of particles that can move relative to each other when stress is applied; however, the fundamental particles, the elements that make up all other bodies, these must be bodies that are perfectly inelastic, undeformable and unchangeable.

The more one considers elasticity, the more it seems to require that the elastic body have parts that can move relative to one another under stress.

Hence, it is more reasonable to assert that the fundamental particles of matter are perfectly hard, rather than to pretend that perfectly hard bodies do not exist in Nature.

Nevertheless, I do not know whether our present knowledge allows us to make either assertion definitely.

However, one of the main reasons for denying that perfectly hard bodies exist was that we were unable to derive the laws of motion transfer for hard bodies.