Proposition 24, Theorem 39

Philosophical Absolute Motion and Rest

For philosophical disquisitions, we should consider things themselves, distinct from our sensible measures of them.

This is because it is possible that nothing is really at rest.

We may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects.

Bodies really at rest do rest in respect to one another. Therefore it is possible that in the remote regions of outerspace there may be some body absolutely at rest. *

But this is impossible to know, from the position of bodies to one another in our regions, whether any of these do keep the same position to that remote body. It follows that absolute rest cannot be determined from the position of bodies in our regions.

A motion is made up of smaller motions.

All the parts of revolving bodies try to move away from the axis of motion.

The impetus of a body moving forward comes from the joint impetus of all the parts.

Therefore, if surrounding bodies are moved, those that are relatively at rest within them will partake of their motion.

This is why the true and absolute motion of a body cannot be determined by the translation of it from those which only seem to rest.

This is because the external bodies should not only appear at rest, but to be really at rest.

Otherwise, all included bodies, besides their translation from near the surrounding ones, partake likewise of their true motions.

Though that translation were not made, they would not be really at rest, but only seem to be so.

The surrounding bodies are like the shell and the actual body is like the kernel. If the shell moves, the kernel will also move, as being part of the whole.

Cause of True and Relative Motion

The difference between true and relative motions are caused by the forces impressed on bodies to generate motion.

True motion is neither generated nor altered, but by some force impressed on the actual body moved.

Relative motion may be generated or altered without any force impressed on the body.

For it is sufficient only to impress some force on other bodies with which the former is compared, that by their giving way, that relation may be changed, in which the relative rest or motion of this other body did consist.

True motion always creates some change on the moving body.

But relative motion does not necessarily cause changes by such forces.

For if the same forces are likewise impressed on those other bodies, with which the comparison is made, that the relative position may be preserved, then that condition will be preserved in which the relative motion consists.

Therefore, any relative motion may be changed when the true motion remains unaltered.

The relative motion may be preserved when the true motion changes.

Thus, true motion by no means consists in such relations.

Effect of True and Relative Motion

The effects which distinguish absolute from relative motion is the centrifugal force.

A circular motion only has true motion.

Hang a pail by a long cord. The pail twists the cord so often. Then fill it with water and whirl it in the opposite direction so that the cord untwists itself. The pail continues for some time in this motion.

The surface of the water will at first be plain, as before the vessel began to move. But after that, the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and move away little and little from the middle and ascend to the sides of the pail.

This forms a concave figure. The swifter the motion, the higher will the water rise until, performing its revolutions in the same times with the pail, it becomes relatively at rest in it.

This ascent of the water shows its endeavour to move away from the axis of its motion.

The true and absolute circular motion of the water, which is here directly contrary to the relative, becomes known, and may be measured.

At first, when the relative motion of the water in the vessel was greatest, it produced no endeavour to recede from the axis; the water showed no tendency to the circumference, nor any ascent towards the sides of the vessel, but remained of a plain surface, and therefore its true circular motion had not yet begun.

But afterwards, when the relative motion of the water had decreased, the ascent thereof towards the sides of the vessel proved its endeavour to recede from the axis.

This showed the real circular motion of the water continually increasing, till it had acquired its greatest quantity, when the water rested relatively in the vessel.

Therefore, this endeavour does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation.

There is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axis of motion, as its proper and adequate effect; but relative motions, in one and the same body, are innumerable, according to the various relations it bears to external bodies, and, like other relations, are altogether destitute of any real effect, any otherwise than they may perhaps partake of that one only true motion.

Therefore, in their system who suppose that our heavens, revolving below the sphere of the fixed stars, carry the planets along with them; the several parts of those heavens, and the planets, which are indeed relatively at rest in their heavens, do yet really move.

For they change their position one to another (which never happens to bodies truly at rest), and being carried together with their heavens, partake of their motions, and as parts of revolving wholes, endeavour to recede from the axis of their motions.

Wherefore relative quantities are not the quantities themselves, whose names they bear, but those sensible measures of them (either accurate or inaccurate), which are commonly used instead of the measured quantities themselves. And if the meaning of words is to be determined by their use, then by the names time, space, place, and motion, their [sensible] measures are properly to be understood; and the expression will be unusual, and purely mathematical, if the measured quantities themselves are meant. On this account, those violate the accuracy of language, which ought to be kept precise, who interpret these words for the measured quantities. Nor do those less defile the purity of mathematical and philosophical truths, who confound real quantities with their relations and sensible measures.

It is very difficult to discover and distinguish, the true motions of particular bodies from the apparent.

This is because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses.

Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common centre of gravity, we might, from the tension of the cord, discover the endeavour of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. And then if any equal forces should be impressed at once on the alternate faces of the globes to augment or diminish their circular motions, from the increase or decrease of the tension of the cord, we might infer the increment or decrement of their motions; and thence would be found on what faces those forces ought to be impressed, that the motions of the globes might be most augmented; that is, we might discover their hindmost faces, or those which, in the circular motion, do follow.

But the faces which follow being known, and consequently the opposite ones that precede, we should likewise know the determination of their motions. And thus we might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared. But now, if in that space some remote bodies were placed that kept always a given position one to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies, whether the motion -did belong to the globes or to the bodies. But if we observed the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest; and then, lastly, from the translation of the globes among the bodies, we should find the determination of their motions. But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it.