Proposition 43, Theorem 34

Every tremulous body in an elastic medium propagates the motion of the pulses on every side right forward.

But in a non-elastic medium excites a circular motion.

Case. 1

The parts of the tremulous body, alternately going and returning, do in going urge and drive before them those parts of the medium that lie nearest, and by that impulse compress and condense them.

In returning, they suffer those compressed parts to go away again, and expand themselves.

Therefore the parts of the medium that lie nearest to the tremulous body move to and fro by turns, in like manner as the parts of the tremulous body itself do.

For the same cause that the parts of this body agitate these parts of the medium, these parts, being agitated by like tremors, will in their turn agitate others next to themselves.

These others, agitated in like manner, will agitate those that lie beyond them, and so on in infinitum.

And in the same manner as the first parts of the medium were condensed in going, and relaxed in returning, so will the other parts be condensed every time they go, and expand themselves every time they return.

Therefore, they will not be all going and all returning at the same instant (for in that case they would always preserve determined distances from each other, and there could be no alternate condensation and rarefaction);

But since, in the places where they are condensed, they approach to, and, in the places where they are rarefied, recede from each other, therefore some of them will be going while others are returning; and so on in infinitum.

The parts so going, and in their going condensed, are pulses, by reason of the progressive motion with which they strike obstacles in their way; and therefore the successive pulses produced by a tremulous body will be propagated in rectilinear directions; and that at nearly equal distances from each other, because of the equal intervals of time in which the body, by its several tremors produces the several pulses.

The parts of the tremulous body go and return in some certain and determinate direction.

Yet the pulses propagated from thence through the medium will dilate themselves towards the sides, by the foregoing Proposition; and will be propagated on all sides from that tremulous body, as from a common centre, in superficies nearly spherical and concentrical.

An example of this we have in waves excited by shaking a finger in water, which proceed not only forward and backward agreeably to the motion of the finger, but spread themselves in the manner of concentrical circles all round the finger, and are propagated on every side. For the gravity of the water supplies the place of elastic force.

Case 2

If the medium is not elastic, then its parts cannot be condensed by the pressure from the vibrating parts of the tremulous body.

The motion will be propagated in an instant towards the parts where the medium yields most easily, that is, to the parts which the tremulous body would otherwise leave vacuous behind it.

The case is the same with that of a body projected in any medium.

A medium yielding to projectiles does not recede in infinitum, but with a circular motion comes round to the spaces which the body leaves behind it.

Therefore as often as a tremulous body tends to any part, the medium yielding to it comes round in a circle to the parts which the body leaves.

As often as the body returns to the first place, the medium will be driven from the place it came round to, and return to its original place.

Though the tremulous body be not firm and hard, but every way flexible, yet if it continue of a given magnitude, since it cannot impel the medium by its tremors any where without yielding to it somewhere else, the medium receding from the parts of the body where it is pressed will always come round in a circle to the parts that yield to it. Q.E.D.

Corollary

Some think that the agitation of a flame conduces to the propagation of a pressure in rectilinear directions through an ambient medium.

This is wrong.

A pressure of that kind must be derived not from the agitation only of the parts of flame, but from the dilatation of the whole.