Isaac Newton

“ Therefore when the height of the quick-silver is at 30 inches, a height of uniform air, whose weight would be sufficient to compress our air to the density we find it to be of, must be equal to 356.700 inches or 29.725 feet of our measure. And this is that very height of the medium, which I have called A in the construction of the foregoing proposition. A circle whose radius is 29.725, feet is 186.768 feet in circumference. And since a pendulum 391/5 inches in length compleats one oscillation, composed of its going and return, in two seconds of time, as is commonly known ”

“ 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; and 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. ”

“ An example of this we have in waves excited by shaking a finger in water, which proceed not only, forwards and backwards 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 be not elastic, then, because its parts cannot be condensed by the pressure arising 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 ”

“ Let a pendulum be constructed, whose length between the point of suspension and the centre of oscillation is equal to the breadth of the waves; and in the time that the pendulum will perform one single oscillation, the waves will advance forward nearly a space equal to their breadth. ”

“ The velocity of the pulses is equal to that which heavy bodies acquire by falling with an equally accelerated motion, and in their fall describing half the altitude A. For the pulse will, in the time of this fall, supposing it to move with the velocity acquired by that fall, run over a space that will be equal to the whole altitude A ”

“ Because the weight of air is to the weight of water as 1 to 870, and because salts are almost twice as dense as water; if the particles of air are supposed to be of near the same density as those of water or salt, and the rarity of the air arises from the intervals of the particles ”

“ Then while the cone ABC, propagating the pressure, urges the conic frustum degf beyond it on the superficies de, and this frustum urges the next frustum fgih on the superficies fg, and that frustum urges a third frustum, and so in infinitum it is manifest (by the third law) that the first frustum defg is, by the reaction of the second frustum fgbi, as much urged and pressed on the superficies fg, as it urges and presses that second frustum. Therefore the frustum degf is compressed on both sides, that is, between the cone Ade and the frustum fhig ”

“ 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; and 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, and these others agitated in like manner, will agitate those that lie beyond them, and so on in infinitum. ”