Isaac Newton

“ Bodies swimming upon fluids, when they move straight forwards, cause the fluid to ascend at their fore parts and subside at their hinder parts, especially if they are of an obtuse figure; and thence they meet with a little more resistance than if they were acute at the head and tail. And bodies moving in elastic fluids, if they are obtuse behind and before, condense the fluid a little more at their fore parts, and relax the same at their hinder parts; and therefore meet also with a little more resistance than if they were acute at the head and tail. ”

“ Proposition XXXIV. Theorem XXVIII. If in a rare medium, consisting of equal particles freely disposed at equal distances from each other, a globe and a cylinder described on equal diameters move with equal velocities, in the direction of the axis of the cylinder: the resistance of the globe will be but half so great as that of the cylinder. ”

“ Besides the globe always recedes from that side of itself which is descending in the oscillation, and by so receding comes nearer to the sides of the vessel so as even to strike against them sometimes. ”

“ In the scholium subjoined to the sixth section, we shewed by experiments of pendulums, that the resistances of equal and equally swift globes moving in air, water, and quicksilver, are as the densities of the fluids. We here prove the same more accurately by experiments of bodies falling in air and water. ”

“ But in continued mediums, as water, hot oil, and quicksilver, the globe as it passes thro them does not immediately strike against all the particles of the fluid that generate the resistance made to it, but presses only the particles that lie next to it, which press the particles beyond, which press other particles, and so on ”

“ Therefore since the resistances of similar and equally swift bodies, in a medium whose distant parts do not fly from each other, are as the squares of the diameters; the resistances made to bodies moving with very great and equal velocities in an elastic fluid, will be as the squares of the diameters, nearly. ”

“ Therefore if we suppose two systems of this kind, the correspondent particles, by reason of the similitude of the motions at their beginning, will continue to be moved with like motions, so long as they move without meeting one another. For if they are acted on by no forces, they will go on uniformly in right lines by the 1st law. But if they do agitate one another, with some certain forces, and those forces are as the diameters of the correspondent particles inversely and the squares of the velocities directly ”

“ So that the motions of correspondent and similar particles will continue similar till their first meeting with each other; and thence will arise similar collisions, and similar reflexions; which will again beget similar motions of the particles among themselves (by what was just now shewn) till they mutually sell upon one another again, and so on ad infinitum. ”