Page:Newton's Principia (1846).djvu/355

 weighed and when they were let fall; because warmth rarefies the wax, and by rarefying it diminishes the weight of the globe in the water; and wax, when rarefied, is not instantly reduced by cold to its former density. Before they were let fall, they were totally immersed under water, lest, by the weight of any part of them that might chance to be above the water, their descent should be accelerated in its beginning. Then, when after their immersion they were perfectly at rest, they were let go with the greatest care, that they might not receive any impulse from the hand that let them down. And they fell successively in the times of 47½, 48½, 50, and 51 oscillations, describing a height of 15 feet and 2 inches. But the weather was now a little colder than when the globes were weighed, and therefore I repeated the experiment another day; and then the globes fell in the times of 49; 49½, 50. and 53; and at a third trial in the times of 49½, 50, 51, and 53 oscillations. And by making the experiment several times over, I found that the globes fell mostly in the times of 49½ and 50 oscillations. When they fell slower, I suspect them to have been retarded by striking against the sides of the vessel.

Now, computing from the theory, the weight of the globe in vacuo is 139$$\scriptstyle \frac{2}{5}$$ grains; the excess of this weight above the weight of the globe in water 132$$\scriptstyle \frac{11}{40}$$ grains; the diameter of the globe 0,99868 of an inch; $$\scriptstyle \frac{8}{3}$$ parts of the diameter 2,66315 inches; the space 2F 2,8066 inches; the space which a globe weighing 7$$\scriptstyle \frac{1}{8}$$ grains falling without resistance describes in a second of time 9,88164 inches; and the time G0″,376843. Therefore the globe with the greatest velocity with which it is capable of descending through the water by the force of a weight of 7$$\scriptstyle \frac{1}{8}$$ grains, will in the time 0″,376843 describe a space of 2,8066 inches, and in one second of time a space of 7,44766 inches, and in the time 25″, or in 50 oscillations, the space 186,1915 inches. Subduct the space 1,386294F, or 1,9454 inches, and there will remain the space 184,2461 inches which the globe will describe in that time in a very wide vessel. Because our vessel was narrow, let this space be diminished in a ratio compounded of the subduplicate ratio of the orifice of the vessel to the excess of this orifice above half a great circle of the globe, and of the simple ratio of the same orifice to its excess above a great circle of the globe; and we shall have the space of 181,86 inches, which the globe ought by the theory to describe in this vessel in the time of 50 oscillations, nearly. But it described the space of 182 inches, by experiment, in 49½ or 50 oscillations.

. 5. Four globes weighing 154$$\scriptstyle \frac{3}{8}$$ grains in air, and 21½ grains in water, being let fall several times, fell in the times of 28½, 29, 29½, and 30, and sometimes of 31, 32, and 33 oscillations, describing a height of 15 feet and 2 inches.

They ought by the theory to have fallen in the time of 29 oscillations, nearly.