Page:Newton's Principia (1846).djvu/358

 that, the pin being removed, the table, which had then no support but the iron hinges, fell downward, and turning round upon the hinges, gave leave to the globes to drop off from it. At the same instant, with the same pull of the iron wire that took out the pin, a pendulum oscillating to seconds was let go, and began to oscillate. The diameters and weights of the globes, and their times of falling, are exhibited in the following table.

But the times observed must be corrected; for the globes of mercury (by Galileo's theory), in 4 seconds of time, will describe 257 English feet, and 220 feet in only 3″42‴. So that the wooden table, when the pin was taken out, did not turn upon its hinges so quickly as it ought to have done; and the slowness of that revolution hindered the descent of the globes at the beginning. For the globes lay about the middle of the table, and indeed were rather nearer to the axis upon which it turned than to the pin. And hence the times of falling were prolonged about 18"'; and therefore ought to be corrected by subducting that excess, especially in the larger globes, which, by reason of the largeness of their diameters, lay longer upon the revolving table than the others. This being done, the times in which the six larger globes fell will come forth 8″ 12‴, 7″ 42‴, 7″ 42‴, 7″ 57‴, 8″ 12" and 7″ 42‴.

Therefore the fifth in order among the globes that were full of air being 5 inches in diameter, and 483 grains in weight, fell in 8″ 12‴, describing a space of 220 feet. The weight of a bulk of water equal to this globe is 16600 grains; and the weight of an equal bulk of air is $$\scriptstyle \frac{16600}{860}$$ grains, or 19$$\scriptstyle \frac{3}{10}$$ grains; and therefore the weight of the globe in vacuo is 502$$\scriptstyle \frac{3}{10}$$ grains; and this weight is to the weight of a bulk of air equal to the globe as 502$$\scriptstyle \frac{3}{10}$$ to 19$$\scriptstyle \frac{3}{10}$$; and so is 2F to $$\scriptstyle \frac{8}{3}$$ of the diameter of the globe, that is, to 13⅓ inches. Whence 2F becomes 28 feet 11 inches. A globe, falling in vacuo with its whole weight of 502$$\scriptstyle \frac{3}{10}$$ grains, will in one second of time describe 193⅓ inches as above; and with the weight of 483 grains will describe 185,905 inches; and with that weight 483 grains in vacuo will describe the space F, or 14 feet 5½ inches, in the time of 57‴ 58⁗, and acquire the greatest velocity it is capable of descending with in the air. With this velocity the globe in 8″ 12‴ of time will describe 245 feet and 5⅓ inches. Subduct 1,3863F, or 20 feet and ½ an inch, and there remain 225 feet 5 inches. This space, therefore, the falling globe ought by the