Page:Newton's Principia (1846).djvu/324

of the lesser globe, which is in the duplicate ratio of the velocity, was to the whole resistance as 0,56752 tor 0,61675, that is, as 45,453 to 49,396; whereas that part of the resistance of the greater globe is almost equal to its whole resistance; and so those parts are nearly as 318,136 and 45,453, that is, as 7 and 1. But the diameters of the globes are 18¾ and 6$\scriptstyle {\frac {7}{8}}$; and their squares 351$\scriptstyle {\frac {9}{16}}$ and 47$\scriptstyle {\frac {17}{64}}$ are as 7,438 and 1, that is, as the resistances of the globes 7 and 1, nearly. The difference of these ratios is scarce greater than may arise from the resistance of the thread. Therefore those parts of the resistances which are, when the globes are equal, as the squares of the velocities, are also, when the velocities are equal, as the squares of the diameters of the globes.

But the greatest of the globes I used in these experiments was not perfectly spherical, and therefore in this calculation I have, for brevity's sake, neglected some little niceties; being not very solicitous for an accurate calculus in an experiment that was not very accurate. So that I could wish that these experiments were tried again with other globes, of a larger size, more in number, and more accurately formed; since the demonstration of a vacuum depends thereon. If the globes be taken in a geometrical proportion, as suppose whose diameters are 4, 8, 16, 32 inches; one may collect from the progression observed in the experiments what would happen if the globes were still larger.

In order to compare the resistances of different fluids with each other, I made the following trials. I procured a wooden vessel 4 feet long, 1 foot broad, and 1 foot high. This vessel, being uncovered, I filled with spring water, and, having immersed pendulums therein, I made them oscillate in the water. And I found that a leaden globe weighing 166$\scriptstyle {\frac {1}{6}}$ ounces, and in diameter 3$\scriptstyle {\frac {5}{8}}$ inches, moved therein as it is set down in the following table; the length of the pendulum from the point of suspension to a certain point marked in the thread being 126 inches, and to the centre of oscillation 134$\scriptstyle {\frac {3}{8}}$ inches.

The arc described in the first descent, by a point marked in the thread was inches.	64	.	32	.	16	.	8	.	4	.	2	.	1	.	½	.	¼
The arc described in the last ascent was inches.	48	.	24	.	12	.	6	.	3	.	1½	.	¾	.	$\scriptstyle {\frac {3}{8}}$	.	$\scriptstyle {\frac {3}{16}}$
The difference of the arcs, proportional to the motion lost, was inches.	16	.	8	.	4	.	2	.	1	.	½	.	¼	.	$\scriptstyle {\frac {1}{8}}$	.	$\scriptstyle {\frac {1}{16}}$
The number of the oscillations in water.					$\scriptstyle {\frac {29}{60}}$	.	1$\scriptstyle {\frac {1}{5}}$	.	3	.	7	.	11¼	.	12⅔	.	13⅓
The number of the oscillations in air.	85½	.	287	.	535