Page:On the connexion of the physical sciences (1834).djvu/18

6 case with a spheroid; but the celestial bodies are so nearly spherical, and at such remote distances from one another, that they attract and are attracted as if each were a dense point situate in its centre of gravity,—a circumstance which greatly facilitates the investigation of their motions.

The attraction of the earth on bodies at its surface in that latitude the square of whose sine is $1⁄3$, is the same as if it were a sphere; and experience shows that bodies there fall through 16·0697 feet in a second. The mean distance of the moon from the earth is about sixty times the mean radius of the earth. When the number 16·0697 is diminished in the ratio of 1 to 3600, which is the square of the moon's distance from the earth's centre, it is found to be exactly the space the moon would fall through in the first second of her descent to the earth, were she not prevented by the centrifugal force arising from the velocity with which she moves in her orbit; so that the moon is retained in lier orbit by a force having the same origin, and regulated by the same law, with that which causes a stone to fall at the earth's surface. The earth may, therefore, be regarded as the centre of a force which extends to the moon; and, as experience shows that the action and re-action of matter are equal and contrary, the moon must attract the earth with an equal and contrary force.