The manor-house of Woolsthorpe, a few miles from Grantham, seated in a little valley near the source of the Witham, was the scene of Newton’s birth. Popular tradition reports, that the fall of an apple from a tree, in the orchard belonging to this house, was the mustard-seed out of which ultimately grew the grand theory of universal gravitation, and the story is not without a leaven of truth. It is certain that, to avoid the plague which ravaged England in 1666, Newton retired from Cambridge; and, when sitting alone, in his garden at Woolsthorpe, his thoughts were directed to that remarkable power which causes all bodies to descend toward the centre of the earth. The supposition presented itself, that as this power extends to the highest altitudes of the earth’s surface, it probably extends much farther into space; so that even the moon may gravitate toward the earth, and be balanced in her orbit by the combined force of attraction and the centrifugal force implied in her motion. If this were true, the planets might be supposed to gravitate toward the sun, and to be restrained thereby from flying off under the action of the centrifugal force. Sixteen years rolled away before this beautiful hypothesis was verified, and difficulties arose in testing it, which seemed to disprove it altogether. It was necessary to calculate the force of gravity at the surface of the earth; to estimate its diminished energy at an increased distance; and, after having found the law of the diminution, to ascertain whether the phenomena of the lunar motions corresponded proportionably with those of falling bodies at the terrestrial surface. Assuming the force of gravity to vary inversely as the square of the distance, it followed that, at the distance of the moon, it would be about 3600 times less than at the surface of the earth. The problem, therefore, to be solved was, whether the versed sine of an arc described by the moon—which measures the space through which in the same time she would fall to the earth, if abandoned to the action of gravity—would be 3600 times less than the space through which in the same time a heavy body falls, at the earth’s surface, [Illustration] A B being the arc of the moon’s orbit, _c d_ the sine of the arc, and _e f_ the versed sine. After a careful study of the lunar observations supplied by Flamstead, and a series of calculations—displaying unexampled originality and industry—Newton fully demonstrated that the versed sine of an arc described by the moon in one minute, was equal to the space traversed in descent by a heavy body at the surface of the earth in one second—the exact proportion that ought to exist, according to the modification to which the intensity of gravity is subject by variation of distance.