intensity of the attraction were inversely as the square of the distance.
It deserves to be noticed, that to solve even this problem, Newton must at the time have been familiar with the doctrine of central forces, though Huyghens' work on that subject was not published until more than six years after.
Though the data which Newton assumed were not precisely those which the planetary systems presented, the result reached was highly interesting and calculated to encourage and direct further inquiry. The next question to be determined was, the law of the variation of the earth's attraction—Was this also inversely as the square of the distance? If so, the universality of the attraction of gravitation varying in intensity according to the law just mentioned, would be almost indubitable.
The method by which Newton undertook to determine the variation of the earth's attractive influence—so simple when once suggested—was entirely original with him, and is one, though but one, of the grounds for attributing to him preeminently the honor of the discovery of the law of gravitation. Hooke, and doubtless others, subsequently labored for years to determine whether the intensity of the earths attraction diminished with an increase of the distance from the center, and if so, according to what law, and yet all their efforts were fruitless. Newton's method was simply this, assuming the supposed distance of the moon from the earth to be correct, the length of the entire orbit of the moon may be readily determined. Moreover, the time of a complete revolution of the moon about the earth being known, the arc which she describes in one minute of time becomes known. Regarding this arc, which differs but little from a straight line, as the diagonal of a parallelogram, by the parallelogram of forces one of the sides of this parallelogram would represent the distance which the moon actually falls toward the earth under the influence of the earth's attraction in one minute of time. The arc just mentioned being known, this distance, which is the versed sine of the arc, may be readily determined. A measure is thus obtained of the intensity, at the moon, of the earth's attraction. By comparing this with the intensity of the attraction at the surface of the earth, as indicated by the distance a body near the surface will fall in one minute, the law of the variation in the intensity may be determined. Upon making the necessary computations the result was not just that which Newton anticipated, or rather hoped for. The distance which the moon ought to have fallen in one minute, according to the hypothesis, was one-sixth greater than that which, as it appeared, she actually did fall. Most men would have regarded this discrepancy as of little account, and accepting the result as, for the time at least, a sufficiently accurate demonstration of the hypothesis, would at once have given it publicity.
