THE LAW OF GRAVITATION. 487 



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 w^as, 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 vary- 

 ing in intensity according to the law just mentioned, would be almost 

 indubitable. 



The method by which Newton undertook to determine the varia- 

 tion 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 dis- 

 covery of the law of gravitation. Hooke, and doubtless others, sub- 

 sequently labored for years to determine whether the intensity of the 

 earth^s 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 sup- 

 posed 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 

 Icnown, the arc which she describes in one minute of time becomes 

 known. Eegarding 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 in- 

 tensity 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. 



