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the sun rules the planets, the attraction of the earthmust rule the moon. What if the very force which drewthe apple to the ground he the same which keeps the dis-tant moon from passing away into space on ' a tangentto her actual orbit !
Whether the idea was suggested in this particularway or otherwise, it is certain that in 1665, at theage of only 23 years, Newton was engaged in the in-quiry whether the earth may not retain the moonin her orbit by the very same inherent virtue or attrac-tive energy whereby she draws bodies to her surfacewhen they are left unsupported.
In order to deal with this question, he required toknow the law according to which the attractive forcediminishes with distance. Assuming it to be identicalin quality with the force by which the sun retains theseveral planets in their orbits, he had, in the observedmotions of the planets, the means of determining thelaw very readily. The reasoning he actually em-ployed is not quite suited to these pages. I substitutethe following, which the reader may if he please omit(passing to the next paragraph), but it is not difficultto grasp. Let us call the distance of a planet (theearth, suppose), unity or 1, its period 1, its velo-city 1. Let the distance of a planet farther from thesun be called D; then the third law of Kepler tells usthat its period will be the square root of D x D x D,or will be D \/D. But regarding the orbits as circlesaround the sun as centre, the circumference of thelarger orbit will exceed that of the smaller in the pro -