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ing bodies on wheels, and made the inclined planes ofhard substances perfectly polished. But other andbetter methods were devised; and when Newton’slabours began, men of science were already familiarwith the fact that a falling body, if unretarded byatmospheric resistance or other cause, passes in thefirst second over l&rV feet, and has acquired at theend of the second a velocity of 32} feet per second;by the end of the second second it has passed over64} feet in all, and has acquired a velocity of 64} feetper second; at the end of the third it has passed over144-fb, and has acquired a velocity of 96| feet per se-cond; and so on,—the law being that the space fallenvaries as the square of the number of elapsed seconds,*while the velocity varies as this number directly.
So much, as I have said, was known before Newtonbegan to inquire into the laws influencing the celestialbodies; so that, if there is any truth in the story ofthe apple, Newton certainly did not inquire why theapple fell to the earth. It is not impossible that onsome occasion, when he was pondering over themotions of the celestial bodies,—and perhaps think-ing of those inviting speculations by which Borelli,Kepler, and others had been led to regard the celes-tial motions as due to attraction,—the fall of an applemay have suggested to Newton that terrestrial gravityafforded a clue which, rightly followed up, might leadto an explanation of the mystery. If the attraction of
* The spaces traversed in successive seconds are proportional tothe numbers 1, 3, 5, 7, &c.
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