Inspiration, comments, and criticisms on this manuscript were gratefully received from Drs. Peter Heimann, David Kubrin, Charles Weiner, and two annonymous referees. An earlier version of section 3, with repetitions of the experiments of Poleni, 'sGravesande, and Desaguliers, was presented to the H. M. Evans History of Science Dinner Club, Berkeley, California, in May 1971.

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And upon these rules of ascending and descending, Galileo demonstrated that projections would, in spaces void of resistance, describe Parabolas. And all Mathematicians (not excepting Mr. Leibniz himself) unanimously agree that he was in the right. And yet Mr. Leibniz would have us measure the force imprest, not by the velocity generated to which it is proportional, but by the space of ascent to which it is not proportional.

In a second fragment Newton wrote (ibid., 119): The [weight or] gravity of the body which by its action impresses these impulsive forces upon the body acts with three times more force in the second part of [the] time than in the first and with five times more force in the third part of the time than in the first and with seven times more force in the fourth part of the time than in the first and so on. Which is as much as to say that the falling body grows heavier and heavier as it falls, and becomes three times heavier in the [middle of the] second part of the time than in the [middle of the] first and so on. Or that the weight of the body is proportional to the time of its falling. And by consequence that in the beginning of the first part of the time the body hath no weight at all. Which is contrary to the hypothesis of uniform gravity and to experience itself.

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