manner that Newton first attempted to verify his theory of gravitation. He knew approximately the velocity produced in falling bodies at the earth’s surface, and if the law of the inverse square of the distance held true, and the reputed distance of the moon was correct, he could infer that the moon ought to fall towards the earth at the rate of fifteen feet in one minute. Now, the actual divergence of the moon from the tangent of its orbit appeared to amount only to thirteen feet in one minute, and there was a discrepancy of two feet in fifteen, which caused Newton to lay “aside at that time any further thoughts of this matter.” Many years afterwards, probably fifteen or sixteen years, Newton obtained more precise data from which he could calculate the size of the moon’s orbit, and he then found the discrepancy to be inconsiderable.
His theory of gravitation was thus verified as far as the moon was concerned; but this was to him only the beginning of a long course of deductive calculations, each ending in a verification. If the earth and moon attract each other, and also the sun and the earth, there is reason to expect that the sun and moon should attract each other. Newton followed out the consequences of this inference, and showed that the moon would not move as if attracted by the earth only, but sometimes faster and sometimes slower. Comparison with Flamsteed’s observations of the moon showed that such was the case. Newton argued again, that as the waters of the ocean are not rigidly attached to the earth, they might attract the moon, and be attracted in return, independently of the rest of the earth. Certain daily motions resembling the tides would then be caused, and there were the tides to verify the reasoning. It was the extraordinary power with which Newton traced out geometrically the consequences of his theory, and submitted them to repeated comparison with experience, which constitutes his pre-eminence over all physicists.