twenty-three years of age, he had already not only mastered all of value that had previously been written on Mathematics, Astronomy and Natural Philosophy, but he had discovered the Binomial Theorem, and had conceived and to an extent developed the Differential Calculus—an achievement with which few other events in the history of science deserve to be compared, after we except his own subsequent brilliant discoveries in Optics, and his successful application of the calculus to the discovery of the law and explanation of many of the most interesting phenomena of gravitation. In the summer of 1665 he left Cambridge on account of the plague which prevailed there at the time and returned to his native town of Woolsthorpe in Lancashire. It was during this visit to Woolsthorpe that the famous incident occurred which, as is generally supposed, first suggested to him the idea of gravitation and was the occasion of his great discovery. The account of it is given by his contemporary and friend Pemberton. One day as he was sitting under an apple tree in the garden an apple fell before him. This turned the currents of his thoughts and led him to reflect upon the nature of that mysterious influence which urges all terrestrial bodies toward the center of the earth, causing them, when free to move, to fall with a constantly accelerated velocity, which continues to act moreover without sensible diminution in intensity at the top of the highest towers or even the summit of the loftiest mountain. The thought was suggested to his mind, why may not this power extend to the moon? And if so, is not this the influence which retains her in her orbit round the earth? He at once applied himself to the determination if possible of the truth of this conjecture. If the moon were really retained in her orbit by terrestrial gravity, he concluded that the planets were probably retained in their orbits by a similar influence of the sun. Moreover, if the attractive influence of the earth extended to the moon and that of the sun to the farthest limits of our system, he concluded that the intensity of the attraction in each case diminished as the distance from the center of attraction increased. If this were so, it would manifest itself by a difference in the velocities of the planets, they being at different distances from the sun, and he accordingly inferred that by a comparison of the velocities of the motions of the several planets with each other, the law of variation of the intensity of the attractive force might be determined. Kepler's third law, that the squares of the times are as the cubes of the mean distances, furnished him at once with the necessary data for the calculation. He was not at the time able to solve the precise problem which the actual phenomena presented, the planetary orbits being elliptical and the attractive force at one of the foci, but assuming the orbits to be circular and the attractive force at the center, he found that Kepler's law would follow, if the variation in the
