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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 inter- 

 esting 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 famoiis inci- 

 dent 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 con- 

 tinues 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 con- 

 cluded 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 deter- 

 mined. 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 



