MOTOR FORCE OF THE WORLD MACHINE 255 



worked out the theory of the moon's halo ; he is deeply inte- 

 rested in astronomy and optics. 



Precisely what set him pondering gravitation we do not 

 know. In any of his own writings he makes no mention of 

 the famous anecdote of the apple that we owe to his niece, 

 who told it to Voltaire, who embalmed it in the celebrated 

 English Letters published a few years after Newton's death. 

 The tree was there ; no doubt the apple fell. It is more likely 

 that the germ of his discovery lay in his reflections over Kepler's 

 laws, or in some passage in Wallis. Among the Portsmouth 

 papers an old manuscript has been found giving his own account 

 giving, too, a glimpse of the amazing activity of his mind 

 at this time. It runs : 



" In the beginning of the year 1665 I found the method of 

 approximating Series and the Rule for reducing any dignity of 

 any Binomial into such a series. The same year in May I 

 found the method of tangents of Gregory and Slusius, and in 

 November had the direct method of Fluxions, and the next 

 year in January had the theory of Colours, and in May following 

 I had entrance into the inverse method of Fluxions. And the 

 same year I began to think of gravity extending to the orb of 

 the Moon, and having found out how to estimate the force with 

 which [a] globe revolving within a sphere presses the surface 

 of the sphere, from Kepler's rule of the periodical times of the 

 Planets being in a sesquialterate proportion of their distances 

 from the centres of their orbs, I deduced that the forces which 

 keep the Planets in their orbs must [be] reciprocally as the 

 squares of their distances from the centres about which they 

 revolve ; and thereby compared the force requisite to keep the 

 Moon in her orb with the force of gravity at the surface of the 

 earth, and found them answer pretty nearly. All this was in 

 the two plague years of 1665 and 1666, for in those days I was 

 in the prime of my age for invention, and minded Mathematicks 

 and Philosophy more than at any time since." * 



The account was written in after years, probably in his old 

 age. It is not likely the discovery came to him with all the 

 heavy armament of mathematical proof in which it appears in 



1 Quoted by Berry from the Preface to the Catalogue of the Ports- 

 mouth Papers. 



