David Gregory, Isaac Newton 53 



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 inven- 

 tion, and minded mathematics and philosophy more than 

 at any time since." 1 



In explanation of this passage it may be noted that the 

 " method of fluxions " was the foundation of the differential 

 calculus, and the " inverse method of fluxions " that of the 

 integral calculus. 



Newton's attention was probably drawn to the study of 

 optics by Barrow. The change of direction of a ray of 

 light on entering a transparent body obliquely had been a 

 favourite subject of investigation in many countries, and 

 the law regulating it was first correctly formulated by Snell 

 (1591-1626), Professor of Mathematics at the University of 

 Leiden. It was reserved to Newton to show that ordinary 

 white light, such as sunlight, consisted of a mixture of 

 different rays. When transmitted through a prism it 

 spreads out into a band of coloured light called the spectrum, 

 because the different rays are deviated to a different degree. 

 With the same transparent material, the measure of the 



1 From a MS. among the Portsmouth Papers, quoted in the 

 preface to the " Catalogue of the Portsmouth Papers." 



