212 A Short History of Astronomy [Cn. IX. 



of Galilei and Kepler. Telescopes on this principle, differ- 

 ing however in some important particulars from Newton's, 

 had already been described in 1663 by James Gregory 

 (1638-1675), with whose i Itas Newton was acquainted, but 

 it does not appear that Gregory had actually made an 

 instrument. Owing to mechanical difficulties in construction, 

 half a century elapsed before reflecting telescopes were 

 made which could compete with the best refractors of the 

 time, and no important astrcno nical discoveries were made 

 with them before the time of William Herschel (chapter XIL), 

 more than a century after the original invention. 



Newton's discovery of the effect of a prism in resolving 

 a beam of white light into different colours is in a sense 

 the basis of the method of spectrum analysis (chapter xin., 

 299), to which so many astronomical discoveries of the 

 last 40 years are due. 



169. The ideas by which Newton is best known in each 

 of his three great subjects gravitation, his theory of 

 colours, and fluxions seem to have occurred to him 

 and to have been partly thought out within less than two 

 years after he took his degree, that is before he was 24. 

 His own account written many years afterwards gives 

 a vivid picture of his extraordinary mental activity at this 

 time : 



" 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 centers 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 centers 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 



