BEGINNINGS OF MODERN MATHEMATICAL SCIENCE 291 



of gravitation by carefully comparing the motion of the moon 

 with that of a falling body near the earth for which however 

 his data were not yet sufficiently accurate. 



Newton took his B. A. degree in the Lent Term, 1665. In 

 that spring the plague appeared, and for a couple of years he lived 

 mostly at home, though with occasional residence at Cambridge. 

 Probably at this time his creative powers were at their highest. His 

 use of fluxions may be traced back to May, 1665 ; his theory of gravi- 

 tation originated in 1666; and the foundation of his optical discov- 

 eries would seem to be only a little later. In an unpublished mem- 

 orandum made some years later (cancelled, but believed to be correct 

 in the part here quoted), he thus described his work of this time : 

 'In the beginning of the year 1665 I found the method of approximat- 

 ing 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 extend- 

 ing to the orb of the Moon, and . . . from Kepler's Rule of the period- 

 ical 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 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.' Ball, Mathematical Gazette, July, 1914. 



OPTICS. Interesting himself in the telescope, Newton suc- 

 ceeded in eliminating the disturbing chromatic aberration due to 

 unequal refraction of the different colors by constructing a reflect- 

 ing telescope with a concave mirror in place of a convex lens. On 

 the other hand, turning his attention to the colors of the solar 

 spectrum, he wrote his Opticks or a Treatise of the Reflections, 

 Refractions, Inflections and Colours of Light, published in 1704. 



