On his return to Cambridge Newton again applied himself to the construction of reflecting telescopes, and succeeded in effecting it in 1668. In the following year Dr. Barrow resigned in his favour the Lucasian professorship of mathematics, which Newton continued to hold till the year 1703, when Whiston, who had been his deputy from 1699, succeeded him in the chair. On January 11, 1672, Newton was elected a Fellow of the Royal Society. He was then best known by the invention of the reflecting telescope; but immediately on his election he communicated to the Society the particulars of his theory of light, on which he had already delivered three courses of lectures at Cambridge, and they were shortly afterwards published in the Philosophical Transactions. It is impossible here to state the various phenomena of light and colours which were first detected and explained by Newton. They entirely changed the science of optics, and every advance which has since been made in it has only added to the importance and confirmed the value of his observations. The success of the new theory was complete. Newton, however, was much vexed and harassed by the discussions which it occasioned. The annoyance which he thus experienced made him even think of abandoning the pursuit of science, and although it failed to withdraw him from the studies to which he was devoted, it confirmed him in his unwillingness to publish their results. The next few years of Newton’s life were not marked by any remarkable events. They were passed almost entirely at Cambridge, in the prosecution of the researches in which he was engaged. The most important incident was the communication to Oldenburgh, and, through him, to Leibnitz, that he possessed a method of determining maxima and minima, of drawing tangents, and performing other difficult mathematical operations. This was the method of fluxions, but he did not announce its name or its processes. Leibnitz, in return, explained to him the principles and processes of the Differential Calculus. This correspondence took place in the years 1676 and 1677: but the method of fluxions had been communicated to Barrow and Collins as early as 1669, in a tract, first printed in 1711, under the title ‘Analysis per equationes numero terminorum infinitas.’ Newton had indeed intended to publish his discovery as an introduction to an edition of Kinckhuysen’s Algebra, which he undertook to prepare in 1672; but the fear of controversy prevented him, and the method of fluxions was not publicly announced till the appearance of the Principia in 1687. The edition of Kinckhuysen’s treatise did not appear; but the same year, 1672, was marked by Newton’s editing the Geography of Varenius.