The appointment of Newton to the Lucasian chair at Cambridge seems to have been coeval with his grandest discoveries. The first of these of which the date is well authenticated is that of the different refrangibility of the rays of light, which he established in 1666. The germ of the doctrine of universal gravitation seems to have presented itself to him in the same year, or at least in 1667; and “in the year 1666 or before”[9] he was in possession of his method of fluxions, and he had brought it to such a state in the beginning of 1669, that he permitted Dr. Barrow to communicate it to Mr. Collins on the 20th of June in that year. Although we have already mentioned, on the authority of a written memorandum of Newton himself, that he purchased a prism at Cambridge in 1664, yet he does not appear to have made any use of it, as he informs us that it was in 1666 that he “procured a triangular glass prism to try therewith the celebrated phenomena of colours.”[10] During that year he had applied himself to the grinding of “optic glasses, of other figures than spherical,” and having, no doubt, experienced the impracticability of executing such lenses, the idea of examining the phenomena of colour was one of those sagacious and fortunate impulses which more than once led him to discovery. Descartes in his _Dioptrice_, published in 1629, and more recently James Gregory in his _Optica Promota_ published in 1663, had shown that parallel and diverging rays could be reflected or refracted, with mathematical accuracy, to a point or focus, by giving the surface a parabolic, an elliptical, or a hyperbolic form, or some other form not spherical. Descartes had even invented and described machines by which lenses of these shapes could be ground and polished, and the perfection of the refracting telescope was supposed to depend on the degree of accuracy with which they could be executed. In attempting to grind glasses that were not spherical, Newton seems to have conjectured that the defects of lenses, and consequently of refracting telescopes, might arise from some other cause than the imperfect convergency of rays to a single point, and this conjecture was happily realized in those fine discoveries of which we shall now endeavour to give some account.