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His early and fast friend, Dr. Barrow—in compass of invention only inferior to Newton—who had been elected Professor of Greek in the University, in 1660, was made Lucasian Professor of Mathematics in 1663, and soon afterward delivered his Optical Lectures: the manuscripts of these were revised by Newton, and several oversights corrected, and many important suggestions made by him; but they were not published till 1669.

In the year 1665, he received the degree of Bachelor of Arts; and, in 1666, he entered upon those brilliant and imposing discoveries which have conferred inappreciable benefits upon science, and immortality upon his own name.

Newton, himself, states that he was in possession of his Method of Fluxions, "in the year 1666, or before." Infinite quantities had long been a subject of profound investigation; among the ancients by Archimedes, and Pappus of Alexandria; among the moderns by Kepler, Cavaleri, Roberval, Fermat and Wallis. With consummate ability Dr. Wallis had improved upon the labours of his predecessors: with a higher power, Newton moved forwards from where Wallis stopped. Our author first invented his celebrated BINOMIAL THEOREM. And then, applying this Theorem to the rectification of curves, and to the determination of the surfaces and contents of solids, and the position of their centres of gravity, he discovered the general principle of deducing the areas of curves from the ordinate, by considering the area as a nascent quantity, increasing by continual fluxion in the proportion of the length of the ordinate, and supposing the abscissa to increase uniformly in proportion to the time. Regarding lines as generated by the motion of points, surfaces by the motion of lines, and solids by the motion of surfaces, and considering that the ordinates, abscissae, &c., of curves thus formed, vary according to a regular law depending on the equation of the curve, he deduced from this equation the velocities with which these quantities are generated, and obtained by the rules of infinite series, the ultimate value required. To the velocities with which every line or quantity is generated, he gave the name of FLUXIONS, and to the lines or quantities themselves, that of FLUENTS. A discovery that successively baffled the acutest and strongest[Pg 15] intellects:—that, variously modified, has proved of incalculable service in aiding to develope the most abstruse and the highest truths in Mathematics and Astronomy: and that was of itself enough to render any name illustrious in the crowded Annals of Science.

At this period, the most distinguished philosophers were directing all their energies to the subject of light and the improvement of the refracting telescope. Newton, having applied himself to the grinding of "optic glasses of other figures than spherical," experienced the impracticability of executing such lenses; and conjectured that their defects, and consequently those of refracting telescopes, might arise from some other cause than the imperfect convergency of rays to a single point. He accordingly "procured a triangular glass prism to try therewith the celebrated phenomena of colours." His experiments, entered upon with zeal, and conducted with that industry, accuracy, and patient thought, for which he was so remarkable, resulted in the grand conclusion, that LIGHT WAS NOT HOMOGENEOUS, BUT CONSISTED OF RAYS, SOME OF WHICH WERE MORE REFRANGIBLE THAN OTHERS. This profound and beautiful discovery opened up a new era in the History of Optics. As bearing, however, directly upon the construction of telescopes, he saw that a lens refracting exactly like a prism would necessarily bring the different rays to different foci, at different distances from the glass, confusing and rendering the vision indistinct. Taking for granted that all bodies produced spectra of equal length, he dismissed all further consideration of the refracting instrument, and took up the principle of reflection. Rays of all colours, he found, were reflected regularly, so that the angle of reflection was equal to the angle of incidence, and hence he concluded that optical instruments might be brought to any degree of perfection imaginable, provided reflecting specula of the requisite figure and finish could be obtained. At this stage of his optical researches, he was forced to leave Cambridge on account of the plague which was then desolating England.

He retired to Woolsthorpe. The old manor-house, in which he was born, was situated in a beautiful little valley, on the west side of the river Witham; and here in the quiet home of his boyhood,[Pg 16] he passed his days in serene contemplation, while the stalking pestilence was hurrying its tens of thousands into undistinguishable graves.

Towards the close of a pleasant day in the early autumn of 1666, he was seated alone beneath a tree, in his garden, absorbed in meditation. He was a slight young man; in the twenty-fourth year of his age; his countenance mild and full of thought. For a century previous, the science of Astronomy had advanced with rapid strides. The human mind had risen from the gloom and bondage of the middle ages, in unparalleled vigour, to unfold the system, to investigate the phenomena, and to establish the laws of the heavenly bodies. Copernicus, Tycho Brahe, Kepler, Galileo, and others had prepared and lighted the way for him who was to give to their labour its just value, and to their genius its true lustre. At his bidding isolated facts were to take order as parts of one harmonious whole, and sagacious conjectures grow luminous in the certain splendour of demonstrated truth. And this ablest man had come—was here. His mind, familiar with the knowledge of past effort, and its unequalled faculties developed in transcendant strength, was now moving on to the very threshold of its grandest achievement. Step by step the untrodden path was measured, till, at length, the entrance seemed disclosed, and the tireless explorer to stand amid the first opening wonders of the universe.

The nature of gravity—that mysterious power which causes all bodies to descend towards the centre of the earth—had, indeed, dawned upon him. And reason busily united link to link of that chain which was yet to be traced joining the least to the vastest, the most remote to the nearest, in one harmonious bond. From the bottoms of the deepest caverns to the summits of the highest mountains, this power suffers no sensible change: may not its action, then, extend to the moon? Undoubtedly: and further reflection convinced him that such a power might be sufficient for retaining that luminary in her orbit round the earth. But, though this power suffers no sensible variation, in the little change of distance from the earth's centre, at which we may place ourselves, yet, at the distance of the moon, may not its force undergo[Pg 17] more or less diminution? The conjecture appeared most probable: and, in order to estimate what the degree of diminution might be, he considered that if the moon be retained in her orbit by the force of gravity, the primary planets must also be carried round the sun by the like power; and, by comparing the periods of the several planets with their distances from the sun, he found that, if they were held in their courses by any power like gravity, its strength must decrease in the duplicate proportion of the increase of distance. In forming this conclusion, he supposed the planets to move in perfect circles, concentric to the sun. Now was this the law of the moon's motion? Was such a force, emanating from the earth and directed to the moon, sufficient, when diminished as the square of the distance, to retain her in her orbit? To ascertain this master-fact, he compared the space through which heavy bodies fall, in a second of time, at a given distance from the centre of the earth, namely, at its surface, with the space through which the moon falls, as it were, to the earth, in the same time, while revolving in a circular orbit. He was absent from books; and, therefore, adopted, in computing the earth's diameter, the common estimate of sixty miles to a degree of latitude as then in use among geographers and navigators. The result of his calculations did not, of course, answer his expectations; hence, he concluded that some other cause, beyond the reach of observation—analogous, perhaps, to the vortices of Descartes—joined its action to that of the power of gravity upon the moon. Though by no means satisfied, he yet abandoned awhile further inquiry, and remained totally silent upon the subject.

These rapid marches in the career of discovery, combined with the youth of Newton, seem to evince a penetration the most lively, and an invention the most exuberant. But in him there was a conjunction of influences as extraordinary as fortunate. Study, unbroken, persevering and profound carried on its informing and disciplining work upon a genius, natively the greatest, and rendered freest in its movements, and clearest in its vision, through the untrammelling and enlightening power of religion. And, in this happy concurrence, are to be sought the elements of those amazing abilities, which, grasping, with equal facility, the[Pg 18] minute and the stupendous, brought these successively to light, and caused science to make them her own.