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time the elements of geometry and analysis, and discovered a calculus which entirely changed the face of the science, effecting a complete revolution. in that and in every branch of philosophy connected with it. Before 1661 he had not read Euclid; in 1665 he had committed to writing the method of fluxions. At 25 years of age he had discovered the law of gravitation, and laid the foundation of celestial dynamics, the science created by him. Before ten years had elapsed he added to his discoveries that of the fundamental properties of light. So brilliant a course of discovery in so short a time, changing and reconstructing analytical, astronomical, and optical science, almost defies belief. The statement can only be deemed possible by an appeal to the incontestible evidence that proves it strictly true. By a rare felicity these doctrines gained the universal assent of mankind as soon as they were clearly understood; and their originality has never been seriously called in question. Some doubts having been raised respecting his inventing the calculus-doubts raised in consequence of his so long withholding the publication of his method-no sooner was the inquiry instituted than the evidence produced proved so decisive, that all men in all countries acknowledged him to have been by several years the earliest inventor, and Leibnitz, at the utmost, the first publisher; the only questions raised being, first, whether or not he had borrowed from Newton; and next, whether, as second inventor, he could have any merit at all; both which questions have long since been decided in favour of Newton. But undeniable though it be that Newton made the great steps of this progress, and made them without any anticipation or participation by others, it is equally certain that there had been approaches in former times by preceding philosophers to the same discoveries. Cavalleri, by his Geometry of Indivisibles (1635), Roberval, by his Method of Tangents (1367), had both given solutions
which Descartes could not attempt; and it is remarkable that Cavalleri regarded curves as polygons, surfaces as composed of lines, while Roberval viewed geometrical quantities as generated by motion; so that the one approached to the differential calculus, the other to fluxions; and Fermat, in the interval between them, comes still nearer the great discovery by his determination of maxima and minima, and his drawing of tangents. More recently Hudden had made public similar methods invented by Schoetin; and what is material, treating the subject algebraically, while those just now mentioned had rather dealt with it geometrically.
It is thus easy to perceive how near an approach had been made to the calculus before the great event of its final discovery. There had in like manner been approaches made to the law of gravitation, and the dynamical system of the universe. Galileo's important propositions on motion, especially on curvilinear motion, and Kepler's laws upon the elliptical form of the planetary orbits, the proportion of the areas to the times, and of the periodic times to the mean distances; and Huygens's theorems on centrifugal forces,-had been followed by still nearer approaches to the doctrine of attraction. Borelli had distinctly ascribed the motion of satellites to their being drawn towards the principal planets, and thus prevented from flying off by the centrifugal force. Even the composition of white light, and the different action of bodies upon its component parts, had been vaguely conjectured by. Ant. de Dominis, archbishop of Spalatro, at the beginning, and more precisely in the middle, of the 17th century by Marcus (Kronland, of Prague), unknown to Newton, who only refers to the archbishop's work; while the treatise of Huygens on light, Grimaldi's observations on colours by inflexion, as well as on the elongation of the image in the prismatic spectrum, had been brought to his attention, although much less near to his own great discovery
than Marcus's experiment. But all this only shows that the discoveries of Newton, great and rapid as were the steps by which they advanced our knowledge, yet obeyed the law of continuity, or rather of gradual progress, which governs all human approaches towards perfection. The limited nature of man's faculties precludes the possibility of his ever reaching at once the utmost excellence of which they are capable. Survey the whole circle of the sciences, and trace the history of our progress in each, you find this to be the universal rule. In chymical philosophy the dreams of the alchymists prepared the way for the more rational, though erroneous, theory of Stahl; and it was by repeated improvements that his errors, so long prevalent, were at length exploded, giving place to the sound doctrine which is now established.
The great discoveries of Black and Priestley on heat and aeriform fluids, had been preceded by the happy conjectures of Newton, and the experiments of others. Nay, Voltaire had well nigh discovered both the absorption of heat, the constitution of the atmosphere, and the oxydation of metals; and by a few more trials might have ascertained it. Cuvier had been preceded by inquirers who took sound views of fossil osteology, among whom the truly original genius of Hunter fills the foremost place. The inductive system of Bacon had been, at least in its practice, known to his predecessors. Observations and even experiments were not unknown to the ancient philosophers, though mingled with gross errors: in early times, almost in the dark ages, experimental inquiries had been carried on with success by Friar Bacon, and that method actually recommended in a treatise, as it was two centuries later by Leonardo da Vinci: and at the latter end of the next century Gilbert examined the whole subject of magnetic action entirely by experiments. So that Lord Bacon's claim to be regarded as the father of modern philosophy, rests upon the important, the in
valuable step of reducing to a system the method of investigation adopted by those eminent men, generalizing it, and extending its application to all matters of contingent truth, exploding the errors, the absurd dogmas, and fantastic subtleties of the ancient schools, above all, confining the subject of our inquiry, and the manner of conducting it, within the limits which our faculties prescribe. Nor is this great law of gradual progress confined to the physical sciences; in the moral it equally governs. Before the foundations of political economy were laid by Hume and Smith, a great step had been made by the French philosophers, disciples of Quesnai; but a nearer approach to sound principles had signalized the labours of Gournay, and those labours had been shared and his doctrines patronized by Turgôt, when chief minister.
Again, in constitutional policy, see by what slow degrees, from its first rude elements, the attendance of feudal tenants at their lord's court, and the summons of burghers, to grant supplies of money, the great discovery of modern times in the science of practical politics has been effected, the representative scheme which enables States of any extent to enjoy popular government, and allows mixed monarchy to be established, combining freedom with order-a plan pronounced by the statesmen and writers of antiquity to be of hardly possible formation, and wholly impossible continuance. The globe itself, as well as the science of its inhabitants, has been explored according to the law which forbids a sudden and rapid leaping forward, and decrees that each successive step, prepared by the last, shall facilitate the next. Even Columbus followed several successful discoverers on a smaller scale, and is by some believed to have had, unknown to him, a predecessor in the great exploit by which he pierced the night of ages, and unfolded a new world to the eyes of the old. The arts afford no exception to the general law. Demos
thenes had eminent forerunners, Pericles the last of them. Homer must have had predecessors of great merit, though doubtless as far surpassed by him as Fra Bartolomeo and Pietro Perugino were by Michael Angelo and Raphael. Dante owed much to Virgil; he may be allowed to have owed, through his Latin Mentor, not a little to the old Grecian; and Milton had both the orators and poets of the ancient world for his predecessors and his masters. The art of war itself is no exception to the rule. The plan of bringing an overpowering force to bear on a given point had been tried occasionally before Frederick II. reduced it to a system; and the Wellingtons and Napoleons of our own day made it the foundation of their strategy, as it had also been previously the mainspring of our naval tactics. It has oftentimes been held that the invention of logarithms stands alone in the history of science, as having been preceded by no step leading towards the discovery. There is, however, great inaccuracy in this statement, for not only was the doctrine of infinitesimals familiar to its illustrious author, and the relation of geometrical to arithemetical series well known, but he had himself struck out several methods of great ingenuity and utility (as that known by the name of Napier's Bones) -methods that are now forgotten, eclipsed as they were by the consummation which has immortalized his name. So the inventive powers of Watt, preceded as he was by Worcester and Newcomen, but far more materially by Causs and Papin, had been exercised on some admirable contrivances, now forgotten, before he made the step which created the steam-engine anew-not only the parallel motion, possibly a corollary to the proposition on circular motion in the Principia, but the separate condensation, and above all, the governor, perhaps the most exquisite of mechanical inventions: and now we have those here present who apply the like principle to the diffusion of knowledge, aware, as they must be, that