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would strongly urge young men who listen to lectures to

lecturing, and our readers shall have the benefit of it. We

PREFACE. The present is the fourth volume of the “ POPULAR LECTURER,” new series. It contains 30 lectures, extending to 384 pages, the average cost being one penny each. The subjects treated comprise Education, Natural History, Language, Mechanics, Industry, Cotton, Pictures, Travels, Biography, Mining, Science, Poetry, Music, &c.

Amongst the authors of these lectures will be found the names of Lord Brougham ; the Rev. Dr. Hook; Dr. Latham; the Dean of Carlisle ; Thomas Bazley, Esq., M.P.; Leo. H. Grindon, Esq.; R. W. Emerson, Esq.; the Rev. Marmaduke Miller; George Dawson, Esq., M.A. ; His Royal Highness the Prince Consort; E. W. Binney, Esq.,

the Right Hon. Sir James Stephen ; and other well-known names in literature and science.

The volume will be found to contain a large fund of valuable and interesting information, of the kind most serviceable to students, and the members of educational institutions generally. A “revival” is taking place in the art of

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study shorthand. Phonography is the system in which

these lectures have been reported by

THE EDITOR.

plating by what steps he ascended. Tracing his course of action may help others to gain the lower eminences lying within their reach, while admiration excited and curiosity satisfied are frames of mind both wholesome and pleasing. Nothing new, it is true, can be given in narrative, hardly anything in reflection, less still perhaps in comment orillustration; but it is .well to assemble in one view various parts of the vast subject, with the surrounding circumstances, whether accidental or intrinsic, and to mark in passing the misconceptions raised by individual ignorance or national prejulice which the historian of science occasionally finds crossing his path.

The remark is common and is obvious, that the genius of Newton did not manifest itself at a very early age. His faculties were not, like those of some great and many ordinary individuals, precociously developed. Among the former, Clairant stands preeminent, who at 19 years of age presented to the Royal Academy a memoir of great originality upon a difficult subject in the higher geometry, and at 18 published his great work on curves of double curvature, composed during the two preceding years. Pascal, too, at 16, wrote an excellent treatise on conic sections, That Newton cannot be ranked in this respect with those extraordinary persons, is owing to the accidents which prevented him from entering upon mathematical study before his 18th year; and then a much greater marvel was wrought than even the Clairants and the Pascals displayed.

His earliest history is involved in some obscurity, and the most celebrated of men has, in this particular, been compared to the most celebrated of rivers (the Nile), as if the course of both in its feebler state had been concealed from mortal eyes.

We have it, however, well ascertained that within four years, between the age of 18 and 22, he had begun to study mathematic science, and had taken his place among its greatest masters; learnt for the first

SIR ISAAC NEWTOX.

Auxions. At 25 years

age

in that and in every branch of philosophy connected 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 reconstructing analytical, astronomical, and optical science, almost defies belief. The statement can only be deemed possible by an appeal to the incontestible mankind as soon as they were clearly understood; cits these doctrines gained the universal assent of 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 pubinstituted 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 had borrowed from Newton; and next, whether, as only questions raised being, first, whether or not he 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 made them without any anticipation or participation Newton made the great steps of this progress, and by others, it is equally certain that there had been approaches in former times by preceding philosophers to the same discoveries. Cavalleri, hy his Method of Tangents (1367), had both given solutions Geometry of Indivisibles (1635), Roberval, by his

cting by what steps he ascended. Tracing his time the elements of geometry and analysis, and irse of action may help others to gain the lower

discovered a calculus which entirely changed the inences lying within their reach, while admiration face of the science, effecting a complete revolution ited and curiosity satisfied are frames of mind h wholesome and pleasing. Nothing new, it is

with it Before 1661 he had not read Euclid ; in # can be given in narrative, hardly anything in 1865 he bad committed to writing the method of Eection, less still perhaps in comment orillustration;

of

he had discovered the it is well to assemble in one view various parts the vast subject, with the surrounding circumres, whether accidental or intrinsic, and to mark grassing the misconceptions raised by individual

evi-uce that proves it strictly true.

By a rare feli

the fundamental properties of light.

So brilliant a surance or national preju-lice which the historian course of discovery in so short a time, changing and science occasionally finds crossing his path. The remark is common and is obvious, that the huius of Newton did not manifest itself at a very ly age. His faculties were not, like those of some at and many ordinary individuals, precociously eloped. Among the former, Clairant stands pre

the nent, who at 19 years of age presented val Academy a memoir of great originality upon

licult subject in the higher geometry, and at 18 blished his great work on curves of double curvae, composed during the two preceding years.

lication of his methodno sooner was the inquiry mal, too, at 16, wrote an excellent treatise on lic sections.

That Newton cannot be ranked in respect with those extraordinary persons, is owing the accidents which prevented him from entering u mathematical study before his 18th year; and n a much greater marvel was wrought than even

Clairants and the Pascals displayed. His earit history is involved in some obscurity, and the si celebrated of men has, in this particular, been L; vared to the most celebrated of rivers (the Nile) if the course of both in its feebler state had on concealed from mortal We have it, however, well ascertained that within T years, between the age of 18 and 22, he had begun study mathematic science, and had taken his place cong its greatest masters; learnt for the first

eyes,

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 aige. braically, while those just now mentioned had rather dealt with it geometrically.

It is thus easy to perceive how near an approach had been madle 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 inportant 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

SIR ISAAC NEWTON.

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which Descartes could not attempt; and it is remarkable that Cavalleri regarded curves as polygons, ->sırfaces as composed of lines, while Roberval viewed wnetrical quantities as generated by motion; 80 that the one approached to the differential calculus, the other to fluxions; and Fermat, in the interval *tween them, comes still nearer the great discosiery by his determination of maxima and minima, sulis drawing of tangents. More recently Hudden hadi maile public similar methods invented by Schotin; and what is material, treating the subject algeraically, while those just now mentioned had rather alt with it geometrically.

It is thus easy to perceive how near an approach ad been made to the calculus before the great event ť its final discovery. There had in like manner pen approaches made to the law of gravitation, and je dynamical system of the universe. Galileo's toportant propositions on motion, especially on cur linear motion, and Kepler's laws upon the elliptical prin of the planetary orbits, the proportion of the reas to the times, and of the periodic times to the iean distances; and Huygens's theorems on centriigal forces,—had been followed by still nearer pproaches to the doctrine of attraction. Borelli Iiad istinctly ascribed the motion of satellites to their eing drawn towards the principal planets, and thus revented from flying off by the centrifugal force. Cven the composition of white light, and the different ction of bodies upon its component parts, had been guely conjectured by Ant. de Dominis

atmosphere, and the oxydation of metals ; and by a The inductive system of Bacon had been, at least Leonardo da Vinci: and at the latter end of the Dext century Gilbert examined the whole subject of magnetic action entirely by experiments. Lord Bacon's claim to be regarded as the father of 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 obered 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 capa; ble

. 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, long prevalent

, were at length exploded, giving place to the sound doctrine which is now established.

modem philosophy, rests upon the important, the in

, archbishop f Spalatro, at the beginning, and more precisely in le middle

, of the 17th century by Marcus (Kronland, f I'rague), unknown to Newton, who only refers to Er archbishop's work; while the treatise of Huygens

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 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. 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

So that

en light, (frimaldi's observations on colours by inflexin, as well as on the elongation of the image in the rismatic spectrum, had been brought to his attention, Ithough much less near to his own great discovery

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