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peculiarly fitted for the business by his singular mathematical and chemical knowledge. It appears that he had always taken great interest in chemistry; for, from the time when, as a child, he had lived with the apothecary at Grantham, till he resided at Cambridge, he had continued to occupy himself occasionally with that science. Of this we have a proof in his philosophical works, which are filled with profound chemical observations. In tracing the order of these labours, we find him, in his first researches about telescopes, in 1672, making a number of experiments on the alloys of metals, in order to discover the combinations most advantageous for optical purposes, and amassing in these essays a number of remarkable peculiarities in the constitution of bodies. Three years afterwards, the paper on the colours in thin plates affords us still more varied experiments on the combinations of different bodies, solid or liquid, with each other, and on the tendency or the repugnancy they have to unite; still later, the same subjects are treated with greater boldness and comprehensiveness in the Treatise on Optics, and particularly in the queries placed at the end of that admirable work; for what, at that time, could be bolder, than to assert that water must contain an inflammable principle, and that a similar one exists in the diamond?

Besides the natural charm a mind like Newton's must have felt, in the various astonishing and mysterious phenomena of chemistry, what additional interest must they have excited in him, when, having discovered the existence of molecular attraction, and the effects of actions exerted at small distances in the motion of light, he was led to see that similar forces, differing only in their law of decrease, or intensity, would be sufficient to produce in the ultimate particles of bodies all those phenomena of union and disunion, that constitute the science of chemistry! With these new and important phenomena, he occupied himself constantly at Cambridge; and, along with the study of chronology and history, they were the only relaxation he allowed himself when fatigued with his mathematical meditations. He had constructed a small laboratory for prosecuting such pursuits; and it would seem that, in the years immediately following the publication of the Principia, he devoted

almost his whole time to them. But a disastrous accident deprived him, in an instant, of the fruits of so much labour, and lost them to science for ever.

Newton had a favourite little dog called "Diamond." One winter's morning, while attending early service, he inadvertently left this dog shut up in his room; on returning from chapel, he found that the animal, by upsetting a taper on his desk, had set fire to the papers on which he had written down his experiments; and thus he saw before him the labours of so many years reduced to ashes. It is said, that on first perceiving this great loss, he contented himself by exclaiming, "Oh, Diamond! Diamond! thou little knowest the mischief thou hast done." But the grief caused by this circumstance, grief which reflection must have augmented, instead of alleviating, injured his health, and, if we may venture to say so, for some time impaired his understanding. This incident in Newton's life, which appears to be confirmed by many collateral circumstances, is mentioned in a manuscript note of Huygens, which was communicated to M. Biot, of the French Institute, by Mr. Vanswinden, in the following letter:

"There is among the manuscripts of the celebrated Huygens, a small journal in folio, in which he used to note down different occurrences; it is side Z., No. 8, page 112, in the catalogue of the library at Leyden: the following extract is written by Huygens himself, with whose hand-writing I am well acquainted, having had occasion to peruse several of his manuscripts and autograph letters.* On the 29th May, 1694, a Scotchman of the name of Colin, informed me, that Isaac Newton, the celebrated mathematician, eighteen months previo::sly, had become deranged in his mind, either from too great application to his studies, or from excessive grief at having lost, by fire, his chemical laboratory and some papers. Having made observations before the Chancellor of Cambridge,

The Latin words used by Huygens are as folScotus, celeberrimum ac rarum geometram, Ism. lows:1694, die 29 Maii, narravit mihi D. Colin, Newtonum, incidisse in phrenitin abhinc anno ac sex mensibus. An ex nimiâ studii assiduitate, an dolore infortunii, quod in incendio laboratorium chemicum et scripta quædam amiserat. Cum ad archiepiscopum Cant. venisset, ea locutum quæ alienationem mentis indicarent; deinde ab amicis cura ejus suscepta, domoque clausâ, remedia volenti nolenti adhibita, quibus jam sanitatem recuperavit, ut jam nunc librum suum Principiorum intelligere incipiat.""

which indicated the alienation of his intellect, he was taken care of by his friends, and being confined to his house, remedies were applied, by means of which he has lately so far recovered his health as to begin to again understand his own Principia. Huygens mentioned this circumstance to Leibnitz, in a letter, dated the 8th of the following June, to which the latter replied on the twenty-third. I am very happy that I received information of the cure of Mr. Newton, at the same time that I first heard of his illness, which, without doubt, must have been most alarming. It is to men like Newton and yourself, Sir, that I desire health and a long life." This account by Huygens is corroborated by the following extract from a MS. at Cambridge, written by Mr. Abraham de la Pryne, dated Feb. 3, 1692, in which, after mentioning the circumstance of the papers being set fire to, he says, "But when Mr. New ton came from chapel, and had seen what was done, every one thought he would have run mad, he was so troubled thereat, that he was not himself for a month after." From these details, it would appear that the mind of this great man was affected, either by excess of exertion, or through grief at seeing the result of its efforts destroyed. In truth, there is nothing extraordinary in either of these suppositions; nor ought we to be astonished that the first sentiments arising from the great affliction which befell Newton were expressed without violence, for his mind was, as it were, prostrated under their weight. But the fact of a derangement in his intellect, whatever may have been the cause, will explain how, after the publication of the Principia, in 1687, Newton, though only forty-five years old, never more gave to the world a new work in any branch of science; and why he contented himself with merely publishing those that he had composed long before this epoch, confining himself to the completion of those parts that required development. We may also remark, that even these explanations appear in every case to be taken from experiments or observations previously made; as for instance, the additions to the second edition of the Principia in 1713, the experiments on thick plates, on diffraction, and the chemical queries placed at the end of the Opties, in 1704; for Newton distinctly announces them to be taken from manuscripts which he had former

ly written; and adds, that though he felt the necessity of extending, or of rendering them more perfect, yet henceforth such subjects were no longer in his way.* Thus it appears, that though he had recovered his health sufficiently to understand all his researches, and even, in some cases, to make additions or useful alterations (as is shown by the second edition of the Principia, for which he kept up a very active mathematical correspondence with Cotes), yet he did not wish to undertake new labours in the department of science where he had done so much, and where he was so well able to conceive what remained to do. But whether this determination were imposed on him by necessity, or merely caused by a sort of moral weariness, the result of so long and severe an exercise of thought, what Newton had already done is sufficient to place him in the first rank of discoverers in every branch of pure and applied mathematics. After having admired him as almost the creator of Natural Philosophy, as one of the chief promoters of mathematical analysis, we must acknowledge, also, that to him we owe the first idea of mechanical chemistry; since he regarded its combinations as the result of molecular action, and by the boldest and most felicitous inductions raised himself to a conception of the composition and variation in the state of bodies, such as before his time was unknown and unthought of. Uniting so much theoretical and experimental knowledge, Newton must have been of the greatest service in superintending the melting down of the old coinage, which, from its worn and depreciated state, it was necessary to call in; and we find, accordingly, that in three years time (1699) he was recompensed for his services by the lucrative appointment of Master of the Mint. Hitherto, his means had been small for his domestic wants. This new accession of fortune, however, did not render him unworthy of it; having gained it by merit, he maintained his title to it by the use he made of it. At this time, all the clouds had disappeared with which the spirit of jealousy had endeavoured to obscure his glory. He had raised himself too high to have a rival remain

Vide Optics, end of second book.

The estates of Woolsthorpe and Sustern were valued, at that period, at about 801. per annum. He derived, also, some revenue from the university and from Trinity College.-Vide Turner,

ing, and due homage was paid from all quarters to his transcendent talents.

In 1699, the Académie des Sciences at Paris being empowered by a new Royal Charter to admit a very small number of foreign associates, hastened to make this distinction yet more honourable by enrolling on its lists the name of Newton. In 1701, the University of Cambridge again elected him to serve in Parliament.

In 1703, he was chosen President of the Royal Society of London, a title which renders the person on whom it is conferred, as it were, the public representative of philosophy and science, and gives to him an influence the more useful, because it proceeds from voluntary confidence. Newton was annually reelected to this honourable office, and continued to fill it during the remainder of his life (a period of twenty-five years); and finally, in 1705, he was knighted by Queen Anne. He now determined to publish himself, or to allow others to publish, his different works. He first gave to the world his Optics, a treatise which comprises all his researches on light. It would appear that, fatigued with the petty attacks that his ideas on these subjects had drawn upon him (in 1672-5), Newton had resolved not to publish this work during the life of Hooke; the latter, however, died in 1702, and the jealous influence he had been able to exercise had previously expired. Newton, having no longer any fear of controversy, did not delay publishing these discoveries, which, though of a different description, and of a less general application than those which the world had admired in the Principia, are not inferior to them in the originality of their conception.

When the Optics appeared, in 1704, it was written in English. Dr. Samuel Clarke, afterwards so celebrated for his controversies with Leibnitz, published a Latin version in 1706, with which Newton was so satisfied, that he presented the translator with 5007. as a testimony of his acknowledgment; many editions of the work itself, and of the translation, rapidly succeeded each other, both in England and on the con tinent. Although the number of editions shows how much this treatise has from that time been admired, yet its whole merit has not been fully appreciated till within these few years, when new discoveries, and particularly that of the polarization of light, have rendered

perceptible all the importance of certain very delicate phenomena, whose general existence Newton had pointed out in the propagation of light, and which, under the names of "fits of easy transmission and reflection," he considered as essential attributes of that principle. These properties being so subtile, that they escape all observations which are not extremely exact, and being at the same time so singular that, in order to admit them, it is necessary to have the fullest conviction of the accuracy of the experiments which establish them, they were, for a long period, regarded merely as ingenious hypotheses; and it has even been thought in some degree necessary to apologize for Newton's having mentioned them. But, in the present day, it is generally acknowledged that these properties, with the laws assigned to them by Newton, are modifications really and incontestably inherent in light, though their existence must be diffe rently conceived and applied, according to the hypothesis we adopt as to the nature of the luminous principle.

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To the first edition of the Optics, Newton added two analytical treatises, the one entitled "Enumeratio linearum tertii ordinis," and the other, "Tractatus de quadratura curvarum." The latter contains an explanation of the method of fluxions, and its application to the quadrature of curves, by means of expansion into infinite series; and the first a very elegant classification of curves of the third order, with a clear and rapid enumeration of their properties, which Newton probably had discovered by the method of expansion, enunciated in the former treatise though he merely indicates the results, without mentioning the process which he had employed in investigating them. These two treatises were withdrawn from the following editions of the Optics, with the subject of which they were not sufficiently connected; but we may presume that Newton's object in inserting them in the edition of 1704 was to insure his right to the discovery and application of those new analytical methods, which, after having been so long in his secret, and as he supposed, sole possession, had now for several years been making their way with much success on the continent, and were the producing new and imports.t results in the hands of foreign analysts, particularly of Leibnitz, and the Bernoullis.

The great renown which Newton had acquired, caused all his productions to be received with avidity. Hence it was that Whiston published in 1707, without the knowledge or consent of Newton, the "Arithmetica universalis," which appears to have been merely the text of the lectures on Algebra, that he delivered at Cambridge, written rapidly for his own use, and not intended for publication. Science, however, must congratulate itself on the transgression of confidence that has fortunately made this work known; for it were impossisible to see a more perfect model of the art by which geometrical or numerical questions may be submitted to algebraical calculation; whether we regard the happy choice of the unknown quantities, or the ingenious combination of analytical formulæ, employed in finding the simplest method of solution. A second and more complete edition was published in London in 1712, according to Gravesande, with the participation of Newton himself-a proof that this production of his youth appeared to him neither unworthy of his name nor of his attention.

It was also, by the care of some other editor, but with his consent, that in 1711 a small treatise, entitled "Methodus differentialis," was published, in which he shows how to draw a parabolic curve through any given number of points-a determination which, when reduced into formulæ, is very useful in the interpolation of series, and in approximating to the quadratures of

curves.

In the same year, by other hands, was published the long-suppressed treatise, "Analysis per equationes numero terminorum infinitus," which he had composed in 1665, and in which, as we have already said, he had explained his first discoveries in fluxions, and in expansions, by means of infinite series. A copy of this dissertation had formerly been taken by Collins, from the original sent to him by Barrow; and having been found among his papers after his death, leave was obtained from Newton to publish it—a permission which he probably gave the more willingly, as the work being of old date, incontestably established his claims to the invention of the new method.

Newton formerly had prepared, on the same subject, a more extensive treatise, entitled "A method of Fluxions," which he proposed to join as an introduction

to a treatise on algebra, by Kinckhuysen, of which he had undertaken to publish an edition in 1672: this, without doubt, would have been more valuable than the book itself, but his fear of scientific quarrels induced him then to keep his manuscript secret. Towards the close of his life, he again thought of publishing it, but it was not printed till after his death. The same apprehension had, as we have already said, prevented him from publishing his " Optical Lectures" delivered at Cambridge. Happily, however, he had entrusted copies to many persons, and among others, to Gregory, professor of astronomy at Oxford, one of which being printed three years after his death, has preserved to us this work. It presents a very detailed experimental exposition of the phenomena of the composition and decomposition of light, with their most usual applications: it is, in fact, the Optics without the most difficult part, viz. the theory of colours produced by thin plates; but, in the other parts, fully developed both by calculations and by numerous experiments. In this form, it was extremely proper for the use to which Newton intended it, and at this day it offers a most valuable model for an elementary exposition of phenomena by experiment.

Here would terminate our account of the works on which the fame of Newton reposes, had not a new literary dispute (about 1712), which, in fact, he did not provoke, and the existence of which, perhaps, he more than once regretted, completely revealed all the fertility of his wonderful genius, and assembled a multitude of analytical discoveries, which we find in the correspondence that ensued. We have seen that Newton, for a long time, obstinately guarded the secret of his discoveries, and particularly that of the method of fluxions, of which he justly foresaw the future utility in calculating the phenomena of nature. However, in 1676, Leibnitz having heard of the new results that Newton was said to have obtained by means of infinite series, testified to Oldenburg the desire he felt to become acquainted with them. The latter induced Newton not to refuse a communication which could not but be honourable to him. In consequence (23rd of June, 1676), Newton sent to Oldenburg a letter to be transmitted to Leibnitz, in which he gave expressions for the expansion in series of binomial powers, of the sine in terms of the arc, of the arc

in terms of its sine, and of elliptical, circular, and hyperbolic functions, without, however, any demonstration or indication of the means he had used for obtaining these results; merely stating that he possessed a method by which, when these series were given, he could obtain the quadratures of the curves from which they were derived, as well as the surfaces and centres of gravity of the solids formed by their rotation. This may in fact be done by considering each term of these series as the ordinate of a particular curve, and by then applying the method previously given by Mercator, for squaring curves, of which the ordinates are expressed rationally in terms of the abscissa. This is precisely what Leibnitz remarked in his answer to Newton on the 27th of the following August, adding that he should be glad to know the demonstration of the theorems on which Newton founded his method of reducing into series; but that, for himself, though he recognized the utility of this method, he employed another, which consisted in decomposing the given curve into its superficial elements, and in transforming these infinitely small elements into others, equivalent to them, but belonging to a curve whose ordinate was expressed rationally in terms of the abscissa, so that the method of Mercator might be applied in squaring it. After giving different explanations of this method, he declares in express terms that he does not believe that "all problems, except those of Diophantes, can be resolved by it alone, or by series," as Newton had affirmed in his letter; and among the problems which elude these processes, he mentions the case of finding curves from their tangents; adding that he had already treated many questions of this sort by means of a direct analysis, and that the most difficult had been thus solved. This was more than enough to show Newton that Leibnitz was at least upon the track of the infinitesimal calculus, if he did not possess it already; and, therefore, in his answer (dated Oct. 24th, though apparently delivered to Leibnitz much later), after giving the explanations requested by Leibnitz on the formation of binomial series, and after stating to him the succession of ideas, by means of which he had discovered them, Newton hastens to declare that he possesses for drawing tangents to curves a method equally applicable to equations, whether disen

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gaged or not of radical quantities; but," he adds, as I cannot push further the explication of this method, I have concealed the principle in this anagram."*

He announced that he had established on this foundation many theorems for simplifying the quadrature of curves, and gave expressions for the areas in terms of the ordinates in several simple cases; but he enveloped both the method and the principle on which it rested in another anagram more complicated than the first.

The evident object of Newton, in this letter, was to place his claims to priority of invention in the hands of Leibnitz himself. The noble frankness of Leibnitz appears on this occasion to the greatest advantage: for in his answer to Newton (21st of June, 1677) he employs neither anagram nor evasion, but details simply and openly the method of the infinitesimal calculus, with the differential notation, the rules of differentiation, the formation of differential equations, and the applications of these processes to various questions in analysis and geometry; and, what mathematicians will consider as far from being unimportant, the figures employed in the exposition of these methods offer precisely the same letters, and the same method of notation, that Leibnitz had used in his first letter of the 14th of April the preceding year. Newton made no reply to this memorable letter, either because he no longer felt the wish, or because, from Oldenburg's death, (which happened in the autumn of the same year,) he had no longer an opportunity of doing so.

Leibnitz published his differential method in the Leipzig Acts for 1684, in a form exactly similar to that which he had sent to Newton. No claim was set up at that time to contest his right of discovery, and Newton himself, three years afterwards, eternalized that right by recognizing it in the Principia, in the following terms.† "In a correspondence which took place about ten years ago, between that very celebrated mathematician G. Leibnitz and myself, I mentioned to him that I possessed a method (which I concealed in an anagram) for determining maxima and

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