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Life of Sir Isaac Newton

The following life is substantially a translation from that in the "Biographie Universelle," by M. Biot, the very learned French mathematician and natural philosopher; and to the kindness of this distinguished individual we feel deeply indebted, for allowing us to present this number to our readers. Those alterations only have been made, which we considered might render the treatise more adapted for the objects which the Society has in view.

Isaac Newton was born at Woolsthorpe, in Lincolnshire, on the 25th December, 1642 (O.S.) the year in which Galileo died. At his birth he was so small and weak that his life was despaired of. At the death of his father, which took place while he was yet an infant, the manor of Woolsthorpe, of which his family had been in possession several years, became his heritage. In a short time his mother married again; but this new alliance did not interfere with the performance of her duties towards her son. She sent him, at an early age, to the school of his native village, and afterwards, on attaining his twelfth year, to the neighbouring town of Grantham, that he might be instructed in the classics. Her intention, however, was not to make her son a mere scholar, but to give him those first principles of education which were considered necessary for every gentleman, and to render him able to manage his own estate. After a short period, therefore, she recalled him to Woolsthorpe, and began to employ him in domestic occupations. For these he soon showed himself neither fitted nor inclined. Already, during his residence at Grantham, Newton, though still a child, had made himself remarkable by a decided taste for various philosophical and mechanical inventions. He was boarded in the house of an apothecary, named Clarke, where, caring but little for the society of other children, he provided himself with a collection of saws, hammers, and other instruments, adapted to his size; these he employed with such skill and intelligence, that he was able to construct models of many kinds of machinery; he also made hour-glasses, acting by the descent of water, which marked the time with extraordinary accuracy. A new windmill, of peculiar construction, having been erected in the vicinity of Grantham, Newton manifested a strong desire to discover the secret of its mechanism; and he accordingly went so often to watch the workmen employed in erecting it, that he was at length able to construct a model, which also turned with the wind, and worked as well as the mill itself; but with this difference, that he had added a mouse in the interior, which he called the miller, because it directed the mill, and ate up the flour, as a real miller might do. A certain acquaintance with drawing was necessary in these operations; to this art, thought without a master, he successfully applied himself. The walls of his closet were soon covered with designs of all sorts, either copied from others, or taken from nature. These mechanical pursuits, which already implied considerable powers of invention and observation, occupied his attention to such a degree, that for them he neglected his studies in language; and, unless excited by particular circumstances, he ordinarily allowed himself to be surpassed by children of very inferior mental capacity. Having however, on some occasion, been surpassed by one of his class fellows, he determined to prevent the recurrence of such a mortification, and very shortly succeeded in placing himself at the head of them all.

It was after Newton had for several years cherished and, in part, unfolded so marked a disposition of mind, that his mother, having taken him home, wished to employ him in the affairs of her farm and household. The reader may easily judge that he had little inclination for such pursuits. More than once <2> he was sent by his mother on market-days to Grantham, to sell corn and other articles of farming produce, and desired to purchase the provisions required for the family; but as he was still very young, a confidential servant was sent with him to teach him how to market. On these occasions, however, Newton, immediately after riding into the town, allowed his attendant to perform the business for which he was sent, while he himself retired to the house of the apothecary where he had formerly lodged, and employed his time in reading some old book, till the hour of return arrived. At other times he did not even proceed so far as the town, but stopping on the road, occupied himself in study, under the shelter of a hedge, till the servant came back. With such ardent desire for mental improvement, we may easily conceive that his repugnance to rural occupations must have been extreme; as soon as he could escape from them, his happiness consisted in sitting under some tree, either reading, or modelling in wood, with his knife, various machines that he had seen. To this day is shewn, at Woolsthorpe, a sun-dial, constructed by him on the wall of the house in which he lived. It fronts the garden, and is at the height to which a child can reach. This irresistible passion, which urged young Newton to the study of science, at last overcame the obstacles which the habits or the prudence of his mother had thrown in his way. One of his uncles having one day found him under a hedge, with a book in his hand, entirely absorbed in meditation, took it from him, and discovered that he was working a mathematical problem. Struck with finding so serious and decided a disposition in so young a person, he urged Newton's mother no longer to thwart him, but to send him once more to pursue his studies at Grantham.

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There he remained till he reached his eighteenth year, when he removed to Cambridge, and was entered at Trinity-College, in 1660. Since the beginning of the seventeenth century, a taste for the cultivation of mathematical knowledge had shown itself among the members of that University. The elements of algebra and geometry generally formed a part of the system of education, and Newton had the good fortune to find Dr. Barrow, professor; a man who, in addition to the merit of being one of the greatest mathematicians of his age, joined that of being the kindest instructor as well as the most zealous protector of the young genius growing up under his care.

Newton, in order to prepare himself for the public lessons, privately read the text books in advance, the better to follow the commentaries of the lecturer. These books were, Bishop Sanderson's Logic,[2] and Kepler's Treatise on Optics, from which it is evident the young learner must have made considerable progress in the elements of geometry when studying at Grantham. After Newton went to Cambridge, the process of the unfolding of his intellect, a subject so interesting in the study of the human mind, fortunately remains to us either described by himself or established in literary monuments, by which we are enabled accurately to trace it progress.

At this epoch, Descartes bore sway both in speculative and in natural philosophy. The authority of the metaphysical systems of his daring and fertile mind having succeeded to the empire which those of Aristotle had previously exercised, caused his method and his works to be adopted also in mathematics. Hence the geometry of Descartes was one of the first books that Newton read at Cambridge.

After Newton's persevering efforts, when reading alone, to make himself master of the elements of this science, explained so unconnectedly and imperfectly by other authors, he must have felt a lively pleasure on entering on the wide career that the French analyst was the first to open, and in which, having shown the connexion between algebraical equations and geometry, he discovers to us the use of that relation in solving, almost at sight, problems which, up to that time, had foiled the efforts of all the ancient and modern mathematicians. It is singular, however, that Newton, in his writings, has never mentioned Descartes favourably; and, on more than one occasion, has treated him with injustice.[3] He next proceeded, when <3> about twenty-one years old, to read the works of Wallis, and appears to have taken peculiar delight in studying the remarkable treatise of this analyst, entitled Arithmetica infinitorum. It was his custom, when reading, to note down what appeared to him capable of being improved; and, by following up the ideas of Wallis, he was led to many important discoveries: for instance, Wallis had given the quadrature of curves, whose ordinates are expressed by any integral and positive power of (1-x2); and had observed, that if, between the areas so calculated, we could interpolate the areas of other curves, the ordinates of which constituted, with the former ordinates, a geometrical progression, the area of the curve, whose ordinate was a mean proportional between 1 and (1-x2) would express a circular surface, in terms of the square of its radius. In order to effect this interpolation, Newton began to seek, empirically, the arithmetical law of the co-efficients of the series already obtained.[4] Having found it, he rendered it more general, by expressing it algebraically. He then perceived that this interpolation gave him the expression in series of radical quantities, composed of several terms; but, not blindly trusting to the induction that had conducted him to this important result, he directly verified it by multiplying each series by itself the number of times required by the index of the root, and he found, in fact, that this multiplication re-produced exactly the quantity form which it had been deduced. When he had thus ascertained that this form of series really gave the development of radical quantities, he was obviously led to consider that they might be obtained still more directly, by applying to the proposed quantities the process used in arithmetic for extracting roots. This attempt perfectly succeeded and again gave the same series, which he had previously discovered by indirect means; but it made them depend on a much more general method, since it permitted him to express, analytically, any powers whatever of polynomials, their quotients, and their roots; by operating upon and considering these quantities as the developments of powers corresponding to integral, negative, or fractional exponents. It is, in fact, in the generality and in the uniformity given to these developments in which the discovery of Newton really consists: for Wallis had remarked before him, with regard to monomial quantities, the analogy of quotients and roots, with integral powers, expressed according to the notation of Descartes; nay, more, Pascal had given a rule for forming, directly, any term of an expanded power of a binomial, the exponent being an integer. But whatever might be the merit of these observations, they were incomplete, and wanted generality, from not being expressed in an algebraical form. In fact, this step made by Newton was indispensable for discovering the development of functions into infinite series. Thus was found out the celebrated formula of such constant use in modern analysis, known by the name of the Binomial Theorem of Newton; and not only did he discover it, but he further perceived that there is scarcely any analytical research in which the use of it is not necessary, or at least possible. He immediately made a great number of the most important of these applications, solving, in this way, by series, with unexampled facility and exactness, questions which, up to that time, had not even been attempted, or of which solutions had been obtained only when the real difficulties of the case were removed by particular limitations. It was thus that he obtained the quadrature of the hyperbola and of many other curves, the numerical values of which he amused himself in computing to as many decimal places nearly as had previously been employed in the case of the circle alone: such pleasure did he take in observing the singular effect of these new analytical expressions, which, when capable of being determined exactly, stopped after a certain number of terms; and, in the opposite case, extended themselves indefinitely, while approximating more and more to the truth. Nor did he confine his application of these formulæ to the <4> areas of curves and their rectification, but extended it to the surfaces of solids, to the determination of their contents, and the situation of their centres of gravity. To understand how this method of reducing into series could conduct him to such results, we must recollect that, in 1665, Wallis, in his Arithmetica infinitorum, had shown that the area of all curves may be found whose ordinate is expressed by any integral power of the abscissa; and he had given the expression for this area in terms of the ordinate. Now, by reducing into series the more complicated functions of the abscissa which represent the ordinates, Newton changed them into a series of monomial terms, to each of which he was able to apply the rule of Wallis. He thus obtained as many portions of the whole areas as there were terms, and by their addition obtained the total. But the far more extensive, and, in some respects, unlimited applications that Newton made of this rule, depended on a general principle which he had made out, and which consisted in the determining, from the manner in which quantities gradually increase, what are the values to which they ultimately arrive. To effect this, Newton regards them not as the aggregates of small homogeneous parts, but as the results of continued motion; so that, according to this mode of conception, lines are described by the movement of points, surfaces by that of lines, solids by that of surfaces, and angles by the rotation of their sides. Again — considering that the quantities so formed are greater or smaller in equal times, according as the velocity with which they are developed is more or less rapid, he endeavours to determine their ultimate values from the expression for these velocities, which he calls Fluxions, naming the quantities themselves Fluents. In fact, when any given curve, surface, or solid is generated in this manner, the different elements to which either compose or belong to it, such as the ordinates, the abscissæ, the lengths of the arcs, the solid contents, the inclinations of the tangent planes, and of the tangents, all vary differently and unequally, but nevertheless according to a regular law depending on the equation of the curve, surface, or solid under consideration.

Hence Newton was able to deduce from this equation the fluxions of all these elements, in terms of any one of the variables, and of the fluxion of this variable, considered as indeterminate; then, by expanding into series, he transformed the expression, so obtained, into finite, or infinite series of monomial terms, to which Wallis's rule became applicable: thus, by applying it successively to each, and taking the sum of the results, he obtained the ultimate value, i.e. the fluent of the element he had been considering. It is in this that the method of fluxions consists, of which Newton from that time laid the foundation; and which, eleven years later, Leibnitz again discovered, and presented to the world in a different form, that, namely, of the modern Differential calculus. It were impossible to enumerate the various discoveries in mathematical analysis, and in natural philosophy, that this calculus has given rise to; it is sufficient to remark, that there is scarcely a question of the least difficulty in pure of mixed mathematics that does not depend on it, or which could be solved without its aid. Newton made all these analytical discoveries before the year 1665, that is, before completing his twenty-third year. He collected and arranged them in a manuscript, entitled "Analysis per æquationes numero terminorum infinitas." He did not, however, publish, or even communicate it to any one, partly, perhaps, from a backwardness to attain sudden notoriety, though more probably from his having already conceived the idea of applying this calculus to the determination of the laws of natural phenomena, anticipating that the analytical methods which he had discovered would be to him instruments for working out the most important results. It is at least certain, that, satisfied with the possession of this treasure, he kept it in reserve, and turned his attention more closely towards objects of natural philosophy. At this time (1665), he quitted Cambridge to avoid the plague, and retired to Woolsthorpe. In this retreat he was able to abandon himself, without interruption, to that philosophical meditation which appears to have been essential to his happiness.

The following anecdote is related by Pemberton, the contemporary and friend of Newton. — Voltaire, in his 'Elements of Philosophy,' says that Mrs. Conduit, Newton's niece, attested the fact.

One day, as he was sitting under an apple-tree, (which is still shown) an apple fell before him; and this incident <5> awakening, perhaps, in his mind, the ideas of uniform and accelerated motion, which he had been employing in his method of fluxions, induced him to reflect on the nature of that remarkable power which urges all bodies to the centre of the earth; which precipitates them towards it with a continually accelerated velocity; and which continues to act without any sensible diminution at the tops of the highest towers, and on the summits of the loftiest mountains. A new idea darted across his mind. "Why," he asked himself, "may not this power extend to the moon, and then what more would be necessary to retain her in her orbit about the earth?" This was but a conjecture; and yet what boldness of thought did it not require to form and deduce it form so trifling an accident! Newton, we may well imagine, applied himself with all his energy to ascertain the truth of this hypothesis. He considered, that if the moon were really retained about the earth by terrestrial gravity, the planets, which move round the sun, ought similarly to be retained in their orbits by their gravity towards that body.[5] Now, if such a force exists, its constancy or variability, as well as its energy at different distances from the centre, ought to manifest itself in the different velocity of the motion in the orbit; and consequently, its law ought to be deducible from a comparison of these motions. Now, in fact, a remarkable relation does exist between them, which Kepler had previously found out by observation, namely, that the squares of the times of revolution of the different planets are proportional to the cubes of their distances from the sun. Setting out with this law, Newton found, by calculation, that the force of solar gravity decreases proportionally to the square of the distance; and it is to be observed that he could not have arrived at this result without having discovered the means of determining from the velocity of a body in its orbit, and the radius of the orbit supposed to be circular, the effort with which it tends to recede from the centre; because it is this effort that determines the intensity of the gravity, (to which, in fact, the effort is equal.) It is precisely on this reasoning, that the beautiful theorems on centrifugal force, published six years afterwards by Huygens, are founded; whence it is plain that Newton himself must necessarily have been acquainted with these very theorems. Having thus determined the law of the gravity of the planets towards the sun, he forthwith endeavoured to apply it to the moon; that is to say, to determine the velocity of her movement round the earth, by means of her distance as determined by astronomers, and the intensity of gravity as shown by the fall of bodies at the earth's surface. To make this calculation, it is necessary to know exactly the distance from the surface to the centre of the earth, expressed in parts of the same measure that is used in marking the spaces described, in a given time, by falling bodies at the earth's surface; for their velocity is the first term of comparison that determines the intensity of gravity at this distance from the centre, which we apply afterwards at the distance of the moon by diminishing it proportionally to the square of her distance. It then only remains to be seen, if gravity, when thus diminished, has precisely the degree of energy necessary to counteract the centrifugal force of the moon, caused by the observed motion in her orbit. Unhappily, at this time, there existed no correct measure of the earth's dimensions. Such as were to be met with, had been made only for nautical purposes, and were extremely imperfect. Newton, having no other resource but to employ them, found that they gave for the force that retains the moon in her orbit, a value greater by 16 than that which results from her observed circular velocity. This difference, which would, doubtless, to any other person, have appeared very small, seemed, to his cautious mind a proof sufficiently decisive against the bold conjecture which he had formed. He imagined that some unknown cause, analogous, perhaps, to the vortices of Descartes,[6] modified, in the case of the moon, the general law of gravity indicated by the movement of the planets. He did not, however, on this account, wholly <6> abandon his leading notion, but, in conformity with the character of his contemplative mind, he resolved not yet to divulge it, but to wait until study and reflection should reveal to him the unknown cause which modified a law indicated by such strong analogies. This took place in 1665-6. During that latter year, the danger of the plague having ceased, he returned to Cambridge, but he did not disclose his secret to any one, not even to his instructor, Dr. Barrow. It was not till two years afterwards, 1668, that Newton communicated to the latter, who was then engaged in publishing his lectures on Optics, certain theorems relating to the optical properties of curved surfaces, of which Barrow makes very honourable mention in his preface. Newton had now become a colleague of his former tutor, having been admitted master of arts the preceding year. At length in the same year (1668) an occurrence in the scientific world compelled him to declare himself. Mercator[7] printed and published, towards the end of this year, a book called Logarithmotechnia, in which he had succeeded in obtaining the area of the hyperbola referred to its asymptotes, by expanding its ordinate into a infinite series; this he did by means of common division, as Wallis had done in the case of fractions of the form 11-x: then, considering each term of this series separately, as representing a particular ordinate, he applied to it Wallis's method for curves, whose ordinates are expressed by a single term, and the sum of the partial areas so obtained, gave him the value of the whole area. This was the first example given to the world of obtaining the quadrature of a curve by expanding its ordinate into an infinite series. And it was also the main secret in the general method which Newton had invented for all problems of this nature. The novelty of the invention caused it to be received with general applause. Collins, a gentleman well known to science and philosophy at that time, hastened to send Mercator's book to his friend Barrow, who communicated it to Newton. The latter had no sooner glanced over it, than recognizing his own fundamental idea, he immediately went home, to find the manuscript; in which he had explained his own method, and presented it to Barrow; this was the treatise Analysis per æquationes numero terminorum infinitas. Barrow was struck with astonishment at seeing so rich a collection of analytical discoveries of far greater importance than the particular one which then excited such general admiration. Perhaps, too, he must have been still more surprised at their young author having been able to keep them so profoundly secret. He immediately wrote about them to Collins, who, in return, entreated Barrow to procure for him the sight of so precious a manuscript. Collins obtained his request, and happily, before returning the work, took a copy of it, which being found after his death, among his papers, and published in 1711, has determined beyond dispute, by the date which it bore, at what period Newton made the memorable discovery of expansion by series, and of the method of fluxions. It would have been natural to suppose that an interference with his own discoveries would at last have induced Newton to publish his methods; but he preferred still to keep them secret. "I suspected," says he, "that Mercator must have known the extraction of roots, as well as the reduction of fractions into series by division, or at least, that others, having learnt to employ division for this purpose, would discover the rest before I myself should be old enough to appear before the public, and, therefore, I began henceforward to look upon such researches with less interest."[8]

It were difficult to explain this reserve and indifference by the feelings of extreme modesty alone; but we may come near the truth by considering what were the habits of Newton, and by figuring to ourselves the new and extraordinary allurements of another discovery which he had just made, and which he already enjoyed in secret; for in general, the effort of thinking was with him so strong, that it entirely abstracted his attention from other matters, and confined him exclusively to one object. Thus we know that he never was occupied at the same time with two different scientific investigations. And we find,[9] even in the most beautiful of his works, the simple, yet expressive avowal of the disgust with which his most curious researches had always finally inspired him, from his ideas being <7> continually, and for a long time, directed to the same object. This might, perhaps, also have in part been caused by a discouraging conviction, that he would seldom be understood and followed in the chain of his reasoning; since others, in order to do so, must be as deeply immersed in the subject and as abstracted from other matters as himself. Be this as it may, when Mercator's work appeared, a new series of discoveries of a totally different nature had taken hold of Newton's thoughts.

In the course of 1666, he had accidentally been led to make some observations on the refraction of light through prisms. These experiments, which he had at first tried merely from amusement, or curiosity, soon offered to him most important results. They led him to conclude that light, as it emanates from radiating bodies, such as the sun, for instance, is not a simple and homogeneous substance, but that it is composed of a number of rays endowed with unequal refrangibility, and possessing different colouring properties. The inequality of the refraction undergone by these rays in the same body, when they enter at the same angle of incidence, enabled him to separate them; and thus, having them unmixed and pure, he was able to study their individual properties. But the breaking out of the plague, which in this year compelled him to take refuge in the country, having separated him from his instruments, and deprived him of the means of making experiments, turned his attention to other objects. More than two years elapsed before he returned to these researches, on finding himself about to be appointed lecturer on optics in room of Dr. Barrow, who in 1669 generously retired in order to make way for him. He then endeavoured to mature his first results, and was led to a multitude of observations no less admirable from their novelty and importance, than for the sagacity, address, and method, with which he perfected and connected them. He composed a complete treatise, in which the fundamental properties of light were unfolded, established, and arranged, by means of experiment alone, without any admixture of hypothesis, a novelty at that time almost as surprising as these properties themselves. This formed the text of the lectures he began in Cambridge 1669, when scarcely twenty-seven years old, and thus we see, from what we have related concerning the succession of his ideas, that the method of Fluxions, the theory of universal gravitation, and the decomposition of light, i.e. the three grand discoveries which form the glory of his life, were conceived in his mind before the completion of his twenty-fourth year.

Although the lectures of Newton on optics must inevitably in the end have given publicity to his labours on light, he still refrained from publishing, wishing probably to reserve to himself the opportunity of adding a complete analysis of certain curious properties, of which, as yet, he had had but a slight glimpse. We refer to the intermittences of reflection and refraction which take place in thin plates, and perhaps in the ultimate particles of all bodies. It was not till two years later, that he made known some of his researches, and soon afterwards he was induced to give them full publicity. In 1671 he had been proposed as a Fellow of the Royal Society of London, and was elected on the 11th of January, 1672. In order that he might be qualified to receive this distinction, the rules of the society required that he should declare himself desirous of becoming a Fellow, and he could not do so in a more honourable manner than by offering some scientific communication. He forwarded to them a description of a new arrangement for reflecting telescopes, which rendered them more commodious in use by diminishing their length without weakening their magnifying powers. With regard to this invention, in which Newton had been preceded, probably without knowing it, by Gregory the Scotch mathematician, and by a Frenchman of the name of Cassegrain, it is merely necessary to observe that the construction offers in practice some inconveniences, which cause it to be little used. Nevertheless, when he presented a model of it,[10] of his own construction, it made a great impression of his favour among the members of the society, to whom probably the construction of Gregory's telescope was not yet well known. The letter which Newton wrote to the society on this occasion, ends with the following characteristic expression: — "I am very sensible of the honour done me by the Bishop of Sarum, in proposing me Candidate, and which I hope will be <8> further conferred upon me by my election into the society, and if so, I shall endeavour to testify my gratitude by communicating what my poor and SOLITARY endeavours can effect towards the promoting philosophical design."[11] The favourable reception which this proposal met with, induced Newton two months afterwards to make to the Royal Society another much more important communication, viz. the first part of his labours on the analysis of light. We can easily imagine the sensation which so great and unexpected a discovery must have produced. The society requested of him, in the most flattering terms, permission to insert this beautiful Treatise in the Philosophical Transactions.[12] Newton accepted this speedy and honourable method of publication; and, in addressing his thanks to Oldenburg, their secretary, he says: — "It was an esteem of the Royal Society, for most candid and able judges in philosophical matters, encouraged me to present them with that discourse of light and colours, which since they have so favourably accepted of, I do earnestly desire you to return them my cordial thanks. I before thought it a great favour to be made a member of that honourable body, but I am now sensible of the advantage: for believe me, Sir, I do not only esteem it a duty to concur with them in the promotion of real knowledge, but a great privilege that, instead of exposing discourses to a prejudiced and censorious multitude, (by which means many truths have been baffled and lost,) I may with freedom apply myself to so judicious and impartial an assembly."[13] It is but fair to say, for the honour of the Royal Society, that it has always shown itself, more than any other, worthy of this noble testimony which the most illustrious of its members has rendered to its justice. But thought the suffrage and esteem of such a society may make amends for, yet they cannot prevent individual attacks. Newton himself was compelled to submit to the common destiny, which ordains that merit, and more particularly success, shall give rise to envy. By unveiling himself, he obtained glory, but at the price of his repose. At this period, Robert Hooke was a fellow of the Royal Society, a man of extensive acquirements, and of an original turn of thought, with great activity of mind and an excessive desire of renown. There were few departments of human knowledge to which he had not paid more or less attention: so much so, indeed, that it was hardly possible to find any subject of research upon which he did not profess to have original views; or to propose any new invention of which he did not claim the prior discovery. There was then the more opportunity of setting in action and of gratifying his jealous spirit, as all the physical and natural sciences were, at that time, mixed up with theoretical opinions; and there were few men then to be met with who could distinguish the difference between a vague perception and a precise idea — between a physical hypothesis and a law of nature rigorously demonstrated. Hooke himself was no exception to this remark; and unfortunately he was not sufficiently familiar with pure mathematics to make use of them as a means of calculation, either in proving or perfecting a theory. A thorough acquaintance with this instrument was the great advantage possessed by Newton, and which assured to his researches a precision and a certainty hitherto unknown in science. The investigation of the properties of light presented by him to the Royal Society, eminently possessed this rigorous character. It consisted in showing experimentally a certain number of physical properties, which were thus established as matters of fact without any admixture of hypothesis, and without requiring any previous knowledge in what the nature of light consisted. When the first feelings of surprise and admiration excited by this noble work had subsided, the Royal Society appointed three members to study the treatise fully, and to give an account of it. Hooke, being one of the number, undertook to draw up the report. Already on the occasion of Newton presenting his telescope, Hooke had announced that he possessed an infallible method of improving all sorts of optical instruments, so that[14] "whatever almost hath been in notion and imagination, or desired in optics, may be performed with great facility and truth." Nevertheless, he did not explain this method, but confined himself, in accordance with the conceits of his <9> day, to masking it under the form of an anagram; of which, however, he appears not to have been able to produce the explanation, since neither he not any other person has ever realised these wonderful promises. His report on Newton's work was, if not of the same kind, yet conceived in the same spirit of personality: for, instead of discussing the new facts, singly, and as compared with the original experiments, he examined them only in relation to an hypothesis which he had formerly imagined, and which consists in regarding light not as an emanation of very small particles, but as the simple effect of vibrations excited and propagated in a very elastic medium. This conception of the nature of light may be in itself as true as any other, since that nature is still unknown to us; but, in order to place such an hypothesis on an equal footing with another hypothesis, shown by calculation to be consistent with experiment and observation, it ought to be detailed with exactness, and to be rigorously accordant with mathematical calculation. The first of these conditions was far from being fulfilled by Hooke, who substituted in its stead a sketch exceedingly vague, and materially contrary to experiment. He supposed, for instance, that there are only two colours essentially distinct, namely, the violet and the red, of which all the others are but mixtures.

With regard to the second condition, viz., an accordance with calculation, it was then far from possible to submit the system of undulations to rigorous mathematical investigation; since that is more than even, at the present time, those mathematicians have been able to accomplish who have been most occupied with the subject. To so vague a theory did Hooke refer, as a standard, the physical truths which Newton had discovered. He concluded by dictatorially allowing all that appeared to him to be reconcileable with his own hypothesis, and by advising him not to seek any other explanation of the facts.[15] Newton replied to this attack in a severe and decisive tone.[16] After refuting an error that Hooke had committed, in supposing the spherical aberration in reflectors greater than that in refracting lenses, he shows that Hooke had judged of the facts he had announced, not by means of the observations that supported them, but by their accordance or discordance with a previously conceived hypothesis; that this hypothesis was vague and unsatisfactory, and that, for his own part, he had not wished to support any hypothesis whatever, as in fact he had no need of one, but that he had only aimed at establishing the real properties of light upon actual observation. Finally, he adduced new experiments, confirming the results which he had already obtained, and refuted the inaccurate assertions of Hooke with respect to the possibility of reducing all colours to two simple ones; as well as his objections to the production of whiteness by the mixture of all the rays. This paper, which nearly completed Newton's investigation into the properties of light, was published by the Royal Society in the Philosophical Transactions of Nov. 1672. Hooke did not reply to this, but presuming, and with good reason, after Newton's first treatise, that such an experimentalist would soon be on the track of all that remained to be discovered concerning the physical properties of light, he hastened to present to the Royal Society several important observations on optics. Among them, we may remark a very precise and faithful account of the changeable colours that appear in the form of rings on soap bubbles, and in the thin plates of air included between pieces of glass pressed together; but without any determination of the physical law or measure even of the breadth and intervals of the rings. Two years afterwards (18th of March, 1674), he read another memoir, in which he detailed the fundamental phenomena of diffraction, which had been already discovered and described by Grimaldi;[17] but, what is still more remarkable, he then announced another principle, which, under the name of the principle of interferences, has since become one of such frequent and advantageous application.

This principle is, that colours are produced when two rays of white light arrive simultaneously at the eye, having directions so little different that this organ takes them to be one ray. We shall afterwards see that (as Hooke had <10> anticipated) Newton was induced subsequently to occupy himself with these new phenomena; but, in the mean time, he was exposed to several absurd attacks upon his experimental analysis of light. Such, for instance, was that of a Jesuit named Pardies, who pretended that the elongation of the refracted image, whence Newton inferred the unequal refrangibility of the rays, was produced entirely by a difference in their original incidences on the first face of the prism: a supposition, the inaccuracy of which the most simple calculation would have been sufficient to show; and which Newton had previous refuted in his own Memoir. But still more foolish was the assertion of one Linus, a physician of Liege, who pretended never to have been able to produce by refraction through a prism an elongated image, but only a round and colourless one; whence he concluded that Newton had been led into error by the accidental passage of some bright cloud, which had elongated and coloured the image; adding also that he himself should not have been astonished had the image been elongated in the longitudinal direction of the prism; but that, without violating the rules of optics, it was impossible to imagine its elongation in the transverse direction. This was accompanied by several authoritative remarks on the improbability of what he called the new hypothesis, which Newton had imagined simply to be a statement of facts. These absurdities, as soon as presented, were printed in the Philosophical Transactions; and Newton was obliged to take the trouble to answer them methodically, to prevent their being accredited by that envy which showed itself so eager to receive them. He was compelled to reply to Huygens, who, though really a man of talent, made objections as unphilosophical nearly as the others, since he compared the properties discovered experimentally by Newton with an hypothesis of his own on the nature of light, in the same manner as Hooke had compared them with his hypothesis, and Pardies and Linus with the ancient ones. In vain did Newton reply that he neither advanced nor admitted any hypothesis whatever, but that his sole object was to establish and connect facts by means of the laws of nature. This severe and abstracted method of reasoning was then too little understood. It is scarcely conceivable into what details he was obliged to enter in the discussion; and such was the disgust with which this inspired him, that he gave up his previous intention of printing his lectures on Optics with his treatise on Series, and determined to commit himself no more with the public.[18] "I was," he afterwards wrote to Leibnitz, "so persecuted with discussions arising from the publication of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet, to run after a shadow." It was, perhaps, the remembrance of these inconsiderate objections of Huygens, that afterwards inclined Newton to regard less favourably than he ought to have done, the law of double refraction in Iceland spar, discovered by this eminent mathematician, probably by experiment after Newton's own manner, though he presented it as a deduction from his own favourite system, and as a confirmation of it. It is easy to understand how much Newton must have been grieved by the opposition of so illustrious an adversary as Huygens, since he might at least have hoped to have been understood and appreciated by minds accustomed to the severity of mathematical investigations. Nevertheless, before quitting the lists, Newton wished finally to complete the account of the results which he had obtained, and of the views which he had formed on the nature of light. This was the object of a later paper addressed to the Royal Society.[19]

We find there an experimental analysis of the colours observed in thin plates — phenomena, which, as we have said, had been previously pointed out and described by Hooke, but without his having either measured the spaces occupied by the colours, or determined the law which they followed. Newton first measured the spaces with admirable precision and nicety, and thence derived the physical laws by which all these results are connected with, and may be deduced from each other.

This treatise, united with his first paper on the analysis of Light, afterwards served as a base for the grand work published in 1704, under the name of Newton's Treatise on Optics; with this difference, however, that in the latter work the experimental investigations of <11> the phenomena is more extensive and more strictly separated from all hypothesis. The new experiments with which Newton enriched it, relate principally to the colours observed in the thick plates of all bodies, when they are presented in a proper manner to the incident ray. Newton reduces them to the same laws as those of the phenomena in thin plates; and then considering these laws as established facts equally certain with the particular experiments form which they are deduced, yet far more universal, he unites them all in one general property of light, each peculiarity of which is characterized with such exactness, as to make the general property a pure expression for all the observed laws. The essence of this property is, that each particle of light, from the instant which it quits the radiating body whence it emanates, is subject periodically and at equidistant intervals, to a continual alternation of dispositions to be reflected from or to be transmitted through the surfaces of the diaphanous bodies it meets with; so that, for instance, if such a surface presents itself to the luminous particle during one of the alternations when the tendency to reflection is in force, which Newton has appropriately termed the fit of easy reflection, this tendency makes it yield more easily to the reflecting power of the surface; while, on the other hand, it yields with more difficulty when it is in the contrary phase, which Newton has termed the fit of easy transmission. We have here an admirable example of the universal application of scientific definitions when framed in strict accordance with experiment. For, though the term fits, inasmuch as it seems to imply a physical property, is applicable in its first intention to material particles only, and thus involves the assumption of the materiality of light, (a fact of which we may reasonably doubt, though Newton has never treated it as doubtful,) yet the characteristics of these fits are described in such exact conformity with experiment, that they would exist without any change, even were it discovered that light is constituted in any other manner — that it consists, for instance, in the propagation of undulations: such is the point of view in which Newton regards these fits in his Optics, 1704, limiting himself to deduce from them his profound inductions, on the intimate constitution of bodies, and on the cause which renders them apt to reflect or transmit a particular colour. But in his paper of 1675, he connected these properties with a very bold hypothesis, so general, that, from it, he deduced the nature of light and of heat, and the explanation of all the phenomena of combination or motion which appear to result from certain intangible and imponderable principles. As this hypothesis (mentioned only in the History of the Royal Society) is little known, and as it appears to have been constantly connected with Newton's thoughts on the constitution of the universe, we may here give a summary of it. We do this without the intention either of defending or combating it, but in order that the reader may see precisely in what the general views of Newton from this time forward consisted, and how, while they continued unchanged by lapse of time, he made a more or less explicit declaration of them according to circumstances. Newton, in the first place, excuses himself for proposing a conjecture as to the nature of light, declaring that he does not need one, and that the properties which he has discovered being physical facts, their being explicable or not by this or that hypothesis, could not in any degree add to or take away from their certainty;[20] "but," says he, "because I have observed the heads of some great virtuosos to run much upon hypotheses, I will give one which I should be inclined to consider as the most probable, if I were obliged to adopt one." He then admits, nearly as Descartes had previously done, the existence of a fluid imperceptible to our senses, which extends everywhere in space, and penetrates all bodies, with different degrees of density. He supposes this fluid to be more dense in bodies which contain in the same volume a less number of constituent material particles; he supposes also that the density of this fluid varies around each different body, and even around each constituent particle, increasing rapidly near their surface, and afterwards more slowly, though by insensible degrees, as the distance from the surface becomes greater. This fluid (which Newton calls ætherial medium or æther, in order to characterize by this denomination its extreme tenuity) he also considered as highly elastic; and consequently by the effort which it makes to spread, that it presses against itself, and against the material parts of <12> other bodies, with an energy more or less powerful according to its actual density, and thus that all these bodies continually tend towards one another; the inequality of the pressure urging them always to pass from the denser into the rarer parts of the æther. Conformably to his opinion respecting the disposition of the æther around each body, and around each of its material constituent particles, he considered that the variations of its density between a body and a vacuum, or between one body and another neighbouring body, were not sudden and discontinuous, but gradual and progressive; and from being very rapid near the surfaces, where the nature or density of the matter instantaneously changes, they a little farther become so slow as soon to cease to be perceptible beyond certain limits of thickness inappreciable to our senses. If, then, this æther be disturbed or agitated, in any one point, by any cause whatever, producing a vibratory movement, this motion must transmit itself by undulations through all the rest of the medium, in the same way that sound it transmitted through air, but much more rapidly, by reason of the æther's greater elasticity; and, if those undulations, successively reiterated, happen to encounter in their passage the material particles forming the substance of any body, they will agitate them with considerable force, by the successive impressions, in precisely the same way that we see solid bodies, and sometimes even the whole mass of a large building, tremble under reiterated impulses of the weak undulations in the air, excited by the sounds of an organ, or by the rolling of a drum.

Now Newton does not suppose that light immediately results from the impression produced by these undulations on the nervous membrane of the retina, as Descartes and Hooke had previously done, and as, in general, has been done by all those who have followed the same system. The principal reason which Newton gives for rejecting this supposition is, that a motion excited in, and transmitted through, an elastic fluid which reposes on another fluid of a different density, does not seem capable of being reflected in the first fluid at their surface of common separation, without being in part transmitted into the second; whereas, in many cases, light, propagated into the interior of bodies, is totally reflected at their second surface, and again returns into their interior without the smallest part of it going out. Newton, therefore, admits that light consists of a peculiar substance different from the æther, but composed of heterogeneous particles, which, springing in all directions from shining bodies, with an excessive though measurable velocity, agitate the æther in their passage, and excite in it undulations; by the meeting of which, they become liable to be in their turn accelerated or retarded. Newton does not attempt to characterize the essence of these particles, but merely the faculty that he attributes to them of agitating the æther, and of being agitated by it; and finally he adds,[21] "those that will, may suppose it, multitudes of unimaginable small and swift corpuscles of various sizes springing from shining bodies at great distances one after another; but yet without any sensible interval of time; and continually urged forward by a principle of motion, which, in the beginning, accelerates them till the resistance of the ætherial medium equal the force of that principle, much after the manner that bodies let fall in water are accelerated, till the resistance of the water equals the force of gravity." Be this as it may, the independence of the particles of light and of æther being admitted, as well as their mutual reaction, Newton takes the case of a ray of light moving through a space in which the ætherial medium is composed of strata of unequal density; and applying to the particles of this ray the general principle established above, he concludes that they ought to be pressed, urged, or generally acted upon, so as to go from the denser to the rarer strata of æther; whence they must receive an accelerated velocity, if this tendency conspire with the proper motion of the ray; and a retarded velocity, if it be contrary to it; and generally a curvilinear deviation when the proper motion of the ray and the impression produced by the elastic medium are oblique to one another.

This is precisely what must happen when rays of light pass from one transparent homogeneous body into another, since the æther is there supposed to be of different densities; and the deviation of the rays takes place only near the common surface of the two bodies, where the sensible variation of density begins, whence results the phenomenon <13> of refraction.[22] "Now," says Newton, "if the motion of the ray be supposed in this passage to be increased of diminished in a certain proportion, according to the difference of the densities of the ætherial mediums, and the addition or detraction of the motion be reckoned in the perpendicular from the refracting superficies, as it ought to be, the sines of incidence and refraction will be proportional, according to what Descartes has demonstrated." This explanation of refraction is exactly the same as Newton afterwards reproduced in the Principia, though without there pronouncing any opinion on the nature of the disturbing force. It is, however, probable, that in his Memoir he deduced it by simple induction, rather than by a mathematical investigation; for it does not appear that, at this epoch, he was acquainted with the calculation of curvilinear motions. It is, however, important to remark, that from this time he had formed a conception of the doctrine of universal gravitation; for he takes care to point out that the unequal density of the æther, at different distances from the surface of bodies, suffices to determine their mutual tendency towards one another; a consideration which he again brought forward in the Queries annexed to his Optics (in 1704), after he had discovered the laws of the system of the world. Nevertheless we may infer, that in 1675, he had not yet formed the idea of attractions at small distances, since, in his paper addressed to the Royal Society, he imagines that the ascent of liquids in capillary tubes is caused by the air being more rare in confined than in open spaces, and the more rare in proportion as the spaces are more confined. While in the Queries he attributes these phenomena to their true cause, viz. to the reciprocal attractions of the tubes and of the fluid; though, even at this later period, he did not know how to calculate their effect. It was reserved for LAPLACE to complete this investigation.

After having thus considered the simple transmission of rays in ætherial strata of unequal densities, Newton examines the modifications produced during this transmission, by their meeting with undulations originally excited in the æther itself, according as such undulations may favour or oppose the actual motion of luminous particles; and by this re-action he is enabled to explain the intermittances in reflection and refraction, which take place in thin plates. We may observe in his Optics, that he has never abandoned this idea; for though in that work he had maintained the most complete reserve with regard to the nature of light, yet, after characterizing the fits as a purely abstract physical property, he gives as a method of rendering it sensible, the same manner of conceiving it that he had given in his Memoir of 1675; the same idea is reproduced in several of the Queries, particularly in the 17th, and those following to the 24th, where Newton asks, as in the paper presented to the Royal Society, if this same æther be not also sufficient to produce universal gravitation, and even all the phenomena of animal motion? Finally, in his paper, he endeavours to apply the same principles to the inflections, undergone by rays of light on passing near the extremities of bodies; which he, in like manner, explains by variations in the density of the æther. It is always thus that he has represented these inflections, both in the Principia, printed in 1687, and in the Queries.

From these examples, taken together, we may see that Newton did not "several times change his ideas on light," as has been asserted by some writers, but that, always preserving the same opinion, he has explained it more or less fully, as different occasions demanded.

The phenomena of diffraction, how ever, were still too imperfectly known, and observed with too little detail for enabling Newton to see precisely whether they agreed or not with his hypothesis. We have reason to believe that, in order to study these properties, he then made a number of experiments, to be afterwards inserted at the end of the Optics; for he there introduces them as part of an investigation which he had formerly undertaken, but from which his thoughts were now so far estranged, that he had lost the taste for resuming it. These observations, like all his others, are presented as matters of fact, without relation to any system. When the hypothesis of Newton on the nature of light was presented, in 1675, to the Royal Society, Hooke, as usual, put in his claims to it. Newton, however, did not again waste his time and repose in a controversy on the subject, but contented himself with writing to Oldenburg (21st December), in order to make <14> him see the injustice of that jealous individual. He first clearly shows that his fundamental idea has nothing in common with that of Hooke, inasmuch as the latter supposes light to consist in the undulations themselves of the æther, transmitted to the organ of vision; while the light of Newton is a substance entirely distinct, which, thrown into the æther, impresses upon, or receives from it, peculiar motions, by means of which it acts upon us. "As to the observations of Hooke on the colours of thin plates, I avow," says Newton, "that I have made use of them, and thank him for the same; but he left me to find out and make such experiments about it, as might inform me of the manner of the production of those colours, to ground an hypothesis on; he having give no further insight into it than this, that the colour depended on some certain thickness of the plate; though what that thickness was at every colour, he confesses, in his Micrography, he had attempted in vain to learn; and, therefore, seeing I was left to measure it myself, I suppose he will allow me to make use of what I took the pains to find out; and this I hope may vindicate me from what Mr. Hooke has been pleased to charge me with."[23] Happily this time the discussion proceeded no further; and Oldenburg had sufficient influence, as well as sufficient sense, to prevent its obtaining notoriety. From this time till the year 1679, four years afterwards, Newton communicated nothing to the Royal Society. Oldenburg, whose kindness had ever encouraged him, unfortunately died in this interval, and was succeeded in the secretaryship by Hooke, an appointment little likely to remove an apprehension of new disputes. We may imagine, however, that Newton did not remain idle; and, in fact, in this interval, it appears, he was principally occupied with astronomical observations. At last, 28th November, 1679,[24] he had occasion to write to Hooke about a System of Physical Astronomy, on which the Royal Society had asked his opinion. In his letter he proposed, as a matter deserving attention, to verify the motion of the earth by direct experiment, viz. by letting bodies fall from a considerable height, and then observing if they follow exactly a vertical direction; for if the earth turns, since the rotary velocity at the point of departure must be greater than that at the foot of the vertical, they will be found to deviate from this line towards the east, instead of following it exactly as they would do if the earth did not revolve. This ingenious idea being very favourably received, Hooke was charged to put it into effect. On reflection, Hooke immediately added the remark that wherever the direction of gravity is oblique to the axis of the earth's rotation, i.e. in all parts of the earth, except at the equator, bodies, in falling, change parallels, and approach the equator: so that in Europe, for instance, the deviation does not take place, rigorously speaking, to the east, but to the south-east of the point of departure. Hooke communicated this remark to Newton, who immediately recognised its correctness in theory; but, in addition to this, Hooke assured the Royal Society that, on repeating the experiment several times, he had actually found that the deviation took place constantly towards the south-east; an accordance which would appear very simple, if Hooke's remarks were merely theoretical; but which must appear very extraordinary if he intended to speak of an actual observed deviation reckoned form the foot of the vertical; for in this case, according to the formulæ of LAPLACE, the tendency to the south is of the second order, relative to the absolute deviation; and in Hooke's observations this very slight deviation must have been excessively difficult to ascertain, since his experiments were made in the open air. It was this, however, which led Newton to consider whether the elliptical motion of the planets could result from a force varying inversely as the square of the distance, and if so, under what circumstances such a result would ensue. In fact, in proposing to the Royal Society his curious experiment, he had considered the motion of the heavy body as determined by a force of constant intensity, and had concluded the trajectory to be a spiral,[25] doubtless, because he imagined the body to fall in a resisting medium, such as the air. Hooke, who for a long time had adopted the hypothesis of a force decreasing as the squares of the distance from the centre, replied that the trajectory ought <15> not to be a spiral, but that in a vacuum it would be an excentric ellipse, which would change into an ovodial curve likewise excentric, if the medium were a resisting one. It is impossible exactly to ascertain how Hooke arrived at these results, for neither then, nor on any subsequent occasion, did he give a demonstration of them; though Halley and Sir Christopher Wren both eagerly pressed him to do so. We might imagine, not without some probability, that the elliptic movement of projectiles was, in his mind, a consequence of the hypothetical, though just, ideas he had formed on the physical cause of the planetary motions; for he attributed them to the existence of a gravitating force, proper to each celestial body, and acting round its centre, with an energy inversely proportional to the square of the distance; so that, in this system, the motion of projectiles round the centre of the earth ought to be elliptical round the sun. Hooke had, for some time, turned his thoughts to this kind of speculation; but not being a sufficiently profound mathematician, rigorously to deduce the nature of the force form the form of the orbits, or to show how this form resulted from the supposed law of attraction, he tried to determine its character by direct physical experiments, and actually to produce the motions which resulted from the law, by means of mechanical contrivances. On the 21st March, 1666, he communicated to the Royal Society certain experiments, which he had attempted, in order to determine whether the weight of a body undergoes any variation at different distances from the earth's centre, at the greatest altitudes or depths which can be attained. These experiments were made with too little precision to give results on which any reliance could be placed. Hooke himself perceived this, and proposed to employ the more delicate process of using a pendulum clock, and successively observing its rate at different heights. This first attempt, though imperfect, shows the object he had in view, which perhaps is more clearly seen in his own words. "Gravity, though it seems to be one of the most universal active principles in the world, and consequently ought to be the most considerable, yet has it had the ill fate to have been always, till of late, esteemed otherwise, even to slighting and neglect. But the inquisitiveness of this latter age hath begun to find sufficient arguments to entertain other thoughts of it. Gilbert began to imagine it a magnetical attractive power, inherent in the parts of the terrestrial globe. The noble Verulam also, in part, embraced this opinion; and Kepler (not without good reason) makes it a property inherent in all celestial bodies, — sun, stars, planets. This supposition we may afterwards more particularly examine; but first it will be requisite to consider, whether this gravitating or attracting power be inherent in the parts of the earth; and, if so, whether it be magnetical, electrical, or of some other nature distant from either. If it be magnetical, any body attracted by it ought to gravitate more, when nearer to its surface, than when further off.[26]"

Two months afterwards, Hooke made before the Royal Society another experiment, which, as he himself observed, without being an exact representation of the planetary orbits, afforded an example, at that time new and remarkable, of a curvilinear motion produced by the combination of a primitive impulse with an attracting power emanating from a centre. He suspended from the ceiling of a room a long wire, to the end of which was attached a ball of wood, to represent a planetary body. On removing this pendulum from the vertical, and giving it a lateral impulse, perpendicular to the plane of deviation, it is acted on by two forces, of which one is the impulse itself, and the other terrestrial gravity, of which the effort when decomposed perpendicularly to the wire, tends always to bring the body back to the vertical. Now when the lateral impulse was nothing, the ball clearly described a plane orbit, viz. that of its free oscillation; if the impulse, without being nothing, were still very weak, the trajectory became a very much elongated ellipse, having its major axis in the plane of oscillation; with a stronger impulse, a more open ellipse was obtained, which, at a particular point, became an exact circle; and lastly, still stronger impulses produced ellipses, whose major axes were no long parallel with, but were perpendicular to the place of free oscillation. Thus these different curves were seen to be produced and to be transformed into each <16> other, by merely changing the relative energies of the two forces (the one impulsive, and the other central) which acted on the pendulum. These ellipses, however, differed much from the planetary ellipses, inasmuch as the central force produced by the decomposition of gravity is constantly directed towards the centre of the ellipse, and is directly proportional to the distance of the body from that centre; whereas, in the planetary orbits, the central force is constantly directed towards one of the foci of the ellipse, and is reciprocally proportional to the square of the distance of the body from that point. Notwithstanding this fundamental distinction, the experiment of Hooke was important and useful, as it gave a perceptible example of the composition of forces. Eight years later, in 1674, Hooke presented the whole of his ideas in a much more explicit and complete manner, at the end of a dissertation, entitled, "An Attempt to prove the Motion of the Earth from Observations."[27] "I shall," says he, "hereafter explain a system of the world, differing in many particulars from any yet known, answering in all things to the common rules of mechanical motions. This depends upon three suppositions: — first, that all celestial bodies whatsoever have an attraction or gravitating power towards their own centres, whereby they attract not only their own parts and keep them from flying from them, as we may observe the earth to do, but that they do also attract all the other celestial bodies that are within the sphere of their activity, and consequently, that not only the sun and moon have an influence upon the body and motion of the earth, and the earth upon them, but that Mercury, Venus, Mars, Jupiter, and Saturn also, by their attractive powers, have a considerable influence upon its motion, as in the same manner the corresponding attractive power of the earth hath a considerable influence upon every one of their motions also. The second supposition is this, that all bodies whatsoever, that are put into a direct and simple motion, will so continue to move forward in a straight line, till they are, by some other effectual powers, deflected and bent into a motion describing a circle, ellipsis, or some other more compounded curve line. The third supposition is, that those attractive powers are so much the more powerful in operating, by how much the nearer body wrought upon is to their own centres. Now what these several degrees are I have not yet experimentally verified; but it is a notion which, if fully prosecuted, as it ought to be, will mightily assist the astronomers to reduce all the celestial motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the circular pendulum and the circular motion will easily understand the whole ground of this principle, and will know where to find directions in nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this inquiry, and are not wanting of industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand, which I would first complete, and therefore cannot so well attend it. But this I durst promise the undertaker, that he will find all the great motions of the world to be influenced by this principle, and that the true understanding thereof will be the true perfection of astronomy."

Without lessening the credit due to the distinct expression of such remarkable ideas, it is proper to observe, that we find in Hooke's work no measured result. We do not allude only to the law of force, which is here entirely omitted: we have said that Hooke supposed it to be reciprocal to the square of the distance; but others before him, and among them Bouillaud,[28] had established the same supposition, on simple metaphysical considerations. Halley again did the same, after Hooke and Bouillaud. We have a convincing proof that Hooke arrived at this conclusion in no other way, from his saying that he had not yet experimentally verified the law of decrease in the attracting force; for he would not have thus expressed himself if he had discovered this law directly, by applying the theorems of Huygens on centrifugal forces to the observed orbits of the planets; for in this case the experiment would have been already made, and the law of the squares, thus obtained, would have needed no other verification. The generalization of the idea of gravity, and its extension to all celestial bodies, decreasing in intensity according to the distance, was formally <17> expressed by Borelli[29] in 1666, in his work on the Satellites of Jupiter; and not only did he announce it as a general principle, but he explained very clearly how the planets may be retained and suspended in empty space round the sun, in the same manner as the satellites round their planets, by the action of a power continually and exactly balanced by the centrifugal force caused by their rotation, without having recourse either to the solid heavens of Aristotle, or to the vortices of Descartes. Borelli even endeavoured to deduce from this combination of forces the elliptical motions of the satellites, and the inequalities in their motions, which he considered as being partly produced by the secondary action of the sun; and though, from his being unacquainted both with the law of this force at different distances, and with the Theorems on Central Forces, published by Huygens six years afterwards, he was, of course, unable rigorously to establish these deductions; yet there was much merit in being the first to guess and perhaps to indicate the possibility of doing so. Newton also, we shall presently see, attributes to Borelli the honour of having first formed the idea of extending the principle of gravitation, and of applying it to the planetary motions; and Huygens renders him the same justice in his Kosmotheoros,[30] where he mentions these happy perceptions, immediately before speaking of the demonstrations of Newton. It is not then by any means impossible that Hooke might have been conducted to the same thoughts by similar, that is by purely physical considerations; and we shall presently see reasons that render this conjecture extremely probable. However, in whatever manner he formed these opinions, it is clear that in 1679, he considered them as undoubtedly correct; for, in writing to Newton on the motion of projectiles, he represents the eccentric ellipse as the consequence of a force reciprocal to the squares of the distances from the centre of the earth. This remarkable relation could not fail of striking a mind which had so long and so constantly studied the motions of the heavens. Newton as we have already said, hastened to examine this result, by means of mathematical calculations, and discovered its truth; that is to say, he found that an attractive force, emanating from a centre, and acting reciprocally to the squares of the distances, necessarily compels the body on which it acts, to describe an ellipse, or in general a conic section, in one of whose foci the centre of force resides. The motions produced by such force exactly resemble the planetary motions, both in regard to the form of the orbit and the velocity of the body at each point. This was evidently the secret of the system of the world; but it still remained to account for the singular discordance which the moon's motion had offered to Newton, when, in 1665, he had wished to extend to her the earth's gravity diminished according to this law. Hence it was that, notwithstanding his inference was confirmed by other inductions, he abstained from publishing any thing upon the subject. Three years afterwards, however, (in June, 1682,) Newton being present at a meeting of the Royal Society, in London, the conversation turned on a new measurement of a terrestrial degree, recently executed in France, by Picard, and much credit was given to the care taken in rendering it exact. Newton, having noted down the length of the degree obtained by Picard, returned home immediately, and taking up his former calculation of 1665, began to recompute it from the new data. Finding, as he advanced, the manifest tendency of these numbers to produce the long wished for results, he suffered so much nervous excitement, that becoming at length unable to go on with the calculation, he entreated one of his friends to complete it for him. This time the agreement of the computed with the observed result was no longer doubtful. The force of gravity at the earth's surface, as determined by experiments on falling bodies, when applied to the moon, after being diminished proportionally to the square of the distance from the centre of the earth, was found to be very nearly equal to the centrifugal force in the moon, as concluded from its distance and angular velocity obtained by observation. The small difference which still existed between the two results, was in itself a new proof of exactness; for if we suppose an attractive power to emanate from all the celestial bodies inversely proportional to the squares of <18> their distances from the bodies which they attract, the motion of the moon ought not only to depend upon its gravity towards the earth, but also to be influenced by the action of the sun; for this effect, though exceedingly weakened by the distance, ought not to be wholly imperceptible in the result.

Thus Newton ceased to doubt; and after having been, during so many years, kept in suspense about this eminently important law, he had no sooner recognized its truth, than he penetrated instantly to its most remote consequences, pursued them all with a vigour, a perseverance, and a boldness of thought, which, till that time, had never been displayed in science. Indeed it seems hardly probable that it will, at any future time, be the destiny of another human being to demonstrate such wonderful truths as these; that all the parts of matter gravitate towards one another, with a force directly proportional to their masses, and reciprocally proportional to the squares of their mutual distances; that this force retains the planets and the comets round the dun, and each system of satellites around their primary planets; and that, by the universally communicated influence which it establishes between the material particles of all these bodies, it determines the nature of their orbits, the forms of their masses, the oscillations in the fluids which cover them, and, in fine, their smallest movements, either in space or in rotation upon their own axes, and all conformably to the actually observed laws. The finding of the relative masses of the different planets, the determination of the ratio of the axes of the earth, the pointing out the cause of the precession of the equinoxes, and the discovery of the force exercised by the sun and the moon in causing the tides, were the sublime objects which unfolded themselves to the meditations of Newton, after he had discovered the fundamental law of the system of the universe. Can we wonder at his having been so much excited as not to have been able to complete the calculation which was leading him to a conviction that the discovery was achieved?

It was now that he must have experienced intense satisfaction at having so profoundly studied the manner in which physical forces act, and at having sought by so many experiments to comprehend, and exactly to measure their different effects. More particularly must he have been delighted at having created that new calculus, by means of which he was enabled to developr the most complicated phenomena, to bring to light the simple elements of motion, and thus to obtain the forces themselves from which the phenomena result; and finally, to re-descend from these forces to the detail of all their effects: for, with equal talent, had he not possessed this instrument of investigation, the complete unfolding of his discovery would have been impossible. But, possessing the means, he had only to apply them; and thus he saw the constant object of his hope attained. Henceforward, he devoted himself entirely to the enjoyment of these delightful contemplations; and during the two years that he spent in preparing and developing his immortal work, Philosophiæ naturalis Principia Mathematica, he lived only to calculate and to think. Oftentimes lost in the contemplation of these grand objects, he acted unconsciously: his thoughts appearing to preserve no connexion with the ordinary concerns of life. It is said that, frequently on rising in the morning, he would sit down on his bedside, arrested by some new conception, and would remain for hours together, engaged in tracing it out, without dressing himself. He would even have neglected to take sufficient nourishment, had be not been reminded by others of the time of his meals.[31]

It was only by the uninterrupted efforts of a solitary and profound meditation, that even Newton was able to unfold all the truths he had conceived, and which were but so many deductions from his great discovery. We may learn from his example, on what severe conditions even the most perfect intellect is able to penetrate deeply into the secrets of nature, and to enlarge the bounds of human attainments. For himself, he well knew, and willingly confessed, the inevitable necessity of perseverance and <19> constancy in the exercise of his attention, in order to develop the power of thought. To one who had asked him on some occasion, by what means he had arrived at his discoveries, he replied, "By always thinking unto them;" and at another time he thus expressed his method of proceeding. "I keep the subject constantly before me, and wait till the first dawnings open slowly by little and little into a full and clear light." Again, in a letter to Dr. Bentley, he says, "If I have done the public any service this way, it is due to nothing but industry and patient thought." With such tastes and habits, the complete command of his own time, and of his own ideas, was his highest enjoyment. Thus notwithstanding the importance of the results he had obtained, Newton was not eager to establish a title to them by publication, and perhaps he would have even longer delayed giving them to the world had an accidental circumstance not induced him to do so. About the beginning of 1684, Halley, one of the greatest of the English astronomers, and at the same time, one of the most enlightened and active minds that have ever cultivated science, formed the idea of employing the Theorems of Huygens on central forces, to determine the tendency in the different planets to recede from the sun, by virtue of their revolutions about that body, their orbits being considered as circular. From the ratios discovered by Kepler between the times of these revolutions, and the major axes of the orbits, he recognized these tendencies to be reciprocally as the square of the distances of each planet from the sun, so that the attraction which this luminary exerts to keep them in their places, must also vary according to the same law. This was precisely the idea that Newton had conceived in 1666, and from which he had drawn the same consequence. But there was yet a long way from this, to the rigorous calculation of curvilinear motions when the law of the force is given. Halley perceived the difficulty of this step, and after having in vain endeavoured to remove it, he consulted Hooke, at Sir Christopher Wren's house, without, however, receiving any light on the subject, although Hooke had boasted before them both that he had completely resolved this grand question. At last, impatient to see an idea unfolded, which appeared to him so fertile in consequences, Halley went to Cambridge in 1692, purposely to confer with Newton on the subject. It was then that Newton showed to him a Treatise on Motion, in which Halley found the desired solution. This treatise, with some additions, afterwards formed the two first books of the Principia. It would appear that, at this time, Newton had already introduced, and explained some parts of it, in his lectures at Cambridge. Halley, delighted at seeing his hopes realized, requested Newton to confide to him a copy for insertion in the registers of the Royal Society, in order to secure to him the honour of so important a discovery. Although Newton had an extreme repugnance to expose himself in the arena of literary intrigue, where he had, on a former occasion, wasted his time, and sacrificed his tranquillity, Halley, by repeated entreaties, at length succeeded in his object. On returning to London, Halley announced his success to the Royal Society, who repeated the request by means of Aston, at that time their secretary. But, though Newton kept his word to Halley, personally, by sending him a copy of his treatise, he did not then wish it to be communicated, having still many things to complete.[32] It was not till the following year, that Dr. Vincent presented, in Newton's name, this work, which was destined to make so great a revolution in science. Newton dedicated it to the Royal Society, who showed itself able to appreciate such an honour. It decided that the work should be printed immediately at its own expense, and addressed to the author, by Halley, a letter of thanks expressed in the most honourable terms.

Hooke, who probably had for some time past conceived in his mind similar ideas, without having been able to bring them to perfection, had no sooner understood the object of Newton's treatise, and heard of the admiration with which it was received, than he claimed for himself the priority of the discovery of the law of attraction varying inversely as the square of the distance. His reclamation was so violent, that Halley thought it necessary to notice it in his official letter to Newton, and to say that Hooke expected Newton to mention in his preface, that the priority was due to him. We will here quote the answer of <20> Newton[33], (dated Cambridge, 26th June, 1686,) especially as it will enable us to trace more clearly the progress and development of his ideas throughout this important research.

"In order to let you know the case between Mr. Hooke and me, I give you an account of what passed between us in our letters, so far as I could remember; for 'tis long since they were writ, and I do not know that I have seen them since. I am almost confident by circumstances, that Sir Christopher Wren knew the duplicate proportion when I gave him a visit; and then Mr. Hooke, by his book Cometa, written afterwards (1678), will prove the last of us three that knew it. I intended in this letter to let you understand the case fully, but it being a frivolous business, I shall content myself to give you the heads of it in short, viz. that I never extended the duplicate proportion lower than to the superficies of the earth, and before a certain demonstration I found the last year, have suspected it not to reach accurately enough down so low; and therefore in the doctrine of projectiles never used it, nor considered the motion of the heavens, and consequently Mr. Hooke could not, from my letters, which were about projectiles, and the regions descending hence to the centre, conclude me ignorant of the theory of the heavens. That what he told me of the duplicate proportion was erroneous, namely that it reaches down from hence to the centre of the earth — that it is not candid to require me now to confess myself in print then ignorant of the duplicate proportion in the heavens, for not other reason but because he had told it me in the case of projectiles, and so upon mistaken grounds accused me of that ignorance; — that, in my answer to his first letter, I refused his correspondence; told him I had laid philosophy aside, sent him only the experiment of projectiles (rather shortly hinted, than carefully described) in compliment, to sweeten my answer, expected to hear no further from him, could scarce persuade myself to answer his second letter, did not answer his third, was upon other things, thought no further of philosophical matters than his letters put me upon it, and therefore may be allowed not to have had my thoughts about me so well at that time. That, by the same reason, he concluded me ignorant of the rest of that theory I had read before in his books. That, in one of my papers, writ (I cannot say what year, but I am sure some time before I had any correspondence with Mr. Oldenburg, and that's above fifteen years ago) the proportion of the forces of the planets to the sun reciprocally duplicate to their distances from him, and the proportion of our gravity to the moon's conatus recedendi a centro terræ is calculated, though not accurately enough. — That, when Huygenius put out his treatise de Horologio Oscillatorio, a copy being presented to me, in my letter of thanks to him I gave those rules in the end thereof a particular commendation for their usefulness in computing the forces of the moon from the earth, and the earth from the sun, in determining a problem about the moon's phase, and putting a limit to the parallax, which shews that I had then my eye upon the forces of the planets arising from their circular motion, and understood it; so that while after, when Mr. Hooke propounded the problems solemnly in the end of his Attempt to prove the motion of the earth, if I had not known the duplicate proportion before, I could not but have found it now. Between ten and eleven years ago, there is an hypothesis of mine registered in your books, wherein I hinted a cause of gravity towards the earth, sun, and planets, with the dependence of the celestial motions thereon; in which the proportion of the decrease of gravity from the superficies of the planet (though for brevity sake not there expressed) can be no other than reciprocally duplicate of the distance from the centre; and I hope I shall not be urged to declare in print that I understood not the obvious mathematical conditions of my own hypothesis; but grant I received it afterwards from Mr. Hooke, yet have I as great a right to it as to the ellipsis. For as Kepler knew the orb to be not circular but oval, I guessed it to be elliptical; so Mr. Hooke, without knowing what I have found out since his letters to me, can know no more but that the proportion was duplicate quam proxime at great distances form the centre, and only guessed it to be so accurately, and guessed amiss in extending that proportion down to the very centre; whereas Kepler guessed right at the ellipsis, and so Hooke found less of the proportion than Kepler did of the <21> ellipse, there is so strong an objection against the accurateness of this proportion, that without my demonstrations, to which Hooke is yet a stranger, it cannot be believed by a judicious philosopher to be anywhere accurate. And so, in stating this business, I do pretend to have done for the proportion as for the ellipse, and to have as much right to the one from Hooke and all men, as to the other from Kepler, and, therefore, on this account also, he must, at least, moderate his pretences. The proof you sent me I like very well: I designed the whole to consist of three books; the second was finished last summer, being short, and only wants transcribing, and drawing the cuts fairly. Some new proportions I have since thought of, which I can as well let alone. The third wants the theory of comets. In autumn last, I spent two months in calculations to no purpose, for want of a good method, which made me afterwards return to the first book, and enlarge it with divers propositions, some relating to comets, others to other things I found out last winter. The third I now design to suppress. Philosophy is such an impertinently litigious lady, that a man had as good be engaged in law-suits, as have to do with her. I found it so formerly, and now I am no sooner come near her again, but she gives me warning. The two first books, without the third, will not bear so well the title of Philosophiæ Naturalis Principia Mathematica; and, therefore, I had altered it to this, De Motû corporum libri duo; but, upon second thoughts, I retain the former title, 'twill help the sale of the book, which I ought not to diminish now 'tis yours."

Newton then adds, in a postscript, "Since my writing this letter, I am told by one who had it from another lately present at one of your meetings, how that Mr. Hooke should make a great stir, pretending I had all from him, and desiring they would see that he had justice done him. This carriage towards me is very strange and undeserved; so that I cannot forbear in stating the point of justice, to tell you further that he has published Borelli's hypothesis in his own name; and the asserting of this to himself, and completing it as his own, seems to me the ground of all the stir he makes. Borelli did something and wrote modestly. He has done nothing, and yet written in such a way, as if he knew, and had sufficiently hinted all but what remained to be determined by the drudgery of calculations and observations, excusing himself from that labour, by reason of his other business; whereas he should rather have excused himself by reason of his inability – for it is very plain, by his words, he knew not how to go about it. Now is not this very fine? Mathematicians that find out, settle, and do all the business, must content themselves with being nothing but dry calculators and drudges; and another that does nothing but pretend and grasp at all things, must carry away all the invention, as well of those that were to follow him, as those that went before. Much after the same manner were his letters writ to me, telling me that gravity in descent from hence to the centre of the earth was reciprocally in a duplicate ratio of the altitude — that the figure described by projectiles in that region would be an ellipsis, and that all the motions of the heavens were thus to be accounted for; and this he did in such a way, as if he had found out all, and knew it most certainly. And upon this information, I must now acknowledge, in print, I had all from him, and so did nothing myself but drudge in calculating, demonstrating, and writing upon the inventions of this great man; and yet, after all, the first of these three things he told me is false, and very unphilosophical; the second is as false; and the third was more than he knew, or could affirm me ignorant of, buy anything that passed between us in our letters. Nor do I understand by what right he claims it as his own; for as Borelli wrote long before him, that, by a tendency of the planets towards the sun, like that of gravity or magnetism, the planets would move in ellipses: so Bullialdus wrote, that all force respecting the sun as its centre, and depending upon matter, must be in a reciprocally duplicate ratio of the distance from the centre, and used that very argument for it, by which you, Sir, in the last Transactions, have proved this ratio in gravity."

The remainder of this letter offering no other historical details, we will not continue the quotation; but the extremely curious reply of Halley to Newton is well worthy of attention. It is dated 29th June, 1686. Halley begins by encouraging Newton not to heed the effects of Hooke's expostulations with the Royal Society, and then continues, <22> "According to your desire, I waited upon Sir C. Wren, to inquire of him, if he had the first notion of the reciprocal duplicate proportion from Mr. Hooke? his answer was, that he himself, very many years since, had had his thoughts upon making out the planet's motions by a composition of a descent towards the sun and an impressed motion; but that at length he gave over, not finding the means of doing it. Since which time Mr. Hooke had frequently told him that he had done it, and attempted to make it out to him, but that he never was satisfied that his demonstrations were cogent. And this I know to be true, that in January, 16834, I having, from the sesquialterate proportion of Kepler, concluded that the centripetal force decreased in the proportion of the squares of the distance reciprocally, came on Wednesday to town, from Islington, where I met with Sir C. Wren and Mr. Hooke, and falling in discourse about it, Mr. Hooke affirmed, that upon that principle all the laws of the celestial motions were to be demonstrated, and that he himself had done it. I declared the ill success of my attempts; and Sir Christopher, to encourage the inquiry, said, that he would give Mr. Hooke, or me, two months time to bring to him a convincing demonstration thereof; and besides the honour, he of us that did it should have from him a present of a book of forty shillings. Mr. Hooke then said he had it, but that he would conceal it for some time, that others, trying and failing, might know how to value it, when he should make it public. However, I remember that Sir Christopher Wren was little satisfied that he could do it; and though Mr. Hooke then promised to show it to him, I do not find that, in that particular, he has been so good as his word. The August following, when I did myself the honour to visit you, I then learned the good news, that you had brought this demonstration to perfection, and you were pleased to promise me a copy thereof, which I received with great satisfaction; and thereupon took another journey to Cambridge, on purpose to confer with you about it, since which time it has been entered upon the register-books of the society. Mr. Hooke, according to the philosophically ambitious temper he is of, would, had he been master of a like demonstration, no longer have concealed it, the reason he told Sir Christopher and me now ceasing. But now he says that it is but one small part of an excellent system of nature; which he has conceived but has not yet completely made out; so that he thinks not fit to publish one part without the other. But I have plainly told him, unless he produce another demonstration, and let the world judge of it, neither I nor any one else can believe it. After the meeting of the Royal Society, at which your book was presented, being adjourned to the Coffee-house, Mr. Hooke did there endeavour to gain belief, that he had some such things by him, and that he gave you the first hint of this invention; but I found they were all of opinion that nothing thereof appearing in print, nor on the books of the Society, you ought to be considered as the inventor. And if in truth he knew it before you, he ought not to blame any one but himself, for having taken no more care to secure a discovery which he puts so much value on." Halley concludes, by conjuring Newton, in the name of science, not to suppress the third volume through disgust at the conduct of an envious rival. Happily he succeeded, and Newton has, in a scholium,[34] generously mentioned Wren, Hooke, and Halley, as having all three recognized in the celestial motions the existence of an attraction reciprocally proportional to the square of the distance.

Newton's Principia appeared complete in 1687. We may form some idea of the novelty and profundity of the discoveries which it contained, on learning that, when it was first published, not more than two or three among Newton's contemporaries were capable of understanding it; that Huygens himself, a man whose mind was particularly suited to appreciate its merit, only in part adopted the idea of gravitation, and that merely as regarded the heavenly bodies, while he rejected its influence between the separate particles of matter — being preoccupied by the hypothetical ideas he had formed respecting the cause of gravity; that Leibnitz, perhaps through rivalry, or perhaps by a prepossession in favour of his own metaphysical system, completely mistook the beauty and the certainty of the method employed by Newton in this work, and even went so far as to publish a dissertation, in which he endeavoured to demonstrate the same truths on different principles; <23> that even many years after the publication of the Principia, several most profound mathematicians (John Bernoulli, for instance) opposed it, and that Fontentelle, though in advance of his age on most subjects of philosophy, expressed somewhat more than doubts concerning the law of attraction, and persisted, during his whole life, in upholding the vortices of Descartes; and in fine, that more than fifty years elapsed before the great physical truth contained and demonstrated in the Principia was, we do not say followed up and developed, but even understood by the generality of learned men. Whatever difficulty, however, the just appreciation of such a work may present, we can here give a brief account of it with entire confidence, by translating the words of that illustrious man, whose genius has so much contributed to Newton's glory, in having by his own discoveries subjected all the movements of the celestial bodies to the law of universal gravitation. After having exhibited him as setting out from the laws of Kepler, in order to discover the nature and the law of the force that governs the motions of the planets and the satellites in their orbits, and afterwards generalizing this idea according to the phenomena that presented themselves until he had ascended to the certain and mathematical knowledge of universal gravitation, "Newton," says LAPLACE,[35] "having arrived at this point, saw all the great phenomena of the universe flow from the principle he had discovered. By considering gravity at the surface of the heavenly bodies as the result of the attractions of all their particles, he discovered this remarkable and characteristical property of a law of attraction reciprocal to the square of the distance, namely, that two spheres formed of concentric layers, and with densities varying according to any law whatever, attract each other mutually, as if their masses were united at their centres. Thus the bodies of the solar system act upon each other, and upon the bodies placed at their surfaces, very nearly as if they were so many centres of attraction — a result which contributes to the regularity of their movements, and which made this illustrious mathematician recognize the gravity of the earth in the force that retains the moon in her orbit. He proved that the earth's movement in rotation must have flattened it at the poles; and he determined the laws of gravitation in the degrees of the meridian, and in the force of gravity at the earth's surface. He saw that the attractions of the sun and moon excite and maintain in the ocean those oscillations which are there observed under the name of tides. He recognized several inequalities in the moon's motion and the retrograde motion of her nodes to be owing to the action of the sun. Afterwards, considering the excess of matter in the terrestrial spheroid at the equator, as a system of satellites adhering to its surface, he found that the combined actions of the sun and of the moon tend to cause a retrogradation, in the nodes of the circles they describe round the axis of the earth; and that the sum of these tendencies being communicated to the whole mass of the planet, ought to produce in the intersection of its equator with the ecliptic that slow retrogradation known by the name of the precession of the equinoxes. The true cause of this great phenomenon could not have even been suspected before the time of Newton, since he was the first who made known the two leading facts on which it depends. Kepler himself, urged by an active imagination to explain every thing by hypothesis, was constrained to avow in this instance the failure of his efforts. But, with the exception of the theory of the elliptical motions of the planets and comets, the attraction of spheres, the ratio of the masses of the planets accompanied by satellites to that of the sun, all the other discoveries respecting the motions and figures of the heavenly bodies were left by him in an incomplete state. His theory of the figures of the planets is limited, by supposing them to be homogeneous. His solution of the problem of the precession of the equinoxes, though very ingenious, and notwithstanding the apparent agreement of its result with observations, is defective in many particulars. Among the numerous perturbations in the motions of the heavenly bodies, he has only considered those of the moon, the greatest of which, viz. evection, has wholly escaped his researches. Newton has well established the existence of the principle he had the merit of discovering; but the development of its consequences and advantages has been the work of the successors of this great mathematician. The imperfection of the infinitesimal calculus when <24> first discovered, did not allow him completely to resolve the difficult problems which the theory of the universe offers; and he was oftentimes forces to give mere hints, which were always uncertain till confirmed by rigorous analysis. Notwithstanding these unavoidable defects, the importance and the generality of his discoveries respecting the system of the universe, and the most interesting points of natural philosophy, the great number of profound and original views which have been the origin of the most brilliant discoveries of the mathematicians of the last century, which were all presented with much elegance, will insure to the Principia a lasting preeminence over all other productions of the human mind."

The great results that Newton has amassed in the Principia are almost all presented in a synthetical form, like that used in the writings of the ancients. Nevertheless we may assert, that he did not discover them by means of synthesis, which is neither sufficiently easy of application, nor sufficiently fertile in results to be employed in discovering such complicated truths, or for foreseeing consequences so remote from their first principle. It is hence evident, from this very impossibility, that Newton attained these great results by the help of analytical methods, of which he had himself so much increased the power; and this conclusion acquires certainty form the correspondence between Newton and Cotes, relating to the second edition[36] of the Principia, for in it we find Cotes, the pupil of Newton, employing the analytical form either in submitting to Newton the difficulties he met with, or in solving them himself. It remains to be explained why Newton preferred setting forth his discoveries by a different method, thus depriving himself of the increase of glory he would infallibly have obtained, by giving to the world the several analytical inventions with which he must have been acquainted in solving the questions he has treated. Among these we may mention the principle of the calculus of variations, which must have been necessary to him in determining the solid of the least resistance. It were difficult to say with certainty what decided him to make such a sacrifice, but if we may hazard a conjecture, it may not be impossible that, from the excessive apprehension which he laboured under of having his results attacked, he preferred the sythetical form, as being a severer method of demonstration, and as being likely to inspire more confidence in those who should read his work at a time when the methods of the infinitesimal analysis were still but little known; and when, from their novelty, they might appear less convincing to many of his readers. Whilst the Principia were preparing for the press, chance produced an incident that drew Newton from his studious retreat, and brought him on the theatre of public affairs. King James II. desiring to re-establish catholicism in England, and thinking fit to attack the usages and rights of the Protestants, had, among other measures, commanded[37] the University of Cambridge to confer the degree of M.A. on Francis, a Benedictine Monk, without requiring of him the oath prescribed by the statutes against the catholic religion. The University asserted its privileges; and Newton (who had shown himself one of the most ardent in encouraging resistance) was one of the delegates sent to maintain their rights before the High Commission Court. These delegates made so firm and unexpected a defence, that the king thought proper to drop the affair. It was this circumstance, perhaps, as much as the personal merit of Newton, that induced the University to elect him, the following year, as their representative to serve in the Convention Parliament, which declared the throne vacant, and called William to the crown. He sat in this parliament until its dissolution, but without acting a remarkable part. C. Montague, afterwards Earl of Halifax, was a member at the same time, and having been educated at Cambridge, was able to appreciate the merit of the genius who formed the glory of the University. Hence, when Halifax, having become Chancellor of the Exchequer, in 1696, conceived the design of a general recoinage, he demanded and obtained for Newton the honourable and lucrative employment of Warden of the Mint, which was at once an act of kindness, and a choice influenced by discernment. In fact, Newton rendered very signal service in executing the important measure which the statesman had determined on; being <25> 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 his 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.[38] On the 29th May, 1694, a Scotchman of the name of Colin, informed me, that Isaac Newton, the celebrated mathematician, eighteenth months previously, 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, <26> 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. Newton 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 Optics, in 1704; for Newton distinctly announces them to be taken from manuscripts which he had formerly 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.[39] 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[40] 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 <27> 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 re-elected 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 that 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 500l. as a testimony of his acknowledgement; many editions of the work itself, and of the translation, rapidly succeeded each other, both in England and on the continent. 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 differently conceived and applied, according to the hypothesis we adopt as to the nature of the luminous principle.

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 there producing new and important results in the hands of foreign analysts, particularly of Leibnitz, and the Bernoullis.

<28>

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 impossible 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 to 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 infinitas," which he had composed in 1665, and in which, as we have already said, he had explained is 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 have 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 them 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 <29> 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 disengaged 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."[41]

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 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 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.[42] "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 <30> minima, for drawing tangents, and for similar operations, which was equally applicable both to rational and irrational quantities: that illustrious man replied that he also had fallen on a method of the same kind (se quoque in ejusmodi methodum incidisse), and communicated to me his method, which scarcely differed from mine, except in the notation and the idea of the generation of quantities."

There is a curious ambiguity in the words, "he replied that he had fallen on a method of the same kind," which, to those who had not seen the letters that were interchanged, might convey the idea, that Leibnitz had discovered the key to Newton's anagram; but this meaning is not to be found in Leibnitz's letter; he only announces a supposition, honourable to his character, viz. that the concealed method of Newton has, perhaps, some connexion with that which he communicates to him. With this explanation, the above passage in the Principia is in truth a formal recognition of Leibnitz's claims. It was so considered by every one when it appeared, and during twenty years Leibnitz was allowed, without any dispute, to develop all the parts of the differential calculus, and to deduce from it an immense number of brilliant applications, which seemed to extend the power of mathematical analysis far beyond any preconceived limits. In this interval, Wallis, by publishing the above-mentioned letters between Leibnitz and Newton, only rendered, if possible, the claims of the former more complete and more incontestable in the eyes of every impartial person. It was not till 1699 that Nicholas Fatio de Duillier,[43] in a Memoir, in which he employed the infinitesimal calculus, claimed, in favour of Newton, the first invention of it; "and," added he, "with regard to what Mr. Leibnitz, the second inventor of this calculus may have borrowed from Newton, I refer to the judgement of those persons who have seen the letters and manuscripts relating to this business." Did Fatio really believe what he was writing, or did he wish to flatter the national pride of the country in which he lived? or was he not in some manner irritated at Leibnitz having rendered so little justice to the Principia, and at his appearing to arrogate to himself a sort of empire over all discoveries made by the aid of the new calculus? These questions we do not pretend to decide; but the two latter suppositions are the most probable. Leibnitz replied, by stating the fact, and quoting his letters, and the testimony rendered to him by Newton himself. Fatio was silent; and thus the matter stood till 1704, when Newton published the Optics. In giving an account of the treatise on the quadrature of curves, which was joined to this work, the editor of the Leipzig Acts naturally mentioned the evident analogy that existed between Newton's method of fluxions and the differential calculus which had been published twenty years previously by Leibnitz, in the same Acts, and which had since become the means of making an infinity of analytical discoveries. In comparing the two methods, the editor (whom Newton supposes to have been Leibnitz himself) did not precisely say, that the method of fluxions was a mere transformation of the differential calculus; but he used terms which might bear such an interpretation. This was the signal for attack, on the part of the English writers; one of the most violent of them, Keil, professor of astronomy at Oxford, said, in a paper printed in the Philosophical Transactions, not only that Newton was the first inventor of the method of fluxions, but also that Leibnitz had stolen it from him, by merely changing the name and the notation used by Newton. This produced an indignant reply from Leibnitz, who had the imprudence to submit the question to the judgement of the Royal Society, that is to say, of a tribunal which was presided over by his rival. The society, with scrupulous fidelity, collected all the original letters that could be found bearing on the matter in question, and thus, with regard to the facts, its conduct was unimpeachable; but the most important and delicate part of the business, viz. the discussion of those papers, and the consequences to be deduced by them, it referred to arbitrators chose by itself, who were not known, and about whose appointment Leibnitz was not consulted. These arbitrators decided that Newton had indubitably been the first discoverer of the method of fluxions, a truth which is certainly incontestable in the sense that discovery and invention are synonymous terms; but they also added two assertions, which can only be considered as the expression of their personal opinion — first, that the differential and <31> fluxional methods are one and the same thing; and, secondly, that Leibnitz must have seen a letter of Newton's, (dated 10th December, 1672,) in which the method of fluxions is described in a manner sufficiently clear for any intelligent person to understand. Now of these two assertions, the second is not proved in any one of its parts, and the letter of Newton alluded to, appears, according to his custom, to have been more intended for establishing his right, than proper for indicating the manner of attaining his method. With regard to the first assertion, that the methods are absolutely identical, it may easily be refuted by the simple consideration, that if the method of fluxions alone existed at the present moment, the invention of the differential calculus with its notation, and its principle of decomposition into infinitely small elements, would still be an admirable discovery, and one which would immediately bring to light a number of applications, which we now possess, but which probably would not have been obtainable without its assistance. Admitting, then, as certain, the priority of Newton's ideas on this subject, we think that the reserve he maintained regarding it left the field open to all other inventors; and that from the general tendency of the mathematical researches of that period, both Leibnitz and Newton might have separately arrived by different means at the knowledge of a method, the want of which was then so sensibly felt in all analytical researches. The quarrel between Newton and Leibnitz has not been without advantage to mathematical science; since it produced the previous collection of letters on infinitesimal analysis, collected by the Royal Society, and published in 1712, under the name of the Commercium Epistolicum. But as regards these two great men themselves, the bitterness with which it inspired the one against the other, became the torment and the misfortune of the remainder of their lives. Newton went so far as to affirm, that Leibnitz had deprived him of the differential calculus, and then that this calculus was identical with Barrow's method of tangents: an assertion of which he could not but have perceived the injustice, since, if he pretended, on the one hand, that the differential calculus and the method of fluxions were the same, he must have also admitted the method of fluxions to be identical with Barrow's method of tangents, an assertion which he was far from admitting. Newton suffered himself to be carried away so far as to pretend that the paragraph inserted in the Principia, by which he had so openly acknowledged the independent rights of Leibnitz, was by no means intended to render him that testimony, but, on the contrary, to establish the priority of the method of fluxions over that of the differential calculus. Newton's animosity was not even calmed by the death of Leibnitz, in 1716: for he immediately afterwards printed two manuscript letters of Leibnitz, written in the preceding year, accompanied with a bitter refutation. Six years later, (in 1722) he caused a new edition of the Commercium Epistolicum to be printed, at the head of which he placed a very partial extract from this Collection. This was apparently made by himself, and had already appeared two years before the death of Leibnitz, in the Philosophical Transactions for 1715. Finally, Newton had the weakness to leave out, or allow to be left out, in the third edition of the Principia, published under his own inspection, 1725, the famous Scholium, in which he had admitted the rights of his rival. To render such conduct, not to say excusable, but even comprehensible, on the part of a man who must so well have known that the only tribunal that can decide on such causes is impartial posterity, it is necessary to say that Leibnitz, on his side, had neither been less passionate nor less unjust. Hurt by the unexpected publication of the Commercium Epistolicum, and irritated by a decision, give without his knowledge, by judges whom he had not appointed, and who had not waited for his defence, he summoned contrary testimonies in his support. Leibnitz had the misfortune to produce proofs equally exaggerated with those brought forward by Newton. He printed, and spread throughout Europe, an anonymous letter (since discovered to have been written by J. Bernoulli), extremely injurious to Newton, whom it represented as having fabricated his method of fluxions from the differential calculus. Leibnitz committed a still greater fault. He was in the habit of corresponding with the Princess of Wales, daughter-in-law to George the First. This princess, endowed with a highly cultivated mind, had received Newton with extreme kindness, and was fond of conversing with him. She declared that she esteemed <32> herself happy in living at a time that enabled her to become acquainted with so great a genius. Leibnitz made use of his correspondence with the princess, to lower Newton in her eyes, and to represent his philosophy to her not only as physically false, but also as dangerous in a religious point of view; and, what is still more inconceivable, he founded these accusations on passages in the Principia, and in the Optics, which Newton had evidently composed and inserted with intentions sincerely religious, and as a genuine professions of his firm belief in a divine Providence. For instance, in explaining the true method to be pursued in natural philosophy, Newton says, in his Twenty-eighth Query, "the main business of this science is to argue from phenomena, without feigning hypotheses, and to deduce causes from effects, till we come to the very First Cause; which certainly is not mechanical: and not only to unfold the mechanism of the world, but chiefly to resolve these and such like questions. What is there in places almost empty of matter, and whence is it, that the sun and planets gravitate towards one another, without dense matter between them? Whence is it that nature doth nothing in vain, and whence arises all that order and beauty, which we see in the world? To what end are comets, and whence is it that planets move all one and the same way, in orbs very eccentric; and what hinders the fixed stars from falling upon one another? How came the bodies of animals to be contrived with so much art? and for what ends were their several parts? was the eye contrived without skill in optics, and the ear without knowledge of sounds? How do the motions of the body follow from the will, and whence is the instinct in animals? Is not the sensory of animals that place to which the sensitive substance is present; and into which the sensible species of things are carried through the nerves and brain, that there they may be perceived, by their immediate presence to that substance? And these things being rightly dispatched, does it not appear from phenomena, that there is a Being incorporeal, living, intelligent, omnipresent, who in infinite space, as it were, in his sensory, sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself; and which things, the images only, carried through the organs of sense into our little sensoriums, are there seen and beheld, by that which in us perceives and thinks; and though every true step made in this philosophy bring us not immediately to the knowledge of the First Cause, yet it brings us nearer to it, and on that account is to be highly valued?"

It is thus that Newton speaks of a Supreme Being; and even those who might dispute the arguments which he gives for such an existence, must still recognize, in this passage, the sentiments of a mind deeply imbued with religious feelings, and convinced of their true foundation. It was upon this ground, however, that Leibnitz attacked him in his correspondence with the princess: "it appears," says he, in one of his letters, "that natural religion is diminishing extremely in England;" and he cites as a proof the works of Locke, and the above passage from Newton; elsewhere he says, "that these principles are precisely those of the materialists." When we see a mind of the order of that of Leibnitz expressing itself with such blind contempt for the grand and incontrovertible discovery of universal gravitation, and employing such arguments in objecting to it, we are disposed to compassionate the occasional weakness of the finest intellects, and to deplore the petty passions which tarnish the splendour of genius. The rank of the person to whom this accusation was addressed increased its importance in those days. The king was informed of the matter, and expressed his expectation that Newton would reply. It would appear that it was this authority that determined Newton personally to enter the lists; but he only undertook the defence of the mathematical part of the question; the philosophical part he left to Dr. Clarke, who, though inferior as a mathematician, was a better metaphysician than himself. From this resulted a great number of letters, written by Clarke and Leibnitz to each other, which were all inspected by the princess. In the course of all this correspondence, as often happens, the original question was lost amidst collateral disquisitions.[44] On reading these letters, it must excite surprise that a woman of rank could amuse herself with discussions of this sort, <33> mixed up as they were with the coarse and erudite jests made use of by Leibnitz. To this taste, however, of the princess for serious matters we owe our acquaintance with a work of Newton, very different from those that we have hitherto mentioned. Conversing one day on some historical subject, Newton explained to her a system of chronology, which he had formerly composed, simply for amusement. The princess was so much pleased with it, that she requested a copy, for her own use, on which latter condition Newton complied with her request: he, however, gave also a copy to the Abbé Conti, who had made himself remarkable by interfering in the disputes between Leibnitz and Newton. No sooner was the Abbé in Paris, than he communicated this manuscript to the world. It was immediately translated and printed, not only without the consent or knowledge of Newton, but even accompanied with a refutation by Fréret. Newton had thus the mortification to hear at the same time of the publication and the reply, without having had any suspicion of the transaction; and was hence obliged, though contrary to his original intention, at least to give a more correct edition; but he was only able to prepare one: it did not appear till after his death in 1728.

This leads us to speak of another work of Newton, which, though appearing to differ much in its title from the one we have just mentioned, is, like it, an historical memoir; the title is, "Observations upon the Prophecies of Holy Writ, particularly the Prophecies of Daniel and the Apocalypse of St. John." Notwithstanding the singularity such a subject appears to offer, when treated of by a mind like that of Newton, we venture to affirm, that more persons have spoken of this dissertation than have given themselves the trouble to read it; it therefore becomes our duty here to point out more particularly the object which Newton had in view, and his manner of proceeding. The groundwork of his reasoning is concisely expressed by the following words in the work itself:[45]

"The folly of interpreters hath been to fortell times and things by this prophecy, as if God designed to make them prophets. By this rashness they have not only exposed themselves, but brought the prophecy also into contempt. The design of God was much otherwise. He gave this and the prophecies of the Old Testament, not to gratify men's curiosities, by enabling them to foreknow things; but that after they were fulfilled, they might be interpreted by the event; and his own Providence, not the interpreters', be then manifested thereby to the world. Now," says Newton, "for understanding the prophecies, we are in the first place to acquaint ourselves with the figurative language of the prophets; this language is taken from the analogy between the world natural and an empire or kingdom considered as a world politic."[46] He then successively enters into all the details of this connexion; first of all considering the heavens and the earth as representing thrones and people; then taking the astronomical phenomena, the rain, the hail, the meteors, the animals, the vegetables, their different parts, their different actions, and those of man himself; and finally, every thing in the material world, as having a peculiar mystic signification which he fixes and defines: "for instance," says he, "when a beast or man is put for a kingdom, his parts and qualities are put for the analogous parts and qualities of the kingdom: as the head of a beast for the great men who precede and govern; the tail for the inferior people who follow and are governed; the heads, if more than one, for the number of capital parts, or dynasties or dominions in the kingdom, whether collateral or successive, with respect to the civil government; the horns on any head for the number of kingdoms in that head, with respect to military power; seeing for understanding and policy; and in matters of religion the επισχοποι, bishops; speaking for making laws; the mouth for a lawgiver, &c. &c."[47] Down to this point we find, in fact, nothing new, except the precise and, in some degree, systematic explanation of the method of interpretation: for at bottom this method is that which has been employed by all commentators; and it is really impossible to employ any other, in applying a prophecy which is not explicit in its terms. The distinguishing character of Newton's work is, that having thus made his glossary beforehand, it often suffices him for explaining a prophecy, to place the figu <34> rative terms word for word opposite to the explanations: by these means he makes a quicker and more extended progress. We will not follow him in the vast career he proposed to go over. Furnished with what he considered a key to prophetical language, he successively questions Daniel and St. John, and endeavours to produce, from their prophecies, the historical events that have taken place since their time. His work is immense; it embraces not only the principal epochs, and the most important events, in the ancient and in a part of the middle ages, but also a multitude of particular facts, of chronological observations, and of researches on civil or ecclesiastical antiquities, showing deep and extensive knowledge, taken from the most authentic sources. To give an idea of the detailed applications by which Newton has allowed himself to be carried away in this singular composition, and at the same time not to leave unnoticed the spirit of prejudice of which unhappily it bears the stamp, we will extract a passage in the seventh and eighth chapters of the first part. Newton has explained the ten horns of the fourth beast of Daniel by the ten kingdoms which the barbarians founded on the ruins of the Roman empire in the west, and has rapidly traced the history of each of these kingdoms, in order to show how it agrees with the prophecies. It remains to explain the eleventh horn of the same beast: the words of scripture are: "Now Daniel considered the horns, and behold there came up among them another horn, before whom there were three of the first horns plucked up by the roots; and behold in this horn were eyes like the eyes of a man, and a mouth speaking great things, and his look was more stout than his fellows, and the same horn made war with the saints, and prevailed against them: and one who stood by, and made Daniel know the interpretation of these things, told him, that the ten horns were ten kings that should arise, and another should arise after them and be diverse from the first, and he should subdue three kings, and speak great words against the Most High, and wear out the saints, and think to change times and laws: and that they should be given into his hands until a time and times and half a time." "Now," says Newton, "kings are put for kingdoms as above; and therefore the little horn is a little kingdom. It was a horn of the fourth beast, and rooted up three of his first horns; and therefore we are to look for it among the nations of the Latin empire, after the rise of the ten horns. But it was a kingdom of a different kind from the other ten kingdoms, having a life or soul peculiar to itself, with eyes and a mouth. By its eyes it was a seer; and by its mouth speaking great things, and changing times and laws, it was a prophet, as well as a king. And such a seer, a prophet, and a king, is the church of Rome." Newton then supports this analogy by an historical account of the rise and progress of the papal power, the details of which he, in succession, compares with the prophecy. Newton carries this investigation no further than the last half of the eighth century, because," says he, "the Pope, by acquiring temporal power, is clearly designated by the prophet:" but carried beyond the limits previously assigned by himself to interpreters, he goes on to predict the epoch of the fall, or at least decline of this temporal power, for translating the expression of Daniel, "a time and times and half a time," by 1260 solar years, and indicating the year 800 as about the point to count from, he fixes the fatal term to be about the year 2060. We must remark, that this conclusion is not, in his work, as in those of some other protestant writers, dictated by any sectarian or party feeling; he states it with all the calm of entire conviction, and with all the simplicity of an evident demonstration. It appears to be not Newton, but St. John and Daniel, who attack the power of modern Rome, who characterize it by injurious terms, and finally predict its ruin.

It will, doubtless, be asked, how a mind of the character and force of Newton's, so habituated to the severity of mathematical considerations, so accustomed to the observation of real phenomena, so methodical, and so cautious, even at his boldest moments in physical speculation, and consequently so well aware of the conditions by which alone truth is to be discovered, could put together such a number of conjectures, without noticing the extreme improbability that is involved in all of them, from the infinite number of arbitrary postulates on which he endeavours to establish his system. The answer to this question must be taken entirely from the ideas and the habits of the age <35> in which Newton lived. Not only was Newton profoundly religious, but his whole life was spent, and all his affections were concentrated in a circle of men, who, holding the same doctrines, considered themselves bound by their station or profession to defend and propagate them. The English philosophers of that period took pleasure in combining the researches of science with theological discussion; to which they were the more inclined, because the cause of protestantism had identified itself with political liberty; and men studied the bible to find weapons against despotism. The choice of Newton by the University of Cambridge as one of the delegates sent to King James, shows clearly that he shared in such sentiments; nor is it a more surprising fact, that Newton wrote upon the Apocalypse, than that R. Boyle, one of the greatest natural philosophers of the same period, published a treatise, entitled "The Christian Virtuoso," of which the object is to show that experimental philosophy conduces to a man being a good Christian, — than that Wallis, the celebrated mathematician, composed a number of tracts on religious subjects, — than that Barrow who reckoned Newton himself among his pupils, and who resigned in his favour the mathematical chair, consecrated his latter years to theology, in order to take the degree of doctor in the faculty — that Hooke, whom we have so often mentioned, composed a work on the Tower of Babel — that Whiston, Newton's pupil and successor at Cambridge, also composed an essay "on the Revelation of St. John," and other treatises on pure theology — that Clarke, another still more illustrious pupil of Newton, the faithful translator of his Optics, the zealous promoter and ingenious defender of his philosophy, was at the same time the most profound theologian and sublime preacher in England; and finally, that Leibnitz himself, to take no other example, in the course of his literary life, voluntarily made numerous excursions into the provinces of natural theology, revelation, and biblical criticism; that he commented on the story of Balaam, treated in various ways the question of grace, and with the laudable intention of uniting Protestants and Catholics, discussed with Bossuet the principal doctrinal points which separate the two churches. This alliance of the exact sciences with religious controversy, at that time so general, is the natural mode of accounting for the theological researches of Newton, however singular they might appear at the present day. There is another tract belonging to the same class of writings, which we must also mention, not only from the importance of the subject in a religious point of view, but also because it affords us a new opportunity of seeing the extensive knowledge which Newton possessed in these matters. The title is "An historical account of two notable corruptions in the Scriptures," in fifty pages 4to.; it contains a critical discussion of two passages in the Epistles of St. John and St. Paul, relating to the doctrine of the Trinity, which Newton supposes to have been altered by the copyists. From the nature of the subject, and from certain indications at the beginning of the pamphlet, it probably was composed when the works of Whiston and of Clarke on the same subject drew upon them the attacks of all the English theologians, that is, about 1712-13. It is certainly very remarkable that a man of the age of seventy-two or seventy-five should be able to compose rapidly, as he himself insinuates, so extensive a piece of sacred criticism, and of literary history, in which the logically connected arguments are always supported by the most varied erudition. At this period of Newton's life, the reading of religious works had become one of his most habitual occupations; and after he had performed the duties of his office, they formed, along with the conversation of his friends, his only amusement. He had now almost ceased to think of science, and as we have already remarked, since the fatal aberration of his intellect in 1693, he gave to the world only three really new scientific productions. One of these had probably been prepared some time previously, and the other must have occupied but little time: the first, published in the Philosophical Transactions, consists of only five, though very important, pages. It contains a comparative scale of temperatures, from the point of melting ice to that of the ignition of charcoal; the lower degrees are observed by means of a thermometer of linseed oil, the scale of which is divided into equal parts; the zero corresponds to the melting point of ice, and the 81st degree to the melting point of tin. The higher degrees are calculated according to the law of cooling in a metallic mass, by supposing the instan <36> taneous decrease in temperature to be proportional to the temperature itself, and by observing the time of the arrival of the fluid at each degree of temperature intended to be marked. These two methods of observation are connected by applying them to the same temperature — for instance, to the fusion of tin, which is the highest in the one series, and the lowest in the other.

We have thus in this paper three important discoveries — first, a method of comparing thermometers, by determining the extreme terms of their scale from phenomena taking place at constant temperatures — secondly, the determination of the laws of cooling in solid bodies at slightly elevated temperatures; and thirdly, the observation of the constancy of temperature in the phenomena of melting and boiling — a constancy which has since become one of the foundations of the modern theory of heat: this important fact is established in Newton's treatise, by numerous and various experiments, made not only on compound bodies, and the simple metals, but on various metallic alloys, which shows us that Newton clearly perceived their importance. There is reason to believe that this paper was one of those composed before the fire in his laboratory.

The second paper we must mention, also dated 1700, was communicated by Newton to Halley, and was a plan for an instrument for reflection to observe with at sea, without the observer being disturbed by the motion of the ship. It has been pretended that this idea, since so generally and so usefully employed by navigators, had been invented a long time previously by Hooke. It is true that in the history of the Royal Society for 1666, there is mentioned an instrument proposed by Hooke, to measure angles by means of the reflection of light; this announcement, however, is unaccompanied by any description to enable us to judge of the nature of the instrument; and if we endeavour to supply this defect by consulting the works of Hooke, written after this period, we shall find, that though he often makes use of reflection, it is always when applied to large fixed instruments; an idea which has no relation to that of employing reflection in moveable instruments, in order to render the angular distance of remote objects under observation independent of small changes of place in the centre of obser
vation from which they are viewed. There is no reason to believe that any one formed this happy and important idea before Newton, though the inexplicable silence of Halley, with regard to Newton's letter to him, left to another man, Hadley, the honour of again conceiving it (in 1731), and of so happily executing it, that mariners have given the name of Hadley's Quadrant to this ingenious and useful invention.

The last labour of Newton that remains to be mentioned, was of another sort, and composed on a totally different occasion. In 1696, J. Bernoulli proposed to the mathematicians of Europe, to discover a curve, down which a heavy body should descend in the quickest time possible, between two given points at unequal heights. Newton having received this problem, presented on the next day a solution of it, but without any demonstration, merely saying that the required curve must be a cycloid, for the determination of which he gave a method. This solution appeared anonymously in the Philosophical Transactions, but J. Bernoulli immediately guessed the author; "tanquam," says he, "ex ungue Leonem." This method of defiance, then in vogue, was again presented some years later to Newton, but by a more formidable adversary, and in a case where victory was of still more importance. In 1716, when the dispute about the invention of the infinitesimal analysis was at his height, Leibnitz wishing to show the superiority of his calculus over Newton's method of fluxions, sent, in a letter to the Abbé Conti, the enunciation of a certain problem, in which it was required to discover a curve such as should cut at right angles an infinity of curves of a given nature, but all expressible by the same equation; "he wished," he said, "to feel the pulse of the English analysts." Of course the question was a very difficult one. It is said that Newton received the problem at four in the afternoon as he was returning from the Mint, and, that though extremely fatigued with business, yet he finished the solution before retiring to rest. It has been, however, justly remarked, that Newton only gave the differential equation for the problem, and not its integral, in which the real difficulty consists. This was his last effort of the kind; and he soon entirely ceased to occupy himself with mathematics: so that during the last ten years of his life, when consulted <37> about any passage in his works, his reply was, "Address yourself to Mr. De Moivre, he knows that better than I do." And then, when his surrounding friends testified to him the just admiration his discoveries had universally excited, he said, "I know not what the world will think of my labours, but, to myself, it seems that I have been but as a child playing on the sea-shore; now finding some pebble rather more polished, and now some shell rather more agreeably variegated than another, while the immense ocean of truth extended itself unexplored before me."[48]

This profound conviction of the numerous discoveries that still remained to be made, did not, however, bring him again on that sea where he had advanced so much farther than any other man. His mind, fatigued by long and painful efforts, had need of complete and entire repose. At least we know, that thenceforward he only occupied his leisure with religious studies, or sought relief in literature or in business. Newton, the greatest of mankind in science, was, if we may dare say so, but an ordinary man in other pursuits; he never distinguished himself in parliament, to which he was twice summoned; and in one instance he appears to have acted with inexplicable timidity.[49] In 1713, a bill was brought in for encouraging the discovery of a method for finding the longitude at sea. Whiston, the author of the bill, and who himself tried to gain the reward proposed in it, obtained the appointment of a committee for discussing the measure; and four members of the Royal Society were invited to attend — Newton, Halley, Cotes, and Dr. Clarke: the three latter gave their opinions verbally, but Newton read his from a paper he had brought with him, without being understood by any one; he then sat down and obstinately kept silence, though much pressed to explain himself more distinctly. At last Whiston, seeing the bill was going to fail, took on himself to say, that Mr. Newton did not wish to explain more through fear of compromising himself, but that he really approved the measure. Newton then repeated word for word what Whiston had said, and the report was brought up. This almost puerile conduct, on such an occasion, tends to confirm the fact of the aberration of Newton's intellect in 1695, though it might have been merely the effect of excessive shyness, produced by the retired and meditative habits of his life. For, to judge from a letter of Newton,[50] written some time before the disastrous epoch, in which he points out the conduct to be pursued by a young traveller, it would appear that he was very ignorant of the habits of society.

From the manner in which his life was spent, we may easily conceive that he was never married, and (as Fontenelle says) that he never had leisure to think about it; that being immersed in profound and continual studies during the prime of his life, and afterwards engaged in an employment of great importance, and ever quite taken up with the company which his merit drew to him, he was not sensible of any vacancy in life, nor of the want of domestic society. His niece, who with her husband lived in his house, supplied the place of children, and attended to him with filial care. From the emoluments of his office — from a wise management of his patrimony – and from his simple manner of living, Newton became very rich, and employed his wealth in doing much good. He thought, says Fontenelle, that a legacy is no gift, and therefore left no will — it was always out of his present fortune that he proved his generosity to his relations, or to the friends whom he knew to be in want. His physiognomy might be called calm rather than expressive, and his manner languid rather than animated: his health remained good and uniform till his eightieth year; he never used spectacles. About that age he began to suffer from an incontinence of urine; but notwithstanding this infirmity, he still had, during his five remaining years, long intervals of health, or at least of freedom from pain, obtained by a strict regimen and other precautions, which till then he had never had occasion for. He was now obliged to rely upon Mr. Conduit, who had married his niece, for the discharge of his official duties at the Mint. Newton was useful to Conduit, even after death: for the honourable confidence that existed between them gave him a sort of claim to the office, which the king eagerly confirmed.

<38>

"Newton," says Fontenelle, "did not suffer much, except in the last twenty days of his life: it was truly judged from the symptoms, that he was afflicted with the stone, and that he could not recover. In the paroxysms of pain, he uttered not a moan, nor gave any sign of impatience; and, as soon as he had a moment of relief, he smiled and spoke with his usual gaiety. Hitherto he had always employed some hours every day in either reading or writing. On Saturday the 18th of March, he read the papers in the morning, and conversed for some time with Dr. Mead, the physician who attended him, having then the perfect use of all his senses and his understanding; but in the evening, he entirely lost them without again recovering, as if the faculties of his mind were not destined to linger by degrees, but at once to vanish. He died the Monday following (March 20th, 1727,) at the age of eighty-five. His corpse lay in state in the Jerusalem Chamber, and was thence conveyed to Westminster Abbey; the funeral ceremony was numerously attended; the pall was supported by six peers; and every honour was paid to his remains."

The family of Newton, justly sensible of the distinction derived from their connexion with so great a genius, erected at a considerable expense a monument to his memory, on which is inscribed an epitaph, ending as follows: — "Sibi gratulentur mortales tale tantumque exstitisse humani generis decus." — "Let mortals congratulate themselves that so great an ornament of the human race has existed" — an eulogy which, though true in speaking of Newton, can be applied to no one else.

Besides the works we have already mentioned, Newton published an edition of the "Geographia Generalis" of Varenius, 8vo, 1672, reprinted in 1681. There is no really complete edition of the works of Newton, though Bishop Horsley published one in five volumes, 4to, to which he has given this title; but he has omitted a number of papers collected by Castillon (4 vols. 4to, Lausanne, 1744). By joining to these two books Newton's scientific letters inserted in the Biographia Britannica, we may make a tolerably complete collection of his works. Among the numerous translations that have appeared of the principal ones, we must not omit that of the Principia in French by Madame Duchâtelet, since it contains excellent notes supposed to be by Clairault. There are also two books in English, viz. H. Pemberton's "View of Sir I. Newton's Philosophy," (London, 1728, 4to), and C. Maclaurin's "Account of Sir I. Newton's Philosophical Discoveries," both of which will well repay the trouble of perusing them. It is, however, in the writings of the modern continental mathematicians, that we find the more complete development of those brilliant discoveries which have shed so much lustre on the name of Newton. It is with the works of LAPLACE, Lagrange, Biôt, Lacroix, Monge, Garnier, Poisson, DELAMBRE, Boucharbat, Carnot, Bailly, Bernouilli, Euler, Bossut, Montucla, De Zach, Lalande, Franœur, Legendre, Poisson, Gauss, Hauy, &c. &c., that the student must become acquainted, before he can hope to attain to a thorough knowledge of the system of the universe. In science, it is perhaps more necessary than in any other species of knowledge intimately to understand what has been done by our predecessors; and it therefore becomes our duty to express our earnest hope, that our readers will not merely content themselves with studying the works of that great man whose discoveries we have in this treatise recorded, but that, endeavouring themselves to enter on the same illustrious career, they will diligently peruse the writings of the distinguished individuals whose names we have just mentioned. A list is given in Hutton's Mathematical Dictionary of the principal MSS. now in existence, that were written by Newton.

[1]

These details of the infancy of Newton are taken chiefly from "Collections for the History of the Town and Soke of Grantham, containing authentic Memoirs of Sir Isaac Newton, &c. by Edmund Turner, (London, 1806.)" And from the Eloge on Newton, written by Fontenelle.

[2]

The title is Logicæ artis Compendium, auctore Robert Sanderson. Oxon. 8vo.

[3]

Particularly in his Optics, where he attributes the discovery of the true theory of the rainbow to Antonius de Dominis, Archbishop of Spalatro, leaving to Descartes only the merit of having "mended the expli <3> cation of the exterior bow;" and yet ever impartial reader, who refers to the original works, will see that the theory of Descartes is exact and complete, either as to the cause of the bow, its formation, or its size, and that he was only unacquainted with the cause of the different colours; and even, notwithstanding his ignorance relative to this part of the phenomenon, Descartes, with great sagacity, refers it to another experimental fact, by assimilating it to the colours formed by prisms. It is this formation of colours that Newton has so completely explained by the unequal refrangibility of the rays of light; but all the rest of the explanation is due to Descartes. The book of Dominis contains absolutely nothing but explications entirely vague, without any calculations or real result.

[4]

These details are mentioned by Newton himself, in a letter sent through Oldenburg to Leibnitz, dated October 24, 1676. It is No. LV. in the Commercium Epistolicum, published by order of the Royal Society of London.

[5]

Newton afterwards shewed the truth of this result, by deducing it from a law observed by Kepler, in the movement of all the planets, which consists in the description of areas proportional to the times, by the radius vector drawn from each planet to the sun; but he did not know how to make use of this law till he had discovered the means of calculating the motion in an elliptic orbit; that is, about the end of the year 1679.

[6]

Vide Whiston's Memoirs of Himself, page 23, &c.

[7]

Born in Holstein: he passed the greater part of his life in England.

[8]

Com. Epist. LVI.

[9]

At the end of the Optics.

[10]

This model, made by Newton himself, is still preserved in the Library of the Royal Society.

[11]

Birch, vol. iii, p. 3.

[12]

At that time published in monthly numbers, by the Royal Society.

[13]

Dated Trinity College, February 10th, 1671.

[14]

Birch, vol. iii. p. 4.

[15]

Birch, Hist. R.S. vol. iii. p. 10.

[16]

Philosoph. Transact. vol. vii. No. 88.

[17]

These discoveries were given to the world in Grimaldi's posthumous work, Physico-mathesis de lumine, &c. (Bononiæ, 1665, in 4to.) — a book also containing the undulatory hypothesis afterwards reproduced by Hooke. Vide Montucla, Histoire des Mathématiques, vol. ii.

[18]

Comm. Epist. LVII.

[19]

Dated 9th Dec. 1675. Birch, vol. iii. pp. 247, 261, 296.

[20]

Birch. Hist. R.S. vol. iii. p. 249.

[21]

Birch, Hist. R.S. vol. iii. pp. 254, 5.

[22]

Birch, Hist. R.S. vol. iii. p. 256.

[23]

Birch, Hist. R.S. vol. iii. p. 279.

[24]

Ibid. vol, iii. p. 512.

[25]

Vide Newton's original Letters in the Biographia Britannica, article Hooke, p. 2659.

[26]

Birch, Hist. R.S. vol. ii., p. 70.

[27]

London, 4to, 1674.

[28]

Bullialdus, Astronomia Philolaica.

[29]

Theoricæ medicearum planetarum ex causis physicis deductæ. (Firenze, 1666.) This same Borelli was the author of the celebrated work de Motu Animalium.

[30]

Vid. lib. ii, p. 141. Christianii Hugenii Kosmotheoros, sive de terris cœlestibus, eorumque ornatu conjecturæ. (4to. Hagæ Comm. 1698.)

[31]

The following anecdote is told on this subject. Dr. Stukely, an intimate friend of Newton, called upon him one day when his dinner was already served up, but before he had appeared in the dining-room. Dr. Stukely having waited some time, and becoming impatient, at length removed the cover from a chicken, which he presently ate, putting the bones back into the dish and replacing the cover. After a short interval, Newton came into the room, and after the usual compliments, sat down to dinner, but on taking up the cover, and seeing only the bones of the bird left, he observed with some little surprise, "I thought I had not dined, but I now find that I have."

[32]

Birch, Hist. R.S. vol. iv. p. 370.

[33]

This letter is printed in the Biographia Britannica. — Art. Hooke.

[34]

Book 1, Prop. 4.

[35]

Exposition du Système du Monde, par Mons. Le Compte LAPLACE. Paris, 1813. 4to. pp. 413, 426.

[36]

M. Biot examined this correspondence at Cambridge.

[37]

Vide Burnet, History of his Own Time, vol. i. p. 698.

[38]

The Latin words used by Huygens are as follows: "1694, die 19 Maii, narravit mihi D. Colin, Scotus, celeberrimum ac rarum geometram, Ism. Newtonum, incidisse in phrenitin abhinc anno ac sex mensibus. An ex nimiâ studii assiduiate, an dolore infortunii, quod in incendio laboratorium chemicum et scripta quædam amiserat. Cum ad archiepiscopum Cant. venisset, ea locutum quæ alienationem mentis indicarent; deindè ab amicis cura ejus suscepta, domoque clausâ, remedia volenti nolenti adhibita, quibus jam sanitatem recuperavit, ut jam nunc librum suum Principiorum intelligere incipiat."

[39]

Vide Optics, end of second book.

[40]

The estates of Woolsthorpe and Sustern were valued, at that period, at about 80l. per annum. He derived, also, some revenue from the university and from Trinity College. — Vide Turnor.

[41]

The letters composing the anagram formed the following sentence – datâ equatione quotcumque fluentes quantitates involvente, fluxiones invenire et vice versâ.

[42]

Scholium, Prop. vii. Lib. 2.

[43]

A Genevese settled in England.

[44]

These letters were published in France by Desmaizeaux.

[45]

Age of Apocalypse.

[46]

Prophecies, part 1. chap. 2.

[47]

Prophecies, part 1. chap. 2. p. 8.

[48]

This anecdote is mentioned in a manuscript of Conduit. Vid. Turner.

[49]

This anecdote is mentioned by Whiston in his work, "Longitude Discovered," – 8vo. London, 1738.

[50]

Biographia Britannica, p. 3242.

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Professor Rob Iliffe
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Scott Mandelbrote,
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