<1>

## 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.

[1]

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 ($1-{\mathit{x}}^{2}$); 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 ($1-{\mathit{x}}^{2}$) 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 $\frac{1}{6}$ 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 $\frac{1}{1-\mathit{x}}$: 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.

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.

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.

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."

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]

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.

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, 168$\frac{3}{4}$, 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.

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."

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.

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."

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]

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.