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 from 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.* 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 Newton afterwards shewed the truth of this re sult, 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. 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 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,* 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 • Vide Whiston's Memoirs of Himself, page 23, &c. 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 the 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 (1608) an occurrence in the scientific world compelled him to declare himself. Mercator* 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 an infinite series; this he did by means of common division, as Wallis had done in the case of fractions of the form 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 1 1 -x 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 Born in Holstein: he passed the greater part of his life in England. 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."* 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; 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, even in the most beautiful of for 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 Com. Epist. LVI. At the end of the Optics 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. 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,* of his own construction, it made a great impression in 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 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 under gone 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 twentyseven years old, and thus we see, preserved in the Library of the Royal Society. This model, made by Newton himself, is still 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." 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.+ 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 more 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." 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 though 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 "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 Birch, vol. iii. p. 4. anagram; day, to masking it under the form of an of which, however, he appears not to have been able to produce the explanation, since neither he nor 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 entirely 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.* Newton replied to this attack in a severe and decisive tone.+ 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 ob servations 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 ;" 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. 事 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 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. |