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## CHAPTER IV.

NEWTON WRITES NOTES ON KINKHUYSEN'S ALGEBRA — AND ON HARMONIC AND INFINITE SERIES — DELIVERS OPTICAL LECTURES AT CAMBRIDGE — IS ELECTED A FELLOW OF THE ROYAL SOCIETY — COMMUNICATES TO THEM HIS DISCOVERIES ON TIIE DIFFERENT REFRANGIBILITY AND NATURE OF LIGHT — POPULAR ACCOUNT OF THEM — THEY INVOLVE HIM IN VARIOUS CONTROVERSIES — HIS DISPUTE WITH PARDIES — WITH LINUS — WITH GASCOIGNE AND LUCAS — THE INFLUENCE OF THESE DISPUTES ON HIS MIND — HIS CONTROVERSY WITH DR. HOOKE AND MONSIEUR HUYGENS, ARISING FROM THEIR ATTACHMENT TO THE UNDULATING THEORY OF LIGHT — HARASSED WITH THESE DISCUSSIONS HE RESOLVES TO PUBLISH NOTHING MORE ON OPTICS — INTIMATES TO OLDENBURG HIS RESOLUTION TO WITHDRAW FROM THE ROYAL SOCIETY FROM HIS INABILITY TO MAKE THE WEEKLY PAYMENTS — THE COUNCIL AGREE TO DISPENSE WITH THESE PAYMENTS — HE IS ALLOWED BY A ROYAL GRANT TO HOLD HIS FELLOWSHIP ALONG WITH THE LUCASIAN CHAIR WITHOUT TAKING ORDERS — HARDSHIP OF HIS SITUATION IN BEING OBLIGED TO PLEAD POVERTY TO THE ROYAL SOCIETY — DRAWS UP A SCHEME FOR EXTENDING THE ROYAL SOCIETY, BY PAYING CERTAIN OF ITS MEMBERS — THE SCHEME WAS FOUND AMONG HIS PAPERS — SOUNDNESS OF HIS VIEWS RELATIVE TO THE ENDOWMENT OF SCIENCE BY THE NATION — ARGUMENTS IN SUPPORT OF THEM.

While Newton was constructing his Reflecting Telescope, and discussing with Gregory and others the question of its superiority to instruments of the Gregorian and Cassegrainian form, his mind was directed to a variety of other subjects. Dr. Barrow had requested him, through Collins, to write some notes to be appended to a Latin translation from the Dutch, of Kinkhuysen's Algebra, a task which he readily undertook, and which occupied some considerable portion of his time during the years <69> 1669 and 1670. He at first did not think the work "worth the pains of a formal comment," and returned the book with his notes, "intermixed with the author's discourse," requesting Collins not to mention his name, but merely to say that "it was enriched by another author" In thanking him for his valuable additions, Collins intimated that the part on surd numbers had been "too lightly handled," and requested Newton to point out in several books on surds which he sent to him, such passages as might be added to Kinkhuysen, to supply the defect. Newton kindly offered to make the necessary additions, and having learned from his correspondent that his "pains" in this matter "would be acceptable to some very eminent grandees of the Royal Society, who must be made acquainted therewith," he got back his MSS., and added only two or three examples more, as upon revising the papers he "judged it (the part on surds) not so imperfect as he thought it had been."[1]

His attention had also been directed by Collins to problems on the summation of harmonic series, and in the determination of the rate per cent. in annuity problems, when all the other quantities were given. In sending the solution of the problems, he gives Collins permission "to insert it in the Philosophical Transactions, so it be without his name to it." "For I see not," he adds, "what there is desirable in public esteem were I able to acquire and maintain it. It would perhaps increase my acquaintance, the thing which I chiefly study to decline."

In the month of July 1670, he had intended, during the Duke of Buckingham's installation as Chancellor of the University of Cambridge, to pay a visit to his friends <70> in London, and to give Mr. Collins "a verbal acknowledgment of his undeserved favours;" but he was prevented "by the sudden surprisal of a fit of sickness, which not long after (God be thanked) I again recovered of."

During the winter of this year, Newton had begun to "methodize his Discourse of Infinite Series,[2] designing to illustrate it with problems," but he was "suddenly diverted from it by some business in the country," and was not able to resume the subject till towards the end of the year, when he was prevented by other avocations from preparing it for the press.

Thus encouraged by the Royal Society, Newton lost no time in making other communications to them. In his very next letter to their secretary, dated 18th January 1672, he announces his optical discoveries in the following manner: — "I desire that in your next letter you would inform me for what time the Society continue their weekly meetings; because, if they continue them for any time, I am purposing them to be considered of and examined on account of a philosophical discovery, which induced me to the making of the said telescope, and which I doubt <72> not but will prove much more grateful than the communication of that instrument, being in my judgment the oddest if not the most considerable detection which hath hitherto been made in the operations of nature."

This "oddest and most considerable detection" was the discovery of the different refrangibility of the rays of light, which it was necessary to explain in a previous chapter, as having been made before the construction of his telescope. It was communicated in a letter to Oldenburg on the 6th of February 1672, and excited great interest when read on the 8th February to "that illustrious company." The "solemn thanks of the meeting were voted to its author for his very ingenious discourse ;" and it was immediately printed in the 80th Number of their Transactions, namely, on the l9th February, both for the purpose of having it well considered by philosophers, and for "securing the considerable notices thereof to the author against the arrogations of others." At the same time a committee, consisting of Dr. Seth Ward, Bishop of Salisbury, Mr. Boyle, and Dr. Hooke, was appointed to peruse and consider it, and to give in a report upon it to the Society.

The kindness of this distinguished body, and the anxiety which they had already shewn for Newton's reputation in the affair of his telescope, excited on his part a reciprocal feeling, and he accepted of their proposal to print his discourse in the following humble terms:-"'Twas an esteem," he says, "of the Royal Society, for candid and able judges in philosophical matters, which encouraged me to present them with that discourse of light and colours, which since it has been so favourably accepted of, I do earnestly desire you to return them my cordial thanks. I before thought it I before thought it a great favour to have been made a member of that honour <73> able 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. As to the printing of that letter, I am satisfied in their judgment, or else I should have thought it too strait and narrow for public view. I designed it only to those that know how to improve upon hints of things, and therefore to shun tediousness, omitted many such remarks and experiments as might be collected by considering the assigned laws of refraction, some of which I believe, with the generality of men, would yet be almost as taking as any of those I described. But yet since the Royal Society have thought it fit to appear publicly, I leave it to their pleasure: and, perhaps, to supply the aforesaid defects, I may send you some more of the experiments, to record it (if it be so thought fit) in the ensuing Transactions."

Having in the preceding chapter given an account of the leading doctrine of the different refrangibility of the rays of light, and of the attempts to improve the reflecting telescope which that discovery suggested, we shall now endeavour to make the reader acquainted with the other discoveries respecting colours, which he at this time communicated to the Royal Society.

We have already seen that a beam of white light emitted from the sun, and refracted by a prism, is decomposed by its action into seven different colours, which compose what is called the Prismatic Spectrum, and which is nothing more than an elongated image of the sun, its length being five time its breadth, and the coloured <74> spaces having the proportions shewn in the annexed figure.

When this spectrum is distinctly formed by a good prism, so that the different colours are clearly separated, Newton found that any particular colour, such as red, was not susceptible of any change either by refraction through prisms, or reflection from mirrors, or from natural bodies, nor by any other cause that he could observe, notwithstanding his utmost endeavours to change it. It might become fainter or brighter, but its colour never changed. Its refrangibility, too, was equally unchangeable, and hence he drew the conclusion that the same degree of refrangibility always belonged to the same colour, and the same colour to the same degree of refrangibility.

But while the colours in the spectrum are original and simple, such as red, orange, yellow, green, blue, indigo, and violet, other colours may be compounded of these, "for a mixture of yellow and blue makes green, and red and yellow makes orange, and orange and yellowish green makes yellow." These compound colours, however, may be separated by the prism into their simple colours, and hence we are enabled by the prism to decompose all such colours, and however similar they may be to the primitive ones, their difference may always be discovered by the different refrangibility of their elements.

But, as Newton remarks, "the most surprising and wonderful composition is that of whiteness. No one sort of rays is alone capable of exhibiting it. It is ever compounded, and for its composition all the primary colours <75> in their due proportion are required." In order to prove this doctrine, which is called the Recomposition of white light, he employed three different methods. When the beam of white light RR, Fig. 8, was separated into its component colours, as in the spectrum MN, he received the refracted pencil R' on a second prism BCD, held either close to the first, or a little behind it, and by the opposite refraction of this prism they were all refracted back into a beam of perfectly white light BW, which projected a white circular spot on the wall at W, exactly similar in form and in colour to the spot formed there by the beam RR, before the prism intercepted it.

Another mode of recomposing white light, which Newton tells us he "often beheld with admiration," is to cause the spectrum to fall upon a large lens at some distance from the prism, and then to converge all the colours into a spot, and mix them again as they were in the light before its incidence on the prism. The light thus reproduced is "entirely and perfectly white," and does not "at all sensibly differ from the direct light of the sun, unless when the glasses used were not sufficiently clear." Hence our author concludes, "that whiteness is the usual colour of light; for light is a confused aggregate of rays endued with all sorts of colour, they are promiscuously darted <76> from the various parts of luminous bodies." When there is a due proportion of the ingredients, that is, of all the simple colours, whiteness is generated, but if any one colour predominate, the light will incline to that colour, as in the yellow flame of a candle, the blue flame of brimstone, and the various colours of the fixed stars.

From a consideration of these facts, our author regards it as very evident how colours are produced by the prism. Since such of the rays constituting white light as differ in colour, differ proportionally in refrangibility, they must in virtue of their unequal refraction be severed and dispersed into an oblong form, as in Fig. 7, in regular succession from the least refracted red to the most refracted violet. "And for the same reason it is," says Newton, "that objects, when looked upon through a prism, appear coloured. For the difform rays, by their unequal refraction, are made to diverge towards several parts of the retina, and there express the images of things coloured, as in the former case they did the sun's image upon a wall."

Having established these principles, Newton applies them to the explanation of several interesting phenomena. He shews that the colours of the primary and secondary rainbow are prismatic spectra, produced by the refraction of the drops of water. He explains the odd phenomena of lignum nephriticum, leaf gold, fragments of coloured glass, and other bodies, which appear in one position of one colour, and of another in another, in consequence of their disposition to reflect one sort of light and transmit another. He assigns the reason of Hooke's beautiful experiment, with two wedge-like transparent vessels, the one filled with a red, the other with a blue liquor. Although they are each very transparent, yet when the two are put together they are opaque; for since the one <77> transimits only red, and the other only blue, no rays whatever can pass through both of them. And without giving more instances, he concludes with this general one, — "That the colours of all natural bodies have no other origin than this; that they are variously qualified to reflect one sort of light in greater plenty than another." For if we illuminate these bodies with uncompounded light of different colours, they always appear of the colour of the light cast upon them, the colour being most vivid in the light of their own daylight colour. Minium, for example, though red, appears indifferently of any colour, though most luminous in red, and bise, though blue, appears indifferently of any colour cast upon it, though most luminous in blue. Hence, since minium reflects most copiously the red rays, it must appear red when illuminated with daylight, that is, with all sorts of rays promiscuously blended, and for the same reason bise appears blue.

No sooner were these important discoveries given to the world, than they were criticised and assailed with a degree of virulence and ignorance which have not often been combined in scientific controversy. The Royal Society unfortunately contained few individuals of pre-eminent talent capable of appreciating the value of his discoveries, and of entering the lists against his envious and ignorant assailants. While they held his labours in the highest esteem, they regarded his discoveries as fair subjects of discussion, and their secretary regularly communicated to him, and even published in their Transactions, almost all the papers which were written in opposition to his views.

The first communication on this subject was the suggestion of four experiments with the prism, which seems to have been made by some friend at Cambridge, as <78> Newton communicated them to the editor of the Philosophical Transactions, with his own observations.[3] This letter was followed by a communication from a Jesuit, Ignatius Pardies, Professor of Mathematics in the Parisian College of Clermont, containing animadversions upon the new Theory of Colours. Although Newton in his original discourse had demonstrated the reverse, yet the French professor pretended that the elongation of the sun's image arose from the unequal incidence of the different rays on the first face of the prism; that the mixture of differently coloured powders was not white, but dull and gray; and that opacity was not produced when the two coloured liquors were mixed in the same vessel. Newton answered these shallow objections in the most satisfactory manner,[4] but this disciple of Descartes, unwilling to be vanquished, took up a new position, and maintained that the elongation of the sun's image by the prism, might be explained by the diffraction of light on the hypothesis of Grimaldi, or by the diffusion of undulations on the hypothesis of Hooke.[5] Newton replied to these silly speculations on the 11th of June; but he contented himself with reiterating his original experiments, and confirming them by more popular arguments. [6] Pardies replied on the 9th July, in terms highly complimentary to Newton.[7] He expressed himself satisfied with Newton's explanations, acknowledged that his only difficulty had been wholly removed, and that he cherished the warmest gratitude for the kindness with which his annotations had been examined and answered.

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About this time Newton seems to have been peculiarly sensitive about the reception of his Doctrine of Colours. On the 8th of July, a month after he had written his second Reply to Pardies, he published in the Philosophical Transactions, with his name, "A Series of Queries, propounded by Mr. Isaac Newton, to be determined by experiment, positively and directly concluding his new Theory of Light and Colours, and here recommended to the industry of the lovers of Experimental Philosophy, as they were generously imparted to the Publisher in a letter of the said Mr. Newton."[8] This paper consists of eight queries, which are merely the different propositions he had established put into that form as if they were still matters of doubt, and it concludes with expressing the wish of the author, "that all objections be suspended taken from Hypotheses, or any other heads than these two; of shewing the insufficiency of experiments to determine these Queries, or prove any other parts of my theory by assigning the flaws and defects in my conclusions drawn from them; or of producing other experiments which directly contradict me, if any such may seem to occur." In order to "invite and gratify foreigners" to consider and put to trial these Queries, the publisher "delivers Mr. Newton's letter in the language also of the learned."

Oldenburg again attempted to prevail upon Newton to answer these observations, but he once more declined, on the ground that the dispute referred merely to simple matters of fact, which could only be decided before competent witnesses. The entreaties of Oldenburg, however, prevailed, and "lest Mr. Linus should make the more stir," this great man condescended to write a grave reply to reasonings utterly contemptible, and to assertions wholly unfounded. In this answer, dated November 13, 1675, and which Linus, who died on the 15th November, probably never saw, Newton gives the most minute and simple instructions for producing the prismatic spectrum. He mentions the size of the hole, "about the bigness of a pease," the position of the prism close to the hole, the mode of turning the prism round till the spectrum is placed in its stationary position, when the rays are equally refracted on both sides of the prism, and the nature and order of the colours. He tells him also that the experiment will not succeed well if the day is not clear, and he begs that "when Mr. Line has tried this he will proceed to try the experimentum crucis, which," he adds, "may be done, though not so perfectly, even without darkening a room, or the expense of any more time than half a quarter of an hour." [10]

After the death of Linus, his pupil, Mr. Gascoigne, entered the field, and declared that Linus had shown to various persons in Liege his experiment, proving the spectrum to be circular, and that Mr. Newton could not <82> be more confident on his side than they were on the other, being fully "persuaded, that unless the diversity of placing the prism, or the bigness of the hole, or some other such circumstance, be the cause of the difference between them, Mr. Newton's experiment will hardly stand." [11] Pleased with "the handsome genius" of Mr. Gascoigne's letter, Newton replied again,[12] exerting himself to discover the reason why the elongated spectrum was not as visible to others as it was to himself. With this view, he describes the three different kinds of images that may be seen upon the wall when a prism refracting the sun's rays is turned round its axis. The first of these is the regular elongated coloured spectrum; the second a round white image formed by reflection from one of the faces of the prism; and the third, an image formed by two refractions and one reflection, which, with a good equi-angular prism, would be a round white image of the aperture, but more or less elongated and coloured, if the two refracting angles were more or less inequal. From this it becomes very probable that Linus never saw the real prismatic spectrum.[13]

As Mr. Gascoigne had not the means of making the experiment thus pointed out, he requested Mr. Anthony Lucas of Liege to make it for him. This ingenious individual, who succeeded Linus in the mathematical chair at Liege, confirmed the leading results of New <83> ton, in so far as the prismatic spectrum was concerned; but he refused to acknowledge the truth of his theory, and made a number of experiments with coloured silks and coloured fluids, which he considered to be subversive of it. His experiments on the length of the spectrum, however, possess a peculiar interest. With a prism having an angle of 60°, and a refractive power of 1.500, he formed the spectrum at the distance of 18 feet from the window. The hole in the shutter was sometimes one-fifth and sometimes one-tenth of an inch, the distance of the prism from the hole about two inches, and the darkness of the room equal to that of the darkest night when the hole was shut. Under these circumstances, he never could find the spectrum longer than thrice the diameter of its breadth, or, at most, three and a half times that diameter when the refractions on both sides of the prism were equal; whereas Newton found it to be five times that diameter, with a prism whose refracting angle was 63° 12′.

In taking into consideration this new difficulty, Newton acknowledges that a difference of 3° 12′ in the refracting angle of the prism, is too little to reconcile the two results, and he conjectures that Mr. Lucas may have set down the round number of 60° as the angle of his prism, in the same manner as he set down its refractive power, or the ratio of the sines, as two to three, or 1.500. "Then," he adds, "if it be two or three degrees less than 60°, if not still less, all this would take away the greatest part of the difference between us." In order however, to determine the point experimentally, he measured the length of the spectrum with prisms of different angles, and obtained the following results: — In the first column of the following table, he gives the six angles <84> of two prisms which he used, and "which were measured as exactly as he could by applying them to the angle of a sector." In the second he gives in inches the length of the image made by each of these angles, its breadth being two inches, its distance from the prism eighteen feet and four inches, and the breadth of the hole in the window-shutter one-fourth of an inch. We have added a third column, showing the ratio of the length to the breadth of the spectrum.

 Angles of the Prism. Length of Image. Ratio of its Length to its Breadth. 56° 10′ $7\frac{3}{4}$ inches. $3\frac{7}{8}$ to 1. The first Prism, 60 24 $9\frac{1}{2}$ " $4\frac{3}{4}$ to 1. 63 26 $10\frac{1}{3}$ " $5\frac{1}{6}$ to 1. 54° 0′ $7\frac{1}{3}$ " $3\frac{2}{3}$ to 1. The second Prism, 62 12 $10\frac{1}{8}$ " $5\frac{1}{16}$ to 1. 63 48 $10\frac{3}{4}$ " $5\frac{3}{8}$ to 1.

On a clearer day, with the second prism, he found the lengths of the spectrum to be as follows, about one-fourth of an inch greater than before: —

 54° 0′ $7\frac{2}{3}$ inches $3\frac{5}{6}$ to 1. The second Prism, 62 12 $10\frac{1}{2}$ " $5\frac{1}{4}$ to 1. 63 48 11 " $5\frac{1}{2}$ to 1.

In noticing the other experiments of Lucas with differently coloured silks, which he placed in a line, and viewing both through a prism and when placed at the bottom of a square vessel of water, Newton found that "unconcerned persons" always saw them in a line as if they had all suffered the same refraction. He does not, however, point out their insufficiency to prove an equality of refraction, but thanks Mr. Lucas for taking so much pains in examining them, "and so much the more, as he was the first that had sent him an experimental examination of them." He even goes so far as to say that, in a little Treatise on <85> the subject, written before his first communication to the Royal Society, he had actually written down the principal of the experiments which Mr. Lucas had now sent him.

We have been thus minute in describing the experiments of Lucas and Newton on the length of the spectrum, because they have a close connexion with the determination of the different dispersive powers of bodies, which was one of the greatest discoveries of the following century, and led to the invention of the achromatic telescope. There are only two ways in which we can account for the shortness of the spectrum observed by Lucas. His eyes may have been to some extent insensible to violet and blue light, and therefore the spectrum would appear to him much shorter than it really was. If we cut off from Newton's spectrum one and a half inches, to reduce it to Lucas's, we cut off the whole of the indigo and violet spaces; and, unless from an imperfection of vision, Lucas could not have failed to see these colours in an apartment so very dark as his. If he had no such imperfection, it becomes highly probable that his prism was made of glass of a low dispersive power. Newton's prisms may have been of flint-glass, and Lucas's of crown-glass; and it is a remarkable circumstance, that in all these controversies the nature of the glass is never once mentioned. Had Newton been less confident than he was, that all other prisms must give a spectrum of the same length as his, in relation to its refracting angle and index of refraction, the invention of the achromatic telescope would have been the necessary result. The objections of Lucas drove Newton to make experiments which he never contemplated, namely, to measure accurately the lengths of spectra formed with prisms of different angles and different re <86> fractive powers; and had the Dutch Professor maintained his opinions with more obstinacy and perseverance, he would have conferred a distinguished favour upon science, and rewarded Newton for all the vexation which had arisen from the minute discussion of his optical discoveries.

Thus terminated the disputes with Pardies, Linus, Gascoigne, and Lucas, and we think it can scarcely be doubted that Newton found it a more difficult task to detect the origin of his adversaries' blunders, and to expose their fallacy, than to establish the great truths which they had attempted to overturn.

Harassing as such a controversy was to a philosopher like Newton, yet it did not touch those deep-seated feelings which characterize the noble and generous mind. It was with ignorance and incapacity only that he had to strive. No personal invective ruffled his equanimity; — no vulgar jealousy roused his indignation; — no charge of plagiarism called in question his veracity or his honour. These aggravations of scientific controversy, however, he was destined to endure, and in the disputes which he was called to maintain against Hooke, Huygens, and Leibnitz, the agreeable consciousness of grappling with minds of kindred power was painfully imbittered by the personal feelings which were thrown into the contest.

Dr. Robert Hooke, born in 1635, was about seven years older than Newton, and was one of the ninety-eight original or unelected Fellows of the Royal Society. He possessed great versatility of talent; yet though his genius was of the most original cast, and his acquirements extensive, he had not devoted himself with fixed purpose to any particular branch of knowledge. His numerous and ingenious inventions, of which we cannot speak too highly, <87> gave to his studies a practical character, unfitting him for that continuous labour which physical researches so imperiously demand. The subjects of light and colours, however, seem to have deeply occupied his thoughts before Newton descended into the same arena, and there can be no doubt that he had made considerable progress in their study. With a mind less divergent in its pursuits, and more fixed in its purpose, he might have unveiled the mystery in which both these subjects were enveloped, and pre-occupied the intellectual throne which was destined for his rival; but the infirm state of his health, the peevishness of temper to which it gave rise, the number of unfinished inventions from which he looked both for fortune and fame, and above all, his inordinate love of reputation, distracted and broke down the energies of his powerful intellect. In the more matured inquiries of his rivals he recognised, and often truly, his own incompleted speculations; and when he saw others reaping the harvest for which he had prepared the ground, and of which he had sown the seed, it was not easy to conceal the mortification which their success inspired. In the arbitraments of science it has always been a difficult task to adjust the rival claims of competitors, when the one was allowed to have completed what the other was acknowledged to have begun. He who commences an inquiry, and publishes its results, often goes much farther than he has announced to the world, and pushing his speculations into the very heart of the subject, frequently submits them to the ear of friendship. From the pedestal of his published labours his rival begins his researches, and brings them to a successful issue, while he has in reality done nothing more than complete the unfinished labours, and demonstrate the imperfect specu <88> lations of his rival or his predecessor. To the world and to himself he is no doubt in the position of the principal discoverer, but there is still some apology for his rival, when he brings forward his unpublished labours, and some excuse for the exercise of personal feeling, when he measures the speed of his rival by his own proximity to the goal.

The conduct of Dr. Hooke would have been viewed with some such feeling, had not his arrogance on other occasions checked the natural current of our sympathy. When Newton presented his Reflecting Telescope to the Royal Society, Dr. Hooke not only criticised the instrument with undue severity, but announced, what was never realized, that he possessed an infallible method of perfecting all kinds 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."

Descartes had long ago maintained that an ethereal medium pervaded all transparent bodies; — that light consists in the action of this medium; — that the ether is less implicated in the parts of solid bodies; — that it moves more freely in them, and transmits light more readily through them, so as to accelerate the rays in a certain proportion; — that refraction arises from this acceleration, and has the sines of incidence and refraction proportional; — that light is at first uniform; — that its colours are some disturbance or new modification of its rays by refraction or reflexion; — that the colours of a prism are made by means of the quiescent medium accelerating some motion of the rays on one side where red appears, and retarding it on the other side where blue appears, and that there are but these two original colours, or colour- <89> making modifications of light, which, by their various degrees or dilutings, as Hooke calls them, produce all intermediate ones.

These views were adopted by Dr. Hooke, who "changed Descartes' pressing or progressive motion of the medium to a vibrating one; — the rotation of the globuli to the obliquation of pulses, and the accelerating their rotation on the one hand, and retarding it on the other, by the quiescent medium to produce colours, to the like action of the medium on the two ends of his pulses for the same end." [14]

Such were Hooke's opinions of the nature of light when Newton published his Theory of Colours, and it was through this theoretical medium that he viewed Newton's discoveries, when he sent his observations upon them to the Royal Society, on the 15th February 1672. Dr. Hooke was thanked "for the pains he had taken in bringing in such ingenious reflections;" but it was not "thought fit to print the two papers together, lest Mr. Newton should look upon it as a disrespect in printing so sudden a refutation of a discourse of his which had met with so much applause at the Society but a few days before."

It is not easy to follow the train of thought which runs through the observations of Dr. Hooke. While he praises "the niceness and curiosity" of Newton's experiments, and expresses an entire agreement with him as to the truth of those which he brought forward, founded on hundreds of trials made by himself, yet he "cannot see in his hypothesis of solving the phenomena of colours thereby, any <90> undeniable argument to convince him of its certainty." He considers them as proving his own hypothesis, which he endeavours, without much success, to explain and establish. This, indeed, seems to be the principal object of his paper, but even if he had succeeded, the truth of his theory would not have invalidated in the slightest degree the doctrines of Newton. "I most readily agree," says he, "with them (Newton's experiments) in every part thereof, and esteem it (his hypothesis) very subtle and ingenious, but I cannot think it to be the only hypothesis, nor so certain as mathematical demonstration." In remonstrating with Newton "on his wholly laying aside the thought of improving telescopes and microscopes by refractions," he is more successful; but though his assertion, that the difficulties of removing the effects of colour are not insuperable, has received ample confirmation, yet the result was not obtained by any of the contrivances which he pretended to possess.

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It would have been well for the progress of science and the tranquillity of its friends, if experiment and observation had been, more than they have, our guides in philosophical inquiry. Even in the present day the disciples of Hooke, who "split pulses" with more success than he did, and whose theory of light has attained a lofty pre-eminence, have not scrupled to imitate their master in measuring optical truths by the undulatory standard, and in questioning and depreciating labours, that it cannot explain, or that run counter to its deductions. There is fortunately, however, a small remnant in the Temple of Science, who, while they give to theory its due honours and its proper place, are desirous, as experimental philosophers, to follow in the steps of their great Master.

After silencing the most powerful of his adversaries, Newton was unexpectedly summoned to defend himself against a new enemy. The celebrated Christian Huygens, an eminent mathematician and natural philosopher, who, like Hooke, had maintained the undulatory theory of light, transmitted to Oldenburg on the 14th January 1673, a letter from Paris, containing some considerations on Newton's Theory of Light; but though his knowledge of optics was of the most extensive kind, his objections were as groundless, and his speculations as erroneous as those of his less enlightened countrymen. Attached to the undulatory hypothesis, he seems, like Dr. Hooke, to have viewed the theory of Newton as calculated to overturn it, and he therefore objects to its two leading doctrines, namely, the composition of white light by the union of all the colours, and the generality of the doctrine of their different refrangibilities. The objection which he urges against the theory of whiteness is, that it may be produced equally well by yellow and blue, and "he does <93> not see why Mr. Newton doth not content himself with these two colours, as it will be much more easy to find a hypothesis by motion that will explicate these two differences, than for so many diversities as there are of other colours, and till he hath found this hypothesis, he has not taught us what it is wherein consists the nature and difference of colours, but only this accident (which certainly is very considerable) of their different refrangibility." He then proposes that the experiment should be tried of stopping all the colours but yellow and blue and green, and then mixing them on paper to see if they make the paper white, "as well as when they all give light." Nay, he adds the following extraordinary opinion, as if it were a new and happy thought. "I even doubt," says he, "whether the lightest place of the yellow colour may not all alone produce that effect, and I mean to try it at the first conveniency; for this thought never came into my mind but just now. Meantime you may see that if these experiments do succeed it can no more be said that all the colours are necessary to compound white; and that 'tis very probable that all the rest are nothing but degrees of yellow and blue more or less changed."

On the subject of the difference of refrangibility, he is equally wrong, though with more reason for his error. He remarks, that the picture formed in a dark room by an object-glass of twelve feet, is too distinct and too well defined to be "produced by rays that would stray the fiftieth part of the aperture; so that (as I believe I have told you heretofore) the difference of the refrangibility doth not, it may be, always follow the same proportion in the great and small inclinations of the rays upon the surface of the glass." [16]

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To these extraordinary objections, Newton replied on the 3d April 1673,[17] and also in another paper which immediately follows the observations of Huygens, the first of these answers having been, as we are informed by the editor, mislaid, otherwise it should have also immediately followed the letter of Huygens. In these answers, Newton shows that the yellows and blues which could produce white, are not simple but compound; and he explains more minutely how the existence of an aberration equal to the fiftieth of the aperture, is compatible with the distinctness of a picture formed by a twelve feet object-glass. Huygens, still dissatisfied with the explanations so patiently given to him, informs Oldenburg that he has still "matter to answer them, but seeing that Newton maintains his opinion with so much concern, he list not to dispute." Newton was not pleased with this criticism upon his explanations, and says in his letter to Oldenburg, — "As for Mr. Huygens' expression, I confess it was a little ungrateful to me to meet with objections which had been answered before, without having the least reason given me why those answers were insufficient."[18]

But though Huygens appears in this controversy as a rash and unreasonable objector to the Newtonian doctrine of colours, it was afterwards the destiny of Newton to play a similar part against the Dutch philosopher. When Huygens published his beautiful law of double refraction, founded on the finest experimental analysis of the phenomena, though presented as a result of the undulatory theory, Newton not only rejected it, but substituted for it another law entirely incompatible with the experiments <95> of Huygens, which Newton himself had praised, but with those of all succeeding philosophers.[19]

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While Newton was harassed with these discussions, and chagrined, it may be, with the loss of the Law Fellowship, he came to the resolution of resigning his place in the Royal Society. On the 8th of March 1673, he writes in the following terms to Oldenburg: — "Sir, — I desire that you will procure that I may be put out from being any longer a member of the Royal Society; for though I honour that body, yet, since I see I shall neither profit them, nor (by reason of this distance) can partake of the advantage of their assemblies, I desire to withdraw." Oldenburg expressed his surprise [23] "at his resigning for no other cause than his distance, which he knew as well at the time of his election ;" and he probably then intimated to him, that he would apply to the Society to excuse him his weekly payments. That such an intimation was made, appears from Newton's letter to Oldenburg, dated June 23, 1673, in which he says, — "For your proffer about my quarterly payments, I thank you, but I would not have you trouble yourself to get them excused, if you have not done it already." Nothing farther seems to have been said on the subject till the 28th January 1675, when Mr. Oldenburg mentioned "to the Society, that Mr. Newton was now in such circumstances that he desired to be excused from the weekly payments."[24] Upon which "it was agreed to by the council that he should be dispensed with, as several others were." It does not appear, from any documents we have seen, what the change of circumstances was to which Oldenburg alludes, but Mr. Edleston thinks it probable that it refers to the expected vacating of <99> his Fellowship, from his being appointed to the Lucasian chair, which, in the usual course of things, would expire in the following autumn. This anticipated event, however, did not take, place, for, on the 27th April 1675, he obtained a patent from the Crown, permitting the Lucasian Professor to hold a Fellowship, without being obliged to go into orders.

This permission seems to have been obtained on the application of Newton; and Mr. Edleston is of opinion, that the draught of it in Newton's own hand, among the Lucasian papers, was composed by himself, and that his visit to London in February may have been connected with this application to the Crown. When the grant was submitted to the King, the following memorandum, found also in Newton's handwriting, was recorded at Whitehall on the 2d March 1674: — "His Majesty, being willing to give all just encouragement to learned men who are and shall be elected into the said Professorship, is graciously pleased to refer this draught of a patent unto Mr. Atturney-Generall to consider the same, and to report his opinion what his Majesty may lawfully do in favour of the said Professors, as to the indulgence and dispensation proposed and desired." The original draught, which has been published by Mr. Edleston, was adopted, excepting in two unimportant particulars, and there is a copy of it in the archives of Trinity College, with the heading, — Indulgentia Regia Professori Mathematico concessa, dignissimo viro Magistro Isaaco Newtono, hujus Collegii Socio, istud munus tunc temporis obeunte.

It is obvious, we think, from these proceedings, that the change in Newton's circumstances must have been of a distressing nature, otherwise he would hardly have per <100> mitted Oldenburg to apply to the Royal Society for a remission of his weekly payments. At no period of his life had he any regard for money, and, as he was always punctual and accurate in his pecuniary concerns, it is very probable, that when the income of his Fellowship[25] and the Lucasian chair were united, he may have resumed his payments to the Royal Society.[26] If he did not do this, it could not have been from poverty, as we find him in 1676 subscribing forty pounds to the new Library of Trinity College.

But however this may be, it cannot fail to be remarked, especially by foreigners, as a singular example of the illiberality of England to her scientific institutions, that a Society, founded by the sovereign, and bearing the name of Royal, should have been established without any provision for the support of its members, for carrying on scientific inquiries, or for the publication of its Transactions. Nor is it less remarkable, that an Institution so useful to the country, so bright with immortal names, and so fitted to promote the intellectual glory of the nation, should have been continued under royal patronage for nearly two hundred years without any attempt being made to extend its usefulness, by placing it in the same advantageous position as the Academy of Sciences in <101> Paris, and other similar institutions in the metropolitan cities of Europe.

If Newton did not feel it a hardship to pay a weekly pittance into the treasury of the Royal Society, he must have felt it a degradation to plead poverty for its remission. His colleagues in the Society, and men of science in a succeeding age, on whom the wealth of this world is never abundantly bestowed, must have often smarted under the injustice of paying for the publication of discoveries which it cost them much time, and frequently much money, to complete. Of all the taxes upon knowledge this is the most oppressive, and not the less oppressive that it is exacted from the feelings and patriotism of its victims.

There is reason to believe that Newton took this view of his own position, and of the inefficiency of any scientific body constituted upon the voluntary principle; and it is not improbable, that he committed to writing his opinions on this subject at the time when he had resolved to withdraw from the Society. In support of this opinion, we have great pleasure in submitting to the reader a very remarkable document in Newton's handwriting, which we found among the family papers at Hurtsbourne Park, entitled "A Scheme for Establishing the Royal Society." We give it without abridgment or change, as the opinions of so competent a judge on the subjects which ought to occupy the attention of a national institute, and on the best method of making it efficient in promoting the advancement of profound science and of useful knowledge, cannot fail to be appreciated by every class of readers.[27]

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"SCHEME FOR ESTABLISHING THE ROYAL SOCIETY.

"Natural Philosophy consists in discovering the frame and operations of Nature, and reducing them, as far as may be, to general Rules or Laws, — establishing these rules by observations and experiments, and thence deducing the causes and effects of things; and for this end it may be convenient, that one or two (and at length perhaps three or four) Fellows of the Royal Society, well skilled in any one of the following branches of Philosophy, and as many in each of the rest be obliged by pensions and forfeitures, (as soon as it can be compassed,) to attend the meetings of the Royal Society. — The Branches are —

"1. Arithmetic, Algebra, Geometry, and Mechanics, with relation to the figures, surfaces, magnitudes, forces, motions, resistances, weights, densities, centres of gravity, and other mathematical affections of solids and fluids; — the composition of forces and motions; — the shocks and reflexions of solids; — the centrifugal forces of revolving bodies; — the motion of pendulums, projected and falling bodies; — the mensuration of time and distance; — the efficacy of the five powers, the running of rivers; — the propagation of light and sound, and the harmony and discord of tunes and colours.

"2. Philosophy relating to the Heavens, the Atmosphere, and the surface of the Earth, viz. Optics, — Astronomy, — Geography, — Navigation, and Meteorology; and what relates to the magnitudes, distances, motions, and centrifugal forces of the heavenly bodies; and to the weight, height, form, and motions of the Atmosphere, and of the things therein, and to instruments for observing the same; and to the figure and motions of the Earth and Sea.

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"3. Philosophy relating to animals, — viz. their species, — qualities, — passions, — anatomy, diseases, &c., and the knowledge of the frame and use of their Stomachs, — entrails, blood-vessels, heart, lungs, liver, spleen, glands, juices, and organs of sensation, motion, and generation.

"4. Philosophy relating to vegetables, and particularly the knowledge of their species, parts, leaves, flowers, seeds, fruits, juices, virtues, and properties, and the manner of their generation, nutrition, and vegetation.

"5. Mineralogy[28] and Chemistry, and the knowledge of the nature of Earths, Stones, Corals, Spars, Metals, semimetals, Marchasites, Arseniates, Bitumens, Sulphurs, Salts, Vitriols, Rain-Water, Springs, Oils, Tinctures, Spirits, Vapours, Fumes, Air, Fire, Flames and their parts, Tastes, Smells, Colours, Gravity, Density, Fixity, Dissolutions, Fermentations, Coalitions, Separations, Congelations, Liquefactions, Volatility, Distillation, Sublimation, Precipitation, Corrosiveness, Electricity, Magnetism, and other qualities; — and the causes of subterraneous Caves, Rocks, Shells, Waters, Petrifactions, Exhalations, Damps, Heats, Fires, and Earthquakes, and the rising or falling of Mountains and Islands.

"To any one or more of these Fellows, such Books, Letters, and things as deserve it, may be referred by the Royal Society at their meetings from time to time; and as often as any such Fellowship becomes void, it may be filled up by the Royal Society with a person who hath already invented something new, or made some considerable improvement in that branch of philosophy, or is eminent for skill therein, if such a person can be found. For the reward will be an encouragement to Inventors; and it will be an advantage to the Royal Society to have <104> such men at their meetings, and tend to make their meetings numerous and useful, and their body famous and lasting."

It is very evident, from this interesting document, that Newton was desirous of converting the Royal Society into an institution like that of the Academy of Sciences in Paris; but we have not been able to learn that he ever communicated this plan either to the Society itself, or to any of its members. During the last twenty years, and long before we could have known the views of so competent a judge, we have cherished the same desire, and embraced every opportunity of pressing it upon the notice of the public.[29] Several years ago we communicated Sir Isaac Newton's scheme to Sir Robert Peel, and it was so far carried into effect by the establishment of the Museum of Practical Geology, which is neither more nor less than an enlargement of the Mineralogical, Geological, and Chemical sections of an Academy of Sciences, or a National Institute. The services of all the members of this important body are of course at the entire disposal of the state, though its members are frequently employed in other duties than those which strictly belong to their office. If mineralogy, geology, and chemistry, therefore, have obtained a national establishment for their improvement and extension, — astronomy, mechanics, natural history, medicine, and literature, and the arts, are entitled to the same protection. If any real objections exist to such an establishment, they can be founded only <105> upon two causes; — on the unwillingness of existing voluntary societies to be merged in a general institution, and on the apprehension that the expense would be a burden to the state. Men will always be found who oppose every change, however salutary, and who regard the reform of existing institutions as dangerous innovations. In political and educational questions, the rights and interests of individuals often obstruct the march of civilisation, but in matters of science and literature, such rights have neither been conferred nor claimed. Were the Royal, the Astronomical, the Geological, the Linnæan, the Zoological, and the Geographical Societies, together with the Society of Civil Engineers, and the Museum of Practical Geology, all united into an Academy of Sciences, and divided into distinct sections as in France, the really working members would occupy a more distinguished position, while the nobility and gentry would preserve all their rights and privileges as honorary members.[30] The Royal Society of Literature, and the Antiquarian Society, would readily coalesce into the Academy of Belles Lettres, and the existing Royal Academy would form the Academy of the Fine Arts, divided, as in France, into the three sections of Painting, Sculpture, and Engraving. In the magnificent grove acquired by Prince Albert and the Royal Commissioners at Kensington Gore, a Palace of Arts would be reared for the Institute, and there would be one library, one museum, and one record of their weekly proceedings. Each member of the now insulated societies would listen to the memoirs and discussions of the assembled Academy, and science and literature would thus receive a new impulse from the number and variety of their worshippers.

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The second difficulty to which we have referred, namely, the expense of endowment, scarcely merits our consideration. A very large sum is annually expended by the State in support of the existing societies, and a considerable number of those who would be members of the General Institute, already enjoy the liberality of Government. But, independently of these considerations, the organization of a National Institute would be a measure of real and direct economy. The inquiries connected with the arts, whether useful or ornamental, which are required by the Government, have hitherto been carried on by Committees of Parliament; and had we a return of all the sums annually spent in scientific inquiries, and for scientific purposes, the amount would be found to exceed greatly that of the annual expense, however liberal, of a National Institution. Every question connected with ship-building, with our steam navy, our light-houses, our harbours, our railways, our mines, our fisheries, our sanatory establishments, our agriculture, our statistics, our fine and useful arts, would be investigated and reported upon by a Committee of Academicians; and while the money of the State would thus be saved, the national resources would be augmented, and all the material interests of the country, under the combined energies of her Art and her Science, would advance with a firm and accelerated step.

But there are grounds higher than utilitarian, on {which} we would plead the national endowment of science and literature. In ancient times, when knowledge had a limited range, and was but slightly connected with the wants of life, the sage stood even on a higher level than the hero and the lawgiver, and History has preserved his name in her imperishable record, when theirs has disap <107> peared from its page. Archimedes lives in the memory of thousands who have forgotten the tyrants of Syracuse, and the Roman consul who subdued it. The halo which encircled Galileo under the tortures of the Inquisition, extinguishes in its blaze even the names of his tormentors; and Newton's glory will throw a lustre over the name of England, when time has paled the light reflected from her warriors. The renown of military achievements appeals but to the country which they benefit and adorn: It lives but in the obelisk of granite: It illuminates but the vernacular page. Subjugated nations turn from the proud monument that degrades them, and the vanquished warrior spurns the record of his humiliation or his shame. Even the patriot traveller makes a deduction from military glory, when he surveys the red track of desolation and of war, and the tears which the widow and the orphan shed corrode the inscription that is written in blood. How different are our associations with the tablet of marble, or the monument of bronze, which emblazon the deeds of the sage and the philanthropist! Their paler lustre irradiates a wider sphere, and excites a warmer sympathy. No trophies of war are hung in the temple which they adorn, and no assailing foe desecrates its shrine. In the anthem from its choir the cry of human suffering never mingles, and in the procession of the intellectual victor, ignorance and crime are alone bound to his car. The achievements of genius, could the wings of light convey them, would be prized in the other worlds of our system, — in the other systems of the universe. They are the bequests which man offers to his race, — a gift to universal humanity — at first to civilisation — at last to barbarism.

Views like these must have influenced the mind of <108> Newton, when, in an elaborate document which he left in duplicate behind him, he recommended the systematic endowment of Science. Were the British Parliament to try this question at its bar, and summon as witnesses the wisest of their race, what name, or what constellation of names, could countervail against the High Priest of Science, when he proposes to rebuild its Temple upon a broader basis, and give its arches a wider span, and its domes a loftier elevation!

[1] Letters to Collins from 1669 to September 27, 1670. — Macclesfield Correspondence , Vol. ii.

[2] This work was never finished. It was published by Horsley, under the title of Geometria Analytica, from three different MSS. — See Newtoni Opera, tom. i. pp. 391-518. A translation of it had been published by Colson in 1736.

[3] The communication is dated 13th April 1672, and is published in the Transactions, No. 82, p. 4059, April 22, 1672.

[4] Phil. Trans., No. 84, p. 4091, June 17, 1672.

[5] Phil. Trans., No. 85, p. 5012, July 15, 1672.

[6] Ibid., p. 5014.

[7] Ibid., p. 5018.

[8] Phil. Trans., No. 84, p. 4080, June 17, 1672. This paper is part of a letter to Oldenburg, dated July 6, 1672, from Stoake Park, Northamptonshire.

[9] Phil. Trans., No. 110, p. 217.

[10] Phil. Trans., No. 121, p. 503.

[11] Phil. Trans., No. 121, p. 503

[12] Ibid., No. 123, p. 556.

[13] A short time before the commencement of this controversy, Linus communicated to the Royal Society a paper entitled Optical Assertions concerning the Rainbow, which appeared in their Transactions, No. 117, p. 386. How such a paper could have been published by so learned a body seems very incomprehensible. Linus was celebrated as a dial-maker. Mr. Charles Ellis mentions one of his dials at Liege, in which the hours were distinguished by touch, and says that they were "the originals of those formerly in our Privy Gardens." — Phil. Trans., No. 283, 1703, vol. xv. p. 1418.

[14] This view of Descartes' theory and of Hooke's opinions, is given by Newton in his letter to Oldenburg, dated 21st December 1675. General Dict. vol. vii. p. 783, or Macclesfield Correspondence, vol. ii. p. 378.

[15] Newtoni Opera, tom. iv. pp. 322-342.

[16] Phil. Trans., vol. viii. No. 96, p. 6086, July 1693.

[17] Phil. Trans., No. 97, p. 6108.

[18] Letter to Oldenburg without a date, but probably in April 1673.

[20] This letter is dated November 18, 1676, and was written after receiving an account of the experiments of Lucas. — Macclesfield Correspondence , vol. ii. p. 405.

[21] Gentleman's Magazine, 1799, Supplement, pp. 1186 and 999.

[22] Correspondence, &c., pp. xlviii. xlix. note, 38.

[23] This appears from a memorandum on the back of Newton's letter to him.

[24] The admission-money to the Royal Society was £2, and the payments one shilling a week.

[25] In reference to an application from Francis Aston for a dispensation similar to that received by Newton, Dr. Barrow, then Master of Trinity, in declining to grant it, says, — "Indeed a Fellowship with us is now so poor, that I cannot think it worth holding by an ingenuous person upon terms liable to so much scruple." — Edleston's Correspondence, p. 1.

[26] In a volume of MSS. in the British Museum relating to the Royal Society, there is, as Mr. Weld informs us, a sheet containing the names of Fellows who will probably pay, and give yearly one entertainment to the society. Opposite the names of Dr. Grew, Hooke, and Newton, are the words, "No pay, but will contribute experiments." The date of this list, if it has any, is not mentioned. See Baily's Life of Flamsteed, p. 90, note, and Weld's Hist. of the Royal Society, vol. i. p. 250, note.

[27] We found two copies of this scheme, one of which is more complete than the other. The first paragraph of the copy given in the text is wanting in the less perfect copy, but in other respects they are nearly the same. There is no date upon either of the copies.

[28] Written by mistake Meteorology; but in the other copy it is Mineralogy.

[29] See especially the Quarterly Review, October 1830, vol. xliii. pp. 305-342; Edinburgh Review, January 1835, vol. lx. p. 363; Edinburgh Journal of Science, passim; North British Review, vol. iv. pp. 410-412; vol. vi. p. 506; vol. xiv. pp. 281-288; from the last of which articles some of the paragraphs in the text are transferred.

[30] Corresponding to the Académiciens Libres of the Academy of Sciences in Paris.