Popular Science Monthly/Volume 17/June 1880/Goethe's Farbenlehre: Theory of Colors I
By Professor JOHN TYNDALL, F. R. S.
IN the days of my youth, when life was strong and aspiration high, I found myself standing one fine summer evening beside a statue of Goethe in a German city. Following the current of thought and feeling started by the associations of the place, I eventually came to the conclusion that, judging even from a purely utilitarian point of view, a truly noble work of art was the most suitable memorial for a great man. Such a work appeared to me capable of exciting a motive force within the mind which no purely material influence could generate. There was then labor before me of the most arduous kind. There were formidable practical difficulties to be overcome, and very small means wherewith to overcome them, and yet I felt that no material means could, as regards the task I had undertaken, plant within me a resolve comparable with that which the contemplation of this statue of Goethe was able to arouse.
My reverence for the poet had been awakened by the writings of Mr. Carlyle, and it was afterward confirmed and consolidated by the writings of Goethe himself. But there was one of the poet's works, which, though it lay directly in the line of my own studies, remained for a long time only imperfectly known to me. My opinion of that work was not formed on hearsay. I dipped into it so far as to make myself acquainted with its style, its logic, and its general aim; but having done this I laid it aside, as something which jarred upon my conception of Goethe's grandeur. The mind willingly rounds off the image which it venerates, and only acknowledges with reluctance that it is on any side incomplete; and believing that Goethe in the "Farbenlehre" was wrong in his intellectual, and perverse in his moral judgments—seeing, above all things, that he had forsaken the lofty impersonal calm which was his chief characteristic, and which had entered into my conception of the godlike in literature—I abandoned the "Farbenlehre," and looked up to Goethe on that side where his greatness was uncontested and supreme.
But in the month of May, 1878, Mr. Carlyle did me the honor of calling upon me twice; and I, not being at home at the time, visited him in Chelsea soon afterward. He was then in his eighty-third year, and, looking in his solemn fashion toward that portal to which we are all so rapidly hastening, he remembered his friends. He then presented to me, as "a farewell gift," the two octavo volumes of letterpress and the single folio volume, consisting in great part of colored diagrams, which are here before you. Exactly half a century ago these volumes were sent by Goethe to Mr. Carlyle. They embrace the "Farbenlehre"—a title which may be translated, though not well translated, "Theory of Colors"—and they are accompanied by a long letter, or rather catalogue from Goethe himself, dated the 14th of June, 1830, a little less than two years before his death. My illustrious friend wished me to examine the book, with a view of setting forth what it really contained. This year for the first time I have been able to comply with the desire of Mr. Carlyle; and as I knew that your wish would coincide with his, as to the propriety of making some attempt to weigh the merits of a work which exerted so great an influence in its day, I have not shrunk from the labor of such a review.
The average reading of the late Mr. Buckle is said to have amounted to three volumes a day. But they could not have been volumes like those of the "Farbenlehre." For the necessity of halting and pondering over its statements was so frequent and the difficulty of coming to any undoubted conclusion regarding Goethe's real conceptions was often so great as to invoke the expenditure of an inordinate amount of time. I can not even now say with confidence that I fully realize all the thoughts of Goethe. Many of them are strange to the scientific man. They demand for their interpretation a sympathy beyond that required or even tolerated in severe physical research. Two factors, the one external and the other internal, go to the production of every intellectual result. There is the evidence without and there is the mind within on which that evidence impinges. Change either factor, and the result will cease to be the same. In the region of politics, where mere opinion comes so much into play, it is only natural that the same external evidence should produce different convictions in different minds. But in the region of science, where demonstration instead of opinion is paramount, such differences ought hardly to be expected. That they nevertheless occur is strikingly exemplified by the case before us; for the very experimental facts which had previously converted the world to Newton's views, on appealing to the mind of Goethe, produced a theory of light and colors in violent antagonism, to that of Newton.
Goethe prized the "Farbenlehre" as the most important of his works. "In what I have done as a poet," he says to Eckermann, "I take no pride, but I am proud of the fact that I am the only person in this century who is acquainted with the difficult science of colors." If the importance of a work were to be measured by the amount of conscious labor expended in its production, Goethe's estimate of the "Farbenlehre" would probably be correct. The observations and experiments there recorded astonish us by their variety and number. The amount of reading which he accomplished was obviously vast. He pursued the history of optics, not only along its main streams, but on to its remotest rills. He was animated by the zeal of an apostle, for he believed that a giant imposture was to be overthrown, and that he was the man to accomplish the holy work of destruction. He was also a lover of art, and held that the enunciation of the true principles of color would, in relation to painting, be of lasting importance. Thus positively and negatively he was stimulated to bring all the strength he could command to bear upon this question.
The greater part of the first volume is taken up with Goethe's own experiments, which are described in nine hundred and twenty paragraphs duly numbered. It is not a consecutive argument, but rather a series of jets of fact and logic emitted at various intervals. I picture the poet in that troublous war-time, walking up and down his Weimar garden, with his hands behind his back, pondering his subject, throwing his experiments and reflections into these terse paragraphs, and turning occasionally into his garden-house to write them down. This first portion of the work embraces three parts, which deal respectively with—Physiological or Subjective Colors, with Physical or Prismatic Colors, and with Chemical Colors and Pigments. To these are added a fourth part, bearing the German title "Allgemeine Ansichten nach innen"; a fifth part, entitled "Nachbarliche Verhältnisse," neighboring relations; and a sixth part, entitled "Sinnlich-sittliche Wirkung der Farbe," sensuously-moral effect of colors. It is hardly necessary to remark that some of these titles, though doubtless pregnant with meaning to the poet himself, are not likely to commend themselves to the more exacting man of science.
The main divisions of Goethe's book are subdivided into short sections, bearing titles more or less shadowy from a scientific point of view: Origin of White; Origin of Black; Excitement of Color; Heightening; Culmination; Balancing; Reversion; Fixation; Mixture real; Mixture apparent; Communication actual; Communication apparent. He describes the colors of minerals, plants, worms, insects, fishes, birds, mammals, and men. Hair on the surface of the human body he considers indicative rather of weakness than of strength. The disquisition is continued under the headings: How easily Color arises; How energetic Color may be; Heightening to red; Completeness of Manifold Phenomena; Agreement of Complete Phenomena; How easily Color disappears; How durable Color remains; Relation to Philosophy; Relation to Mathematics; Relation to Physiology and Pathology; Relation to Natural History; Relation to General Physics; Relation to Tones. Then follows a series of sections dealing with the primary colors and their mixtures. These sections relate less to science than to art. The writer treats, among other things, of—Æsthetic Effects; Fear of the Theoretical; Grounds and Pigments; Allegorical, Symbolical, and Mystical Use of Colors. The headings alone indicate the enormous industry of the poet; showing at the same time an absence of that scientific definition which he stigmatized as "pedantry" in the case of Newton.
In connection with this subject, Goethe charged himself with all kinds of kindred knowledge. He refers to ocular spectra, quoting Boyle, Buffon, and Darwin; to the paralysis of the eye by light; to its extreme sensitiveness when it awakes in the morning; to irradiation—quoting Tycho Brahe on the comparative apparent size of the dark and the illuminated moon. He dwells upon the persistence of impressions upon the retina, and quotes various instances of abnormal duration. He possessed a full and exact knowledge of the phenomena of subjective colors, and described various modes of producing them. He copiously illustrates the production by red of subjective green, and by green of subjective red. Blue produces subjective yellow, and yellow subjective blue. He experimented upon shadows, colored in contrast to surrounding light. The contrasting subjective colors he calls "geforderte Farben," colors "demanded" by the eye. Goethe gives the following striking illustration of these subjective effects: "I once," he said, "entered an inn toward evening, when a well-built maiden, with dazzlingly white face, black hair, and scarlet bodice and skirt came toward me. I looked at her sharply in the twilight, and when she moved away, saw upon the white wall opposite a black face with a bright halo round it, while the clothing of the perfectly distinct figure appeared of a beautiful sea-green." With the instinct of the poet, Goethe discerned in these antitheses an image of the general method of nature. Every action, he says, implies an opposite. Inhalation precedes expiration, and each systole has its corresponding diastole. Such is the eternal formula of life. Under the figure of systole and diastole the rhythm of nature is represented in other portions of the work.
Goethe handled the prism with great skill, and his experiments with it are numberless. He places white rectangles on a black ground, black rectangles on a white ground, and shifts their apparent positions by prismatic refraction. He makes similar experiments with colored rectangles and disks. The shifted image is sometimes projected on a screen, the experiment being then "objective." It is sometimes looked at directly through the prism, the experiment being then "subjective." In the production of chromatic effects, he dwells upon the absolute necessity of boundaries—"Gränzen." The sky may be looked at and shifted by a prism without the production of color; and if the white rectangle on a black ground be only made wide enough, the center remains white after refraction, the colors being confined to the edges. Goethe's earliest experiment, which led him so hastily to the conclusion that Newton's theory of colors was wrong, consisted in looking through a prism at the white wall of his own room. He expected to see the whole wall covered with colors, this being, he thought, implied in the theory of Newton. But to his astonishment it remained white, and only when he came to the boundary of a dark or a bright space did the colors reveal themselves. This question of "boundaries" is one of supreme importance to the author of the "Farbenlehre"; the end and aim of his theory being to account for the colored fringes produced at the edges of his refracted images.
Darkness, according to Goethe, had as much to do as light with the production of color. Color was really due to the commingling of both. Not only did his white rectangles upon a black ground yield the colored fringes, but his black rectangles on a white ground did the same. The order of the colors seemed, however, different in the two cases. Let a visiting-card, held in the hand between the eye and a window facing the bright firmament, be looked at through a prism, then supposing the image of the card to be shifted upward by refraction, a red fringe is seen above and a blue one below. Let the back be turned to the window and the card so held that the light shall fall upon it; on being looked at through the prism, blue is seen above and red below. In the first case the fringes are due to the decomposition of the light adjacent to the edge of the card, which simply acts as an opaque body, and might have been actually black. In the second case the light decomposed is that coming from the white surface of the card itself. The first experiment corresponds to that of Goethe with a black rectangle on a white ground; while the second experiment corresponds to Goethe's white rectangle on a black ground, Both these effects are immediately deducible from Newton's theory of colors. But this, though explained to him by physicists of great experience and reputation, Goethe could never be brought to see, and he continued to affirm to the end of his life that the results were utterly irreconcilable with the theory of Newton.
In his own explanations Goethe began at the wrong end, inverting the true order of thought, and trying to make the outcome of theory its foundation. Apart from theory, however, his observations are of great interest and variety. He looked to the zenith at midnight, and found before him the blackness of space, while in daylight he saw the blue firmament overhead; and he rightly adopted the conclusion that this coloring of the sky was due to the shining of the sun upon a turbid medium with darkness behind. He by no means understood the physical action of turbid media, but he made a great variety of experiments bearing upon this point. Water, for example, rendered turbid by varnish, soap, or milk, and having a black ground behind it, always appeared blue when shone upon by white light. When, instead of a black background, a bright one was placed behind, so that the light shone, not on, but through the turbid liquid, the blue color disappeared, and he had yellow in its place. Such experiments are capable of endless variation. To this class of effects belongs the painter's "chill." A cold, bluish bloom, like that of a plum, is sometimes observed to cover the browns of a varnished picture. This is due to a want of optical continuity in the varnish. Instead of being a coherent layer it is broken up into particles of microscopic smallness, which virtually constitute a turbid medium and send blue light to the eye.
Goethe himself describes a most amusing illustration, or, to use his own language, "a wonderful phenomenon," due to the temporary action of a turbid medium on a picture: "A portrait of an esteemed theologian was painted several years ago by an artist specially skilled in the treatment of colors. The man stood forth in his dignity clad in a beautiful black velvet coat, which attracted the eyes and awakened the admiration of the beholder almost more than the face itself. Through the action of humidity and dust, however, the picture had lost much of its original splendor. It was therefore handed over to a painter to be cleaned and newly varnished. The painter began by carefully passing a wet sponge over the picture. But he had scarcely thus removed the coarser dirt, when to his astonishment the black velvet suddenly changed into a light-blue plush; the reverend gentleman acquiring thereby a very worldly, if, at the same time, an old-fashioned appearance. The painter would not trust himself to wash further. He could by no means see how a bright blue could underlie a dark black, still less that he could have so rapidly washed away a coating capable of converting a blue like that before him into the black of the original painting."
Goethe inspected the picture, saw the phenomenon, and explained it. To deepen the hue of the velvet coat the painter had covered it with a special varnish, which, by absorbing part of the water passed over it, was converted into a turbid medium, through which the black behind instantly appeared as blue. To the great joy of the painter, he found that a few hours' continuance in a dry place restored the primitive black. By the evaporation of the moisture the optical continuity of the varnish (to which essential point Goethe does not refer) was reëstablished, after which it ceased to act as a turbid medium.
This question of turbid media took entire possession of the poet's mind. It was ever present to his observation. It was illustrated by the azure of noonday, and by the daffodil and crimson of the evening sky. The inimitable lines written at Ilmenau—
"Ueber allen Gipfeln
suggest a stillness of the atmosphere which would allow the columns of fine smoke from the foresters' cottages to rise high into the air. He would thus have an opportunity of seeing the upper portion of the column projected against bright clouds, and the lower portion against dark pines, the brownish yellow of the one and the blue of the other being strikingly and at once revealed. He was able to produce artificially at will the colors which he had previously observed in nature. He noticed that when certain bodies were incorporated with glass this substance also played a double part, appearing blue by reflected and yellow by transmitted light. The action of turbid media was to Goethe the ultimate fact—the Urphänomen—of the world of colors. "We see on the one side Light, and on the other side Darkness. We bring between both Turbidity, and from these opposites develop all colors."
As long as Goethe remained in the region of fact his observations are of permanent value. But by the coercion of a powerful imagination he forced his turbid media into regions to which they did not belong, and sought to overthrow by their agency the irrefragable demonstrations of Newton. Newton's theory, as known by everybody, is that white light is composed of a multitude of differently refrangible rays, whose coalescence in certain proportions produces the impression of white. By prismatic analysis these rays are separated from each other, the color of each ray being strictly determined by its refrangibility. The experiments of Newton, whereby he sought to establish this theory, had long appealed with overmastering evidence to every mind trained in the severities of physical investigation. But they did not thus appeal to Goethe. Accepting for the most part the experiments of Newton, he rejected with indignation the conclusions drawn from them, and turned into utter ridicule the notion that white light possessed the composite character ascribed to it. Many of the naturalists of his time supported him, while among philosophers Schelling and Hegel shouted in acclamation over the supposed defeat of Newton. The physicists, however, gave the poet no countenance. Goethe met their scorn with scorn, and under his lash these deniers of his theory, their master included, paid the penalty of their arrogance.
How, then, did he lay down the lines of his own theory? How, out of such meager elements as his yellow, and his blue, and his turbid medium, did he extract the amazing variety and richness of the Newtonian spectrum? Here we must walk circumspectly, for the intellectual atmosphere with which Goethe surrounds himself is by no means free from turbidity. In trying to account for his position, we must make ourselves acquainted with his salient facts, and endeavor to place our minds in sympathy with his mode of regarding them. He found that he could intensify the yellow of his transmitted light by making the turbidity of his medium stronger. A single sheet of diaphanous parchment placed over a hole in his window-shutter appeared whitish. Two sheets appeared yellow, which by the addition of other sheets could be converted into red. It is quite true that by simply sending it through a medium charged with extremely minute particles we can extract from white light a ruby red. The red of the London sun, of which we have had such fine and frequent examples during the late winter, is a case to some extent in point. Goethe did not believe in Newton's differently refrangible rays. He refused to entertain the notion that the red light obtained by the employment of several sheets of parchment was different in quality from the yellow light obtained with two. The red, according to him, was a mere intensification—"Steigerung"—of the yellow. Colors in general consisted, according to Goethe, of light on its way to darkness, and the only difference between yellow and red consisted in the latter being nearer than the former to its final goal.
But how in the production of the spectrum do turbid media come into play? If they exist, where are they? The poet's answer to this question is subtile in the extreme. He wanders round the answer before he touches it, indulging in various considerations regarding penumbra? and double images, with the apparent aim of breaking down the repugnance to his logic which the mind of his reader is only too likely to entertain. If you place a white card near the surface of a piece of plate-glass, and look obliquely at the image of the card reflected from the two surfaces, you observe two images, which are hazy at the edges and more dense and defined where they overlap. These hazy edges Goethe pressed into his service as turbid media, He fancied that they associated themselves indissolubly with his refracted rectangles—that in every case the image of the rectangle was accompanied by a secondary hazy image, a little in advance of the principal one. At one edge, he contended, the advanced secondary image had black behind it, which was converted into blue; while at the other edge it had white behind it, and appeared yellow. When the refracted rectangle is made very narrow, the fringes approach each other and finally overlap. Blue thus mingles with yellow, and the green of the spectrum is the consequence. This, in a nutshell, is the theory of colors developed in the "Farbenlehre." Goethe obviously regarded the narrowing of the rectangle, of the cylindrical beam, or of the slit of light passing through the prism, which, according to Newton, is the indispensable condition requisite for the production of a pure spectrum, as an impure and complicated mode of illustrating the phenomenon. The elementary fact is, according to Goethe, obtained when we operate with a wide rectangle the edges only of which are colored, while the center remains white. His experiments with the parchment had made him acquainted with the passage of yellow into red as he multiplied his layers; but how this passage occurs in the spectrum he does not explain. That, however, his hazy surfaces—his virtual turbid media—produced, in some way or other, the observed passage and intensification, Goethe held as firmly, and enunciated as confidently, as if his analysis of the phenomena had been complete.
The fact is, that between double images and turbid media there is no kinship whatever. Turbidity is due to the diffusion, in a transparent medium, of minute particles having a refractive index different from that of the medium. But the act of reflection which produced the penumbral surfaces, whose aid Goethe invoked, did not charge them with such discrete particles. On various former occasions I have tried to set forth the principles on which the chromatic action of turbid media depends. When such media are to be seen blue, the light scattered by the diffused particles, and that only, ought to reach the eye. This feeble light may be compared to a faint whisper which is easily rendered inaudible by a louder noise. The scattered light of the particles is accordingly overpowered, when a stronger light comes, not from the particles, but from a bright surface behind them. Here the light reaches the eye, minus that scattered by the particles. It is therefore the complementary light, or yellow. Both effects are immediately deducible from the principles of the undulatory theory. As a stone in water throws back a larger fraction of a ripple than of a larger wave, so do the excessively minute particles which produce the turbidity scatter more copiously the small waves of the spectrum than the large ones. Light scattered by such particles will therefore always contain a preponderance of the waves which produce the sensation of blue. During its transmission through the turbid medium the white light is more and more robbed of its blue constituents, the transmitted light which reaches the eye being therefore complementary to the blue.
Some of you are, no doubt, aware that it is possible to take matter in the gaseous condition, when its smallest parts are molecules, incapable of being either seen themselves or of scattering any sensible portion of light which impinges on them; that it is possible to shake these molecules asunder by special light-waves, so that their liberated constituents shall coalesce anew and form, not molecules, but particles; that it is possible to cause these particles to grow, from a size bordering on the atomic, to a size which enables them to copiously scatter light. Some of you are aware that in the early stages of their growth, when they are still beyond the grasp of the microscope, such particles, no matter what the substance may be of which they are composed, shed forth a pure firmamental blue; and that from them we can manufacture in the laboratory artificial skies which display all the phenomena, both of color and polarization, of the real firmament.
With regard to the production of the green of the spectrum by the overlapping of yellow and blue, Goethe, like a multitude of others, confounded the mixture of blue and yellow lights with that of blue and yellow pigments. This was an error shared by the world at large. But in Goethe's own day, Wünsch, of Leipsic, who is ridiculed in the "Farbenlehre," had corrected the error, and proved the mixture of blue and yellow lights to produce white. Any doubt that might be entertained of Wünsch's experiments—and they are obviously the work of a careful and competent man—is entirely removed by the experiments of Helmholtz and others in our own day. Thus, to sum up, Goethe's theory, if such it may be called, proves incompetent to account even approximately for the Newtonian spectrum. He refers it to turbid media, but no such media come into play. He fails to account for the passage of yellow into red and of blue into violet; while his attempt to deduce the green of the spectrum from the mixture of yellow and blue is contradicted by facts which were extant in his own time.