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
Ist Ruh’,
In allen Wipfeln
Spurest Du
Kaum einen Hauch”
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.
II.
One hole Goethe did find in Newton’s armor, through which he incessantly worried the Englishman with his lance. Newton had committed himself to the doctrine that refraction without color was impossible. He therefore thought that the object-glasses of telescopes must for ever remain imperfect, achromatism and refraction being incompatible. This inference was proved by Dollond to be wrong. With the same mean refraction, flint-glass produces a longer and richer spectrum than crown-glass. By diminishing the refracting angle of the flint-glass prism, its spectrum may be made equal in length to that of the crown-glass. Causing two such prisms to refract in opposite directions, the colors may be neutralized, while a considerable residue of refraction continues in favor of the crown. Similar combinations are possible in the case of lenses; and hence, as Dollond showed, the possibility of producing a compound achromatic lens. Here, as elsewhere, Goethe proves himself master of the experimental conditions. It is the power of interpretation that he lacks. He flaunts this error regarding achromatism incessantly in the face of Newton and his followers. But the error, which was a real one, leaves Newton’s theory of colors perfectly unimpaired.
Newton’s account of his first experiment with the prism is for ever memorable. “To perform my late promise to you,” he writes to Oldenburg, “I shall without further ceremony acquaint you that in the year 1666 (at which time I applied myself to the grinding of optick-glasses of other figures than spherical) I procured me a triangular glass prism, to try therewith the celebrated phenomena of colors. And in order thereto, having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the sun’s light, I placed my prism at its entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colors produced thereby; but after a while applying myself to consider them more circumspectly, I became surprised to see them in an oblong form, which, according to the received laws of refractions, I expected should have been circular. They were terminated at the sides with straight lines, but at the ends the decay of light was so gradual that it was difficult to determine justly what was their figure, yet they seemed semicircular. “Comparing the length of this colored spectrum with its breadth, I found it about five times greater; a disproportion so extravagant that it excited me to a more than ordinary curiosity of examining from whence it might proceed.” This curiosity Newton gratified by instituting a series of experimental questions, the answers to which left no doubt upon his mind that the elongation of his spectrum was due to the fact “that light is not similar or homogeneal, but consists of difform rays, some of which are more refrangible than others; so that, without any difference in their incidence on the same medium, some shall be more refracted than others; and therefore that, according to their particular degrees of refrangibility, they were transmitted through the prism to divers parts of the opposite wall. When,” continues Newton, “I understood this, I left off my aforesaid glass-works; for I saw that the perfection of telescopes was hitherto limited, not so much for want of glasses truly figured according to the prescriptions of optick authors, as because that light itself is an heterogeneous mixture of differently refrangible rays; so that were a glass so exactly figured as to collect any one sort of rays into one point, it could not collect those also into the same point, which, having the same incidence upon the same medium, are apt to suffer a different refraction.”
Goethe harped on this string without cessation. “The Newtonian doctrine,” he says, “was really dead the moment achromatism was discovered. Gifted men, our own Klügel, for example, felt this, but expressed themselves in an undecided way. On the other hand, the school which had been long accustomed to support, patch up, and glue their intellects to the views of Newton, had surgeons at hand to embalm the corpse, so that even after death, in the manner of the Egyptians, it should preside, at the banquets of the natural philosophers.”
In dealing with the chromatic aberration of lenses, Goethe proves himself to be less heedful than usual as an experimenter. With the clearest perception of principles, Newton had taken two pieces of cardboard, the one colored a deep red, the other a deep blue. Around those cards he had wound fine black silk, so that the silk formed a series of separate fine dark lines upon the two colored surfaces. He might have drawn black lines over the red and blue, but the silk lines were finer than any that he could draw. Illuminating both surfaces, he placed a lens so as to cast an image of the surfaces upon a white screen. The result was that, when the dark lines were sharply defined upon the red, they were undefined upon the blue; and that, when, by moving the screen, they were rendered distinct upon the blue, they were indistinct upon the red. A distance of an inch and a half separated the focus of red rays from the focus of blue rays, the latter being nearer to the lens than the former. Goe
the appears to have attempted a repetition of this experiment; at all events he flatly contradicts Newton, ascribing his result not to the testimony of his bodily eyes, but to that of the prejudiced eyes of his mind. Goethe always saw the dark lines best defined upon the brighter color. It was to him purely a matter of contrast, and not of different refrangibility. He argues caustically that Newton proves too much; for, were he correct, not only would a dioptric telescope be impossible, but, presented to our naked eyes, differently colored objects must appear utterly confusing. Let a house, he says, be supposed to stand in full sunshine; let the roof-tiles be red, the walls yellow, with blue curtains behind the open windows, while a lady with a violet dress steps out of the door. Let us look at the whole from a point in front of the house. The tiles we will suppose appear distinct, but on turning to the lady we should find both the form and the folds of her dress undefined. We must move forward to see her distinctly, and then the red tiles would appear nebulous. And so with regard to the other objects, we must move to and fro in order to see them clearly if Newton’s pretended second experiment were correct. Goethe seems to have forgotten that the human eye is not a rigid lens, and that it is able to adjust itself promptly and without difficulty to differences of distance enormously greater than that due to the different refrangibility of the differently colored rays.
Works of Johann Wolfgang von Goethe Page 350