FROM THE HISTORY OF PHYSICS

NEWTON’S THEORY OF COLORS

M. M. Gurevich

1. INTRODUCTION

The history of color science has scarcely been illuminated at all in our literature. For this reason alone it deserves attention and at least a brief consideration.

The founder of the physico-mathematical treatment of questions of color is Isaac Newton, who devoted to it a considerable part of his optical investigations.

The theory of colors constitutes one of the finest adornments of Newton’s works on optics.

Newton’s views in the field of color have not lost their significance to this day, and one should think that acquaintance with them may serve as a good beginning for many who wish to become familiar with contemporary ideas about color.

We owe to Academician S. I. Vavilov the possibility of reading Newton’s principal optical works in Russian. Yet it is difficult for an unprepared reader to find his bearings in Newton’s writings; much in them at first seems obscure, and their inner coherence easily escapes notice. The reason for this situation is obvious. The two hundred and fifty years that have passed since the publication of Newton’s Opticks, and the almost three hundred years that separate us from the time when his Lectures on Optics were written, have covered for us both Newton’s time and the circumstances of his work with a dense veil of time, behind which not only the outlines of individual details but even the contours of major events are lost.

From our school days we have become so accustomed to the idea that the white light of the Sun contains within itself a multitude of simple, monochromatic rays, each of which has its own color, that it is difficult for us to take any other point of view and to imagine what an overwhelming impression this discovery must have made on contemporaries. It is therefore quite natural that, before speaking about Newton’s color science, it is necessary to pause at least briefly over the exposition of the system of views of his predecessors.

M. M. Gurevich

2. CONCEPTIONS OF COLOR BEFORE NEWTON

There was no generally accepted point of view on colors before Newton at all. Every major scholar put forward his own theory, which in most cases was not based on experimental results and in which it was almost always possible to notice echoes of Aristotle’s view, expressed as early as the fourth century before our era.

Aristotle’s conceptions of color were extremely vague. He believed that color is inseparably connected with the transparency of the medium through which the eye sees objects. Aristotle distinguishes actual transparency from potential transparency, the latter being transformed into the former under the action of the fire of heavenly or earthly bodies. Color is the moving principle of the actually transparent. Everything visible is color. Colorless objects are invisible.

On the other hand, Aristotle taught that color is a mixture of light with darkness in different quantities. Light, which from Aristotle’s point of view had a heavenly origin, met with the darkness of earthly matter, and as a result colors arose, alluring in their splendor, the quality of which depended on the amount of darkness mixed with the light. The simplicity and vividness of this latter conception ensured it extraordinary vitality.

After Aristotle’s authority had been completely overthrown, his theory of color continued to retain its place and significance chiefly because there was nothing with which to replace it. It should be noted that in favor of this theory there also speaks the simple testimony of everyday experience, which clearly demonstrates that every colored surface is always darker than a white one located next to it.

Kepler still adhered to Aristotle’s point of view; in 1609 he wrote that color is “light in possibility,” or “light hidden in transparent matter.” The difference of colors, in his conception, is determined by the different “arrangement” of the matter of the transparent with respect to light and darkness, and accordingly by its thickness.

In 1611 Bishop Antonio de Dominis tried to introduce here an element of quantitative assessment. He believed that if bodies containing pure light, such as stars or fire, for some reason lose their radiance, then they appear white to us. If some darkness is mixed with the light, but without thereby destroying all the light completely, then colors arise. Fire therefore becomes red because it is connected with smoke, which darkens it. The Sun and the stars, approaching the horizon, weaken their light in the intervening medium and therefore turn red. There are three intermediate colors: 1) red—the lightest of them, 2) green—

...—darker, and 3) violet—the darkest. These colors arise when light passes through a triangular prism. Light that has passed through a small thickness near the edge of the prism becomes bright red; light that has passed through the middle part becomes green; and light that has passed through the thick layer at the base becomes violet. All the remaining colors are composed of these three colors.

Marcus Marci de Kronland, who published his results in 1648 in Prague, came closer than others to Newton in the study of prismatic colors. He, like Newton, recommends observing prismatic colors in a darkened room, describes in detail the divergence of a beam of solar rays after its passage through a prism, and, like Newton, connects the appearance of colors with the refraction of light. To each refraction there corresponds its own definite color, and different refractions are connected with different colors.

Marci, however, understood these phenomena quite differently from Newton. Whereas in Newton each solar ray falling on a prism is divided into all possible colors, Marci believes that a simple ray of white light is transformed into one or another prismatic color depending on the angle at which it falls on the prism. Rays coming from one edge of the Sun, after refraction, form a red beam, and rays coming from the other edge—a violet one.

Apparently, these considerations later led Newton to set up a special experiment with the prismatic decomposition of light from Venus, which is visible at a much smaller angle of vision than the Sun.

In trying to explain the transformation of some white rays into red ones and others into violet ones, Marci draws attention to the unequal “condensation,” as he calls it, of light, which occurs when it is refracted into an optically denser medium. This different “condensation,” preventing the full development of its brilliance, leads to different self-attenuation, which our eye perceives as a difference in colors. In this explanation it is not difficult to notice traces of the ancient Aristotelian view of the origin of colors as a mixture of light with darkness.

Thus, proceeding from premises that would seem to be correct, Marci ultimately arrived at the same Aristotle, though in a disguised form.

In 1662 there appeared a work by Isaac Vossius, On the Nature of Light. Holding that light cannot be a substance, Vossius thought that the cause of light is fire, which likewise has nothing material in itself, but is only a high degree of heat arising from strong concussions of a solid body. Although light is immaterial, it has real existence, just as sounds, smells, magnetic force, and so on.

Empty space is completely transparent. Bodies are transparent in proportion to the amount of color that they contain. The cause of color is sulfur, which is contained in all bodies and assumes different coloring depending on the degree of combustion. At first it appears green, then yellow, further red, then purple, and, finally, black.

In Fossa’s views we see, perhaps, a natural mixture of advanced ideas and old notions already outliving themselves.

Of great interest to us are Descartes’ views (1664). According to his ideas, the substance filling all space consists of three kinds of particles, or of three elements. The first element consists of the finest particles of elongated shape, the second of equally small particles of spherical shape, and the third element of coarser and larger particles, which are aggregations of particles of the first kind that have combined. Inside every luminous body, particles of the first kind are in energetic motion, the result of which is the pressure exerted by them on the spherical particles. This pressure does not cause any translational motion, since space is entirely filled, but leads to the instantaneous transmission of pressure (or tendency to motion) in all directions and to any distance. Reaching the eye, this pressure—or tendency to motion—causes the impression of light.

Descartes explains the phenomena of color by the fact that, when a beam falls obliquely on the surface of an optically denser medium, the motions of the spherical particles become rotational, and the speed of rotation proves to be different in different parts of the beam. The different speed of rotation of the spheres leads to different colors. The greatest speed corresponds to red, the smallest to violet.

Among Newton’s older contemporaries the greatest interest is undoubtedly presented by his compatriot and frequent opponent—Robert Hooke. Hooke proceeded from wave conceptions of the nature of light and was the first to give an interference interpretation of the colors of thin plates. Nevertheless, in Hooke’s theory of colors one can still find the influence of the old Aristotelian ideas about the interaction of light and darkness.

Hooke (1665) believed that the refraction of light in an optically denser medium is accompanied by an increase in the speed of propagation of the wave. From this he arrives at the idea that refraction is accompanied by a change in the angle between the ray and the surface of the wave. In a homogeneous medium, where light propagates in all directions with the same speed, the rays turn out to be perpendicular to the spherical wave, which at large distances from the source becomes plane. In this case, Hooke believes, we observe white light. The coloration of light observed upon refraction of a beam falling obliquely on the surface of separation Hooke connects above all with a change in the angle between the ray and the pos-

NESS OF THE WAVE, which upon passing into a denser medium becomes sharp (Fig. 1). However, this circumstance still does not create the coloredness of the ray, which Hooke explains in the following way. If (Fig. 2) two rays, coming from the edges of the solar disk, fall upon the surface of the water in a vessel, then the color difference of the extreme rays after refraction is connected with the fact that they border on darkness.

The darkness located next to the extreme rays weakens and retards them, whereas, on the other side, they are in contact not with darkness but with the remaining rays, which, moving together with the extreme ones, cannot retard and weaken them to the same extent. In this case the effect of darkness on the extreme rays limiting the refracted bundle will be different because, on one edge, that part of the wave is retarded which is in front, while on the other it is the part which remains behind.

In the first case, Hooke believes, the eye perceives violet; in the second, red. All the other colors of the spectrum lying between them are obtained by the mixing of these two extreme or primary colors.

Fig. 1. Change of the wave front upon refraction according to Hooke’s ideas.

Fig. 2. Formation of the spectrum upon refraction according to Hooke.

Thus, in all the enumerated theories of color we see a great variety of hypotheses, at times very ingenious, concerning the essence of the phenomenon.

At the basis of each theory lies one or another arbitrary assumption which the author considers necessary to invoke in order to explain the observed phenomena.

The very multiplicity of the theories testifies more eloquently than any other evidence to the fact that not one of them had gained serious currency. At the same time, the number of theories also indicates the persistence and energy with which the best minds sought solutions to this most interesting and “eye-catching” riddle of everyday experience.

For the period preceding the beginning of Newton’s work, the situation may be characterized, for example, by the fact that Newton’s teacher Isaac Barrow presents the nature of color only very briefly, and in a very cautious and skeptical form. “Since colors have come up,” he writes in his Lectures, “one must (according to custom and order) say a little about them as well.”

So cautious a scholar as Robert Boyle, in his work Experiments and Considerations Touching Colours (1665), lists all existing views on the nature of color and leaves it to the reader himself to choose the one he likes best. He himself agreed in believing that “nature has buried these, like other phenomena, in the deep darkness of human ignorance.” So pessimistic a view of the possibility of revealing the essence of color was the natural consequence of the long failures of science in this field.

It is clear that such a state of affairs required change. Yet it took the genius of the young Newton to find the right path and to give a simple solution to this seemingly insoluble problem.

3. NEWTON’S THEORY OF COLORS

Newton set forth his theory of color in two places: in the book Lectures on Optics, written by him in 1669–1671 in Cambridge and published only after the author’s death, in 1729, and in the Opticks, published in 1704.*)

The Lectures on Optics consist of two parts: the first of them is entitled “On the Refraction of the Rays of Light,” the second—“On the Origin of Colors.” Although in the preface to the Opticks Newton recommends it as his final opinion on the question of the refraction and composition of colors, many observations made by the young investigator in his Lectures (in 1669 Newton was 27 years old) are of very great interest to us, since in them one senses the connection between what is set forth and the tasks of practice, and Newton’s objections to his predecessors are plainly expressed.

*) Both books have been translated into Russian by Academician S. I. Vavilov. Isaac Newton’s Opticks was published in 1927 by the State Publishing House in Moscow in the series “Classics of Natural Science” on the occasion of the bicentenary of Newton’s death. Lectures on Optics was issued by the Publishing House of the Academy of Sciences of the USSR in 1946 in the series “Classics of Science.” All further quotations from these books are made according to S. I. Vavilov’s translations.

NEWTON’S THEORY OF COLORS

It is difficult not to quote the first phrase with which Newton begins his Lectures. Establishing for the first time the different refrangibility of the rays that make up sunlight, Newton writes: “The recent invention of telescopes has so sharpened the wits of most geometers that in optics, it seems, nothing untried remains and there is no room for new discoveries.”

The second part of the Lectures likewise begins with considerations about telescopes, which undoubtedly were the chief reason for Newton’s interest in optics. “Those engaged with telescopes,” he writes, “complain of the colors that usually tinge objects observed through glass. This coloration is the greater and more noticeable the smaller the spheres from which the eyepiece glass is made, or the wider the objective glass is opened to the incident rays.” “Since at present the principal improvements desired in perspectives*,” Newton continues, “are those that would allow objects to be magnified more and made brighter, it is therefore worth taking pains over the investigation of the nature of colors, in order to determine the cause of their appearance and of the indistinctness they introduce into objects.”

Newton then enters into sharp polemics with his predecessors, beginning with the adherents of Aristotle’s views (the Peripatetics) and ending with his contemporaries, whose names, incidentally, he does not mention. It should be noted that the passage quoted below is one of the very few in which Newton explicitly criticizes others’ opinions and expresses his own judgments. For this reason it is especially interesting.

“Those who have taught about colors up to the present,” he writes in the introduction to the second part of the Lectures, “have done so either as the Peripatetics did, or have endeavored to investigate their nature and causes, like the Epicureans and other more recent authors. What was handed down about colors by the Peripatetics, even if true, has no significance whatever for our purpose, for it concerned neither the manner in which colors arise nor the causes of their variety… Thus, they omitted that whose explanation is the highest business of philosophers and the only thing that can satisfy a mind eager for natural science… It is also said that in some colors more white is admixed than in others, but this is insufficient for producing them, for no color arises from whiteness and blackness mixed together, except intermediate dark ones, and the amount of light does not change the kind of color. A red body, for example, always appears red, both in twilight and at brightest noon.”

“Further, even the very definition that the Peripatetics assign to colors is so inconsistent with their nature that even

* In the seventeenth and eighteenth centuries telescopes were sometimes called “perspectives.”

8 UFN, vol. LII, issue 2.

by its name does not express them; Aristotle asserts: “Color is the surface of a bounded transparent body.” This is rather a description of a colored surface than of color... But colors are often visible where there is no such boundary as in the rainbow and the prism, in glasses and liquids slightly tinted with some color, in sea water, which often appears green and produces colors not at the boundary of the water but throughout its entire thickness, in air, which is especially transparent and is not bounded by any dense body, yet on a clear night appears blue, and in flame, no less clear and more transparent to light than air”...

The objections which Newton advances against the ancient authors reduce, as we see, to the fact that their speculative judgments are in no way connected with the data of scientific experience and rest only on arguments that say nothing about the causes of the physical difference of colors or about their origin. Naturally, nothing can be drawn from this for explaining the colors that appear in telescopes.

Turning to consideration of the opinions of more recent authors, Newton writes further: “As for the opinion of other philosophers, they assert that colors are born either from the various mixture of shadow with light, or from the rotation of globules or from their different pressure, or, finally, from various modes of vibration of a certain ethereal medium, if light is regarded as arising from the impulse of a vibrating medium propagating in the reticular tissue. I would have had to expand at great length if I were to refute these opinions separately. I shall not do this, since all of them converge in a common error, namely in that the modification of light which manifests the separate colors is not proper to it by its origin, but is acquired upon reflection or refraction.

“Before falling upon some colored body, they think, the rays of light do not differ in any way, and according to the predisposition of this body they are reflected or refracted in various ways and, corresponding to the kind of modification thereby acquired, they then manifest to the observer various phantasms of color. The mixture of light and shadow, the rotation of globules, or the various vibrations of a medium are not assumed to be inherent in the rays before their reflections and refractions; they are considered to be generated by these very actions. Likewise the Peripatetics derive the origin of colors from the bodies of which, they assert, colors are qualities. How greatly, however, this contradicts the truth is more than evident from what follows. I have found that the modification of light from which colors arise is innate in light, and does not arise upon reflection or refraction, or from the qualities of bodies, or in any other way, and cannot be destroyed or in any way changed.”

Having then set forth in concise form his principal discoveries in the field of color, Newton continues:

“I see no obstacles to undertaking an investigation of the nature of colors, in which nothing has been regarded as pertaining to mathematics.”

“Just as astronomy, geography, navigation, optics, and mechanics,” he writes further, “are considered mathematical sciences, since they deal with physical things—sky, earth, ships, light, and local motion—so also colors belong to physics, and the science of them should be considered mathematical, since it is set forth by mathematical reasoning. An exact science of colors belongs among the most difficult of those that would be desirable for the philosopher.”

Thus Newton resolutely removes the science of color from the realm of unfounded conjectures and transfers it to that domain of mathematics which he himself ranks among the most difficult. If we take into account that, after Newton, such scholars as M. V. Lomonosov, Young, Helmholtz, Grassmann, Maxwell, and Schrödinger successively worked on the theory of color, and that they did not succeed in exhausting its inner content, then one must marvel at Newton’s extraordinary perspicacity.

The exposition of the same theory of colors in the later, more mature, and considerably drier Opticks already has an entirely different character. Here there is none of the sharp polemical form that so distinguished the exposition of the Lectures—Newton’s first scientific work. The Opticks is constructed in a far stricter style. It begins with eight definitions indicating how one should understand the terms Newton uses in the book. Then follow the axioms. In the eight axioms Newton sets forth the basic data of optics obtained by science before him. Then come “Propositions,” “Theorems,” “Observations,” “Problems,” and “Experiments,” in the form of which Newton presents the results of his experiments and the conclusions drawn from them.

Color is made the basis of the construction of the whole book. The first proposition, which constitutes the starting point of the exposition, speaks of the relation between color and refraction. It is formulated as follows:

“Rays differing in color differ also in degree of refrangibility.”

This proposition is proved by two experiments.

In the first of them Newton observes through a prism a strip of cardboard, one half of which is painted red and the other blue. Through the prism the strip of cardboard appears displaced, with the blue half displaced more than the red. In a second experiment Newton established that a lens, which gives an image of the same strip of cardboard, gathers blue rays at a somewhat shorter distance than red ones. In this experiment he described for the first time the chromatic aberration of a lens as we understand it today.

The second part of the first book is wholly devoted to the theory of color. And here, despite the strict form of exposition of the book, the discussion—

The treatment of questions of color begins with a proposition that is wholly negative in character and is devoted to the refutation of the erroneous views of predecessors:

“The phenomena of colors in refracted and reflected light are not produced by any new modifications of light, brought about in different ways by the various boundaries of light and shadow.”

The proposition is proved by four experiments. In order to demonstrate the subtlety, ingenuity, and persuasiveness of Newton’s experimental proofs, we shall present two of them in the form in which they were given by the author.

“Experiment 1. Let the sun shine into a very dark room through an oblong aperture \(F\) (Fig. 3), the breadth of which is one sixth or one eighth of an inch, or somewhat less, and let the beam of light \(FH\) after this pass first through a very large prism \(ABC\) at a distance of about 20 feet from the aperture, placed parallel to the aperture;

Fig. 3. Diagram of Newton’s experiment proving that color does not change from the boundary with darkness.

then (with its white part) the light goes through the oblong aperture \(H\), the breadth of which is about a fourth or a sixth of an inch and which is made in a black opaque body \(OI\) and placed at a distance of two or three feet from the prism in a position parallel to the prism and to the first aperture; the white light, passed in this way through the aperture \(H\), then falls upon white paper \(pt\), placed behind the screen \(H\) at a distance of three or four feet from it, and casts upon it the usual colors of the prism: let us put red at \(t\), yellow at \(s\), green at \(r\), blue at \(q\), and violet at \(p\); then with an iron wire or with some other similar thin dark object, whose breadth is about one tenth of an inch, one can, by stopping the rays at \(k, l, m, n\), or \(o\), cause one of the colors at \(t, s, r, q\) to disappear ...

or \(p\), while the other colors remain on the paper as before; by means of a somewhat wider obstacle one may extract two or three, or four colors together and leave the rest. Thus any color, just like violet, may become the extreme one at the boundary of the shadow at \(p\), and any color may become extreme, like red, at the boundary of the shadow at \(t\); each of them may likewise border on a shadow obtained between the colors when some intermediate part of the light is intercepted by the obstacle, and, finally, each of the colors, remaining alone, may be bounded by shadow on both sides. All colors are equally related to any boundaries of shadow, and therefore the difference of one color from another does not arise from different boundaries of shadow, in consequence of which light would be modified in different ways, as philosophers have thought up to now.”

It may be supposed that the principal purpose of this experiment was to refute Hooke’s views, who, as we have seen, regarded the contact of the refracted beam with darkness as the principal cause of the formation of violet on one side and red on the other*). If Hooke’s theory had been correct, then the appearance of a dark band in the middle of the spectrum \(pt\) ought to have led not only to the disappearance, for example, of the green color at \(r\), but also to the remaining parts of the spectrum being transformed into two independent, shorter spectra with violet colors above and red below. In any case, the introduction of one or even several dark bands into the spectrum ought to have caused a change in the remaining colors, connected with a change in the proportions of light and darkness. Meanwhile the experiment showed the complete independence of the colors of the spectrum from the adjacency of light or shadow, so that Hooke’s views had to be regarded as completely refuted.

The second experiment, described by Newton with the same purpose, demonstrates that, on the other hand, a change of color can be observed without the slightest participation of boundaries of light and shadow.

“Experiment 2. Sunlight, admitted into a dark room through a round aperture \(F\) (Fig. 4) half an inch wide, first passed through the prism \(ABC\), placed near the aperture, and then through the lens \(PT\), a little more than four inches wide and situated at a distance of about eight feet from the prism; next the light converged at \(O\)—the focus of the lens—at a distance of about three feet from it, and here fell upon the white paper \(DE\). If the paper was perpendicular to this light falling upon it, as pred—

) The supposition expressed finds some confirmation in the fact that in the “Lectures,” written in the years preceding Newton’s clash with Hooke, this proposition and the corresponding experiments are not contained. Moreover, Newton’s Opticks* was published in 1704, while Hooke died in 1703.

set at position \(DE\), then all the colors on the paper at \(O\) appeared white. But if the paper was rotated about an axis parallel to the prism, becoming very inclined to the light, as represented by the positions \(de\) and \(\delta\varepsilon\), then the same light in one case appeared yellow and red, in another—blue. Here one and the same part of the light, in one and the same place, corresponding to different inclinations of the paper, appeared in one case white, in another—yellow or red, in a third—blue, although the boundary of light and shadow and of the refraction of the prism remained exactly the same in all cases».

Fig. 4. Diagram of Newton’s experiment showing that color can change when the angle of incidence of a beam on a surface is changed.

Newton further explains why these changes of color, occurring when the illuminated surface is inclined, are observed. He points out that rays less inclined illuminate a surface more strongly than rays more inclined to the surface. It should be noted that this was printed 25 years before Bouguer’s first work on the gradation of light and almost simultaneously with the arguments of the French monk François Marie on the possibility of measuring light.

There is no need to quote Newton further. The third experiment is a modification of the second; the fourth sets forth observations on the colors of “soap bubbles, with which children play,” and whose appearance is likewise not connected with any boundaries of light and shadow or with the refraction of light.

Proposition II, which is in essence the first positive assertion in the field of the theory of colors, expresses the fact that Newton himself apparently considered the most essential and fundamental. This proposition is formulated as follows:

“Every homogeneous light* has its own color, corresponding to the degree of its refrangibility, and such a color cannot be changed by reflections and refractions.”

*) In Definition VII, prefixed to the whole book, Newton says: “Light whose rays are all equally refrangible I call simple, homogeneous, and similar; but light whose rays are some more refrangible than others I call complex, heterogeneous, and dissimilar.”

The second proposition Newton proves by two experiments, of which one speaks of the invariability of color under arbitrary refraction, and the other of the invariability of color upon reflection.

This kind of invariability of the color of radiation under reflections or refractions is decisive evidence against any notions of a “modification” of light occurring under the influence of the matter with which the rays enter into interaction.

“In homogeneous light of any color,” writes Newton, “all bodies appeared to be of exactly the same color, with only this difference, that some of them reflected this light more strongly, others more weakly. I, however, never found a body which, on reflecting homogeneous light, noticeably changed its color.”

“From all this it is evident,” Newton concludes, “that if sunlight consisted of only one kind of rays, there would be only one color in the whole world, and it would be impossible to obtain any new color by means of reflections and refractions; consequently, the variety of colors depends on the complexity of light.”

It should be noted that, although the phenomenon of the spectral decomposition of light had been observed long before Newton, Newton was the first to understand and decipher it, i.e., to show that a whole series of properties of light rays, and first and foremost their color, depends on the degree of their refrangibility. Later, with the development of wave conceptions, the degree of refrangibility was replaced by wavelength.

Having established the principal fact in the domain of his theory of color, Newton interrupts his exposition with a definition intended to explain what content he puts into the words “color” or “colored rays.” This definition is given in the following form.

“Homogeneous light and rays which appear red, or, rather, cause objects to appear so, I call creators of red color; rays which cause objects to appear yellow, green, blue, or violet, I call creators of yellow, creators of green, creators of blue, creators of violet color, and likewise with respect to the rest. And if at times I speak of light or rays as colored or having color, it should not be understood that I am speaking philosophically and precisely—I am expressing myself roughly and in accordance with those notions which ordinary people may acquire on seeing all these experiments. For rays, to speak precisely, are not colored. In them there is nothing else except a definite force or predisposition to excite this or that color. For, just as the sound of a bell, or of a musical string, or of other sounding bodies is nothing other than vibratory motion, and in the air there is propagated from the object nothing other than this motion, which produces in the sensorium the sensation of such motion in the form of sound, so likewise the coloration of an object is nothing other than a predisposition

...to propagate this or that motion into the sensorium, and in the latter there appears a sensation of these motions in the form of colors.”

These remarks of Newton may be regarded as a strictly materialist definition of color. Indeed, Newton asserts that rays, differing physically in their refrangibility (other differences were not known to him), acting upon the organs of vision, evoke in them different reactions, perceived by us in the form of various colors.

By the power of his genius Newton overcame the testimony of his own perceptions, which convince everyone of what scholars had maintained since the time of Aristotle: namely, that color is a property of the observed object. Newton came to the conclusion that color is our sensation, determined by the composition of the ray flux entering the eye.

It is not difficult to see that Newton’s point of view on the nature of color coincides with the views expressed by V. I. Lenin in Materialism and Empirio-Criticism, where one may read ):
“If color is a sensation only depending on the retina (as natural science compels you to admit), then this means that rays of light, falling upon the retina, produce the sensation of color. This means that outside us, independently of us and of our consciousness, there exists a motion of matter, let us say, ether waves of a definite length and a definite velocity, which, acting on the retina, produce in man the sensation of this or that color. That is precisely how natural science regards it. It explains the different sensations of this or that color by the different lengths of light waves existing outside the human retina, outside man and independently of him. This is materialism: matter, acting upon our sense organs, produces sensation” *).

Further, Lenin says still more clearly that color is a sensation, i.e., the product of the specially organized matter of our sense organs. On p. 45 of the same book it is written: “... color is the result of the action of a physical object on the retina—sensation is the result of the action of matter on our sense organs.”

Let us return, however, to the theory of colors.

) V. I. Lenin, Collected Works, vol. 14, 4th ed., Gospolitizdat, 1947, p. 43.
*) A splendid confirmation of the dependence of color perception on the structure of the visual apparatus is provided by the well-known cases of anomalies of color vision, in which the color perceptions of a person possessing eyesight that is entirely normal in all other respects differ substantially from the color perceptions of the vast majority. Sometimes the anomaly is manifested in the fact that a person does not see, for example, the red berries of wild strawberries among green grass or cannot distinguish the red light of a traffic signal from the green one. The need to ensure the safety of transport has compelled serious attention to be paid to detecting such kinds of anomalies in the structure of the eyes of persons mastering the profession of engine driver or chauffeur.

Having established the correspondence between the color of homogeneous (monochromatic) light and its refrangibility, and having established, moreover, the invariability of colors under any reflections and refractions, Newton naturally had to raise the question of what colors can be obtained by mixing homogeneous colors in various combinations and in various proportions. Propositions IV and V are devoted to answering these questions. In the first of them it is shown, above all, that by mixing homogeneous rays one can obtain colors similar “in appearance” to the colors of a certain homogeneous light, but not similar to it with respect to invariability under refraction. By mixing homogeneous yellow with homogeneous red, one can obtain an orange color, similar in appearance to the orange color of homogeneous rays. However, when observed through a prism, the mixture is decomposed into its constituent parts, whereas homogeneous light remains unchanged.

When homogeneous rays are mixed, colors may also be obtained that are not similar to the colors of homogeneous light. It is interesting to note the following passage from the Opticks.

“Thus, if white sunlight, composed of all sorts of rays, is added to the color of any homogeneous light, the color will not disappear and will not change its character—it will only be diluted; with a further addition of white it will be diluted more and more. Finally, if red is mixed with violet, then, according to their different proportions, various purples will be obtained, resembling in appearance none of the colors of homogeneous light; from the mixture of these purples with yellow and blue other new colors can be obtained.” (Opticks, p. 108.)

Proposition V, based on seven experiments, is directed toward proving the complex structure of the white light of the sun. In the process of this proof Newton combined colors optically, superposing different radiations on one another and then decomposing them again by one or another method. He also combined colors by mixing colored powders. And although Newton could not fail to notice the great difference between these two methods of combining colors, for some reason he did not establish that their results often contradict one another. He writes, for example: “... trying to compose white by mixing colored powders, used by painters, I noticed that all colored powders suppress and retain within themselves a very considerable part of the light by which they are illuminated.” And further: “Therefore, by mixing such powders, we cannot expect such a strong and full white as from paper,—the color will be somewhat dusky, as when light and darkness, or white and black, are mixed, that is, gray, brownish, or reddish-brown, like the color of human nails, mice, ashes, common stones, dust and dirt on highways, and the like.”

Not having noticed the fundamental difference between the addition of luminous fluxes and the mixing of colored powders,* Newton nevertheless arrives at correct conclusions. Having substantiated one of the main propositions of his theory of color, consisting in the recognition of the complexity of the composition of white sunlight, Newton cuts the ground from under all previous theories, which had sought the explanation of color in one or another modification (change) of sunlight, simple from their point of view, occurring upon reflections and refractions and introducing into the nature of the incident light something that had not originally been there.

Here the paths of further development of Newton’s theory are also indicated. If the white light of the sun contains within itself all the colors of homogeneous radiations, if, moreover, the colors of these radiations are not changed by any refractions or reflections, and the only thing that changes is the quantity of one or another homogeneous light in the mixture, then there naturally emerges the possibility of predicting the color, if the composition of the radiation is known. But how such a calculation can be carried out is still quite invisible from all these premises. The Opticks contains no indication of the paths by which Newton’s genius approached the solution of the problem. Proposition VI, which poses and solves it, is formulated as follows:

“In a certain mixture of primary colors the quantity and quality of each of them are given. To find the color of the mixture.”

Proceeding from obviously incorrect assumptions about certain connections between the colors of the spectrum and the seven tones of the musical scale, and using the mixing of powders as the addition of radiations, Newton gave a method for calculating the color of a mixture by which he was ahead of his time by at least 150 years.

Only in 1853 was Grassmann able to decipher the principles that underlie Newton’s graphical method, and only in 1854 and 1855 were Helmholtz and Maxwell able to give experimental confirmation of Newton’s method.

The method itself consists in the following. All the colors into which a prism decomposes the white light of the Sun are arranged along a circumference. The prismatic spectrum contains seven colors: red, orange, yellow, green, blue, indigo, and violet. To each of them is assigned a part of the circumference in correspondence with the seven musical tones contained in the octave. The arc \(DE\) (Fig. 5) represents the red color, the arc \(EF\)—orange, the arc \(FG\)—yellow, and so on, the arc \(CD\)—violet. These colors must be imagined, like prismatic colors, as gradually

* In the first case radiations are indeed added, while in the second much more complex phenomena take place, in which it would be more correct to speak not of the addition of radiations, but of the addition of absorptions. This distinction was first described by Helmholtz in 1852.

...passing one into another. Between the points \(D\) and \(E\) are found all degrees of red, at \(E\) is the mean color between red and orange; from \(E\) to \(F\) are all degrees of orange, at \(F\) the mean between orange and yellow, etc. “Let,” writes Newton, “\(p\) be the center of gravity of the arc \(DE\), \(q, r, s, t, v, x\) respectively the centers of gravity of the arcs \(EF, FG, GA, AB, BC\) and \(CD\); describe around these centers of gravity circles proportional to the number of rays of each color in the given mixture, i.e. circle \(p\), proportional to the number of rays in the mixture that produce the red color, circle \(q\), proportional to the number of rays in the mixture that produce the orange color, and so on with respect to the rest. Find the common center of gravity of all these circles \(p, q, r, s, t, v, x\). Let this center be \(z\); from the center of the circle \(ADF\), through \(z\) to the circumference draw the straight line \(OY\): the position of the point \(Y\) on the circumference will indicate the color arising from the composition of all the colors of the given mixture, while the line \(Oz\) will be proportional to the fullness or intensity of the color, i.e. to its distance from whiteness. Thus, if \(Y\) falls midway between \(F\) and \(G\), the mixed color will be the best yellow; if \(Y\) deviates from the middle toward \(F\) or \(G\), then the mixed color will be, respectively, yellow tending toward orange or toward green. If \(z\) lies on the circumference, the hue will be intense and flowering in the highest degree; if \(z\) lies midway between the circumference and the center, the hue will be half as intense, i.e. that color which is obtained by dissolving the most intense yellow with an equal quantity of white; if \(z\) lies at the center \(O\), then the hue will lose all its intensity and become white”*).

Fig. 5. Newton’s color circle. The spectral colors are arranged along the circumference, at the center of which lies white. The extreme red coincides with the extreme violet.

) In books and articles published about 20 years ago, in which the number of colors was increased to seven or which, generally speaking, were written with a good knowledge of the subject, N. D. Nyberg made the error of asserting that the graphic representation of colors by means of a triangle “was first used by the famous physicist Newton and therefore bears his name.” N. D. Nyberg, Course of Color Science*, Gizelektroprom, 1932, p. 45). As is evident from the preceding exposition, all references to “Newton’s triangle” should be regarded as incorrect.

For the level of our knowledge in the history of color science, characteristic is not only the appearance of such an error, but also the fact that for 20 years no one, so far as is known, paid attention to this misunderstanding.

It may be added that Grassmann, who wrote in the second half of the nineteenth century, also used Newton’s circle, although he may have known about the color triangle given by Young (at the beginning of the century) in his Lectures on Physics.

If, in this passage, some terms are replaced, the exposition of the basic properties of the color diagram will not differ from the modern one. Indeed, the point at which the straight line intersects the line of spectral colors characterizes what at present is customarily called the hue. The “fullness or intensity of the color,” measured by the distance \(Oz\), is quite analogous to what we call purity or saturation, while the “gravity,” “weight,” or “quantity of rays” by which Newton measures the quantity of color coincides entirely with what in a number of cases is customarily called the modulus of a color.

It is further easy to see that if the quantity of a spectral color is determined, according to Newton, by its “weight” or “quantity of rays,” then the quality of the color is specified by the position of the corresponding point on the diagram. Thus, color is determined by three independent numbers: by the two coordinates of the position of a point on the plane, and by one number determining its quantity. The three-dimensionality of color should therefore be considered as having been established already by Newton.

People often speak of Newton’s seven primary colors, opposing them to the three colors of later theories. However, these seven colors, which appeared in Newton as the result of an erroneous analogy with acoustic phenomena, did not prevent him from representing all qualitative differences of colors by an aggregate of points on a plane diagram, and not, for example, in space, and from reducing the whole variety of colors to a set of three, and no greater number, of measurements, for which the seven primary colors provided, it would seem, little basis.

It is easy to understand that however many principal colors Newton might have marked in the spectrum—seven, eight, or more—when summing them according to the rule of the center of gravity proposed by him, he always finds one common center on the plane of the diagram, which, as has already been noted, inevitably leads to the three-dimensionality of color, which is only superficially masked by the seven colors of the solar spectrum.

Meanwhile, nowadays, for some reason, it is customary to suppose that the three-dimensionality of color was established by Grassmann.

The second law of color mixture, which it is also customary to ascribe to Grassmann, asserting that a continuous change in the composition of radiation corresponds to a continuous change in color, is likewise a direct consequence of the method, described by Newton, of finding the center of gravity.

If the rule of addition indicated by Newton for simple colors is extended to compound colors, then the third law of color mixture as well, establishing the independence of the mixture from the spectral composition of the components being mixed, must be regarded as a simple consequence of the very same method of finding the center of gravity.

It is difficult to understand how Newton, who began the construction of his theory of color with a refutation of Aristotle’s views, could arrive at the formulation of a proposition containing all

the principal propositions of what we call the lower metric of color, on the further development of which mankind spent almost two and a half centuries. It must not be overlooked that Newton could use as a basis only experiments carried out by himself, for which he had at his disposal only the most elementary, one might say naïve, means. It is quite obvious that Newton could have had neither colorimetric nor even the simplest photometric instruments.

The one thing lacking in Newton’s theory is the law for adding “weights,” or “quantities of rays,” although simple summation suggests itself even from the mechanical analogy. Nevertheless, Newton did not consider it possible to give any indication of the quantity of color obtained as a result of the composition of given quantities of homogeneous components.

In this connection it should be added that Newton himself did not regard the rule of the center of gravity as entirely exact. “I consider,” he writes at the end of Proposition VI, “this rule sufficiently accurate for practice; however, it is not mathematically exact...”

And, finally, Proposition VII, summing up everything said earlier, was formulated by Newton as follows:

“All colors in the universe, produced by light and not dependent on the power of imagination, will be either colors of homogeneous light, or mixtures of them; moreover they will mix exactly or almost exactly according to the rule of the preceding problem.”

Having briefly repeated the results obtained, Newton establishes the fundamental proposition that color is determined only by the composition of the homogeneous, simple rays entering into it. “And therefore, if it is asked what the cause of any color is, we need only reason in what manner the rays of sunlight separated from one another or mixed during reflections, refractions, or owing to other causes: in other words, it is necessary to find the kinds of rays of which the given color is composed, and their proportions, and then, by means of the last problem, to find the color that must result when these rays (or their colors) are mixed in this proportion.”

4. CONCLUSION

In concluding this exposition of Newton’s theory of colors, we must naturally pose several questions to ourselves. Indeed, why is the three-dimensionality of color considered to have been discovered in 1853 by Grassmann, who, with regard to the laws of mixture, essentially did not go beyond commenting on what Newton had done in 1704? Why are the continuity of color and the possibility of composing colors independently of their spectral composition likewise attributed to Grassmann, although both are a simple consequence

possibility of mixing colors according to the center-of-gravity rule? Why did Grassmann do more than Newton, if, without carrying out a single experiment and proceeding from Newton’s works, he set forth in a more explicit form a number of propositions on which Newton’s center-of-gravity rule is based?

It is difficult to guess the true causes of various historically formed misconceptions. One can only suppose that the results obtained by Newton were not properly appreciated not only by his contemporaries, but also by a number of subsequent generations. It may be thought that Grassmann was one of the first who fully understood Newton. Even Helmholtz, in his work of 1852, did not reckon with Newton’s old results, stating that in the spectrum there is only one pair of complementary colors—yellow and indigo. This assertion also provoked an objection from Grassmann, who used the occasion (1853) for the systematic development of the foundations of Newton’s method, applying to it the vector method of finding the center of gravity that he had found earlier (in his work Ausdehnungslehre, “Theory of Extension”).

One should not, of course, underestimate Grassmann’s role in the history of the science of color. Having deciphered the mathematical foundations of Newton’s geometrical construction, which Newton himself did not consider entirely exact, Grassmann strengthened in the minds of his contemporaries the logical necessity of a number of consequences following from Newton’s ideas, and directed along the proper course the work of such scientists as Helmholtz and Maxwell. In this lies his indisputable merit. At the same time, is it not time to raise the question of restoring Newton to the role of founder of the modern theory of color, since the three-dimensionality of color, the laws of mixture, and the methods for calculating a color from its known composition are set forth by Newton quite clearly in his Opticks, published in 1704?