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§ 6. PURE SENSATIONS
1. The concept "pure sensation" as shown in § 5 is the product of a twofold abstraction: 1) from the ideas in which the sensation appears, and 2) from the simple feelings with which it is united. We find that pure sensations, defined in this way, form a number of disparate systems of quality; each of these systems, such as that of sensations of pressure, of tone, or of light, is either a homogeneous or a complex continuity (§ 5, 5) from which no transition to any other system can be found.
2. The rise of sensations, as physiology teaches us, is regularly dependent on certain physical processes that have their origin partly in the external world surrounding us, partly in certain bodily organs. We designate these processes with a name borrowed from physiology as sense-stimuli or sensation-stimuli. If the stimulus is a process in the outer world we call it physical; if it is a process in our own body we call it physiological. Physiological stimuli may be divided, in turn, into peripheral and central, according as they are processes in the various bodily organs outside of the brain, or processes in the brain itself. In many cases a sensation is attended by all three forms of stimuli. Thus, to illustrate, an external impression of light acts as a physical, stimulus on the eye; in the eye and optic nerve there arises a peripheral physiological stimulation; finally a central physiological stimulation takes place in the corpora quadrigemina and in the occipital regions of the cerebral cortex, where the optic nerve terminates. In many cases the physical stimulus may be wanting, while both forms of physiological stimuli are present; as, when we perceive a flash of light in consequence of a violent ocular movement. In still other cases the central stimulus alone is present; as, when we recall a light [p.39] impression previously experienced. The central stimulus is, accordingly, the only one that always accompanies sensation. When a peripheral stimulus causes a sensation, it must be connected with a central stimulus, and a physical must be connected with both a peripheral and a central stimulus.
3. The physiological study of development renders it probable that the differentiation of the various sensational systems has been effected in part in the course of general development. The original organ of sense is the outer skin with the sensitive inner organs adjoining it. The organs of taste, smell, hearing, and sight, on the other hand, are later differentiations of it. It may, therefore, be surmised that the sensational systems corresponding to these special sense-organs, have also gradually arisen through differentiation from the sensational systems of the general sense, from sensations of pressure, hot, and cold. It is possible, too, that in lower animals some of the systems now so widely differentiated are even yet more alike. From a physiological standpoint the primordeal character of the general sense is also apparent in the fact that it has for the transfer of sense-stimuli to the nerves either very simple organs or none at all. Pressure, temperature, and pain-stimuli can produce sensations at points in the skin where, in spite of the most careful investigation, no special end-organs can be found. There are, indeed, special receiving organs in the regions most sensitive to pressure (touch-corpuscles, end-bulbs, and corpuscles of Vater), but their structure renders it probable that they merely favor the mechanical transfer of the stimulus to the nerve-endings. Special end-organs for hot, cold, and pain-stimuli have not been found at all.
In the later developed special sense-organs, on the other hand, we find everywhere structures which not only effect the suitable transfer of the stimuli to the sensory nerves, but generally bring about a physiological transformation of the [p. 40] stimulation which is indispensable for the rise of the peculiar sensational qualities. But even among the special senses there are differences in this respect.
The receiving organ in the ear, in particular, appears to be of a character different from that of the organs of smell, taste, and sight. In its most primitive forms it consists of a vesicle filled with one or more solid particles (otoliths), and supplied with nerve-bundles distributed in its walls. The particles are set in motion through sound-vibrations, and must cause a rapid succession of weak pressure-stimulations in the fibres of the nerve-bundles. The auditory organ of the higher animals shows an extraordinary complexity, still, in its essential structure it recalls this primitive type. In the cochlea of man and the higher animals the auditory nerve passes at first through the axis, which is pierced by a large number of fine canals, and then emerges through the pores which open into the cavity of the cochlea. Here the branches are distributed on a tightly stretched membrane, which extends through the spiral windings of the cochlea and is weighted with special rigid arches (arches of Corti). This membrane - the basilar membrane, as it is called - must, according to the laws of acoustics, be thrown into sympathetic vibrations whenever sound-waves strike the ear. It seems, therefore, to play the same part here as the otoliths do in the lower forms of the auditory organ. At the same time one other change has taken place which accounts for the enormous differentiation of the sensational system. The basilar membrane has a different breadth in its different parts, for it grows continually wider from the base to the apex of the cochlea. In this way it acts like a system of stretched chords of different lengths. And just as in such a system, other conditions remaining the same, the longer chords are tuned to lower and the shorter to higher tones, so we may assume the same to [p. 41] be true for the different parts of the basilar membrane. We may surmise that the simplest auditory organs with their otoliths have a homogeneous sensational system, analogous perhaps to our systems of sensations of pressure. The special development of the organ as seen in the cochlea of higher animals explains the evolution of an extraordinarily complex sensational system from this originally homogeneous system. Still, the structure remains similar in this respect, that it seems adapted, in the latter case as in the former, to the best possible transfer of the physical stimulus to the sensory nerve rather than to any transformation of the stimulus. This view agrees with the observed fact that, just as sensations of pressure may be perceived, on regions of the skin not supplied with special receiving organs, so, in the case of certain animals, such as birds, where the conditions are specially favorable for their transmission, sound-vibrations are transferred to the auditory nerve and sensed even after the removal of the whole auditory organ with its special receiving structure.
With smell, taste, and sight the case is essentially different. Organs are present which render direct action of the stimuli on the sensory nerves impossible. The external stimuli are here received through special organs and modified before they excite the nerves. These organs are specially metamorphosed epithelial cells with one end exposed to the stimulus and the other passing into a nerve fibre. Everything goes to show that the receiving organs here are not merely for the transfer of the stimuli, but rather for their transformation. In the three cases under discussion it is probable that the transformation is a chemical process. In smell and taste we have external chemical agencies, in sight we have light as the causes of chemical disintegrations in the sensory cells; these processes in the cells then serve as the real stimuli. [p. 42]
These three senses may, as chemical senses, be distinguished from the mechanical senses of pressure and sound. It is impossible to say with any degree of certainty, to which of these two classes sensations of cold and hot belong. One indication of the direct relation between stimuli and sensation in mechanical senses, as contrasted with the indirect relation in chemical senses, is that in the first case the sensation lasts only a very little longer than the external stimulus, while in the latter case it persists very much longer. Thus, in a quick succession of pressures and more especially of sounds, it is possible to distinguish clearly the single stimuli from one another; lights, tastes, and smells, on the other hand, run together at a very moderate rate of succession.
4. Since peripheral and central stimuli are regular physical concomitants of elementary sensational processes, the attempt to determine the relation between stimuli and sensations is very natural. In attempting to solve this problem, physiology generally considers sensations as the result of physiological stimuli, but assumes at the same time that in this case any proper explanation of the effect from its cause is impossible, and that all that can be undertaken is to determine the constancy of the relations between particular stimuli, and the resulting sensations. Now, it is found in many cases that different stimuli acting on the same end-organ produce the same sensations; thus, for example, mechanical and electrical stimulations of the eye produce light sensations. This result was generalized in the principle, that every receiving element of a sense-organ and every simple sensory nerve-fibre together with its central terminus, is capable of only a single sensation of fixed quality; that the various qualities of sensation are, therefore, due to the various physiological elements with different specific energies.
This principle, generally called the "law of specific energy [p. 43] of nerves", is untenable for three reasons, even if we neglect for the moment the fact that it simply refers the causes of the various differences in sensations to a qualtalitas occutlta of sensory and nervous elements.
1) It is contradictory to the physiological doctrine of the development of the senses. If, as we must assume according to this doctrine, the complex sensational systems are derived from systems originally simpler and more homogeneous, the physiological sensory elements must have undergone a change also. This, however, is possible only under the condition that organs may be modified by the stimuli which act upon them. That is to say, the sensory elements determine the qualities of sensations only secondarily, as a result of the properties which they acquire through the processes of stimulation aroused in them. If, then, these sensory elements have undergone, in the course of time, radical changes due to the nature of the stimuli acting upon them, such changes could have been possible only under the condition that the physiological stimulations in the sensory elements varied to some extent with the quality of the stimulus.
2) The principle of specific energy is contradictory to the fact that in many senses the number of different sensory elements does not correspond at all to that of different sensational qualities. Thus, from a single point in the retina we can receive all possible sensations of brightness and color; in the organs of smell and taste we find no clearly distinguishable forms of the sensory elements, while even a limited area of their sensory surfaces can receive a variety of sensations, which, especially in the case of the olfactory organ, is very large. Where we have every reason to assume that qualitatively different sensations actually do arise in different sensory elements, as in the case of the auditory organ, the structure of the organ goes to show that this difference [p. 44] is not due to any attribute of the nerve-fibres or of other sensory elements, but that it comes originally from the way in which they are arranged. Different fibres of the auditory nerve will, of course, be stimulated by different tone-vibrations, because the different parts of the basilar membrane are tuned to different tones; but this is not due to some original and inexplicable attribute of the single auditory nerve-fibres, but to the way in which they are connected with the end-organ.
3) Finally, the sensory nerves and central elements can have no original specific energy, because the peripheral sense-organ must be exposed to the adequate stimuli for a sufficient interval, or must at least have been so exposed at some previous period, before the corresponding sensations can arise through their stimulation. Persons congenitally blind and deaf do not have any sensations of light or tone whatever, so far as we know, even when the sensory nerves and centres were originally present.
Everything goes to show that the differences in the qualities of sensations are conditioned by the differences in the processes of stimulation that arise in the sense-organs. These processes are dependent, primarily on the character of the physical stimuli, and only secondarily on the peculiarities of the receiving organ, which are due to its adaptation to these stimuli. As a result of this adaptation, however, it may happen that even when some stimulus other than that which has effected the original adaptation of the sensory elements, that is, when an inadequate stimulus acts, the sensation corresponding to the adequate stimulus may arise. Still, this does not hold for all stimuli or for all sensory elements. Thus, hot and cold stimulations can not cause cutaneous sensations of pressure or sensations in the special sense-organs; chemical and electrical stimuli produce sensations of light only when they act upon the retina, not when they act on [p. 45] the optic nerve; and, finally, these general stimuli can not arouse sensations of smell or taste. When an electric current causes chemical disintegration, it may, indeed, arouse such sensations, but it is through the adequate chemical stimuli produced.
5. From the very nature of the case, it is impossible to explain the character of sensations from the character of physical and physiological stimuli. Stimuli and sensations can not be compared with one another at all; the first belong to the mediate experience of the natural sciences, the second to the immediate experience of psychology. An interrelation between sensations and physiological stimuli must necessarily exist, however, in the sense that different kinds of stimulation always correspond to different sensations. This principle of the parallelism of changes in sensation and in physiological stimulation is an important supplementary principle in both the psychological and physiological doctrines of sensation. In the first case it is used in producing definite changes in the sensation by means of intentional variation of the stimulus; in the second it is used in inferring the identity or non-identity of physiological stimulations from the identity or non-identity of the sensations. Furthermore, the same principle is the basis of our practical life and of our theoretical knowledge of the external world.
A. SENSATIONS OF THE GENERAL SENSE.
6. The definition of the "general sense" includes two factors. In point of time, the general sense is that which precedes all others and therefore belongs to all beings, endowed with mind. In its spacial attributes, the general sense is distinguished from the particular senses in having the most extensive sensory surface exposed to stimuli. It includes not only the whole external skin and the adjoining areas of [p. 46] the mucous membrane, but a large number of internal organs supplied with sensory nerves, such as joints, muscles, tendons, and bones, which are accessible to stimuli either always, or at certain times, under special conditions, as is the case with bones. The general sense includes four specific, distinct sensational systems: sensations of pressure, hot, cold, and pain. Not infrequently a single stimulus arouses more than one, of these sensations. The sensation is then immediately recognized as made up of a mixture of components from the different systems; for example, from sensations of pressure and pain, or from sensations of hot and pain. In a similar manner as a result of the extension of the sense-organ, we may often have mixtures of the various qualities of one and the same system, for example, qualitatively different sensations of pressure, when an extended region of the skin is touched.
The four systems of the general sense are all homogenous systems (§ 5, 5). This shows that the sense is genetically earlier than the others, whose systems are all complex. The sensations of pressure from the external skin, and those due to the tensions and movements of the muscles, joints, and tendons, are generally grouped together under the name touch-sensations, and distinguished from the common sensations, which include sensations of hot, cold, and pain, and those sensations of pressure that sometimes arise in the other internal organs. This distinction, however, has its source in the relation of the sensations to ideas and concomitant feelings, and has nothing to do with the qualities of the sensations in themselves.
7. The ability of the different parts of the general sense-organ to receive stimulations and give rise to sensations, can be tested with adequate exactness only on the external skin. The only facts that can be determined in regard to [p. 47] the internal parts, are that the joints are in a high degree sensitive to pressures, while the muscles and tendons are much less so, and that sensations of hot, cold, and pain in the internal organs are exceptional, and noticeable only under abnormal conditions. On the other hand, there is no point of the external skin and of the immediately adjoining parts of the mucous membrane, which is not sensitive at once to stimulations of pressure, hot, cold, and pain. The degree of sensitivity may, indeed, vary at different points, in such a way that the points most sensitive to pressure, to hot, and to cold, do not, in generally, coincide. Sensitivity to pain is everywhere about the same, varying at most in such a way that in some places the pain-stimulus acts on the surface, and in others not until it has penetrated deeper. On the other hand, certain approximately punctiform cutaneous regions appear to be most favorable for stimulations of pressure, hot, and cold. These points are called respectively, pressure-spots, hot-spots, and cold-spots. They are distributed in different parts of the skin in varying numbers. Spots of different modality never coincide; still, temperature-spots always receive sensations of pressure and pain as well; and a pointed hot stimulus applied to a cold spot, always causes a sensation of hot, while hot-spots do not seem to be stimulated by pointed cold stimuli. Furthermore, hot-spots and cold-spots react with their adequate sensations to properly applied mechanical and electrical stimuli.
8. Of the four qualities mentioned sensations of pressure and pain form closed systems which show no relations either to each other or to the two systems of temperature-sensations. These last two, on the other hand, stand in the relation of opposites; we apprehend hot and cold not merely as different, but as contrasted sensations. It is, however, very probable that this is not due to the original nature of the sensations, [p. 48] but partly to the conditions of their rise, and partly to the accompanying feelings. For, while the other qualities may be united without limitation to form mixed sensations -- as, for example, pressure and hot, pressure and pain, cold and pain - hot and cold exclude each other because, under the conditions of their rise, the only possibilities for a given cutaneous region are a sensation of hot or one of cold, or else an absence of both. When one of these sensations passes continuously into the other, the change regularly takes place in such a way that either the sensation of hot gradually disappears and a continually increasing sensation of cold arises, or vice versa the sensation of cold disappears and that of hot gradually arises. Then, too, elementary feelings of opposite character are connected with hot and cold, the point where both sensations are absent corresponding to their indifferent zone.
In still another respect the two systems of temperature-sensations are peculiar. They are to a great extent dependent on the varying conditions under which the stimuli act upon the sense-organ. A considerable increase above the temperature of the skin is perceived as hot, while a considerable decrease below the same is perceived as cold, but the temperature of the skin itself, which is the indifference zone between the two, can adapt itself rapidly to the existing, external temperature within fairly wide limits. The fact that in this respect too, both systems are alike, favors the view that they are interconnected and also antagonistic.
B. SENSATIONS OF SOUND.
9. We possess two independent systems of simple auditory sensations, which are generally, however, connected as a result of the mixture of the two kinds of impressions. They are [p. 49] the homogeneous system of simple noise-sensations and the complex system of simple tone-sensations.
Simple noise-sensations can be produced only under conditions that exclude the simultaneous rise of tonal sensations, as when air-vibrations are produced whose rate is either too rapid or too slow for tone-sensations to arise, or when the sound-waves act upon the ear for too short a period. Simple sensations of noise, thus produced, may vary in intensity and duration, but apart from these differences they are qualitatively alike. It is possible that small qualitative differences also exist among them, due to the conditions of their rise, but such differences are too small to be marked by distinguishing names. The noises commonly so called are compound ideas made up of such simple noise-sensations and of a great many irregular tonal sensations (cf. § 9, 7). The homogeneous system of simple noise-sensations is probably the first to develop. The auditory vesicles of the lower animals, with their simple otoliths, could hardly produce anything but these. In the case of man and the higher animals it may be surmised that the structures found in the vestibule of the labyrinth receive only homogeneous stimulations, corresponding to simple sensations of noise. Finally, experiments with animals deprived of their labyrinths, make it probable that even direct stimulations of the auditory nerve can produce such sensations (p. 41). In the embryonic development of the higher animals, the cochlea develops from an original, vestibular vesicle, which corresponds exactly to a primitive auditory organ. We are, therefore, justified in supposing that the complex system of tonal sensations is a product of the differentiation of the homogeneous system of simple noise-sensations, but that in every case where this development, has taken place, the simple system has remained along with the higher. [p. 50]
10. The system of simple tone-sensation is a continuity of one dimension. We call the quality of the single simple tones pitch. The one-dimensional character of the system finds expression in the fact that, starting with a given pitch, we can vary the quality only in two opposite directions: one we call raising the pitch, the other lowering it. In actual experience simple sensations of tone are never presented alone, but always united with other tonal sensations and with accompanying simple sensations of noise. But since, according to the scheme given above (§ 5, 1), these concomitant elements can be varied indefinitely, and since in many cases they are relatively weak in comparison with one of the tones, the abstraction of simple tones was early reached through the practical use of tonal sensations in the art of music. The names c, c#, d#, and d stand for simple tones, though the clangs of musical instruments or of the human voice by means of which we produce these different pitches, are always accompanied by other, weaker tones and often, too, by noises. But since the conditions for the rise of such concomitant tones can be so varied that they become very weak, it has been possible to produce really simple tones of nearly perfect purity. The simplest means of doing this is by using a tuning-fork, and a resonator tuned to its fundamental tone. Since the resonator increases the intensity of the fundamental only, the other, accompanying tones are so weak when the fork sounds, that the sensation is generally apprehended as simple and irreducible. If the sound-vibrations corresponding to such a tonal sensation are examined, they will be found to correspond to the simplest possible form of vibration, the pendulumoscillation, so called because the vibrations of the atmospheric particles follow the same laws as a pendulum oscillating in [p. 51] a very small amplitude.  That these relatively simple sound-vibrations correspond to sensations of simple tones, and that we can even distinguish the separate tones in compounds, can be explained, on the basis of the physical laws of sympathetic vibration, from the structure of the organs in the cochlea. The basilar membrane in the cochlea is in its different parts tuned to tones of different pitch, so that when a simple oscillatory sound-vibration strikes the ear, only the part tuned to that particular pitch will vibrate in sympathy. If the same rate of oscillation comes in a compound sound-vibration, again only the part tuned to it will be affected by it, while the other components of the wave will set in vibration other sections of the membrane, which correspond in the same way to their pitch.
11. The system of tonal sensations shows its character as a continuous series in the fact that it is always possible to pass from a given pitch to any other through continuous changes in sensation. Music has selected at option from this continuity single sensations separated by considerable intervals, thus substituting a tonal scale for the tonal line. This selection, however, is based on the relations of tonal sensations themselves. We shall return to the discussion of these relations later, in taking up the ideational compounds arising from these sensations (§ 9). The natural tonal line has two extremities, which are conditioned by the physiological capacity of the ear for receiving sounds. These extremities are the lowest and highest tones; the former corresponds to 8-10 double vibrations per second, the latter to 40,000-50,000. [p.52]
C. SENSATIONS OF SMELL AND TASTE.
12. Sensations of smell form a complex system whose arrangement is still unknown. All we know is that there is a very great number of olfactory qualities, between which there are all possible transitional forms. There can, then, be no doubt that the system is a continuity of many dimensions.
12a. Olfactory qualities may be grouped in certain classes, each of which contains classes sensations which are more or less related. This fact may be regarded as an indication of how these sensations may perhaps be reduced to a small number of principal qualities. Such classes are for examples, sensations like those from ether, balsam, musk, benzine, those known as aromatic, etc.
It has been observed in a few cases that certain olfactory sensations which come from definite substances, can also be produced by mixing others. But these observations are still insufficient to reduce the great number of simple, qualities contained in each of the classes mentioned, to a limited number of primary qualities and their mixtures. Finally, it has been observed that many odors neutralize each other, so far as the sensation is concerned, when they are mixed in the proper intensities. This is true not only of substances that neutralize each other chemically, as acetic acid and ammonia, but also of others, such as caoutchoue and wax or tolu-balsam, which do not act on each other chemically outside of the olfactory cells. Since this neutralization takes place when the two stimuli act on entirely differerent olfactory surfaces, one on the right and the other on the left mucous membrane of the nose, it is probable that we are dealing, not with phenomena analogous to those exhibited by complementary colors (22), but with a reciprocal central inhibition of sensations. Another observed fact tells against the notion that they are complementary. One and the same olfactory quality can neutralize several entirely different qualities, sometimes even those which in turn neutralize one another, while among colors it is always only two fixed qualities that are complementary. [p. 53]
13. Sensations of taste have been somewhat more thoroughly investigated, and we can here distinguish four, distinct primary qualities. Between these there, are all possible transitional tastes, which are to be regarded is mixed sensations. The primary qualities are sour, sweet, bitter, and saline. Besides these, alkaline and metallic are sometimes regarded as independent qualities. But alkaline qualities show an unmistakeable relationship with saline, and metallic with sour, so that both are probably mixed sensations, (alkaline made up perhaps of saline and sweet, metallic of sour and saline). Sweet and saline are opposite qualities. When these two sensations are united in proper intensifies, the result is a mixed sensation (commonly known as "insipid"), even though the stimuli that here reciprocally neutalize each other do not enter into a chemical combination. The system of taste-sensations is, accordingly, in all probability to be regarded as a two-dimensional continuity, which may be geometrically represented by a circular surface on whose circumference, the four primary, and their intermediate, qualities are arranged, while the neutral mixed sensation is in the middle, and the other transitional taste-qualities on the surface, between this middle point and the saturated qualities on the circumference.
13a. In these attributes of taste-qualities we seem to have the fundamental type of a chemical sense. In this respect taste is perhaps the antecedent of sight. The obvious interconnection with the chemical nature of the stimulation, makes it probable even here that the reciprocal neutralization of certain sensations, with which the two-dimensional character of the sensational system is perhaps connected, depends, not on the sensations in themselves, but on the relations between the physiological stimulations, just as in the case of sensations of hot and cold (p. 48). It is well known that very commonly the chemical effect of certain substances can be neutralized through the action of certain other substances. Now, we do not know what the chemical [p. 54] changes are that are produced by the gustatory stimuli in the taste-cells. But from the neutralization of sensations of sweet and saline we way conclude, in accordance with the principle of the parallelism of changes in sensation and in stimuli (p. 45), that the chemical reactions which sweet and saline substances produce in the sensory cells, also counteract each other. The same would hold for their sensations for which similar relations could be demonstrated. In regard to the physiological conditions for gustatory stimulations, we can draw only this one conclusion from the facts mentioned, namely, that the chemical processes of stimulation corresponding to the sensations which neutralize each other in this way, probably take place in the same cells. Of course, the possibility is not excluded that several different processes liable to neutralization through opposite reactions, could arise in the same cells. The known anatomical facts and the experiments of physiology in stimulating single papillae separately, give lie certain conclusions in this matter. Whether we are here dealing with phenomena that are really analogous to those exhibited by complementary colors (v. inf. 22) is still a question.
D. SENSATIONS OF LIGHT.
14. The system of light-sensations is made up of two partial systems: that of sensation of achromatic light and that of sensations of chromatic light. Between the qualities in these two, all possible transitional forms exist.
Sensations of achromatic light, when considered alone, form a complex system of one dimension, which extends, like the tonal line, between two limiting qualities. The sensations in the neighborhood of one of these limits we call black; in the neighborhood of the other white, while between the two we insert grey in its different shades (dark grey, grey, and light grey). This one-dimensional system of achromatic sensations differs from that of tones in being at once a system of quality and of intensity for every qualitative change in the direction from black to white is seen at the [p. 55] same time as an increase in intensity, an every qualitative change in the direction from white to black is seen as a decrease intensity. Each point in the series, which thus has a definite quality and intensity, is called a degree of brightness of the achromatic sensations. The whole system may, accordingly, be designated as the sensations of pure brightness. The use of the word "pure" indicates the absence of all sensations of color. The system of pure brightness is absolutely one-dimensional for, both the variations in quality and those in intensity belong to one and the same dimension. It differs essentially, in this respect, from the tonal line, in which each point is merely a degree of quality, and has also a whole series of gradations in intensity. Simple tone-sensations thus form a two-dimensional continuity so soon as we take into account both determinants, quality and intensity, while the system of pure brightness is always one-dimensional, even when we attend to both determinants. The whole system may, therefore, be regarded as a continuous series of grades of brightness, in which the lower grades are designated black so far as quality is concerned, and weak in point of intensity, while the higher grades are called white and strong.
15. Sensations of color also form a one-dimensional system when their qualities alone are taken into account. Unlike the system of sensations of pure brightness, this system returns upon itself from whatever point we start, for at first, after leaving a given quality, we pass gradually to a quality that shows the greatest difference, and going still further we find that the qualitative differences become smaller again, until finally we reach the starting point once more. The color-spectrum obtained by refracting sunlight through a prism, or that seen in the rainbow, shows this characteristic, though not completely. If in these cases we start from the red end of the spectrum, we come first to orange, then to yellow, yellow- [p. 56] green, green-blue, blue, indigo-blue, and finally to violet which is more like red than any of the other colors except orange, which lies next to red. The line of colors in the spectrum does not return quite to its starting-point, because it does not contain all of colors that we have in sensation. Purple-red shades, which can be obtained by the objective mixture of red and violet rays, are wanting in the spectrum. Only when we fill out the spectral series with them, is the system of actual color-sensations complete, and then the system is a closed circle. This characteristic is not to be attributed to the circumstance that the spectrum actually presents for our observation a series returning nearly to its beginning. The same order of sensations can be found by arranging according to their subjective relationship, colored objects presented in any irregular order. Even children who have never observed attentively a solar spectrum or a rainbow, and can, therefore, begin the series with any other color just as well as with red, always arrange them in the same order.
The system of pure colors is, then, to be defined as one-dimensional. It does not extend in a straight line, however, but returns upon itself. Its simplest geometrical representation would be a circle. From a given point in this system we pass, when the sensation is gradually varied, first to sensations, then to those most markedly different, and finally to others similar to the first quality, but in the opposite direction. Every color must, accordingly, be related to one other particular color as a maximum of difference in sensation. This color may be called the opposite color, and in the representation of the color-system by a circle, two opposite colors are to be placed at the two extremities of the same diameter. Thus, for example, purple-red and green, yellow and blue, light green and violet, are opposite colors, that is, colors which exhibit the greatest qualitative differences. [p. 57]
The quality determined by the position of a sensation in the color-system, in distinction to other qualitative determinations, is called color-tone, a figurative name borrowed from tonal sensations. In this sense the simple names of colors; such as red, orange, yellow, etc., denote merely color tones. The color-circle is a representation of the system of color-tones abstracted from all the other attributes belonging to the sensations. In reality, every color-sensation has two other attributes, one we call its saturation, the other its brightness. Saturation is peculiar to chromatic sensations, while brightness belongs to achromatic sensations as well.
16. By saturation we mean the attribute of color-sensations by virtue of which they appear in all possible stages of transition to sensations of pure brightness, so that a continuous passage is possible from every color to any point in the series of whites, greys, and blacks. The term "saturation" is borrowed from the common method of producing these transitional colors objectively, that is, by the more or less intense saturation of some colorless soluble with color-pigment. A color may be ever so saturated, yet it is possible to think of a still greater saturation of the same color-tone, and, on the other hand, pure brightness always denotes the end of the series of diminishing grades of saturation for any color whatever. A degree of saturation may, therefore, be thought of as an attribute of all color-sensations, and, at the same time, as the attribute by which the system of color-sensations is directly united with that of sensations of pure brightness. If, now, we represent some particular sensation of white, grey, or black by the central point of the color-circle, all the grades of saturation that can arise as transitional stages from any particular color to this particular sensation of pure brightness, will obviously be represented by that radius of the circle which connects the centre with [p. 58] the color in question. If the shades of saturation corresponding to the continuous transitional stage, from all the colors to a particular sensation of pure brightness are thus geometrically represented, we have the system of saturation-grades as a circular surface whose circumference is a system of simple color-tones, and whose centre is the sensation of pure brightness, corresponding to the absence of all saturation. For the formation of such a system of saturation-grades any point whatever in the series of sensations of pure brightness may be taken, so long as the condition is fulfilled that white is not too bright or the black too dark, for in such differences in both saturation and color disappear. Systems of saturation which are arranged about different points in the series of pure brightness, always have different grades of brightness. A pure system of saturation, accordingly, call be made for only one particular grade of brightness at a time, that is, for only one point in the series of sensations of pure brightness. When such systems are made for all possible points, the system of saturation will be supplemented by that of grades of brightness.
17. Brightness is just as an attribute of color-sensation as it is of achromatic sensations, and is in this case, too, at once a quality and degree of intensity. Starting from a given grade, if the brightness increases, every color approaches white, in quality, while at the same time the intensity increases; if the brightness decreases, the colors approach black in quality, and the intensity diminishes. The grades of brightness for any single color thus form a system of intensive qualities, analogous to that of pure brightness, only in place of the achromatic gradations between white and black, we have the corresponding grades of saturation. From the point of greatest saturation there are two opposite for variation in saturation: one positive, towards [p. 59] white, accompanied by an increase in the intensity of the sensation, and the other negative, towards black, with a corresponding decrease in intensity. As limits for these two directions we have, on the one hand, the pure sensation white, on the other, the pure sensation black; the first is at the same time the maximum, the second the minimum of intensity. White and black are in this way opposite extremities of the system of sensations of pure brightness, and also of the system of color-sensations arranged according to grades of brightness. It follows obviously that there is a certain medium brightness for every color, at which its saturation is greatest. From this point, the saturation diminishes in the positive direction when the brightness increases, and in the negative direction when the brightness decreases. The grade of brightness most favorable for the saturation is not the same for all colors, but varies from red to blue, in such a way that it is most intense for red and least intense for blue. This accounts for the familiar phenomenon that in twilight, when the degree of brightness is small, the blue color-tones -- of paintings, for example -- are still clearly visible, while the red color-tones appear black.
18. If we neglect the somewhat different position of the maximal saturation of the various colors in the line of brightness, the relation that exists between sensations of chromatic brightness and those of pure, or achromatic, brightness, by virtue of the gradual transition of colors into white on the one hand, and into black on the other, may be represented in the simplest manner as follows. First, we may represent the system of pure color-tones, that is, of the colors at their maximal saturation, by a circle, as above. Then we may draw through the centre of this circle, perpendicular to its plane, the straight line of pure brightness, in such a way that where it cuts the plane of the circular surface, [p. 59] it represents the sensation of pure brightness corresponding to the minimum of saturation for the colors with which we started. In like manner, the other color-circles for increasing and decreasing grades of brightness, may be arranged perpendicularly along this line, above and below the circle of greatest saturation. But the decreasing saturation of the colors in these latter circles must be expressed in the shortening of their radii; just as in the first circle, the shorter the distance from the centre, the less the saturation. These radii grow continually shorter, until finally, at the two extremities of the line, the circles disappear entirely. This corresponds to the fact that for every color the maximum of brightness corresponds to the sensation white, while its minimum corresponds to black 
19. The whole system of sensations of chromatic brightness may, accordingly, be most simply represented by a spherical surface whose equator represents the system of pure color-tones, or colors of greatest saturation, while the two poles correspond to white and black, the extremities of the sensations of chromatic brightness. Of course, any other geometrical figure with similar attributes, as, for example, two cones with a common base and apexes pointing in different directions, would serve the same purpose. The only thing essential for the representation, is the gradual transition to white and black, and the corresponding decrease in the variety of the color-tones, which finds its expression in the continual decrease in the length of the radii of the color-circles. Now, as above shown, the system of saturations corresponding to [p. 61] a particular sensation of pure brightness, may be represented by a circular surface which contains all the sensations of light belonging to one grade of brightness. When we unite grades of saturation and brightness to a single system, the total system of light sensations may be represented by a solid sphere. The equator is the system of pure color-tones; the polar axis is the system of pure brightnesses; the surface represents the system of chromatic brightnesses, and, finally, every circular plane perpendicular to the polar axis, corresponds to a system of saturations of equal brightness. This representation by means of a sphere is indeed arbitrary, in the sense that any other solid figure with analogous attributes may be chosen in its place; still, it presents to view the psychological fact that the total system of light sensations is a closed continuity of three dimensions. The three-dimensional character of the system arises from the fact that every concrete sensation of light has three determinants: color-tone, saturation, and brightness. Pure, or achromatic, brightness and pure, or saturated, colors are to be regarded as the two extreme cases in the series of saturations. The closed form of the system comes from the circular character of the color-line, on the one hand, and, on the other, from the termination of the system of chromatic brightness in the extremes of pure brightness. A special characteristic of the system is that only the changes in the two dimensions, or those of color-tones and saturations, are pure variations in quality, while every movement in the third dimension, or that of brightness, is at once a modification of both quality and intensity. As a consequence of this circumstance, the whole three-dimensional system is required to represent the qualities of light-sensations, but it includes also the intensities of these sensations.
20. Certain principal senses are prominent in this [p. 62] system, because we use them as points of reference for the arrangement of all the others. These are, white and black, in the achromatic series, and the four principal colors, red, yellow, green, and blue, in the chromatic. Only these six sensations have clearly distinguished names in the early development of language. All other sensations are then named eiher with reference to these or with modifications of the names themselves. Thus, we regard grey as a stage in the achromatic series lying between white and black, We designate the different grades of saturation according to their brightness, as whitish or blackish, light or dark color-tones; an we generally choose compound names for the colors between the four principal ones, as, for example, purple-red, orange-yellow, yellow-green, etc. These all show their relatively late origin by their ver composition.
20a. From the early origin of the names for the six qualities mentioned, the conclusion has been drawn that they are fundamental qualities of vision, and that the others are compounded from them. Grey is declared to be a mixture of black and white, violet and purple-red to be mixtures of blue and red, etc. Psychologically there is no justification for calling any light-sensations compound in comparison with others. Grey is a simple sensation just as much as white or black; such colors as orange and purple-red are just as much simple colors as red and yellow; and any grade of saturation which we have placed in the system between a pure color and white, is by no means, for that reason, a compound sensation. The closed, continuous character of the system makes it necessary for language to pick out certain especially marked differences in reference to which all other sensations are then arranged, for the simple reason that it is impossible to have an unlimited number of names. It is most natural that white and black should be chosen as such points of reference for the achromatic series, since they designate the greatest differences. When once these two are given, however, all other achromatic sensations will be considered as transitional [p. 63] sensations between them, since the extreme differences are connected by a series of all possible grades of brightness. The case of color-sensations is similar; only here, on account of the circular form of the color-line, it is impossible to choose directly two absolutely greatest differences. Other motives besides the necessary qualitative difference, are decisive in the choice of the principal colors. We may regard as such motives, the frequency and affective intensity of certain light-impressions due to the natural conditions of human existence. The red color of blood, the green of vegetation, the blue of the sky, and the yellow of the heavenly bodies in contrast with the blue of the sky, and the yellow heavenly bodies may well have furnished the earliest occasions for the choice of certain colors as those to receive names. Language generally names the sensation from the object that produced it, not the object from the sensation. In this case too, when certain principal qualities were once determined, all others must, on account of the continuity of the series of sensations, seem to be intermediate color-tones. The difference between principal colors and transitional colors is, therefore, very probably due entirely to external conditions. If these conditions had been other, red might have been regarded as a transitional color between purple and orange, just as orange is now placed between red and yellows 
21. The attributes of the system of light-sensations above described, are so peculiar as to lead us to expect a priori that the relation between these psychological attributes and the objective processes of stimulation, is essentially different from that in the cases of the sensational systems discussed before, especially those of the general and auditory senses. Most [p. 64] striking, in this respect, is the difference between the system in question and that of tones. In the latter case, the principle of parallelism between sensation and stimulus (p. 45), holds not only for the physiological processes of. stimulation, but to a great extent for the physical processes as well. A simple sensation corresponds to a simple form of sound-vibration, and a plurality of simple sensations to compound form. Furthermore, the intensity of the sensation varies in proportion to the amplitude of the vibrations, and its quality with their form, so that in both directions the subjective difference between sensations increases with the growing difference between the objective physical stimuli. The relation in the case of light-sensations is entirely different. Like objective sound, objective light also consists of vibrations in some medium. To be sure, the actual form of these vibrations is still a question, but from physical experiments on the phenomena of interference we know that the consist of very short and rapid waves. Those seen as light vary in wave-length from 688 to 393 millionths of a millimetre, and in rate from 450 to 790 billion vibrations per second. In this case, too, simple sensations correspond to simple vibrations, that is, vibrations of like wave-length; and the quality of the sensation varies continuously with the rate: red corresponds to the longest and slowest wives, and violet to the shortest and most rapid, while the other color-tones form a continuous series between these, varying with the changes in wave-length. Even here, however, an essential difference appears, for the colors red and violet, which are the most different in wave-length, are more similar in sensation than those which lie between 
There are also other differences. 1) Every change in the amplitude of the physical vibrations corresponds to a subjective change in both intensity and quality, as we noted above in the discussion of sensations of brightness. 2) All light, even though it be made up of all the different kinds of vibration, is simple in sensation, just as much as objectively simple light, which is made up of only one kind of waves, as is immediately apparent if we make a subjective comparison of sensations of chromatic light with those of achromatic light. From the first of these facts it follows that light which is physically simple may produce not only chromatic, but also achromatic sensations, for it approaches white when the amplitude of its vibrations increases, and black when the amplitude decreases. The quality of an achromatic sensation does not, therefore, determine unequivocally its source; it may be produced either through a change in the amplitude of objective light-vibrations or through a mixture of simple vibrations of different wave-lengths. In the first case, however, there is always connected with the change in amplitude a change in the grade of brightness, which does not necessarily take place when a mixture is made.
22. Even when the grade of brightness remains constant, this achromatic sensation may have one of several sources. A sensation of pure brightness of a given intensity may result not only from a mixture of all the rates of vibration contained in solar light, as, for example, in ordinary daylight, but it may also result when only two kinds of light-waves, namely those which correspond to sensations sub- [p. 66] jectively the most different, that is, to opposite colors, are mixed in proper proportions. Since opposite colors, when mixed objectively, produce white, they are called complementary colors. As examples of such opposite or complementary colors we may mention spectral red and green-blue, orange and sky-blue, yellow and indigo-blue.
Like achromatic sensations, each of the color-sensations may also, though to a more limited extent, have one of several sources. When two objective colors which lie nearer each other in the color-circle than opposites, are mixed, the mixture appears, not white, but of a color which in the series of objectively simple qualities lies between the two with which we started. The saturation of the resulting color is, indeed, very much diminished when the components of the mixture approach opposite colors; but when they are near each other, the diminution is no longer perceptible, and the mixture and the corresponding simple color are generally subjectively alike. Thus, the orange of the spectrum is absolutely indistinguishable from a mixture of red and yellow rays. In this way, ,all the colors in the color-circle between red and green can be obtained by mixing red and green, all between green and violet by mixing green and violet, and, finally, purple, which is not in the solar spectrum, can be produced by mixing red and violet. The whole series of color-tones possible in sensation can, accordingly, be obtained from three objective colors. By means of the same three colors we can also produce white with its intermediate stages. The mixture of red and violet gives purple, and this is the complementary color of green; and the white secured by mixing these complementary colors, when mixed in different proportions with the various colors, gives the different grades of saturation.
23. The three objective colors that may be used in this way to produce the whole system of light-sensations, are [p. 67] called fundamental colors. In order to indicate their significance, a triangular surface is chosen to represent the system of saturation, rather than the circular surface which is derived from the psychological relations alone. The special significance of the fundamental colors is then expressed by placing then at the angles of the triangle. Along the sides are arranged the color-tones in their maximal saturation, just as on the circumference of the color-circle, while the other grades of saturation in their transitions to white, which lies in the centre, are on the triangular surface. Theoretically, any set of three colors could be chosen as fundamental colors, provided they were suitably distant from one another. Practically, those mentioned, red, green, and violet, are preferable for two reasons. First, by using them we avoid having as one of the three, purple, which can not be produced by objectively simple light. Secondly, at the two ends of the spectrum sensations vary most slowly in proportion to the period of vibration, so that when the extreme colors of the spectrum are used as fundamental colors, the result obtained by mixing two neighboring ones is most like the intermediate, objectively simple color. 
24. These phenomena show that in the system of light sensations a simple relation does not exist between the physical stimuli and the sensations. This can be understood from what has been said above (3) as to the, character of the physiological stimulation. The visual sense is to be [p. 68] reckoned among the chemical senses, and we can expect a simple relation only between the photochemical processes ill the retina and the sensations. Now, we know from experience that different kinds of physical light produce like chemical disintegrations, and this explains in general the possibility mentioned above, of having the same sensation from many different kinds of objective light. According to the principle of parallelism between changes in sensation and in the physiological stimulation (p. 45), it may be assumed that the various physical stimuli which cause the same sensation all produce the same photochemical stimulation in the retina, and that altogether there are just as many kinds and varieties of the photochemical processes as kinds and varieties of distinguishable sensations. In fact, all that we know, up to the present time, about the physiological substratum of light-sensations is based upon this assumption. The investigation of the physiological processes of stimulation through light, has not yet given any further result than that the stimulation is in all probability a chemical process.
25. The relatively long persistence of the sensation after the stimulation that originated it, is explicable on the assumption that the light-stimulations are due to chemical processes in the retina (3, p. 42). This persistence is called, with reference to the object used as stimulus, the after-image of the impression. At first this after-image appears in the same brightness and color as the object: white when the object is white, black when it is black, and if it is colored, in the same color. These are the positive and like-colored after-images. After a short time it passes, in the case of achromatic impressions, into the opposite grade of brightness, white into black, or black into white; in the case of colors, it passes into the opposite or complementary color. These are the negative and complementary after-images. If light-stimuli of short duration [p. 69] act upon the eye in darkness, this transition may be repeated several times. A second positive after-image follows the negative, and so on, so that an oscillation between the two phases takes place. The positive after-image may be readily explained by the fact that the photochemical disintegration caused by any kind of light, lists a short time after the action of the light. The negative and complementary after-images can be explained by the fact that disintegration in a given direction causes a partial consumption of the photochemical substance most directly concerned, and this results in a corresponding modification of the photochemical processes when the stimulation of the retina continues.
26. The origin of a part of the phenomena included under the name light contrasts and color-contrasts is very probably the same as that of the negative and complementary after-images. These phenomena consist in the appearance of simultaneous sensations of opposite brightness and color in the neighborhood of any light-impression. Thus, a white surface appears to be surrounded by a dark margin, a black surface by a bright margin, and a colored surface by a margin of the complementary color. These phenomena, which are called "marginal contrasts" when they are limited to the immediate neighborhood of the object, are in part at least nothing but negative or complementary after-images that are simultaneously visible in the immediate neighborhood of the impression as a result of continual weak ocular movements. Whether there is also an irradiation of the stimulation is a question; its existence still wants certain proof. The fact that these contrasts increase as the light becomes more intense, just as after-images do, speaks for their interconnection with the latter. In this respect, this physioloical contrast differs essentially from certain psychological contrast-phenomena, with which it is generally confused. The latter are closely connected in [p. 70] their rise, with numerous other forms of psychological contrast, so that we will not discuss them until later, when we enter into the general treatment (§17, 9) of such phenomena.
26a. If we take the priciple of parallelism between sensation and physiological stimulation as the basis of our suppositions in regard to the processes that occur in the retina, we may conclude that analogous independence in the photochemical processes corresponds to the relative independence which appears between achromatic and chromatic sensations. Two facts, one belonging to the subjective sensational system, the other to the objective phenomena of color-sensation can be most naturally explained on this basis. The first is the, tendency that every color-sensation shows, of passing into one of pure brightness when the grade of its brightness decreases or increases. This tendency is most simply interpreted on the assumption that every color-stimulation is made up of two physiological components, one corresponding to the chromatic, the other to the achromatic stimulation. To this assumption we may easily add the further condition, that for certain medium intensifies of the stimuli the chromatic components are the strongest, while for greater and smaller intensifies the achromatic components come more and more to the front. The second fact, is that any two opposite colors are complementary; that is, when mixed in suitable proportions, they produce an achromatic sensation. This phenomenon is most easily understood when we assume that opposite colors, which are subjectively the greatest possible differences, represent objective photochemical processes that neutralize each other. The fact that as a result of this neutralization an achromatic stimulation arises, is very readily explained by the presupposition that such a stimulation accompanies every chromatic stimulation from the first, and is therefore all that is left when antagonistic chromatic stimulations counteract each other. This assumption of a relative independence between the chromatic and achromatic photochemical processes, is supported in a very striking way by the existence of an abnormity of vision, sometimes congenital, sometimes acquired through pathological changes in the retina, namely total color-blindness. In such cases all stimulations are, either on the whole [p. 71] retina or on certain parts of it, seen as pure brightness, without any admixture of color. This is an incontrovertible proof that the chromatic and achromatic stimulations are separable physiological processes.
If we apply the principle of parallelism to the chromatic stimulation, two facts present themselves. The first is that two colors separated by limited, short distance, when mixed give a color that is like the intermediate simple color. This indicates that color-stimulation is a process that varies with the physical stimulus, not continuously, as the tonal stimulation, but in short stages, and in such a way that the stages in red and violet are longer than in green, where the mixture of colors fairly near each other, shows the effects of complementary action. Such a non-continuous variation of the process corresponds entirely with its chemical nature, for chemical disintegration and synthesis must always have to do with qroups of atoms or molecules. The second fact is that certain definite colors, which correspond to rather large differences in the stimuli, are subjectively opposite colors, that is, are maximal differences, and the same colors are objectively complementary, that is, mutually neutralizing, processes. Chemical processes, however, can neutralize each other only when they are in some way opposite in character. Any two complementary color-stimulations must, therefore, stand in a relation to each other similar to that which exists between the neutralizing processes operative in the case of antagonistic achromatic stimulations. Still, there are two very essential differences here. First, this opposition in the character of color-stimulations is not limited to one case, but appears for every color distinguishable in sensation, so that we must conclude, according to our presupposition, that for every stage of the photochemical process of. chromatic stimulation which is to be assumed on the ground of the results obtained by mixing neighboring colors, there is a certain complementary process. Secondly, the difference between two opposite colors, which is subjectively the greatest possible difference, is mediated by transitional forms, not merely in one direction from each color, as in the case of black and white, but in two opposite directions. In a similar way, the objective complementary action of two colors gradually diminishes as, starting from opposite colors, they approach each other in either of [p. 72] these two directions. We may, then, infer from this twofold elimination of complementary action that the return of the color-line to its starting point corresponds to a repetition of related photochemical processes, on the same grounds that led us to infer the opposite character of the processes corresponding to opposite colors, from the fact that they are complementary. The whole process of chromatic stimulation, beginning with red and passing beyond violet through purple mixtures to its starting point, running parallel, as it does., with continuous changes in the wavelength of objective light, is to be regarded as an indefinitely long succession of photochemical processes. All these processes together, form a closed circle in which, for every stage there is a neutralizing opposite and a possible transition to this opposite in two different directions.
We know nothing about the total number of photochemical stages in this circle of processes. The numerous attempts made to reduce all color-sensations to the smallest possible number of such stages, lack adequate foundation. Sometimes they indiscriminately translate the results of physical color-mixing into physiological processes, as in the assumption of three fundamental colors, red, green, and violet, from the different mixtures of which all sensations of light, even the achromatic, are to be derived (Young-Helmholtz hypothesis). Sometimes they start with the psychologically untenable assumption that the naming of colors is not due to the influence of certain external objects, but to the real significance of the corresponding sensations (v. sup. p. 63), and assume accordingly four fundamental colors as the sources of all color-sensations. The four fundamental colors here assumed are the two pairs red and green, yellow and blue, to which are added the similar pair of sensations of pure brightness, black and white. All other light-sensations such as grey, orange, violet, etc., are regarded as subjectively and objectively mixed colors (Hering's hypothesis). The evidence in support of the first as of the second of these hypotheses has been derived for the most part from the riot infrequent cases of partial color-blindness. Those who accept three fundamental colors, assert that all these cases are to be explained as a lack of the red or green sensations, or else as a lack of both. Those who accept four, hold that partial color-blindness always includes two fundamental colors that belong together as opposites, and is, therefore, either [p. 73] red-green-blindness or yellow-blue-blindness. An unprejudiced examination of color-blindness does not justify either of these assertions. The three-color theory can not explain total color blindness, and the four-color theory is in contradiction to cases of pure red-blindness and pure green-blindness. Finally, both theories are overthrown by the cases that unquestionably occur, in which such parts of the spectrum as do not correspond to any of the three or four fundamental colors, appear colorless. The only thing that our present knowledge justifies us in saying, is that every simple sensation of light is conditioned physiologically by a combination of two photochemical processes, a monochromatic and a chromatic. The first is made up, in turn, of a process mainly of disintegration, when the light is more intense, and a process of restitution, when the light is weaker. The chromatic process varies by stages in such a way that the whole series of photochemical color-disintegrations forms a circle of processes in which the products of the disintegration for any two relatively most distant stages, neutralize each other. 
Various changes as a result of the action of light have been observed in the living retina, all of which go to support the assumption of a photochemical process. Such are the gradual change into a colorless state, of a substance which in the retina not exposed to light is red (bleaching of the visual purple); microscopical movements of the pigmented protoplasm between the sensitive elements, or rods and cones; and, finally, changes in the form of the rods and cones themselves. Attempts to use these phenomena in any way for a physiological theory of light stimulation, are certainly premature. The most probable conclusion which we can now draw is that the difference in the [p. 74] forms of the rods and cones is connected with a difference in function. The centre of the retina, which is the region of direct vision in the human eye, has only cones, while in the eccentric parts the rods are more numerous; furthermore, in the centre (which also wants the visual purple) the discrimination of colors is much better than in the eccentric regions, while the latter are much more sensitive to brightness. The natural conclusion from these facts is that the differences in sensitivity are connected with the photochemical properties of the rods and cones. Still, we lack here too any particular evidence.
 Pendulum-oscillations may be represented by a sine-curve, because the distance from the position of rest is always proportional to the sine of the time required to swing to the point in question.
 It must be observed, however, that the actual coincidence of these sensations can be empirically proved only for the minimum of brightness. Grades of brightness which approach the maximum are so injurious to the eye that the general demonstration of the approach to white must be accepted as sufficient.
 The same false reasoning from the names of sensations, has even led some scholars to assume that the sensation blue developed later than other color-sensations, because, for example, even in Homer the word for blue is the same as that for "dark". Tests of the color-sensations of uncivilized peoples whose languages are much more deficient in names for colors than that of the Greeks at the time of Homer, have given us a superabundance of evidence that this assumption is utterly without ground.
 Many physicists, to be sure, believe that an analogous relation is to be found between tones of different pitch, in the fact that every tone has in its octave a similar tone. But this similarity, as we shall see (§ 9), does not exist between simple tones, but depends on the actual sympathetic vibration of the octave in all compound clangs. Attempts to support this supposed analogy by finding in the color-line intervals corresponding to the various tonal intervals, third, fourth, fifth, etc., have all been entirely futile.
 In the neighborhood of green this advantage does not exist, and the mixtures always appear less saturated than the intermediate simple colors. This is a clear proof that the choice of the three fundamental colors mentioned is indeed the most practical, but nevertheless arbitrary, and at bottom due to the familiar geometrical principle that a triangle is the simplest figure that can enclose a finite number of points in the same plane.
 The further assumption is made by the defenders of the four fundamental colors, that two opposite colors are related just as bright and dark achromatic stimulations, that is, that one of these colors is due to a photochemical disintegration (dissimilation), the other to a restitution (assimilation). This is an analogy that contradicts the actual facts. The result obtained by mixing complementary colors is on its subjective side a suppression of the color-sensation, while the mixture of white and black, on the other band, produces an intermediate sensation.