§ 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 such a sensation 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, either is homogeneous or it is 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 conditioning processes by a name borrowed from physiology, as sense stimuli or sensation stimuli. If the stimulus is a process in the outer world we call it a physical stimulus; if it is a process in our own body we call it a physiological stimulus. 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, 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 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 when a physical stimulus causes a sensation it 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 the skin structure. 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, that is, from sensations of pressure, heat, and cold. It is possible, too, that in lower animals some of the systems now so clearly differentiated in human beings are more alike. From a physiological standpoint the primordial character of the general sense is also apparent in the fact that it has either very simple organs or none at all for the transfer of sense stimuli to the nerves. Pressure stimuli, temperature stimuli, 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, Fig. 2 A, end-bulbs B, corpuscles of Vater), but the structure of these organs renders it probable that they merely favor the mechanical transfer of the stimulus to the nerve-endings. Special end-organs for heat, cold, and pain have not been found at all.

In the more highly developed special sense-organs we find, on the other hand, elaborate structures which not only effect the suitable transfer of the stimuli to the sensory nerves, but generally bring about a physiological transformation of the stimulation, which transformation seems to be indispensable for the rise of the particular sensational qualities. But even among the special senses there are differences in this respect.

In the auditory organ in particular the receptive parts do not seem to possess the same significance as do the receptive parts in the organs of smell, taste and vision. In their lowest stage of development auditory organs are not distinguished either in structure or function from the sense-organ of equilibration and of kinesthetic impression. The organ of equilibration and kinesthetic impression is the sense-organ which supplies position-sensations and movement-sensations of the body and is probably to be regarded as an inner modification of the general touch sense, although it is not improbable that as a primitive organ of hearing it is also capable of receiving impressions from sound waves. A primitive organ of this kind consists usually of a single vesicle which contains one or more small otoliths and has spread out in its walls a bundle of nerve-fibers (C). When the otoliths are set in oscillation by a movement of the animal's body or by a strong sound vibration, we may assume that they produce a rapid sequence of faint pressure stimulations on the fibers of the nerve bundles. Among the vertebrates this organ for kinesthetic sensations is differentiated from the auditory organ. The two organs remain, however, in close spatial relation to each other. The semicircular canals take over the function of the kinesthetic sense and the cochlea the function of the auditory organ. Though the auditory organ in the higher animals and in man is extremely complicated in its structure, yet it resembles in its essential structures the organs of the simplest type. In the cochlea 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 do the otoliths in the lowest and undifferentiated forms of the auditory organ. There is, however, another change which appears with the development of the membrane which makes it easy to understand the great manifold of tone sensations. The basilar membrane of the cochlea has in its different parts different dimensions, its width at the base of the cochlea being less than its width at the upper end of the canal. The membrane thus behaves like a system of stretched wires of different lengths; and just as in such a system, other conditions being the same, the longer wire is tuned to a lower tone and the shorter wire to a higher tone, so, we may assume, the different parts of the basilar membrane are differently tuned. While we may believe, then, that the sensation system of the simplest auditory organs supplied with otoliths was a homogeneous system, not clearly distinguishable from pressure sensations, we see, on the other hand, that the development of the basilar membrane and its attached organs in the cochleas of the higher animals has resulted in the development of the original homogeneous group of sensations into a manifold system of the greatest complexity. The receiving organ remains the same in type in the two cases in that both of them are organs for the complete transmission of the physical stimulus to the sensory nerves, not organs for the transformation of the stimulus.

The organs of smell, taste and vision differ essentially from the auditory organs. In these organs the physiological structures render the direct action of the stimulus upon the sensory nerves impossible. They interpose between the direct stimulus and the nerve cell specialized structures which modify the external stimuli. The energy as thus modified becomes the stimulus acting upon the sensory nerves. The modifying organs in the three senses under discussion are specially developed cells derived from the external layer of the body and known as sensory cells. One end of such sensory cells is turned toward the stimulus while the other is in communication with the nerve-fibers. In the olfactory organ in the nose these sensory cells, which can be distinguished by their narrow fiber-like endings, are distributed among certain broader insensitive cells, (E). In the tongue, the sensory cells are organized into certain bulb-shaped organs made up of compact layers of these cells and known as taste-bulbs, (F). Finally, in the eye, the sensory cells are developed into two classes: first, the large cones distributed chiefly through the middle of the retina, and second, the rods, which are slender organs and are most numerous in the peripheral regions of the retina. These rods and cones with their connecting fibers, which pass into the nerve-fibers, constitute a unique membrane known as the retina, (G). Everything goes to show that these receiving structures are not merely transmitting organs but transforming organs which modify the character of the stimulus. The transformation process in the three organs under discussion is probably of a chemical character. In the case of the olfactory and gustatory organs, the true chemical reagents produce changes in the nerve cells, which then become the true sensory stimuli. In the case of the eye, the chemical process is produced by the action of light.

These three senses may be distinguished as chemical senses, 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 heat 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 case of the mechanical senses, the sensation lasts only a very little longer than the external stimulus, while in the case of the chemical senses, the sensation persists much longer. Thus, in a quick succession of pressures and more especially in a quick succession of sounds, it is possible to distinguish clearly the single stimuli from one another; lights, tastes and smells, on the other hand, run together even when given at a very moderate rate of succession. Temperature stimuli received by the skin seem to behave in this respect like chemical stimuli. We are probably justified for this reason in regarding the mode of action as indirect.

4. Since 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 determine this relation, 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 both 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-fiber 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 their different specific energies.

This principle, generally called the "law of specific energy 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 qualitas occulta 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 also have undergone a change. Such a change is, however, possible only under the condition that organs may be modified by the stimuli which act upon them. That is to say, the sensory organs 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 organs 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 organs themselves varied to some extent with the quality of the stimulus.

2) The concept of specific energy is contradictory to the fact that in many senses there are no distinct sensory elements corresponding to the 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 the sensory surfaces in both these senses 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 auditory organ, the structure of the organ shows that this difference is not due to any attribute of the nerve-fibers or of other sensory elements, but that it comes originally from the way in which these elements are arranged. Different fibers 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-fibers. It is due to the way in which the single nerve-fibers 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 appropriate stimuli for a sufficient interval, or at least must have been so exposed at some previous period, before the corresponding sensations can arise through the excitation of the central organs. 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 centers 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 which 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. And even then peculiarities are due to the adaptation of the sense-organ to the physical stimuli. As a result of this adaptation, however, it may come to be true 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, a sensation may arise which corresponds to the adequate stimulus. This does not hold, however, for all stimuli, or for all sensory elements. Thus, heat 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 the optic nerve; and, finally, mechanical and electrical 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, for stimuli belong to the mediate experience of the natural sciences, while sensations belong 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 psychology it is used in producing definite changes in sensation, by means of intentional variation of the stimulus. In physiology 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.

5a. The principle of "specific energy" appears as the implicit assumption in many of the earlier physiological discussions, but it remained for johannes MÜLLER to give it a definite formulation. The principle was later employed, especially by helmholtz in his theories of hearing and vision. In the later expositions the form of the principle has been somewhat modified. As a rule the nerve-fibers themselves are no longer considered as the seats of the specific energy; they are looked upon rather as indifferent conductors. It is the peripheral sensory elements (rods and cones of the retina, the endings of the auditory fibers in the cochlea, etc.) or sometimes the nerve cells in the central sensory centers, or both of these, which are regarded as the seats of specific energy. Such views are, however, entirely hypothetical. Our knowledge of the processes in either the peripheral sensory cells, or in the central nerve cells, and even the greater part of our knowledge of the anatomy of these cells, is so very incomplete that we are not able to base any conclusions upon such knowledge. The only ground for the principle is, therefore, to be found in the phenomena of like sensations arising from different stimuli, and these phenomena, as already remarked, do not give the principle any adequate ground for general application. Wherever the principle seems to apply, the facts are much better explained by referring them to the general principle of the adaptation of the sensory elements to stimuli.

References. J. Müller, Lehrbuch der Physiologie des Menschen, 4th ed. 1844, vol. I, p. 667. Helmholtz , Physiologische Optik, 2nd ed., p. 233, and (Engl. trans. by Ellis) Sensations of Tone, Sect. 3 and 4. Goldscheider, Ges. Abhandlungen, I. 1, 1898. Weinmann, Die Lehre von den spezifischen Sinnesenergien, 1895. W. Nagel, Allg. Einleitung zur Physiologie der Sinne in Handbuch der Physiol. des Menschen, III, 1904. Wundt, Grundz. 5th ed., vol. I, Chap. 8, Sect. 4.

A. SENSATIONS OF THE GENERAL SENSE.

6. The definition of the "general sense" includes a spatial and a temporal factor. In point of time the general sense is that which precedes all others and therefore belongs to all beings endowed with mind. In point of spatial attributes, the general sense has the most extensive sensory surface exposed to stimuli. This surface includes not only the whole external skin and the adjoining areas of the mucous membrane, but also a large number of internal organs supplied with sensory nerves, such as joints, muscles, tendons, and bones, which are accessible to stimuli either regularly, or at least at certain times and under special conditions, as is the case with bones.

The general sense includes four specific, distinct sensational systems, namely sensations of pressure, heat, 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, we may have together sensations of pressure and pain, or sensations of heat 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, we may experience qualitatively different sensations of pressure when an extended region of the skin is touched.

The four systems of general sense are all homogeneous systems (§ 5, 5). This shows that the sense is genetically earlier than the others, the systems of which 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 heat, cold and pain, and the sensations of pressure which sometimes arise in the other internal organs (stomach, intestines, lungs, etc.). Touch sensations may in turn be divided into external touch sensations and internal touch sensations. The first include the external skin impressions of pressure, the second, the impressions arising in the joints, muscles, and tendons during movement. The internal touch sensations are again subdivided, with reference to the physiological organs from which they rise, as joint sensations and muscle sensations, with reference to the conditions which produce them, as sensations of movement or contraction, and as sensations of tension or effort.

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 which can be determined in regard to 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 heat, cold, and pain, in the internal organs are exceptional and rise to a noticeable intensity only under abnormal conditions. On the other hand, there is no point of the external skin, or of the immediately adjoining parts of the mucous membrane, which is not sensitive to stimulations of pressure, heat, 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 heat, and to cold, do not, in general, 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 regions of the skin appear to be most favorable for stimulations of pressure, heat and cold. These points are called respectively, pressure-spots, heat-spots and cold-spots. They are distributed in different parts of the skin in varying numbers. Spots of different modality do not coincide; yet, temperature-spots can always receive pressure sensations and pain sensations; and moderate warm stimulations produce, as a rule, warm sensations on the cold-spots, while strong heat stimulations produce on these cold-spots a so-called paradoxical sensation of cold. The warm-spots not infrequently react to cold with a sensation of cool which has been described as a contrary sensation, but they never react to cold with the sensation warm. Finally, both the heat-spots and the cold-spots respond with their appropriate sensory qualities to definitely limited mechanical and electrical stimulations.

8. Of the four qualities mentioned, sensations of pressure and those of pain form closed systems which show no relations either to each other or to the two systems of temperature sensations. The temperature qualities, on the other hand, stand in the relation of opposites; we apprehend heat and cold, not merely as different, but also as contrasted sensations. It is very probable that this is due in part to the conditions under which the sensations arise, and partly to the accompanying feelings. For, while the other qualities may be united without limitation to form mixed sensations as, for example, pressure with pain, cold with pain heat, and cold tend to exclude each other, because under the conditions of their rise, the only possibilities for a given cutaneous region is either a sensation of heat, or one of cold, or else an absence of both. Then, too, elementary feelings of opposite character are connected with heat and cold, the absence of both sensations corresponding to the indifference-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 heat, while a considerable decrease below the temperature of the skin is perceived as cold. The temperature of the skin itself, which is thus the indifference-zone between the two forms of sensation, can, within fairly wide limits, adapt itself rapidly to the existing external temperature. The fact that in this respect too, both sensations are alike, favors the view that they are interconnected and also antagonistic.

References. E. H. Weber, Tastsinn und Gemeingefühl, Handwörterb. der Physiol. Ill, 2. Blix, Zeitschr. f. Biologie 20, 21. Goldscheider, Archiv f. Physiol., 1885, 1886, and 1887, and also Ges. Abhandlungen 1898, I (pressure-spots, heat-spots, and cold-spots), and Ges. Abhandl. II (muscle sense). Kiesow, Phil. Stud. vol. 6. von Frey, Ber. der sächs. Ges. der Wiss., vols. 46 and 47, and Abhandl. der math.-phys. Cl. vol. 23. alrutz, Skandin. Archiv. f. Physiol., vol. 7 and 10. thunberg, same, vol. II. Wundt, Grundz. 5th ed., vol. II, Chap. 10; Lectures, lecture 5.
 
 

B. SENSATIONS OF SOUND.

9. We possess two independent systems of simple auditory sensations, which are, however, generally connected with each other as a result of the mixture of the two kinds of impressions. The two systems are, the system of noise sensations, and that of tone sensations.

Simple noise sensations can be produced only under conditions under which the simultaneous rise of a tone sensation is impossible, as for example when a sound vibration acts upon the ear for so short a time that a tone sensation can not arise. The simple noise sensations which are aroused in this way may differ very notably in intensity, but they seem always to be relatively uniform in quality. It is possible that small qualitative differences 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 experiences made up of such simple noises 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 simple noise sensations. Many of these vesicles serve either in addition to their other functions, or exclusively, the function of an inner tactual, or kinesthetic sense and give rise to sensations which vary with the position and movement of the body. In the case of the higher vertebrates and man, the functions of the kinesthetic sense are differentiated from those of hearing. The vestibule and the semicircular canal function in these animals only as kinesthetic organs (cf. § 10, 12), while the cochlea is devoted entirely to the auditory functions. These facts indicate clearly the genetic relation of hearing to touch.

10. The system of simple tone sensations is a continuity of one dimension. We call the quality of a single simple tone its pitch. The one-dimensional character of this system shows itself in the fact that, starting with a given pitch, we can vary the quality only in two opposite directions: in the direction of raising the pitch, and in the direction of lowering the pitch. In actual experience simple sensations of tone are never presented alone, but always united with other tone sensations and with accompanying simple sensations of noise. But since, according to the scheme given above (p. 32), 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 tone 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 these concomitants 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 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 tone sensation are examined, they will be found to correspond to the simplest possible form of vibration, namely, to the so-called pendulum oscillation. This name is used because the vibrations of the atmospheric particles follow the same laws as a pendulum oscillating in a very small amplitude 1). 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 from the structure of the organs in the cochlea, as an application of the law of sympathetic vibration. Since the basilar membrane, which extends through the whole cochlea and upon which the auditory nerve fibers terminate, changes its width continuously from top to bottom, we may assume that its different parts are tuned to the tones of various pitch (p. 42). This is the "resonance hypothesis" which was first formulated by HELMHOLTZ. According to this view 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 of the membrane tuned to that particular rate of vibration 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. (Compare § 9, 7a.).
 
 

1) 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.
 
 

11. The system of tone sensations shows its character as a continuous series in the fact that it is always possible to pass from a given pitch such as c to any other such as c' through continuous changes in sensation. (Fig. 3.) Music has selected at option from this continuity, single sensations separated by considerable intervals, thus substituting a tonal scale (c, d, e, f, g, a, b) for the tonal line. This selection, however, is based on the relations of tone sensations themselves. We shall return to the discussion of these relations later, in taking up the ideational compounds arising from these sensations (§9).

In the different scales of our musical system the tonal intervals correspond in each scale to different points in the continuous line of tonal sensations. Those instruments which have their notes set at a fixed tone, as for example the piano, are tuned to what is known as a tempered scale. This scale has five half-tones in the octave and permits an approximate, though not exact, transition from one scale to the other, as for example from C major to B minor or B major. The tonal line has two extremities, which are conditioned by the physiological sensitivity of the ear. These extremities are the lowest and highest tones; the former corresponds to 1216 double vibrations per second, the latter to 40,00050,000. The limit defined by these latter figures is, however, doubtful, since both the subjective recognition of intervals and the objective determination of the rate of vibration of the sounding body (tuning-fork or pipe) are very uncertain for these high pitches. For tones of medium pitch (from 200 to 1000 vibrations) we can distinguish differences in the pitch of tones which are given in succession, even when these tones differ only about one fifth of a vibration per second; and the difference thus necessary for discrimination remains in this part of the scale an absolute, fixed quantity, even though the pitch of the tone varies. Another fact which stands in full accord with that just described is the fact that if, depending entirely upon our recognition of tonal intervals, we bisect a certain tonal interval, that is, if we try to place a tone B in such a position that it will seem to us to be equally distant from a lower tone A and a higher tone C, it will be found that in every case, even when the interval is entirely inharmonious, the tone B will lie half-way between A and C in the number of its objective vibrations. Such a comparison of the tones is possible here, as in every other form of sensation, only when the distance between the sensations is not too large. Thus the distance may not exceed to any great extent the range of a single octave. The ability to discriminate diminishes also very rapidly when we experiment with low tones and even more so when we experiment with the higher tones. The ability to discriminate the intensity of tones and noises is very incomplete. It differs from ability to discriminate qualities in that it is constant, not for absolute differences in intensity, but for relative differences only. The ratio of just noticeable differences between successive sound impressions is 1/3 of the objective intensity of the original impression.

References. Helmholtz, (Engl. trans.) Sensations of Tone, Sects. 1, 4, and 9. Hensen, Physiol. des Gehörs, in Hermann's Sects. 1, 4, and 9. Hensen, Physiol. des Gehörs, in Hermanns Handbuch der Physiol., vol. III, Pt. 2 (1880). Stumpf, Tonpsychologie, vol.II, § 28 on noise and clangs (1890). K. L. Schaefer, Gehörssinn in Nagel's Handbuch der Physiol., vol. 3, pt. 2. Wundt, Grundz. 5th ed., vol. II, Chap. 10; Lectures, lecture 5. Preyer, Die Grenzen der Tonwahrnehmung, 1876. luft, Unterscheidung von Tonhöhen, Phil. Stud., vol. 4. Schischmanow, Unterscheidung von Intervallen, Phil. Stud., vol. 5. Lorenz, Einteilung von Tonstrecken, Phil. Stud., vol. 6. For a discussion of sensitivity for differences in sound intensity see also § 17, 10. For a discussion of the limits of tone sensations and of the weakest audible Tones see: Schwendt, Archiv f. Ohrenheilkunde, vol. 49. Zwaardemaker-quitt, Arch. f. Physiol., 1902. Suppl. Pflüger's Archiv, vol. 97, M. Wien. For further references on tone perception see § 9 below.
 
 

C. SENSATIONS OF SMELL AND TASTE.
12. Sensations of smell form a complex system the arrangement of which is still unknown. All we know is that there are a great many different 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 those 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 example, 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 other substances. 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 which neutralize each other chemically, as acetic acid and ammonia, but also of others, such as caoutchouc 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 different 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 such neutralizing qualities 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 two fixed qualities, and only two, that are in each case complementary.

13. Sensations of taste have been somewhat more thoroughly investigated than those of smell, and we can here distinguish four distinct primary qualities. Between these primary qualities there are all possible transitional tastes, which are to be regarded as 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 unmistakable relationship to saline, and metallic to sour, so that both are probably mixed sensations (alkaline made up of saline and sweet, metallic of sour and saline). Sweet and saline are opposite qualities. When these two sensations are united in proper intensities, the result is a neutral mixed sensation (commonly known as "insipid"), even though the stimuli that here reciprocally neutralize 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 rectangular surface at the angles of which the four primary qualities are placed, the various mixed qualities being placed along the sides and on the inner surface.

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 relation to 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 heat and cold (p. 54). It is well known that very commonly the chemical effect of certain substances can be neutralized through the action of certain other substances. We do not know what the chemical changes are which are produced by the gustatory stimuli in the taste-cells, but from the neutralization of sensations of sweet and saline we may conclude, in accordance with the principle of the parallelism of changes in sensation and in stimuli (p. 49), that the chemical reactions which sweet and saline substances produce in the sensory cells, also counteract each other. 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 subject 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 no certain conclusion in this matter. Whether we are here dealing with phenomena really analogous to those exhibited by complementary colors (v. inf. 22) is still an open question.

References. On smell: Zwaardemaker, Physiologie des Geruchs, 1895. On taste, W. Nagel, in Bibl. zool., 18, 1894, and in Pflüger's Archiv f. Physiol. vol. 54. oehrwall, Skand. Archiv f. Physiol. vol. 2. Kiesow, Phil. Stud., vols. 9, 10, and 12. Haenig, Phil. Stud., vol. 17.

D. SENSATIONS OF LIGHT.

14. The system of light sensations is made up of two partial systems: that of sensations of achromatic light and that of sensations of chromatic light. Between the qualities in these two systems, all possible transitional forms exist.

Sensations of achromatic light, when considered alone, form a 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, those in the neighborhood of the other we call white, while between the two we insert gray in its different shades (dark gray, gray, and light gray). This one-dimensional system of achromatic sensations differs from that of tones in being at once a system of quality and of intensity; since every qualitative change in the direction from black to white is seen at the same time as an increase in intensity, and every qualitative change in the direction from white to black is seen as a decrease in intensity. Each point in the series, which thus has a definite quality and intensity, is called a degree of brightness. The whole system may, accordingly, be designated as that of 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; both the variations in quality and those in intensity belong to one and the same dimension. This system differs essentially, in this respect, from the tonal line, in which each point is merely a degree of quality, and has by itself 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 so far as intensity is concerned, while the higher grades are called white and strong. Our sensitivity for differences in brightness is, especially for medium intensities, very great. The ratio is from 1/100 to 1/150 of the brightness with which we start in the comparison of two intensities. Like the ratios of sound intensities (p. 59), this ratio of brightness intensities is constant in its relative magnitude. (weber's Law 17, 10.)

15. Sensations of color also form a one-dimensional system when their qualities alone are taken into account. Unlike 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 characteristics again become like those with which we began, until finally we reach the starting point once more. The color spectrum obtained by refracting sunlight through a prism, or that found in the rainbow, shows this characteristic, though not completely. If in these cases we start from the red end of the spectrum (Fig. 5) we come first to orange, then to yellow, yellow-green, green-blue, blue, indigo-blue, and finally to violet, which last 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 the colors which we have in sensation. Purple 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 spectrum series with purple, is the system of actual color sensations complete, and then the system constitutes a line which returns upon itself. This can be represented most easily by a circle such as is used in the color circle in Fig. 5.

From a given point in this system we pass, when the sensation is gradually varied, first to similar sensations, then to those most markedly different, and finally to others similar to the first quality, but lying on the opposite side. Every color must, accordingly, be related to some other color which constitutes a maximum of difference in sensation (p. 36, Fig. 1, E' E"). Such pairs of colors may be called opposite colors, and in the representation of the color system by a circle, two opposite colors are to be placed at the two extremities of a diameter. Thus, for example, purple and green, yellow and blue, light green and violet, are pairs of opposite colors, that is, colors which exhibit the greatest qualitative differences. Sensitivity for either absolute or relative objective color differences as expressed in the number of vibrations, is entirely irregular, changing constantly from point to point on the color line. Sensitivity is generally at its maximum in yellow and blue, at its minimum in red and violet. It has a third relatively low point between yellow and blue, that is, in green. A regularity such as is to be found in the case of tonal qualities (p. 58), or in the case of different degrees of brightness (p. 63), is entirely wanting here.

The quality determined by the position of a sensation in the color circle, as distinguished from other qualitative determinations is called color-tone, a figurative term borrowed from tone sensations. In addition to color-tone, every color sensation has two other attributes, one we call chromatic character or saturation of the color, the other its brightness. Of these two attributes saturation is peculiar to chromatic or color sensations, while brightness belongs to both chromatic and achromatic sensations.

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, grays, and blacks. The term "saturation" is borrowed from the common method of producing these transitional colors objectively, that is, by the saturation of some colorless soluble with color-pigment. Since the end of every series of diminishing grades of saturation of any color quality is thus an achromatic sensation, the degree of saturation may 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 united with the system of sensations of pure brightness. If, now, we represent some particular sensation of white, gray, or black by the central point of the color circle, all the grades of color saturation which 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 center with the color in question. If the grades of color saturation corresponding to the continuous transitional stages from all the colors to a sensation of pure brightness, are thus geometrically represented, we have the system of saturation-grades as a circular surface, the circumference of which is the system of simple color-tones and the center of which is the sensation of pure brightness (Fig. 5). For the formation of such a system of saturation-grades any point whatever in the series of sensations of pure brightness may be chosen, so long as the condition is fulfilled that the white is not too bright, or the black too dark, for in such extreme cases differences in both saturation and color disappear. 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 necessary an attribute of a color sensation as it is of achromatic sensations, and is in the case of color sensations also, both a quality and a 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 the system of pure brightnesses, 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 directions for variation in saturation: one positive, towards 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. It follows obviously that there is a certain medium brightness for every color, at which its saturation is greatest. From this point, the saturation decreases in the positive direction, that is, towards white, when the brightness increases, and in the negative direction, that is, towards black when the brightness decreases. The grade of brightness most favorable for 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 fact 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 (purkinje's phenomenon).

18. If we neglect for the moment the somewhat different relations of the maximal saturations of the various colors with respect to the line of brightness, we may represent the general relation which exists by virtue of the gradual transition of colors into white and black, that is, we may represent the general relation between sensations of chromatic brightness and sensations of pure, or achromatic, brightness in the simplest manner by the following figure. First, we may represent the system of pure color-tones, that is, of the colors at their maximal saturation, by a circle, as above. (Fig. 5.) Then we may draw through the center of this circle, perpendicular to its plane, the straight line of pure brightness (Fig. 4), in such a way that where it cuts the plane of the circular surface, it represents the sensation of pure brightness corresponding to the minimum of saturation of the colors with which we started. In like manner, the other color circles for increasing and decreasing grades of brightness, may be arranged at right angles along this line, above and below the circle of greatest saturation. The decreasing saturation of the colors in these latter circles must also be expressed, and this can be done by the shortening of their radii; just as in the first circle, the shorter the distance from the center, the less the saturation. The radii in successive circles grow continually shorter, until finally, at the two extremities of the line of brightness the circles disappear entirely. This corresponds to the fact that for every color the maximum of brightness passes into the sensation white, while its minimum passes into black2).

2) 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 whole system of color sensations and brightness sensations can be represented by a closed solid figure in the form of two cones which are placed with their bases together (Fig. 6), or by a sphere, one of the poles of which corresponds to the darkest black, the other to the brightest white. In these geometrical representations there is a complete exhibition of the fact that the system of light sensations is a three-dimensional and closed continuum. The three-dimensional character of this system arises from the fact that every light sensation is made up of three determining characteristics, namely, color-tone, saturation, and brightness. Pure colorless brightness sensations and color sensations of maximum saturation are to be looked upon as the two limiting cases in the complete series of color variations. The fact that the system is closed grows out of the two facts that the color sensations can be arranged in a single circle and the fact that colorless brightness qualities are bounded by the same pure brightness sensations as are the grades of saturation. A special peculiarity of the system consists in the fact that only variations in the two dimensions of color-tone and saturation grade are pure qualitative changes, while every variation in the third dimension, that is, in the direction of brightness sensations, is at once a qualitative and intensive variation. In view of this last fact, the whole three-dimensional system is required in order to show the qualitative characteristics of light sensations in their completeness. The system includes, however, at the same time, not only the qualitative characteristics but also sensation intensity.

19. Certain principal sensations are prominent in this 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 in the chromatic series the four principal colors: red, yellow, green and blue. This group of four colors was first pointed out as important by leonardo da vinci. Only these six sensations have clearly distinguished names in the early development of language. All other sensations are then named either with reference to these or even with modifications of the names themselves. Thus, we regard gray 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; and we generally choose compound names for the colors between the principal ones, as, for example, purple-red, orange-yellow, yellow-green, etc. These all show their relatively late origin by their very composition.

19a. 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. Gray is declared to be a mixture of black and white, violet and purple to be mixtures of blue and red, etc. Psychologically there is no justification for calling any light sensations compound in comparison with others. Gray is a simple sensation just as much as white or black; such colors as orange and purple 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, all other achromatic sensations will be considered as transitional 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, 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 which 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 yellow 3).
 
 

3) The same false reasoning from the names of sensations, has even led to the assumption 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" (L. geiger, Zur Entwicklungsgeschichte der Menschheit, 1871). 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 (grant allen, On Color, 1880).
 
 

References. Purkinje, Beobachtungen und Versuche zur Physiologie der Sinne, 2 vols., 18191823. Helmholtz, Physiol. Optik, § 1921. Hering, Zur Lehre vom Lichtsinn, 5 and 6, 18741878. (Hering holds to the view that the naming of the colors is due to their subjective characters and then proceeds to draw conclusions from this view for the theory of light sensations.) Wundt, Die Empfindung des Lichts und der Farben, Phil. Stud., vol. 4; Grundz, 5th ed., vol. II, Chap. 10, sect. 4; Lectures, lecture 6. On sensitivity for color-differences: A. König and dieterici, Archiv f. Ophthalm., vol. 30, no. 2. König, Zeitschr. f. Psych. vol. 3.

20. The attributes of the system of light sensations above described, are so peculiar that they lead us to expect a priori that the relation between the psychological attributes and the objective processes of stimulation, is essentially different from that which we inferred in the cases of the sensational systems discussed before, especially in the case of the general sense and auditory sense. Most striking in this respect, is the difference between the system of colors and that of tones. In the case of tones the principle of parallelism between sensation and stimulus (p. 49), 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 corresponds to a compound form of vibration. Furthermore, the intensity of the sensation varies in proportion to the amplitude of the vibrations, and its quality varies with the 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 of a certain 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 they 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. For light, as for sound, simple sensations correspond to simple vibrations, that is, to vibrations of like wave-length; and the quality of the sensations varies continuously with the wavelength and with the rate of vibration. Thus, red corresponds to the longest and slowest waves, and violet to the shortest and most rapid, while the other color-tones form a 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 like each other in sensation than are most of the colors which lie between 4). There are also other differences. 1) Every change in the amplitude of the physical vibrations corresponds, as we noted above in the discussion of sensations of brightness, to a subjective change in both intensity and quality. 2) All light, even though it be made up of all the different kinds of vibrations, is simple in sensation, just as much as objectively simple light, which is made up of only one kind of waves. This 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 the sensation from such simple light 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; such a sensation 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.
 
 

4) 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.
 
 

21. Even when the grade of brightness remains constant, an 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 lightwaves are mixed in proper proportions. The kinds of light necessary to thus produce a sensation of pure brightness are those which correspond to sensations subjecti vely the most different, that is, to opposite colors, or at least to colors very nearly opposite in quality. Whenever the objective mixture of two colors produces white, these colors are called complementary colors. As examples of such complementary colors, we may mention spectral red and green-blue, orange and sky-blue, yellow and indigo-blue. (Fig. 5.)

Each of the color sensations may, like achromatic sensations, 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 complementary colors; but when the component colors are near each other, the diminution in saturation 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 the three objective colors, red, green and violet. 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, finally, the white secured by mixing purple and green gives, when mixed in different proportions with the various colors, the different grades of saturation.

22. The three objective colors which may be used in this way to produce the whole system of light sensations, are called fundamental colors. In order to indicate their significance, a triangular surface is chosen to represent the system of saturations, 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 them at the angles of the triangle. Along the sides are arranged the color-tones in their maximal saturation, while on the triangular surface are the other grades of saturation in their transitions to white, the white lying in the center (Fig. 7). Theoretically any set of three colors could be chosen as fundamental colors, provided they were suitably distant from one another. Practically, those mentioned, namely red, green, and violet, are preferable because 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 colors is most like the intermediate, objectively simple color 5).

5) 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.

23. 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 classified as one of the chemical senses, and we can expect a simple relation only between the photochemical processes in 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. 49), 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 conditions of light sensations is based upon this assumption. The investigation of the physiological processes of light stimulation, has not yet given any further result than that the stimulation is in all probability a chemical process.

24. The relatively long time required for a light sensation to arise and the relatively long after-effect of such a sensation, which continues after the stimulus has been withdrawn, can be explained on the assumption that light stimulation is a chemical process in the retina (p. 46). The time during which a light stimulus must act, in order that it may produce the maximum sensation of which it is capable, is on the average for colorless light 0,268 sec., for colored lights it is 0.530 sec., little or no difference appearing for different wavelengths. These intervals are the same for different intensities of light. The short period required for the development of colorless excitation, as compared with the time required for the development of color stimulations from all parts of the spectrum, points unmistakably to a fundamental difference between the processes of colorless excitation and those which come from the different colors, and at the same time, the uniformity of the period for all colors shows that there is an intimate relationship between these processes of color excitation. Similar results appear through the investigation of the after-effects of stimulation, which after-effects are commonly designated as after-images because of the fact that objects were used as the sources of stimulation. At first the after-image appears in the same brightness and color as the object: white when the object is white, black when the object is black, and if the object is colored, the after-image appears in the same color. These are the positive and like-colored after-images. After a short time the afterimage 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 act upon the eye in darkness, this transition from positive to negative after-images 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, lasts 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. This view is confirmed by the fact that when the retina which is gradually passing through the successive stages of an after-image is stimulated by a sudden light stimulus, the effect is always the sum of the new stimulus and the after-image, that is, the effect is the same as that which would be produced on the unfatigued retina by the new stimulus plus the remnant of the after-effect. (fechner-helmholtz law of negative and complementary after-images.) The rate of subsidence of chromatic and achromatic afterimages differs. The rate for all chromatic after-images of whatever color is essentially the same.

25. The phenomena of color induction and light induction are very closely related to positive and negative after-mages. These phenomena consist in the appearance of simultaneous sensations of opposite brightness and color in the neighborhood of any light impression. Positive light induction is the less common of these two kinds of phenomena. It appears most noticeably in those cases in which one part of the retina is intensely stimulated and a contiguous region is left entirely unstimulated. In such a case the positive light stimulation, or color stimulation, seems to spread out over the unstimulated area. In all other cases the opposite form of induction, namely, negative induction, appears. In consequence of such negative induction 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 are, furthermore, accompanied by psychological contrast phenomena which belong under the general principle to be explained later (§ 17, 11), namely, the principle of emphasis of opposites. Indeed, the term "contrast" is, as a rule, applied to the total effects of such combined physiological and psychological influences. Such a use of the term is justified to a certain degree by the impossibility of separating the two kinds of influences from each other, but it would be much more appropriate to use the term induced excitation for the physiological factor, and to reserve the term contrast for the psychological factor. For this psychological factor corresponds fully to the psychological emphasizing of opposites which can be demonstrated in other spheres, especially among spatial and temporal ideas, and among the feelings. Light induction and color induction, in this purely physiological sense, consist probably in a kind of negative irradiation of the stimulation, in which the stimulation is not carried over directly to contiguous regions in its own proper quality as it is in the case of positive induction, but rather excites in these neighboring regions a stimulation process of opposite character. Such negative irradiation may possibly be due to the fact that the photochemical substances which are used up in the stimulation of a certain region of the retina, are replaced in part through an influx of other similar substances from the surrounding regions. If, then, a light impression is applied to these impoverished neighboring regions, the result would be the same as that which would appear in the case of an after-image on the originally stimulated area (p. 77). Evidence in favor of assuming this connection between the facts of induction and after-images, appears in the fact that in both cases the effects are heightened by an increase in the intensity of the light impressions. But just at this point there shows itself a very fundamental difference between these physiological processes of light induction and the psychological processes of contrast with which they are usually erroneously classified. To this fundamental difference we shall return when we come to the general treatment of contrasts (§ 17, 10).

25a. If we take the principle 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 the photochemical processes corresponding to chromatic and achromatic sensations, are relatively independent of each other, in a way analogous to that in which the corresponding sensations are relatively independent. Two facts, one belonging to the subjective sensational system, the other to the objective phenomena of color-mixing, can be very naturally explained on this basis. The first is the fact that every color sensation tends to pass into one of pure brightness when the grade of its brightness undergoes a marked decrease or increase. (Fig. 6). This fact 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 must add the further condition, that for certain medium intensities of the stimuli the chromatic components are relatively the strongest, while for greater and smaller intensities the achromatic components predominate more and more. The second fact is, that there are complementary colors. This fact is most easily understood when we assume that opposite colors, which are subjectively the greatest possible differences in sensation (Fig. 5), depend upon objective photochemical processes which 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 an achromatic 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 by the existence of an abnormality of vision, sometimes congenital, sometimes acquired through pathological changes in the retina, namely total color-blindness. In such cases all stimulations are seen, either on the whole retina or on certain parts of it, as pure achromatic brightness. This is proof that the chromatic and achromatic stimulations are separable physiological processes.

If we apply the principle of parallelism to the chromatic stimulations, two facts present themselves. The first is that two colors separated by a limited, short distance, when mixed give a color that is like the intermediate simple color. This indicates that color stimulation is a process which 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 pronounced effects of complementary action. The second fact is that certain colors which correspond to rather large differences in stimulation, namely, the complementary colors, evidently depend upon processes which neutralize each other. Now, let it be remembered that chemical processes can neutralize each other only when they are in some way opposite in character, and that for every color recognizable in sensation there is an opposite quality, it will then be seen that for every stage in the photochemical process of color stimulation there must be a stage of complementary action. The whole series of chromatic stimulations, beginning with red and passing beyond violet through purple mixtures back to its first point, running parallel, as it does, with continuous changes in the wave-length of objective light, is to be regarded as an indefinitely long succession of photochemical disintegrations. All these processes together form a closed circle in which there is, for every stage, a neutralizing opposite, and in which there are two possible paths of transition in different directions to this neutralizing opposite.

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 indiscriminatingly 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 sensations themselves (v. sup. p. 71), 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 gray, 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 not infrequent cases of partial color-blindness. Those who accept three fundamental colors, assert that all these cases are to be explained as a total lack of the red, green, or violet sensations, or else as a partial lack of these. Those who accept four, hold that partial color-blindness always includes two fundamental colors which belong together as opposites; that color-blindness is, accordingly, either 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 which 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 probably conditioned by a combination of two photochemical processes, an achromatic 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 6).

6) 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 hand, produces the intermediate sensation, gray.
 
 

Various changes in the living retina have been observed as a result of the action of light, all of which go to support the assumption of a photochemical process. Such changes are, first, the gradual change into a colorless state, of a substance which in the retina not exposed to light is purple (bleaching of the visual purple); second, 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 forms of the rods and cones is connected with a difference in function. The center of the human retina, which is the region of direct vision, has only cones, while in the peripheral regions the rods predominate. Correspondingly, the ability to distinguish colors is more complete in the center which has no visual purple than it is in the peripheral regions, and in the extreme periphery the ability to distinguish colors is entirely lost, while the sensitivity for brightness is greater than it is at the center. In like fashion the sensitivity of the retina for changes in brightness increases in the dark, while the sensitivity for colors decreases, so that colors of faint intensity, when seen in the dark are colorless, and appear in comparison with the surroundings, according to the degree of their brightness, either as white or black. The condition of the retina just described is known as dark adaptation of the retina. This condition appears in different degrees of intensity according to the degree of darkness or the length of time in which the eye is exposed to darkness. The sensitivity for the colors at the lower end of the spectrum, namely, red and yellow, decreases in the retina adapted to darkness more rapidly than the sensitivity for the colors at the upper end of the spectrum, namely blue and violet. The maximum adaptation is reached in a totally dark room in from twenty to thirty minutes. The sensitivity for brightness increases steadily at the same time that the sensitivity for colors decreases. It is possible that these phenomena are directly connected with the photochemical processes of the rods and cones, the cones being primarily the organs for color sensations and the rods the organs for brightness sensation. This division of functions is, however, evidently not an absolute division.
 
 

References. Helmholtz, Physiol. Optik, § 2025. Hering, Zur Lehre vom Lichtsinn, 16. von Kries, Die Gesichtsempfindungen und ihre Analyse, 1882. Wundt, Grundz. 5th ed., vol. I, Chap. 8, and vol. II, Chap. 10; Lectures, lectures 6 and 7. On the rise of processes of stimulation; Dürr, Phil. Stud., vol. 18. On After-images: Fechner, Poggendorff's Ann. der Physik, vols 44 and 50. Hering, Pflüger's Archiv f. Physiol., vol. 43. Charpentier, Compt. rend., 1881, no. 113. Wirth, Phil. Stud., vols. 1618. On light induction (contrast): Brücke, Denkschr. der Wiener Akad. Math.-naturw. CL, vol. 3. Fechner, Poggendorff's Ann., vol. 50. Hering, Pflüger's Archiv, vol. 41. Kirschnann, Phil. Stud., vol. 6. Köhler, Arch. f. Psych., vol. 2. On color-blindness: holmgren, Die Farbenblindheit 1878. König and Dieterici, Zeitschr. f. Psych., vol. 4. Brodhun, Zeitschr. f. Psych., vols. 3 and 5. König, same journal, vol. 20. von Kries, same journal, vols. 13 and 19. Kirschmann, Phil. Stud., vol. 8. On light sensations in indirect vision and Purkinje's Phenomenon: Schön, Die Lehre vom Gesichtsfeld, 1874. A. E. Fick, Pflüger's Archiv, vol. 43. Kirschmann, Phil. Stud., vol. 8. Hellpach, Phil. Stud., vol. 15. peters, Archiv f. Psych., vol. 3 v. Kries, Zeitsch. f. Psychol., vols. 9 and 15. Sherman, Phil. Stud., vol. 13. Tschermak, Pflüger's Archiv, vol. 82.