VI – CHAPTER I
THE INTENSITY OF PSYCHIC STATES
It is usually admitted that states of consciousness, sensations, feelings, passions, efforts, are capable of growth and diminution; we are even told that a sensation can be said to be twice, thrice, four times as intense as another sensation of the same kind. This latter thesis, which is maintained by psychophysicists, we shall examine later; but even the opponents of psychophysics do not see any harm in speaking of one sensation as being more intense than another, of one effort as being greater than another, and in thus setting up differences of quantity between purely internal states. Common sense, moreover, has not the slightest hesitation in giving its verdict on this point; people say they are more or less warm, or more or less sad, and this distinction of more and less, even when it is carried over to the region of subjective facts and unextended objects, surprises nobody. But this involves a very obscure point and a much more important problem than is usually supposed.
When we assert that one number is greater than another number or one body greater than another body, we know very well what we mean.
For in both cases we allude to unequal spaces, as shall be shown in detail a little further on, and we call that space the greater which contains the other. But how can a more intense sensation contain one of less intensity? Shall we say that the first implies the second, that we reach the sensation of higher intensity only on condition of having first passed through the less intense stages of the same sensation, and that in a certain sense we are concerned, here also, with the relation of container to contained? This conception of intensive magnitude seems, indeed, to be that of common sense, but we cannot advance it as a philosophical explanation without becoming involved in a vicious circle. For it is beyond doubt that, in the natural series of numbers, the later number exceeds the earlier, but the very possibility of arranging the numbers in ascending order arises from their having to each other relations of container and contained, so that we feel ourselves able to explain precisely in what sense one is greater than the other. The question, then, is how we succeed in forming a series of this kind with intensities, which cannot be superposed on each other, and by what sign we recognize that the members of this series increase, for example, instead of diminishing: but this always comes back to the inquiry, why an intensity can be assimilated to a magnitude.
It is only to evade the difficulty to distinguish, as is usually done, between two species of quantity, the first extensive and measurable, the second intensive and not admitting of measure, but of which it can nevertheless be said that it is greater or less than another intensity. For it is recognized thereby that there is something common to these two forms of magnitude, since they are both termed magnitudes and declared to be equally capable of increase and diminution. But, from the point of view of magnitude, what can there be in common between the extensive and the intensive, the extended and the unextended? If, in the first case, we call that which contains the other the greater quantity, why go on speaking of quantity and magnitude when there is no longer a container or a contained? If a quantity can increase and diminish, if we perceive in it, so to speak, the less inside the more, is not such a quantity on this very account divisible, and thereby extended? Is it not then a contradiction to speak of an inextensive quantity? But yet common sense agrees with the philosophers in setting up a pure intensity as a magnitude, just as if it were something extended. And not only do we use the same word, but whether we think of a greater intensity or a greater extensity, we experience in both cases an analogous impression; the terms “greater” and “less” call up in both cases the same idea. If we now ask ourselves in what does this idea consist, our consciousness still offers us the image of a container and a contained. We picture to ourselves, for example, a greater intensity of effort as a greater length of thread rolled up, or as a spring which, in unwinding, will occupy a greater space. In the idea of intensity, and even in the word which expresses it, we shall find the image of a present contraction and consequently a future expansion, the image of something virtually extended, and, if we may say so, of a compressed space. We are thus led to believe that we translate the intensive into the extensive, and that we compare two intensities, or at least express the comparison, by the confused intuition of a relation between two extensities. But it is just the nature of this operation which it is difficult to determine.
The solution which occurs immediately to the mind, once it has entered upon this path, consists in defining the intensity of a sensation, or of any state whatever of the ego, by the number and magnitude of the objective, and therefore measurable, causes which have given rise to it. Doubtless, a more intense sensation of light is the one which has been obtained, or is obtainable, by means of a larger number of luminous sources, provided they be at the same distance and identical with one another. But, in the immense majority of cases, we decide about the intensity of the effect without even knowing the nature of the cause, much less its magnitude: indeed, it is the very intensity of the effect which often leads us to venture an hypothesis as to the number and nature of the causes, and thus to revise the judgment of our senses, which at first represented them as insignificant. And it is no use arguing that we are then comparing the actual state of the ego with some previous state in which the cause was perceived in its entirety at the same time as its effect was experienced. No doubt this is our procedure in a fairly large number of cases; but we cannot then explain the differences of intensity which we recognize between deep-seated psychic phenomena, the cause of which is within us and not outside. On the other hand, we are never so bold in judging the intensity of a psychic state as when the subjective aspect of the phenomenon is the only one to strike us, or when the external cause to which we refer it does not easily admit of measurement. Thus it seems evident that we experience a more intense pain at the pulling out of a tooth than of a hair; the artist knows without the possibility of doubt that the picture of a master affords him more intense pleasure than the signboard of a shop; and there is not the slightest need ever to have heard of forces of cohesion to assert that we expend less effort in bending a steel blade than a bar of iron. Thus the comparison of two intensities is usually made without the least appreciation of the number of causes, their mode of action or their extent.
There is still room, it is true, for an hypothesis of the same nature, but more subtle. We know that mechanical, and especially kinetic, theories aim at explaining the visible and sensible properties of bodies by well defined movements of their ultimate parts, and many of us foresee the time when the intensive differences of qualities, that is to say, of our sensations, will be reduced to extensive differences between the changes taking place behind them. May it not be maintained that, without knowing these theories, we have a vague surmise of them, that behind the more intense sound we guess the presence of ampler vibrations which are propagated in the disturbed medium, and that it is with a reference to this mathematical relation, precise in itself though confusedly perceived, that we assert the higher intensity of a particular sound? Without even going so far, could it not be laid down that every state of consciousness corresponds to a certain disturbance of the molecules and atoms of the cerebral substance, and that the intensity of a sensation measures the amplitude, the complication or the extent of these molecular movements? This last hypothesis is at least as probable as the other, but it no more solves the problem. For, quite possibly, the intensity of a sensation bears witness to a more or less considerable work accomplished in our organism; but it is the sensation which is given to us in consciousness, and not this mechanical work. Indeed, it is by the intensity of the sensation that we judge of the greater or less amount of work accomplished: intensity then remains, at least apparently, a property of sensation. And still the same question recurs: why do we say of a higher intensity that it is greater? Why do we think of a greater quantity or a greater space?
Perhaps the difficulty of the problem lies chiefly in the fact that we call by the same name, and picture to ourselves in the same way, intensities which are very different in nature, e.g. the intensity of a feeling and that of a sensation or an effort.
The effort is accompanied by a muscular sensation, and the sensations themselves are connected with certain physical conditions which probably count for something in the estimate of their intensity: we have here to do with phenomena which take place on the surface of consciousness, and which are always connected, as we shall see further on, with the perception of a movement or of an external object. But certain states of the soul seem to us, rightly or wrongly, to be self-sufficient, such as deep joy or sorrow, a reflective passion or an aesthetic emotion. Pure intensity ought to be more easily definable in these simple cases, where no extensive element seems to be involved. We shall see, in fact, that it is reducible here to a certain quality or shade which spreads over a more or less considerable mass of psychic states, or, if the expression be preferred, to the larger or smaller number of simple states which make up the fundamental emotion.
For example, an obscure desire gradually becomes a deep passion. Now, you will see that thee feeble intensity of this desire consisted at first in its appearing to be isolated and, as it were, foreign to the remainder of your inner life. But little by little it permeates a larger number of psychic elements, tingeing them, so to speak, with its own colour: and lo! your outlook on the whole of your surroundings seems now to have changed radically. How do you become aware of a deep passion, once it has taken hold of you, if not by perceiving that the same objects no longer impress you in the same manner? All your sensations and all your ideas seem to brighten up: it is like childhood back again. We experience something of the kind in certain dreams, in which we do not imagine anything out of the ordinary, and yet through which there resounds an indescribable note of originality. The fact is that, the further we penetrate into the depths of consciousness, the less right we have to treat psychic phenomena as things which are set side by side. When it is said that an object occupies a large space in the soul or even that it fills it entirely, we ought to understand by this simply that its image has altered the shade of a thousand perceptions or memories, and that in this sense it pervades them, although it does not itself come into view. But this wholly dynamic way of looking at things is repugnant to the reflective consciousness, because the latter delights in clean cut distinctions, which are easily expressed in words, and in things with well-defined outlines, like those which are perceived in space. It will assume then that, everything else remaining identical, such and such a desire has gone up a scale of magnitudes, as though it were permissible still to speak of magnitude where there is neither multiplicity nor space! But just as consciousness (as will be shown later on) concentrates on a given point of the organism the increasing number of muscular contractions which take place on the surface of the body, thus converting them into one single feeling of effort, of growing intensity, so it will hypostatize under the form of a growing desire the gradual alterations which take place in the confused heap of co-existing psychic states. But that is a change of quality rather than of magnitude.
What makes hope such an intense pleasure is the fact that the future, which we dispose of to our liking, appears to us at the same time under a multitude of forms, equally attractive and equally possible. Even if the most coveted of these becomes realized, it will be necessary to give up the others, and we shall have lost a great deal. The idea of the future, pregnant with an infinity of possibilities, is thus more fruitful than the future itself, and this is why we find more charm in hope than in possession, in dreams than in reality.
Let us try to discover the nature of an increasing intensity of joy or sorrow in the exceptional cases where no physical symptom intervenes. Neither inner joy nor passion is an isolated inner state which at first occupies a corner of the soul and gradually spreads. At its lowest level it is very like a turning of our states of consciousness towards the future. Then, as if their weight were diminished by this attraction, our ideas and sensations succeed one another with greater rapidity; our movements no longer cost us the same effort. Finally, in cases of extreme joy, our perceptions and memories become tinged with an indefinable quality, as with a kind of heat or light, so novel that now and then, as we stare at our own self, we wonder how it can really exist. Thus there are several characteristic forms of purely inward joy, all of which are successive stages corresponding to qualitative alterations in the whole of our psychic states. But the number of states which are concerned with each of these alterations is more or less considerable, and, without explicitly counting them, we know very well whether, for example, our joy pervades all the impressions which we receive in the course of the day or whether any escape from its influence. We thus set up points of division in the interval which separates two successive forms of joy, and this gradual transition from one to the other makes them appear in their turn as different intensities of one and the same feeling, which is thus supposed to change in magnitude. It could be easily shown that the different degrees of sorrow also correspond to qualitative changes. Sorrow begins by being nothing more than a facing towards the past, an impoverishment of our sensations and ideas, as if each of them were now contained entirely in the little which it gives out, as if the future were in some way stopped up. And it ends with an impression of crushing failure, the effect of which is that we aspire to nothingness, while every new misfortune, by making us understand better the uselessness of the struggle, causes us a bitter pleasure.
The aesthetic feelings offer us a still more striking example of this progressive stepping in of new elements, which can be detected in the fundamental emotion and which seem to increase its magnitude, although in reality they do nothing more than alter its nature. Let us consider the simplest of them, the feeling of grace. At first it is only the perception of a certain ease, a certain facility in the outward movements. And as those movements are easy which prepare the way for others, we are led to find a superior ease in the movements which can be foreseen, in the present attitudes in which future attitudes are pointed out and, as it were, prefigured. If jerky movements are wanting in grace, the reason is that each of them is self-sufficient and does not announce those which are to follow. If curves are more graceful than broken lines, the reason is that, while a curved line changes its direction at every moment, every new direction is indicated in the preceding one. Thus the perception of ease in motion passes over into the pleasure of mastering the flow of time and of holding the future in the present. A third element comes in when the graceful movements submit to a rhythm and are accompanied by music. For the rhythm and measure, by allowing us to foresee to a still greater extent the movements of the dancer, make us believe that we now control them. As we guess almost the exact attitude which the dancer is going to take, he seems to obey us when he really takes it: the regularity of the rhythm establishes a kind of communication between him and us, and the periodic returns of the measure are like so many invisible threads by means of which we set in motion this imaginary puppet. Indeed, if it stops for an instant, our hand in its impatience cannot refrain from making a movement, as though to push it, as though to replace it in the midst of this movement, the rhythm of which has taken complete possession of our thought and will. Thus a kind of physical sympathy enters into the feeling of grace. Now, in analysing the charm of this sympathy, you will find that it pleases you through its affinity with moral sympathy, the idea of which it subtly suggests. This last element, in which the others are merged after having in a measure ushered it in, explains the irresistible attractiveness of grace. We could hardly make out why it affords us such pleasure if it were nothing but a saving of effort, as Spencer maintains. But the truth is that in anything which we call very graceful we imagine ourselves able to detect, besides the lightness which is a sign of mobility, some suggestion of a possible movement towards ourselves, of a virtual and even nascent sympathy. It is this mobile sympathy, always ready to offer itself, which is just the essence of higher grace. Thus the increasing intensities of aesthetic feeling are here resolved into as many different feelings, each one of which, already heralded by its predecessor, becomes perceptible in it and then completely eclipses it. It is this qualitative progress which we interpret as a change of magnitude, because we like simple thoughts and because our language is ill-suited to render the subtleties of psychological analysis.
To understand how the feeling of the beautiful itself admits of degrees, we should have to submit it to a minute analysis. Perhaps the difficulty which we experience in defining: it is largely owing to the fact that we look upon the beauties of nature as anterior to those of art: the processes of art are thus supposed to be nothing more than means by which the artist expresses the beautiful, and the essence of the beautiful remains unexplained. But we might ask ourselves whether nature is beautiful otherwise than through meeting by chance certain processes of our art, and whether, in a certain sense, art is not prior to nature. Without even going so far, it seems more in conformity with the rules of a sound method to study the beautiful first in the works in which it has been produced by a conscious effort, and then to pass on by imperceptible steps from art to nature, which may be looked upon as an artist in its own way. By placing ourselves at this point of view, we shall perceive that the object of art is to put to sleep the active or rather resistant powers of our personality, and thus to bring us into a state of perfect responsiveness, in which we realize the idea that is suggested to us and sympathize with the feeling that is expressed. In the processes of art we shall find, in a weakened form, a refined and in some measure spiritualized version of the processes commonly used to induce the state of hypnosis. Thus, in music, the rhythm and measure suspend the normal flow of our sensations and ideas by causing our attention to swing to and fro between fixed points, and they take hold of us with such force that even the faintest imitation of a groan will suffice to fill us with the utmost sadness. If musical sounds affect us more powerfully than the sounds of nature, the reason is that nature confines itself to expressing feelings, whereas music suggests them to us. Whence indeed comes the charm of poetry? The poet is he with whom feelings develop into images, and the images themselves into words which translate them while obeying the laws of rhythm. In seeing these images pass before our eyes we in our turn experience the feeling which was, so to speak, their emotional equivalent: but we should never realize these images so strongly without the regular movements of the rhythm by which our soul is lulled into self-forgetfulness, and, as in a dream, thinks and sees with the poet. The plastic arts obtain an effect of the same kind by the fixity which they suddenly impose upon life, and which a physical contagion carries over to the attention of the spectator. While the works of ancient sculpture express faint emotions which play upon them like a passing breath, the pale immobility of the stone causes the feeling expressed or the movement just begun to appear as if they were fixed for ever, absorbing our thought and our will in their own eternity. We find in architecture, in the very midst of this startling immobility, certain effects analogous to those of rhythm. The symmetry of form, the indefinite repetition of the same architectural motive, causes our faculty of perception to oscillate between the same and the same again, and gets rid of those customary incessant changes which in ordinary life bring us back without ceasing to the consciousness of our personality: even the faint suggestion of an idea will then be enough to make the idea fill the whole of our mind. Thus art aims at impressing feelings on us rather than expressing them; it suggests them to us, and willingly dispenses with the imitation of nature when it finds some more efficacious means. Nature, like art, proceeds by suggestion, but does not command the resources of rhythm. It supplies the deficiency by the long comradeship, based on influences received in common by nature and by ourselves, of which the effect is that the slightest indication by nature of a feeling arouses sympathy in our minds, just as a mere gesture on the part of the hypnotist is enough to force the intended suggestion upon a subject accustomed to his control. And this sympathy is shown in particular when nature displays to us beings of normal proportions, so that our attention is distributed equally over all the parts of the figure without being fixed on any one of them: our perceptive faculty then finds itself lulled and soothed by this harmony, and nothing hinders any longer the free play of sympathy, which is ever ready to come forward as soon as the obstacle in its path is removed.
It follows from this analysis that the feeling of the beautiful is no specific feeling, but that every feeling experienced by us will assume an aesthetic character, provided that it has been suggested, and not caused. It will now be understood why the aesthetic emotion seems to us to admit of degrees of intensity, and also of degrees of elevation. Sometimes the feeling which is suggested scarcely makes a break in the compact texture of psychic phenomena of which our history consists; sometimes it draws our attention from them, but not so that they become lost to sight; sometimes, finally, it puts itself in their place, engrosses us and completely monopolizes our soul. There are thus distinct phases in the progress of an aesthetic feeling, as in the state of hypnosis; and these phases correspond less to variations of degree than to differences of state or of nature. But the merit of a work of art is not measured so much by the power with which the suggested feeling takes hold of us as by the richness of this feeling itself: in other words, besides degrees of intensity we instinctively distinguish degrees of depth or elevation. If this last concept be analysed, it will be seen that the feelings and thoughts which the artist suggests to us express and sum up a more or less considerable part of his history. If the art which gives only sensations is an inferior art, the reason is that analysis often fails to discover in a sensation anything beyond the sensation itself. But the greater number of emotions are instinct with a thousand sensations, feelings or ideas which pervade them: each one is then a state unique of its kind and indefinable, and it seems that we should have to re-live the life of the subject who experiences it if we wished to grasp it in its original complexity. Yet the artist aims at giving us a share in this emotion, so rich, so personal, so novel, and at enabling us to experience what he cannot make us understand. This he will bring about by choosing, among the outward signs of his emotions, those which our body is likely to imitate mechanically, though slightly, as soon as it perceives them, so as to transport us all at once into the indefinable psychological state which called them forth. Thus will be broken down the barrier interposed by time and space between his consciousness and ours: and the richer in ideas and the more pregnant with sensations and emotions is the feeling within whose limits the artist has brought us, the deeper and the higher shall we find the beauty thus expressed. The successive intensities of the aesthetic feeling thus correspond to changes of state occurring in us, and the degrees of depth to the larger or smaller number of elementary psychic phenomena which we dimly discern in the fundamental emotion.
The moral feelings might be studied in the same way. Let us take pity as an example. It consists in the first place in putting oneself mentally in the place of others, in suffering their pain. But if it were nothing more, as some have maintained, it would inspire us with the idea of avoiding the wretched rather than helping them, for pain is naturally abhorrent to us. This feeling of horror may indeed be at the root of pity; but a new element soon comes in, the need of helping our fellow-men and of alleviating their suffering. Shall we say with La Rochefoucauld that this so-called sympathy is a calculation, “a shrewd insurance against evils to come”? Perhaps a dread of some future evil to ourselves does hold a place in our compassion for other people’s evil. These however are but lower forms of pity. True pity consists not so much in fearing suffering as in desiring it. The desire is a faint one and we should hardly wish to see it realized; yet we form it in spite of ourselves, as if Nature were committing some great injustice and it were necessary to get rid of all suspicion of complicity with her. The essence of pity is thus a need for self-abasement, an aspiration downwards. This painful aspiration nevertheless has a charm about it, because it raises us in our own estimation and makes us feel superior to those sensuous goods from which our thought is temporarily detached. The increasing intensity of pity thus consists in a qualitative progress, in a transition from repugnance to fear, from fear to sympathy, and from sympathy itself to humility.
We do not propose to carry this analysis any further. The psychic states whose intensity we have just defined are deep-seated states which do not seem to have any close relation to their external cause or to involve the perception of muscular contraction. But such states are rare. There is hardly any passion or desire, any joy or sorrow, which is not accompanied by physical symptoms; and, where these symptoms occur, they probably count for something in the estimate of intensities. As for the sensations properly so called, they are manifestly connected with their external cause, and though the intensity of the sensation cannot be defined by the magnitude of its cause, there undoubtedly exists some relation between these two terms. In some of its manifestations consciousness even appears to spread outwards, as if intensity were being developed into extensity, e.g. in the case of muscular effort. Let us face this last phenomenon at once: we shall thus be transported at a bound to the opposite extremity of the series of psychic phenomena.
If there is a phenomenon which seems to be presented immediately to consciousness under the form of quantity or at least of magnitude, it is undoubtedly muscular effort. We picture to our minds a psychic force imprisoned in the soul like the winds in the cave of Aeolus, and only waiting for an opportunity to burst forth: our will is supposed to watch over this force and from time to time to open a passage for it, regulating the outflow by the effect which it is desired to produce. If we consider the matter carefully, we shall see that this somewhat crude conception of effort plays a large part in our belief in intensive magnitudes. Muscular force, whose sphere of action is space and which manifests itself in phenomena admitting of measure, seems to us to have existed previous to its manifestations, but in smaller volume, and, so to speak, in a compressed state: hence we do not hesitate to reduce this volume more and more, and finally we believe that we can understand how a purely psychic state, which does not occupy space, can nevertheless possess magnitude. Science, too, tends to strengthen the illusion of common sense with regard to this point. Bain, for example, declares that “the sensibility accompanying muscular movement coincides with the outgoing stream of nervous energy:” it is thus just the emission of nervous force which consciousness perceives. Wundt also speaks of a sensation, central in its origin, accompanying the voluntary innervation of the muscles, and quotes the example of the paralytic “who has a very distinct sensation of the force which he employs in the effort to raise his leg, although it remains motionless.” Most of the authorities adhere to this opinion, which would be the unanimous view of positive science were it not that several years ago Professor William James drew the attention of physiologists to certain phenomena which had been but little remarked, although they were very remarkable.
When a paralytic strives to raise his useless limb, he certainly does not execute this movement, but, with or without his will, he executes another. Some movement is carried out somewhere: otherwise there is no sensation of effort. Vulpian had already called attention to the fact that if a man affected with hemiplegia is told to clench his paralysed fist, he unconsciously carries out this action with the fist which is not affected. Ferrier described a still more curious phenomenon. Stretch out your arm while slightly bending your forefinger, as if you were going to press the trigger of a pistol; without moving the finger, without contracting any muscle of the hand, without producing any apparent movement, you will yet be able to feel that you are expending energy. On a closer examination, however, you will perceive that this sensation of effort coincides with the fixation of the muscles of your chest, that you keep your glottis closed and actively contract your respiratory muscles. As soon as respiration resumes its normal course the consciousness of effort vanishes, unless you really move your finger. These facts already seemed to show that we are conscious, not of an expenditure of force, but of the movement of the muscles which results from it. The new feature in Professor James’s investigation is that he has verified the hypothesis in the case of examples which seemed to contradict it absolutely. Thus when the external rectus muscle of the right eye is paralysed, the patient tries in vain to turn his eye towards the right; yet objects seem to him to recede towards the right, and since the act of volition has produced no effect, it follows, said Helmholtz, that he is conscious of the effort of volition. But, replies Professor James, no account has been taken of what goes on in the other eye. This remains covered during the experiments; nevertheless it moves and there is not much trouble in proving that it does. It is the movement of the left eye, perceived by consciousness, which produces the sensation of effort together with the impression that the objects perceived by the right eye are moving. These and similar observations lead Professor James to assert that the feeling of effort is centripetal and not centrifugal. We are not conscious of a force which we are supposed to launch upon our organism: our feeling of muscular energy at work “is a complex afferent sensation, which comes from contracted muscles, stretched ligaments, compressed joints, an immobilized chest, a closed glottis, a knit brow, clenched jaws,” in a word, from all the points of the periphery where the effort causes an alteration.
It is not for us to take a side in the dispute. After all, the question with which we have to deal is nοt whether the feeling of effort comes from the centre or the periphery, but in what does our perception of its intensity exactly consist? Now, it is sufficient to observe oneself attentively to reach a conclusion on this point which Professor James has not formulated, but which seems to us quite in accord with the spirit of his teaching. We maintain that the more a given effort seems to us to increase, the greater is the number of muscles which contract in sympathy with it, and that the apparent consciousness of a greater intensity of effort at a given point of the organism is reducible, in reality, to the perception of a larger surface of the body being affected.
Try, for example, to clench the fist with increasing force. You will have the impression of a sensation of effort entirely localized in your hand and running up a scale of magnitudes. In reality, what you experience in your hand remains the same, but the sensation which was at first localized there has affected your arm and ascended to the shoulder; finally, the other arm stiffens, both legs do the same, the respiration is checked; it is the whole body which is at work. But you fail to notice distinctly all these concomitant movements unless you are warned of them: till then you thought you were dealing with a single state of consciousness which changed in magnitude. When you press your lips more and more tightly against one another, you believe that you are experiencing in your lips one and the same sensation which is continually increasing in strength: here again further reflection will show you that this sensation remains identical, but that certain muscles of the face and the head and then of all the rest of the body have taken part in the operation. You felt this gradual encroachment, this increase of the surface affected, which is in truth a change of quantity; but, as your attention was concentrated on your closed lips, you localized the increase there and you made the psychic force there expended into a magnitude, although it possessed no extensity. Examine carefully somebody who is lifting heavier and heavier weights: the muscular contraction gradually spreads over his whole body. As for the special sensation which he experiences in the arm which is at work, it remains constant for a very long time and hardly changes except in quality, the weight becoming at a certain moment fatigue, and the fatigue pain. Yet the subject will imagine that he is conscious of a continual increase in the psychic force flowing into his arm. He will not recognize his mistake unless he is warned of it, so inclined is he to measure a given psychic state by the conscious movements which accompany it! From these facts and from many others of the same kind we believe we can deduce the following conclusion: our consciousness of an increase of muscular effort is reducible to the twofold perception of a greater number of peripheral sensations, and of a qualitative change occurring in some of them.
We are thus led to define the intensity of a superficial effort in the same way as that of a cases there is a qualitative progress and an increasing complexity, indistinctly perceived. But consciousness, accustomed to think in terms of space and to translate its thoughts into words, will denote the feeling by a single word and will localize the effort at the exact point where it yields a useful result: it will then become aware of an effort which is always of the same nature and increases at the spot assigned to it, and a feeling which, retaining the same name, grows without changing its nature. Now, the same illusion of consciousness is likely to be met with again in the case of the states which are intermediate between superficial efforts and deep-seated feelings. A large number of psychic states are accompanied, in fact, by muscular contractions and peripheral sensations. Sometimes these superficial elements are co-ordinated by a purely speculative idea, sometimes by an idea of a practical order. In the first case there is intellectual effort or attention; in the second we have the emotions which may be called violent or acute: anger, terror, and certain varieties of joy, sorrow, passion and desire. Let us show briefly that the same definition of intensity applies to these intermediate states.
Attention is not a purely physiological phenomenon, but we cannot deny that it is accompanied by movements. These movements are neither the cause nor the result of the phenomenon; they are part of it, they express it in terms of space, as Ribot has so remarkably proved. Fechner had already reduced the effort of attention in a sense-organ to the muscular feeling “produced by putting in motion, by a sort of reflex action, the muscles which are correlated with the different sense organs.” He had noticed the very distinct sensation of tension and contraction of the scalp, the pressure from without inwards over the whole skull, which we experience when we make a great effort to recall something. Ribot has studied more closely the movements which are characteristic of voluntary attention. “Attention contracts the frontal muscle: this muscle … draws the eyebrow towards itself, raises it and causes transverse wrinkles on the forehead…. In extreme cases the mouth is opened wide. With children and with many adults eager attention gives rise to a protrusion of the lips, a kind of pout.” Certainly, a purely psychic factor will always enter into voluntary attention, even if it be nothing more than the exclusion by the will of all ideas foreign to the one with which the subject wishes to occupy himself. But, once this exclusion is made, we believe that we are still conscious of a growing tension of soul, of an immaterial effort which increases. Analyse this impression and you will find nothing but the feeling of a muscular contraction which spreads over a wider surface or changes its nature, so that the tension becomes pressure, fatigue and pain.
Now, we do not see any essential difference between the effort of attention and what may be The intensity called the effort of psychic tension: acute desire, uncontrolled anger, passionate love, violent hatred. Each of these states may be reduced, we believe, to a system of muscular contractions co-ordinated by an idea; but in the case of attention, it is the more or less reflective idea of knowing; in the case of emotion, the unreflective idea of acting. The intensity of these violent emotions is thus likely to be nothing but the muscular tension which accompanies them. Darwin has given a remarkable description of the physiological symptoms of rage. “The action of the heart is much accelerated…. The face reddens or may turn deadly pale. The respiration is laboured, the chest heaves, and the dilated nostrils quiver. The whole body often trembles. The voice is affected. The teeth are clenched or ground together and the muscular system is commonly stimulated to violent, almost frantic action. The gestures … represent more or less plainly the act of striking or fighting with an enemy.” We shall not go so far as to maintain, with Professor James, that the emotion of rage is reducible to the sum of these organic sensations: there will always be an irreducible psychic element in anger, if this be only the idea of striking or fighting, of which Darwin speaks, and which gives a common direction to so many diverse movements. But, though this idea determines the direction of the emotional state and the accompanying movements, the growing intensity of the state itself is, we believe, nothing but the deeper and deeper disturbance of the organism, a disturbance which consciousness has no difficulty in measuring by the number and extent of the bodily surfaces concerned. It will be useless to assert that there is a restrained rage which is all the more intense. The reason is that, where emotion has free play, consciousness does not dwell on the details of the accompanying movements, but it does dwell upon them and is concentrated upon them when its object is to conceal them. Eliminate, in short, all trace of organic disturbance, all tendency towards muscular contraction, and all that will be left of anger will be the idea, or, if you still insist on making it an emotion, you will be unable to assign it any intensity.
“Fear, when strong,” says Herbert Spencer, “expresses itself in cries, in efforts to escape, in palpitations, in tremblings.” We go further, and maintain that these movements form part of the terror itself: by their means the terror becomes an emotion capable of passing through different degrees of intensity. Suppress them entirely, and the more or less intense state of terror will be succeeded by an idea of terror, the wholly intellectual representation of a danger which it concerns us to avoid. There are also high degrees of joy and sorrow, of desire, aversion and even shame, the height of which will be found to be nothing but the reflex movements begun by the organism and perceived by consciousness. “When lovers meet,” says Darwin, “we know that their hearts beat quickly, their breathing is hurried and their faces flushed.” Aversion is marked by movements of repugnance which we repeat without noticing when we think of the object of our dislike. We blush and involuntarily clench the fingers when we feel shame, even if it be retrospective. The acuteness of these emotions is estimated by the number and nature of the peripheral sensations which accompany them. Little by little, and in proportion as the emotional state loses its violence and gains in depth, the peripheral sensations will give place to inner states; it will be no longer our outward movements but our ideas, our memories, our states of consciousness of every description, which will turn in larger or smaller numbers in a definite direction. There is, then, no essential difference from the point of view of intensity between the deep-seated feelings, of which we spoke at the beginning, and the acute or violent emotions which we have just passed in review. To say that love, hatred, desire, increase in violence is to assert that they are projected outwards, that they radiate to the surface, that peripheral sensations are substituted for inner states: but superficial or deep-seated, violent or reflective, the intensity of these feelings always consists in the multiplicity of simple states which consciousness dimly discerns in them.
We have hitherto confined ourselves to feelings and efforts, complex states the intensity of which does not absolutely depend on an external cause. But sensations seem to us simple states: in what will their magnitude consist? The intensity of sensations varies with the external cause of which they are said to be the conscious equivalent: how shall we explain the presence of quantity in an effect which is inextensive, and in this case indivisible? To answer this question, we must first distinguish between the so-called affective and the representative sensations. There is no doubt that we pass gradually from the one to the other and that some affective element enters into the majority of our simple representations. But nothing prevents us from isolating this element and inquiring separately, in what does the intensity of an affective sensation, a pleasure or a pain, consist?
Perhaps the difficulty of the latter problem is principally due to the fact that we are unwilling to see in the affective state anything but the conscious expression of an organic disturbance, the inward echo of an outward cause. We notice that a more intense sensation generally corresponds to a greater nervous disturbance; but inasmuch as these disturbances are unconscious as movements, since they come before consciousness in the guise of a sensation which has no resemblance at all to motion, we do not see how they could transmit to the sensation anything of their own magnitude. For there is nothing in common, we repeat, between superposable magnitudes such as, for example, vibration-amplitudes, and sensations which do not occupy space. If the more intense sensation seems to us to contain the less intense, if it assumes for us, like the physical impression itself, the form of a magnitude, the reason probably is that it retains something of the physical impression to which it corresponds. And it will retain nothing of it if it is merely the conscious translation of a movement of molecules; for, just because this movement is translated into the sensation of pleasure or pain, it remains unconscious as molecular movement.
But it might be asked whether pleasure and pain, instead of expressing only what has just occurred, or what is actually occurring, in the organism, as is usually believed, could not also point out what is going to, or what is tending to take place. It seems indeed somewhat improbable that nature, so profoundly utilitarian, should have here assigned to consciousness the merely scientific task of informing us about the past or the present, which no longer depend upon us. It must be noticed in addition that we rise by imperceptible stages from automatic to free movements, and that the latter differ from the former principally in introducing an affective sensation between the external action which occasions them and the volitional reaction which ensues. Indeed, all our actions might have been automatic, and we can surmise that there are many organized beings in whose case an external stimulus causes a definite reaction without calling up consciousness as an intermediate agent. If pleasure and pain make their appearance in certain privileged beings, it is probably to call forth a resistance to the automatic reaction which would have taken place: either sensation has nothing to do, or it is nascent freedom. But how would it enable us to resist the reaction which is in preparation if it did not acquaint us with the nature of the latter by some definite sign? And what can this sign be except the sketching, and, as it were, the prefiguring of the future automatic movements in the very midst of the sensation which is being experienced? The affective state must then correspond not merely to the physical disturbances, movements or phenomena which have taken place, but also, and especially, to those which are in preparation, those which are getting ready to be.
It is certainly not obvious at first sight how this hypothesis simplifies the problem. For we are trying to find what there can be in common, from the point of view of magnitude, between a physical phenomenon and a state of consciousness, and we seem to have merely turned the difficulty round by making the present state of consciousness a sign of the future reaction, rather than a psychic translation of the past stimulus. But the difference between the two hypotheses is considerable. For the molecular disturbances which were mentioned just now are necessarily unconscious, since no trace of the movements themselves can be actually perceived in the sensation which translates them. But the automatic movements which tend to follow the stimulus as its natural outcome are likely to be conscious as movements: or else the sensation itself, whose function is to invite us to choose between this automatic reaction and other possible movements, would be of no avail. The intensity of affective sensations might thus be nothing more than our consciousness of the involuntary movements which are being begun and outlined, so to speak, within these states, and which would have gone on in their own way if nature had made us automata instead of conscious beings.
If such be the case, we shall not compare a pain
of increasing intensity to a note which grows
louder and louder, but rather to a
symphony, in which an increasing number
of instruments make themselves
heard. Within the characteristic sensation,
which gives the tone to all the others,
consciousness distinguishes a larger or smaller
number of sensations arising at different points
of the periphery, muscular contractions, organic
movements of every kind: the choir of these
elementary psychic states voices the new demands
of the organism, when confronted by a new situation.
In other words, we estimate the intensity
of a pain by the larger or smaller part of the
organism which takes interest in it. Richet
has observed that the slighter the pain, the more
precisely is it referred to a particular spot; if it
becomes more intense, it is referred to the whole
of the member affected. And he concludes by
saying that “the pain spreads in proportion as
it is more intense.” We should rather reverse
the sentence, and define the intensity of the pain
by the very number and extent of the parts of
the body which sympathize with it and react,
and whose reactions are perceived by consciousness.
To convince ourselves of this, it will be
enough to read the remarkable description of
disgust given by the same author: “If the stimulus
is slight there may be neither nausea nor
vomiting…. If the stimulus is stronger, instead
of being confined to the pneumo-gastric
nerve, it spreads and affects almost the whole
organic system. The face turns pale, the smooth
muscles of the skin contract, the skin is covered
with a cold perspiration, the heart stops beating:
in a word there is a general organic disturbance
following the stimulation of the medulla oblongata,
and this disturbance is the supreme expression
of disgust.” But is it nothing more than
its expression? In what will the general sensation
of disgust consist, if not in the sum of these
elementary sensations? And what can we understand
here by increasing intensity, if it is not
the constantly increasing number of sensations
which join in with the sensations already experienced?
Darwin has drawn a striking picture
of the reactions following a pain which becomes
more and more acute. “Great pain urges all
animals … to make the most violent and
diversified efforts to escape from the cause of
suffering…. With men the mouth may
be closely compressed, or more commonly the
lips are retracted with the teeth clenched or
ground together…. The eyes stare wildly
… or the brows are heavily contracted.
Perspiration bathes the body…. The circulation and respiration are much affected.” Now, is it not by this very contraction of the muscles affected that we measure the intensity of a pain? Analyse your idea of any suffering which you call extreme: do you not mean that it is unbearable, that is to say, that it urges the organism to a thousand different actions in order to escape from it? I can picture to myself a nerve transmitting a pain which is independent of all automatic reaction; and I can equally understand that stronger or weaker stimulations influence this nerve differently. But I do not see how these differences of sensation would be interpreted by our consciousness as differences of quantity unless we connected them with the reactions which usually accompany them, and which are more or less extended and more or less important. Without these subsequent reactions, the intensity of the pain would be a quality, and not a magnitude.
We have hardly any other means of comparing several pleasures with one another. What do we mean by a greater pleasure except a pleasure that is preferred? And what can our preference be, except a certain disposition of our organs, the effect of which is that, when two pleasures are offered simultaneously to our mind, our body inclines towards one of them? Analyse this inclination itself and you will find a great many little movements which begin and become perceptible in the organs concerned, and even in the rest of the body, as if the organism were coming forth to meet the pleasure as soon as it is pictured. When we define inclination as a movement, we are not using a metaphor. When confronted by several pleasures pictured by our mind, our body turns towards one of them spontaneously, as though by a reflex action. It rests with us to check it, but the attraction of the pleasure is nothing but this movement that is begun, and the very keenness of the pleasure, while we enjoy it, is merely the inertia of the organism, which is immersed in it and rejects every other sensation. Without this vis inertiae of which we become conscious by the very resistance which we offer to anything that might distract us, pleasure would be a state, but no longer a magnitude. In the moral as in the physical world, attraction serves to define movement rather than to produce it.
We have studied the affective sensations separately, but we must now notice that many representative sensations possess an affective character, and thus call forth a reaction on our part which we take into account in estimating their intensity. A considerable increase of light is represented for us by a characteristic sensation which is not yet pain, but which is analogous to dazzling. In proportion as the amplitude of sound-vibrations increases, our head and then our body seem to us to vibrate or to receive a shock. Certain representative sensations, those of taste, smell and temperature, have a fixed character of pleasantness or unpleasantness. Between flavours which are more or less bitter you will hardly distinguish anything but differences of quality; they are like different shades of one and the same colour. But these differences of quality are at once interpreted as differences of quantity, because of their affective character and the more or less pronounced movements of reaction, pleasure or repugnance, which they suggest to us. Besides, even when the sensation remains purely representative, its external cause cannot exceed a certain degree of strength or weakness without inciting us to movements which enable us to measure it. Sometimes indeed we have to make an effort to perceive this sensation, as if it were trying to escape notice; sometimes on the other hand it obsesses us, forces itself upon us and engrosses us to such an extent that we make every effort to escape from it and to remain ourselves. In the former case the sensation is said to be of slight intensity, and in the latter case very intense. Thus, in order to perceive a distant sound, to distinguish what we call a faint smell or a dim light, we strain all our faculties, we “pay attention.” And it is just because the smell and the light thus require to be reinforced by our efforts that they seem to us feeble. And, inversely, we recognize a sensation of extreme intensity by the irresistible reflex movements to which it incites us, or by the powerlessness with which it affects us. When a cannon is fired off close to our ears or a dazzling light suddenly flares up, we lose for an instant the consciousness of our personality; this state may even last some time in the case of a very nervous subject. It must be added that, even within the range of the so-called medium intensities, when we are dealing on even terms with a representative sensation, we often estimate its importance by comparing it with another which it drives away, or by taking account of the persistence with which it returns. Thus the ticking of a watch seems louder at night because it easily monopolizes a consciousness almost empty of sensations and ideas. Foreigners talking to one another in a language which we do not understand seem to us to speak very loudly, because their words no longer call up any ideas in our mind, and thus break in upon a kind of intellectual silence and monopolize our attention like the ticking of a watch at night. With these so-called medium sensations, however, we approach a series of psychic states, the intensity of which is likely to possess a new meaning. For, in most cases, the organism hardly reacts at all, at least in a way that can be perceived; and yet we still make a magnitude out of the pitch of a sound, the intensity of a light, the saturation of a colour. Doubtless, a closer observation of what takes place in the whole of the organism when we hear such and such a note or perceive such and such a colour has more than one surprise in store for us. Has not C. Féré shown that every sensation is accompanied by an increase in muscular force which can be measured by the dynamometer? But of an increase of this kind there is hardly any consciousness at all, and if we reflect on the precision with which we distinguish sounds and colours, nay, even weights and temperatures, we shall easily guess that some new element must come into play in our estimate of them.
Now, the nature of this element is easy to determine. For, in proportion as a sensation loses its affective character and becomes representative, the reactions which it called forth on our part tend to disappear, but at the same time we perceive the external object which is its cause, or if we do not now perceive it, we have perceived it, and we think of it. Now, this cause is extensive and therefore measurable: a constant experience, which began with the first glimmerings of consciousness and which continues throughout the whole of our life, shows us a definite shade of sensation corresponding to a definite amount of stimulation. We thus associate the idea of a certain quantity of cause with a certain quality of effect; and finally, as happens in the case of every acquired perception, we transfer the idea into the sensation, the quantity of the cause into the quality of the effect. At this very moment the intensity, which was nothing but a certain shade or quality of the sensation, becomes a magnitude. We shall easily understand this process if, for example, we hold a pin in our right hand and prick our left hand more and more deeply. At first we shall feel as it were a tickling, then a touch which is succeeded by a prick, then a pain localized at a point, and finally the spreading of this pain over the surrounding zone. And the more we reflect on it, the more clearly shall we see that we are here dealing with so many qualitatively distinct sensations, so many varieties of a single species. But yet we spoke at first of one and the same sensation which spread further and further, of one prick which increased in intensity. The reason is that, without noticing it, we localized in the sensation of the left hand, which is pricked, the progressive effort of the right hand, which pricks. We thus introduced the cause into the effect, and unconsciously interpreted quality as quantity, intensity as magnitude. Now, it is easy to see that the intensity of every representative sensation ought to be understood in the same way.
The sensations of sound display well marked degrees of intensity. We have already spoken of the necessity of taking into account the affective character of these sensations, the shock received by the whole of the organism. We have shown that a very intense sound is one which engrosses our attention, which supplants all the others. But take away the shock, the well-marked vibration, which you sometimes feel in your head or even throughout your body: take away the clash which takes place between sounds heard simultaneously: what will be left except an indefinable quality of the sound which is heard? But this quality is immediately interpreted as quantity because you have obtained it yourself a thousand times, e.g. by striking some object and thus expending a definite quantity of effort. You know, too, how far you would have to raise your voice to produce a similar sound, and the idea of this effort immediately comes into your mind when you transform the intensity of the sound into a magnitude. Wundt has drawn attention to the quite special connexions of vocal and auditory nervous filaments which are met with in the human brain. And has it not been said that to hear is to speak to oneself? Some neuropaths cannot be present at a conversation without moving their lips; this is only an exaggeration of what takes place in the case of every one of us. How will the expressive or rather suggestive power of music be explained, if not by admitting that we repeat to ourselves the sounds heard, so as to carry ourselves back into the psychic state out of which they emerged, an original state, which nothing will express, but which something may suggest, viz., the very motion and attitude which the sound imparts to our body?
Thus, when we speak of the intensity of a sound of medium force as a magnitude, we allude principally to the greater or less effort which we should have ourselves to expend in order to summon, by our own effort, the same auditory sensation.
Now, besides the intensity, we distinguish another characteristic property of the sound, its pitch. Are the differences in pitch, such as our ear perceives, quantitative differences? I grant that a sharper sound calls up the picture of a higher position in space. But does it follow from this that the notes of the scale, as auditory sensations, differ otherwise than in quality? Forget what you have learnt from physics, examine carefully your idea of a higher or lower note, and see whether you do not think simply of the greater or less effort which the tensor muscle of your vocal chords has to make in order to produce the note? As the effort by which your voice passes from one note to another is discontinuous, you picture to yourself these successive notes as points in space, to be reached by a series of sudden jumps, in each of which you cross an empty separating interval: this is why you establish intervals between the notes of the scale. Now, why is the line along which we dispose them vertical rather than horizontal, and why do we say that the sound ascends in some cases and descends in others? It must be remembered that the high notes seem to us to produce some sort of resonance in the head and the deep notes in the thorax: this perception, whether real or illusory, has undoubtedly had some effect in making us reckon the intervals vertically. But we must also notice that the greater the tension of the vocal chords in the chest voice, the greater is the surface of the body affected, if the singer is inexperienced; this is just the reason why the effort is felt by him as more intense. And as he breathes out the air upwards, he will attribute the same direction to the sound produced by the current of air; hence the sympathy of a larger part of the body with the vocal muscles will be represented by a movement upwards. We shall thus say that the note is higher because the body makes an effort as though to reach an object which is more elevated in space. In this way it became customary to assign a certain height to each note of the scale, and as soon as the physicist was able to define it by the number of vibrations in a given time to which it corresponds, we no longer hesitated to declare that our ear perceived differences of quantity directly. But the sound would remain a pure quality if we did not bring in the muscular effort which produces it or the vibrations which explain it.
The experiments of Blix, Goldscheider and Donaldson have shown that the points on the surface of the body which feel cold are not the same as those which feel heat. Physiology is thus disposed to set up a distinction of nature, and not merely of degree, between the sensations of heat and cold. But psychological observation goes further, for close attention can easily discover specific differences between the different sensations of heat, as also between the sensations of cold. A more intense heat is really another kind of heat. We call it more intense because we have experienced this same change a thousand times when we approached nearer and nearer a source of heat, or when a growing surface of our body was affected by it. Besides, the sensations of heat and cold very quickly become affective and incite us to more or less marked reactions by which we measure their external cause: hence, we are inclined to set up similar quantitative differences among the sensations which correspond to lower intensities of the cause. But I shall not insist any further; every one must question himself carefully on this point, after making a clean sweep of everything which his past experience has taught him about the cause of his sensations and coming face to face with the sensations themselves. The result of this examination is likely to be as follows: it will be perceived that the magnitude of a representative sensation depends on the cause having been put into the effect, while the intensity of the affective element depends on the more or less important reactions which prolong the external stimulations and find their way into the sensation itself.
The same thing will be experienced in the case of pressure and even weight. When you say that a pressure on your hand becomes stronger, see whether you do not mean that there first was a contact, then a pressure, afterwards a pain, and that this pain itself, after having gone through a series of qualitative changes, has spread further and further over the surrounding region. Look again and see whether you do not bring in the more and more intense, i.e. more and more extended, effort of resistance which you oppose to the external pressure. When the psychophysicist lifts a heavier weight, he experiences, he says, an increase of sensation. Examine whether this increase of sensation ought not rather to be called a sensation of increase. The whole question is centred in this, for in the first case the sensation would be a quantity like its external cause, whilst in the second it would be a quality which had become representative of the magnitude of its cause. The distinction between the heavy and the light may seem to be as old-fashioned and as childish as that between the hot and the cold. But the very childishness of this distinction makes it a psychological reality. And not only do the heavy and the light impress our consciousness as generically different, but the various degrees of lightness and heaviness are so many species of these two genera. It must be added that the difference of quality is here translated spontaneously into a difference of quantity, because of the more or less extended effort which our body makes in order to lift a given weight. Of this you will soon become aware if you are asked to lift a basket which, you are told, is full of scrap-iron, whilst in fact there is nothing in it. You will think you are losing your balance when you catch hold of it, as though distant muscles had interested themselves beforehand in the operation and experienced a sudden disappointment. It is chiefly by the number and nature of these sympathetic efforts, which take place at different points of the organism, that you measure the sensation of weight at a given point; and this sensation would be nothing more than a quality if you did not thus introduce into it the idea of a magnitude. What strengthens the illusion on this point is that we have become accustomed to believe in the immediate perception of a homogeneous movement in a homogeneous space. When I lift a light weight with my arm, all the rest of my body remaining motionless, I experience a series of muscular sensations each of which has its “local sign,” its peculiar shade: it is this series which my consciousness interprets as a continuous movement in space. If I afterwards lift a heavier weight to the same height with the same speed, I pass through a new series of muscular sensations, each of which differs from the corresponding term of the preceding series. Of this I could easily convince myself by examining them closely. But as I interpret this new series also as a continuous movement, and as this movement has the same direction, the same duration and the same velocity as the preceding, my consciousness feels itself bound to localize the difference between the second series of sensations and the first elsewhere than in the movement itself. It thus materializes this difference at the extremity of the arm which moves; it persuades itself that the sensation of movement has been identical in both cases, while the sensation of weight differed in magnitude. But movement and weight are but distinctions of the reflective consciousness: what is present to consciousness immediately is the sensation of, so to speak, a heavy movement, and this sensation itself can be resolved by analysis into a series of muscular sensations, each of which represents by its shade its place of origin and by its colour the magnitude of the weight lifted.
Shall we call the intensity of light a quantity, or shall we treat it as a quality? It has not perhaps been sufficiently noticed what a large number of different factors co-operate in daily life in giving us information about the nature of the luminous source. We know from long experience that, when we have a difficulty in distinguishing the outlines and details of objects, the light is at a distance or on the point of going out. Experience has taught us that the affective sensation or nascent dazzling that we experience in certain cases must be attributed to a higher intensity of the cause. Any increase or diminution in the number of luminous sources alters the way in which the sharp lines of bodies stand out and also the shadows which they project. Still more important are the changes of hue which coloured surfaces, and even the pure colours of the spectrum, undergo under the influence of a brighter or dimmer light. As the luminous source is brought nearer, violet takes a bluish tinge, green tends to become a whitish yellow, and red a brilliant yellow. Inversely, when the light is moved away, ultramarine passes into violet and yellow into green; finally, red, green and violet tend to become a whitish yellow. Physicists have remarked these changes of hue for some time; but what is still more remarkable is that the majority of men do not perceive them, unless they pay attention to them or are warned of them. Having made up our mind, once for all, to interpret changes of quality as changes of quantity, we begin by asserting that every object has its own peculiar colour, definite and invariable. And when the hue of objects tends to become yellow or blue, instead of saying that we see their colour change under the influence of an increase or diminution of light, we assert that the colour remains the same but that our sensation of luminous intensity increases or diminishes. We thus substitute once more, for the qualitative impression received by our consciousness, the quantitative interpretation given by our understanding. Helmholtz has described a case of interpretation of the same kind, but still more complicated: “If we form white with two colours of the spectrum, and if we increase or diminish the intensities of the two coloured lights in the same ratio, so that the proportions of the combination remain the same, the resultant colour remains the same although the relative intensity of the sensations undergoes a marked change…. This depends on the fact that the light of the sun, which we consider as the normal white light during the day, itself undergoes similar modifications of shade when the luminous intensity varies.”
But yet, if we often judge of variations in the luminous source by the relative changes of hue of the objects which surround us, this is no longer the case in simple instances where a single object, e.g. a white surface, passes successively through different degrees of luminosity. We are bound to insist particularly on this last point. For the physicist speaks of degrees of luminous intensity as of real quantities: and, in fact, he measures them by the photometer. The psychophysicist goes still further: he maintains that our eye itself estimates the intensities of light. Experiments have been attempted, at first by Delbœuf, and afterwards by Lehmann and Neiglick, with the view of constructing a psychophysical formula from the direct measurement of our luminous sensations. Of these experiments we shall not dispute the result, nor shall we deny the value of photometric processes; but we must see how we have to interpret them.
Look closely at a sheet of paper lighted e.g. by four candles, and put out in succession one, two, Photometric three of them. You say that the surface remains white and that its brightness diminishes. But you are aware that one candle has just been put out; or, if you do not know it, you have often observed a similar change in the appearance of a white surface when the illumination was diminished. Put aside what you remember of your past experiences and what you are accustomed to say of the present ones; you will find that what you really perceive is not a diminished illumination of the white surface, it is a layer of shadow passing over this surface at the moment the candle is extinguished. This shadow is a reality to your consciousness, like the light itself. If you call the first surface in all its brilliancy white, you will have to give another name to what you now see, for it is a different thing: it is, if we may say so, a new shade of white. We have grown accustomed, through the combined influence of our past experience and of physical theories, to regard black as the absence, or at least as the minimum, of luminous sensation, and the successive shades of grey as decreasing intensities of white light. But, in point of fact, black has just as much reality for our consciousness as white, and the decreasing intensities of white light illuminating a given surface would appear to an unprejudiced consciousness as so many different shades, not unlike the various colours of the spectrum. This is the reason why the change in the sensation is not continuous, as it is in the external cause, and why the light can increase or decrease for a certain period without producing any apparent change in the illumination of our white surface: the illumination will not appear to change until the increase or decrease of the external light is sufficient to produce a new quality. The variations in brightness of a given colour—the affective sensations of which we have spoken above being left aside—would thus be nothing but qualitative changes, were it not our custom to transfer the cause to the effect and to replace our immediate impressions by what we learn from experience and science. The same thing might be said of degrees of saturation. Indeed, if the different intensities of a colour correspond to so many different shades existing between this colour and black, the degrees of saturation are like shades intermediate between this same colour and pure white. Every colour, we might say, can be regarded under two aspects, from the point of view of black and from the point of view of white. And black is then to intensity what white is to saturation.
The meaning of the photometric experiments will now be understood. A candle placed at a certain distance from a sheet of paper illuminates it in a certain way: you double the distance and find that four candles are required to produce the same effects, sensation. From this you conclude that if you had doubled the distance without increasing the intensity of the luminous source, the resultant illumination would have been only one-fourth as bright. But it is quite obvious that you are here dealing with the physical and not the psychological effect. For it cannot be said that you have compared two sensations with one another: you have made use of a single sensation in order to compare two different luminous sources with each other, the second four times as strong as the first but twice as far off. In a word, the physicist never brings in sensations which are twice or three times as great as others, but only identical sensations, destined to serve as intermediaries between two physical quantities which can then be equated with one another. The sensation of light here plays the part of the auxiliary unknown quantity which the mathematician introduces into his calculations, and which is not intended to appear in the final result.
But the object of the psychophysicist is entirely different: it is the sensation of light itself which he studies, and claims to measure. Sometimes he will proceed to integrate infinitely small differences, after the method of Fechner; sometimes he will compare one sensation directly with another. The latter method, due to Plateau and Delbœuf, differs far less than has hitherto been believed from Fechner’s: but, as it bears more especially on the luminous sensations, we shall deal with it first. Delbœuf places an observer in front of three concentric rings which vary in brightness. By an ingenious arrangement he can cause each of these rings to pass through all the shades intermediate between white and black. Let us suppose that two hues of grey are simultaneously produced on two of the rings and kept unchanged; let us call them A and B. Delbœuf alters the brightness, C, of the third ring, and asks the observer to tell him whether, at a certain moment, the grey, B, appears to him equally distant from the other two. A moment comes, in fact, when the observer states that the contrast A Β is equal to the contrast Β C, so that, according to Delbœuf, a scale of luminous intensities could be constructed on which we might pass from each sensation to the following one by equal sensible contrasts: our sensations would thus be measured by one another. I shall not follow Delbœuf into the conclusions which he has drawn from these remarkable experiments: the essential question, the only question, as it seems to me, is whether a contrast A B, formed of the elements A and B, is really equal to a contrast Β C, which is differently composed. As soon as it is proved that two sensations can be equal without being identical, psychophysics will be established. But it is this equality which seems to me open to question: it is easy to explain, in fact, how a sensation of luminous intensity can be said to be at an equal distance from two others.
Let us assume for a moment that from our birth onwards the growing intensity of a luminous source had always called up in our consciousness, one after the other, the different colours of the spectrum. There is no doubt that these colours would then appear to us as so many notes of a gamut, as higher or lower degrees in a scale, in a word, as magnitudes. Moreover it would be easy for us to assign each of them its place in the series. For although the extensive cause varies continuously, the changes in the sensation of colour are discontinuous, passing from one shade to another shade. However numerous, then, may be the shades intermediate between the two colours, A and B, it will always be possible to count them in thought, at least roughly, and ascertain whether this number is almost equal to that of the shades which separate Β from another colour C. In the latter case it will be said that Β is equally distant from A and C, that the contrast is the same on one side as on the other. But this will always be merely a convenient interpretation: for although the number of intermediate shades may be equal on both sides, although we may pass from one to the other by sudden leaps, we do not know whether these leaps are magnitudes, still less whether they are equal magnitudes: above all it would be necessary to show that the intermediaries which have helped us throughout our measurement could be found again inside the object which we have measured. If not, it is only by a metaphor that a sensation can be said to be an equal distance from two others.
Now, if the views which we have before enumerated with regard to luminous intensities are accepted, it will be recognized that the different hues of grey which Delbœuf displays to us are strictly analogous, for our consciousness, to colours, and that if we declare that a grey tint is equidistant from two other grey tints, it is in the same sense in which it might be said that orange, for example, is at an equal distance from green and red. But there is this difference, that in all our past experience the succession of grey tints has been produced in connexion with a progressive increase or decrease in illumination. Hence we do for the differences of brightness what we do not think of doing for the differences of colour: we promote the changes of quality into variations of magnitude. Indeed, there is no difficulty here about the measuring, because the successive shades of grey produced by a continuous decrease of illumination are discontinuous, as being qualities, and because we can count approximately the principal intermediate shades which separate any two kinds of grey. The contrast A Β will thus be declared equal to the contrast Β C when our imagination, aided by our memory, inserts between A and Β the same number of intermediate shades as between Β and C. It is needless to say that this will necessarily be a very rough estimate. We may anticipate that it will vary considerably with different persons. Above all it is to be expected that the person will show more hesitation and that the estimates of different persons will differ more widely in proportion as the difference in brightness between the rings A and Β is increased, for a more and more laborious effort will be required to estimate the number of intermediate hues. This is exactly what happens, as we shall easily perceive by glancing at the two tables drawn up by Delbœuf. In proportion as he increases the difference in brightness between the exterior ring and the middle ring, the difference between the numbers on which one and the same observer or different observers successively fix increases almost continuously from 3 degrees to 94, from 5 to 73, from 10 to 25, from 7 to 40. But let us leave these divergences on one side: let us assume that the observers are always consistent and always agree with one another; will it then be established that the contrasts A Β and Β C are equal? It would first be necessary to prove that two successive elementary contrasts are equal quantities, whilst, in fact, we only know that they are successive. It would then be necessary to prove that inside a given tint of grey we perceive the less intense shades which our imagination has run through in order to estimate the objective intensity of the source of light. In a word, Delbœuf’s psychophysics assumes a theoretical postulate of the greatest importance, which is disguised under the cloak of an experimental result, and which we should formulate as follows: “When the objective quantity of light is continuously increased, the differences between the hues of grey successively obtained, each of which represents the smallest perceptible increase of physical stimulation, are quantities equal to one another. And besides, any one of the sensations obtained can be equated with the sum of the differences which separate from one another all previous sensations, going from zero upwards.” Now, this is just the postulate of Fechner’s psychophysics, which we are going to examine.
Fechner took as his starting-point a law discovered by Weber, according to which, given a certain stimulus which calls forth a certain sensation, the amount by which the stimulus must be increased for consciousness to become aware of any change bears a fixed relation to the original stimulus. Thus, if we denote by Ε the stimulus which corresponds to the sensation S, and by ΔΕ the amount by which the original stimulus must be increased in order that a sensation of difference may be produced, we shall have ΔΕ/E = const. This formula has been much modified by the disciples of Fechner, and we prefer to take no part in the discussion; it is for experiment to decide between the relation established by Weber and its substitutes. Nor shall we raise any difficulty about granting the probable existence of a law of this nature. It is here really a question not of measuring a sensation but only of determining the exact moment at which an increase of stimulus produces a change in it. Now, if a definite amount of stimulus produces a definite shade of sensation, it is obvious that the minimum amount of stimulus required to produce a change in this shade is also definite; and since it is not constant, it must be a function of the original stimulus. But how are we to pass from a relation between the stimulus and its minimum increase to an equation which connects the “amount of sensation” with the corresponding stimulus? The whole of psychophysics is involved in this transition, which is therefore worthy of our closest consideration.
We shall distinguish several different artifices in the process of transition from Weber’s experiments, or from any other series of similar observations, to a psychophysical law like Fechner’s. It is first of all agreed to consider our consciousness of an increase of stimulus as an increase of the sensation S: this is therefore called S. It is then asserted that all the sensations ΔS, which correspond to the smallest perceptible increase of stimulus, are equal to one another. They are therefore treated as quantities, and while, on the one hand, these quantities are supposed to be always equal, and, on the other, experiment has given a certain relation ΔΕ = ⨍(E) between the stimulus Ε and its minimum increase, the constancy of ΔS is expressed by writing ΔS = C ΔE/⨍(E), C being a constant quantity. Finally it is agreed to replace the very small differences ΔS and ΔΕ by the infinitely small differences dS and dE, whence an equation which is, this time, a differential one: dS = C dE/⨍(E). We shall now simply have to integrate on both sides to obtain the desired relation: S=C ⨍Eo dE/⨍(E). And the transition will thus be made from a proved law, which only concerned the occurrence of a sensation, to an unprovable law which gives its measure.
Without entering upon any thorough discussion of this ingenious operation, let us show in a few words how Fechner has grasped the real difficulty of the problem, how he has tried to overcome it, and where, as it seems to us, the flaw in his reasoning lies.
Fechner realized that measurement could not be introduced into psychology without first defining what is meant by the equality and addition of two simple states, e.g. two sensations. But, unless they are identical, we do not at first see how two sensations can be equal. Undoubtedly in the physical world equality is not synonymous with identity. But the reason is that every phenomenon, every object, is there presented under two aspects, the one qualitative and the other extensive: nothing prevents us from putting the first one aside, and then there remains nothing but terms which can be directly or indirectly superposed on one another and consequently seen to be identical. Now, this qualitative element, which we begin by eliminating from external objects in order to measure them, is the very thing which psychophysics retains and claims to measure. And it is no use trying to measure this quality Q by some physical quantity Q’ which lies beneath it: for it would be necessary to have previously shown that Q is a function of Q’, and this would not be possible unless the quality Q had first been measured with some fraction of itself. Thus nothing prevents us from measuring the sensation of heat by the degree of temperature; but this is only a convention, and the whole point of psychophysics lies in rejecting this convention and seeking how the sensation of heat varies when you change the temperature. In a word, it seems, on the one hand, that two different sensations cannot be said to be equal unless some identical residuum remains after the elimination of their qualitative difference; but, on the other hand, this qualitative difference being all that we perceive, it does not appear what could remain once it was eliminated.
The novel feature in Fechner’s treatment is that he did not consider this difficulty insurmountable. Taking advantage of the fact that sensation varies by sudden jumps while the stimulus increases continuously, he did not hesitate to call these differences of sensation by the same name: they are all, he says, minimum differences, since each corresponds to the smallest perceptible increase in the external stimulus. Therefore you can set aside the specific shade or quality of these successive differences; a common residuum will remain in virtue of which they will be seen to be in a manner identical: they all have the common character of being minima. Such will be the definition of equality which we were seeking. Now, the definition of addition will follow naturally. For if we treat as a quantity the difference perceived by consciousness between two sensations which succeed one another in the course of a continuous increase of stimulus, if we call the first sensation S, and the second S + ΔS, we shall have to consider every sensation S as a sum, obtained by the addition of the minimum differences through which we pass before reaching it. The only remaining step will then be to utilize this twofold definition in order to establish, first of all, a relation between the differences ΔS and ΔΕ, and then, through the substitution of the differentials, between the two variables. True, the mathematicians may here lodge a protest against the substitution of differential for difference; the psychologists may ask, too, whether the quantity ΔS, instead of being constant, does not vary as the sensation S itself; finally, taking the psychophysical law for granted, we may all debate about its real meaning. But, by the mere fact that ΔS is regarded as a quantity and S as a sum, the fundamental postulate of the whole process is accepted.
Now it is just this postulate which seems to us open to question, even if it can be understood. Assume that I experience a sensation S, and that, increasing the stimulus continuously, I perceive this increase after a certain time. I am now notified of the increase of the cause: but why should I call this notification an arithmetical difference? No doubt the notification consists in the fact that the original state S has changed: it has become S’; but the transition from S to S’ could only be called an arithmetical difference if I were conscious, so to speak, of an interval between S and S’, and if my sensation were felt to rise from S to S’ by the addition of something. By giving this transition a name, by calling it ΔS, you make it first a reality and then a quantity. Now, not only are you unable to explain in what sense this transition is a quantity, but reflection will show you that it is not even a reality; the only realities are the states S and S’ through which I pass. No doubt, if S and S’ were numbers, I could assert the reality of the difference S’—S even though S and S’ alone were given; the reason is that the number S’—S, which is a certain sum of units, will then represent just the successive moments of the addition by which we pass from S to S’. But if S and S’ are simple states, in what will the interval which separates them consist? And what, then, can the transition from the first state to the second be, if not a mere act of your thought, which, arbitrarily and for the sake of the argument, assimilates a succession of two states to a differentiation of two magnitudes?
Either you keep to what consciousness presents to you or you have recourse to a conventional mode of representation. In the first case you will find a difference between S and S’ like that between the shades sense. Of rainbow, and not at all an interval of magnitude. In the second case you may introduce the symbol ΔS if you like, but it is only in a conventional sense that you will speak here of an arithmetical difference, and in a conventional sense, also, that you will assimilate a sensation to a sum. The most acute of Fechner’s critics, Jules Tannery, has made the latter point perfectly clear. “It will be said, for example, that a sensation of 50 degrees is expressed by the number of differential sensations which would succeed one another from the point where sensation is absent up to the sensation of 50 degrees…. I do not see that this is anything but a definition, which is as legitimate as it is arbitrary.”
We do not believe, in spite of all that has been said, that the method of mean gradations has set psychophysics on a new path. The novel feature in Delbœuf’s investigation was that he chose a particular case, in which consciousness seemed to decide in Fechner’s favour, and in which common sense itself played the part of the psychophysicist. He inquired whether certain sensations did not appear to us immediately as equal although different, and whether it would not be possible to draw up, by their help, a table of sensations which were double, triple or quadruple those which preceded them. The mistake which Fechner made, as we have just seen, was that he believed in an interval between two successive sensations S and S’, when there is simply a passing from one to the other and not a difference in the arithmetical sense of the word. But if the two terms between which the passing takes place could be given simultaneously, there would then be a contrast besides the transition; and although the contrast is not yet an arithmetical difference, it resembles it in a certain respect; for the two terms which are compared stand here side by side as in a case of subtraction of two numbers. Suppose now that these sensations belong to the same genus and that in our past experience we have constantly been present at their march past, so to speak, while the physical stimulus increased continuously: it is extremely probable that we shall thrust the cause into the effect, and that the idea of contrast will thus melt into that of arithmetical difference. As we shall have noticed, moreover, that the sensation changed abruptly while the stimulus rose continuously, we shall no doubt estimate the distance between two given sensations by a rough guess at the number of these sudden jumps, or at least of the intermediate sensations which usually serve us as landmarks. To sum up, the contrast will appear to us as a difference, the stimulus as a quantity, the sudden jump as an element of equality: combining these three factors, we shall reach the idea of equal quantitative differences. Now, these conditions are nowhere so well realized as when surfaces of the same colour, more or less illuminated, are simultaneously presented to us. Not only is there here a contrast between similar sensations, but these sensations correspond to a cause whose influence has always been felt by us to be closely connected with its distance; and, as this distance can vary continuously, we cannot have escaped noticing in our past experience a vast number of shades of sensation which succeeded one another along with the continuous increase in the cause. We are therefore able to say that the contrast between one shade of grey and another, for example, seems to us almost equal to the contrast between the latter and a third one; and if we define two equal sensations by saying that they are sensations which a more or less confused process of reasoning interprets as such, we shall in fact reach a law like that proposed by Delbœuf. But it must not be forgotten that consciousness has here passed through the same intermediate steps as the psychophysicist, and that its judgment is worth here just what psychophysics is worth; it is a symbolical interpretation of quality as quantity, a more or less rough estimate of the number of sensations which can come in between two given sensations. The difference is thus not as great as is believed between the method of least noticeable differences and that of mean gradations, between the psychophysics of Fechner and that of Delbœuf. The first led to a conventional measurement of sensation; the second appeals to common sense in the particular cases where common sense adopts a similar convention. In a word, all psychophysics is condemned by its origin to revolve in a vicious circle, for the theoretical postulate on which it rests condemns it to experimental verification, and it cannot be experimentally verified unless its postulate is first granted. The fact is that there is no point of contact between the unextended and the extended, between quality and quantity. We can interpret the one by the other, set up the one as the equivalent of the other; but sooner or later, at the beginning or at the end, we shall have to recognize the conventional character of this assimilation.
In truth, psychophysics merely formulates with precision and pushes to its extreme consequences a conception familiar to common sense. As speech dominates over thought, as external objects, which are common to us all, are more important to us than the subjective states through which each of us passes, we have everything to gain by objectifying these states, by introducing into them, to the largest possible extent, the representation of their external cause. And the more our knowledge increases, the more we perceive the extensive behind the intensive, quantity behind quality, the more also we tend to thrust the former into the latter, and to treat our sensations as magnitudes. Physics, whose particular function it is to calculate the external cause of our internal states, takes the least possible interest in these states themselves: constantly and deliberately it confuses them with their cause. It thus encourages and even exaggerates the mistake which common sense makes on the point. The moment was inevitably bound to come at which science, familiarized with this confusion between quality and quantity, between sensation and stimulus, should seek to measure the one as it measures the other: such was the object of psychophysics. In this bold attempt Fechner was encouraged by his adversaries themselves, by the philosophers who speak of intensive magnitudes while declaring that psychic states cannot be submitted to measurement. For if we grant that one sensation can be stronger than another, and that this inequality is inherent in the sensations themselves, independently of all association of ideas, of all more or less conscious consideration of number and space, it is natural to ask by how much the first sensation exceeds the second, and to set up a quantitative relation between their intensities. Nor is it any use to reply, as the opponents of psychophysics sometimes do, that all measurement implies superposition, and that there is no occasion to seek for a numerical relation between intensities, which are not superposable objects. For it will then be necessary to explain why one sensation is said to be more intense than another, and how the conceptions of greater and smaller can be applied to things which, it has just been acknowledged, do not admit among themselves of the relations of container to contained. If, in order to cut short any question of this kind, we distinguish two kinds of quantity, the one intensive, which admits only of a “more or less,” the other extensive, which lends itself to measurement, we are not far from siding with Fechner and the psychophysicists. For, as soon as a thing is acknowledged to be capable of increase and decrease, it seems natural to ask by how much it decreases or by how much it increases. And, because a measurement of this kind does not appear to be possible directly, it does not follow that science cannot successfully accomplish it by some indirect process, either by an integration of infinitely small elements, as Fechner proposes, or by any other roundabout way. Either, then, sensation is pure quality, or, if it is a magnitude, we ought to try to measure it.
To sum up what precedes, we have found the notion of intensity to present itself under a double aspect, according as we study the states of consciousness which represent an external cause, or those which are self-sufficient. In the former case the perception of intensity consists in a certain estimate of the magnitude of the cause means of a certain quality in the effect: it is, as the Scottish philosophers would have said, an acquired perception. In the second case, we give the name of intensity to the larger or smaller number of simple psychic phenomena which we conjecture to be involved in the fundamental state: it is no longer an acquired perception, but a confused perception. In fact, these two meanings of the word usually intermingle, because the simpler phenomena involved in an emotion or an effort are generally representative, and because the majority of representative states, being at the same time affective, themselves include a multiplicity of elementary psychic phenomena. The idea of intensity is thus situated at the junction of two streams, one of which brings us the idea of extensive magnitude from without, while the other brings us from within, in fact from the very depths of consciousness, the image of an inner multiplicity. Now, the point is to determine in what the latter image consists, whether it is the same as that of number, or whether it is quite different from it. In the following chapter we shall no longer consider states of consciousness in isolation from one another, but in their concrete multiplicity, in so far as they unfold themselves in pure duration. And, in the same way as we have asked what would be the intensity of a representative sensation if we did not introduce into it the idea of its cause, we shall now have to inquire what the multiplicity of our inner states becomes, what form duration assumes, when the space in which it unfolds is eliminated. This second question is even more important than the first. For, if the confusion of quality with quantity were confined to each of the phenomena of consciousness taken separately, it would give rise to obscurities, as we have just seen, rather than to problems. But by invading the series of our psychic states, by introducing space into our perception of duration, it corrupts at its very source our feeling of outer and inner change, of movement, and of freedom. Hence the paradoxes of the Eleatics, hence the problem of free will. We shall insist rather on the second point; but instead of seeking to solve the question, we shall show the mistake of those who ask it.
Footnotes – Chapter I
 Essays, (Library Edition, 1891), Vol. ii, p. 381.
 The Senses and the Intellect,4th ed., (1894), p. 79.
 Grundzüge der Physiologischen Psychologie,2nd ed. (1880), Vol. i, p. 375.
 W. James, Le sentiment de l’effort (Critique philosophique, 1880, Vol. ii,) cf. Principles of Psychology, (1891), Vol. ii, chap, xxvi.
 Functions of the Brain, 2nd ed. (1886), p. 386.
 Handbuch der Physiologischen Optik, 1st ed. (1867), pp. 600-601.
 Le mécanisme de l’attention. Alcan, 1888.
 The Expression of the Emotions, 1st ed., (1872), p. 74.
 “What is an Emotion?” Mind,1884, p. 189.
 Principles of Psychology, 3rd. ed., (1890), Vol. i, p. 482.
 The Expression of the Emotions, 1st ed., p. 78.
 L’homme et l’intelligence, p. 36.
 Ibid. p. 37.
 Ibid. p. 43.
 The Expression of the Emotions, 1st ed., pp. 72, 69, 70.
 C. Féré, Sensation et Mouvement. Paris, 1887.
 Grundzüge der Physiologischen Psychologie, 2nd ed., (1880), Vol. ii, p. 437.
 “On the Temperature Sense,” Mind, 1885.
 Rood, Modern Chromatics,(1879), pp. 181-187.
 Handbuch der Physiologischen Optik, 1st ed. (1867), pp. 318-319.
 Éléments de psychophysique. Paris, 1883.
 See the account given of these experiments in the Revue philosophique, 1887, Vol. i, p. 71, and Vol. ii, p. 180.
 Éléments de psychophysique, pp. 61, 69.
 In the particular case where we admit without restriction Weber’s Law ΔE/E=const., integration gives S=C log. E/Q. Q being a constant. This is Fechner’s “logarithmic law.”
 Latterly it has been assumed that ΔS is proportional to S.
 Revue scientifique, March 13 and April 24, 1875.