Chapter I Said a Good Deal on This Subject; but We Must Now See a

little more closely just what happens in this instance of it. The content of the joint-feeling, to begin with, is an object, and is in itself a place. For it to be placed, say in the elbow, the elbow as seen or handled must already have become another object for the mind, and with its place as thus known, the place which the joint-feeling fills must coalesce. That the latter should be felt 'in the elbow' is therefore a 'projection' of it into the place of another object as much as its being felt in the finger-tip or at the end of a cane can be. But when we say 'projection' we generally have in our mind the notion of a there as contrasted with a here. What is the here when we say that the joint-feeling is there? The 'here' seems to be the spot which the mind has chosen for its own post of observation, usually some place within the head, but sometimes within the throat or breast--not a rigorously fixed spot, but a region from any portion of which it may send forth its various acts of attention. Extradition from either of these regions is the common law under which we perceive the whereabouts of the north star, of our own voice, of the contact of our teeth with each other, of the tip of our finger, of the point of our cane on the ground, or of a movement in our elbow-joint.

But for the distance between the 'here' and the 'there' to be felt, the entire intervening space must be itself an object of perception. The consciousness of this intervening space is the sine quâ non of the joint-feeling's projection to the farther end of it. When it is filled by our own bodily tissues (as where the projection only goes as far as the elbow or finger-tip) we are sensible of its extent alike by our eye, by our exploring movements, and by the resident sensations which fill its length. When it reaches beyond the limits of our body, the resident sensations are lacking, but limbs and hand and eye suffice to make it known. Let me, for example, locate a feeling of motion coming from my elbow-joint in the point of my cane a yard beyond my hand. Either I see this yard as I flourish the cane, and the seen end of it then absorbs my sensation just as my seen elbow might absorb it, or I am blind and imagine the cane as an object continuing my arm, either because I have explored both arm and cane with the other hand, or because I have pressed them both along my body and leg. If I project my joint-feeling farther still, it is by a conception rather than a distinct imagination of the space. I think: 'farther,' 'thrice as far,' etc.; and thus get a symbolic image of a distant path at which I point. But the 'absorption' of the joint-feeling by the distant spot, in whatever terms the latter may be apprehended, is never anything but that coalescence into one 'thing' already spoken of on page 184, of whatever different sensible objects interest our attention at once.

2. Feelings of Muscular Contraction.

Readers versed in psychological literature will have missed, in our account thus far, the usual invocation of 'the muscular sense.' This word is used with extreme vagueness to cover all resident sensations, whether of motion or position, in our members, and even to designate the supposed feeling of efferent discharge from the brain. We shall later see good reason to deny the existence of the latter feeling. We have accounted for the better part at least of the resident feelings of motion in limbs by the sensibility of the articular surfaces. The skin and ligaments also must have feelings awakened as they are stretched or squeezed in flexion or extension. And I am inclined to think that the sensations of our contracting muscles themselves probably play as small a part in building up our exact knowledge of space as any class of sensations which we possess. The muscles, indeed, play an all-important part, but it is through the remote effect of their contractions on other sensitive parts, not through their own resident sensations being aroused. In other words, muscular contraction is only indirectly instrumental, in giving us space-perceptions, by its effects on surfaces. In skin and retina it produces a motion of the stimulus upon the surface; in joints it produces a motion of the surfaces upon each other--such motion being by far the most delicate manner of exciting the surfaces in question. One is tempted to doubt whether the muscular sensibility as such plays even a subordinate part as sign of these more immediately geometrical perceptions which are so uniformly associated with it as effects of the contraction objectively viewed.

For this opinion many reasons can be assigned. First, it seems a priori improbable that such organs as muscles should give us feelings whose variations bear any exact proportion to the spaces traversed when they contract. As G. E. Müller says, their sensory nerves must be excited either chemically or by mechanical compression whilst the contractions last, and in neither case can the excitement be proportionate to the position into which the limb is thrown. The chemical state of the muscle depends on the previous work more than on the actually present contraction; and the internal pressure of it depends on the resistance offered more than on the shortening attained. The intrinsic muscular sensations are likely therefore to be merely those of massive strain or fatigue, and to carry no accurate discrimination with them of lengths of path moved through.

Empirically we find this probability confirmed by many facts. The judicious A. W. Volkmann observes that:

"Muscular feeling gives tolerably fine evidence as to the existence of movement, but hardly any direct information about its extent or direction. We are not aware that the contractions of a supinator longus have a wider range than those of a supinator brevis; and that the fibres of a bipenniform muscle contract in opposite directions is a fact of which the muscular feeling itself gives not the slightest intimation. Muscle-feeling belongs to that class of general sensations which tell us of our inner states, but not of outer relations; it does not belong among the space-perceiving senses."

E. H. Weber in his article Tastsinn called attention to the fact that muscular movements as large and strong as those of the diaphragm go on continually without our perceiving them as motion.

G. H. Lewes makes the same remark. When we think of our muscular sensations as movements in space, it is because we have ingrained with them in our imagination a movement on a surface simultaneously felt.

"Thus whenever we breathe there is a contraction of the muscles of the ribs and the diaphragm. Since we see the chest expanding, we know it as a movement and can only think of it as such. But the diaphragm itself is not seen, and consequently by no one who is not physiologically enlightened on the point is this diaphragm thought of in movement. Nay, even when told by a physiologist that the diaphragm moves at each breathing, every one who has not seen it moving downward pictures it as an upward movement, because the chest moves upward."

A personal experience of my own seems strongly to corroborate this view. For years I have been familiar, during the act of gaping, with a large, round, smooth sensation in the region of the throat, a sensation characteristic of gaping and nothing else, but which, although I had often wondered about it, never suggested to my mind the motion of anything. The reader probably knows from his own experience exactly what feeling I mean. It was not till one of my students told me, that I learned its objective cause. If we look into the mirror while gaping, we see that at the moment we have this feeling the hanging palate rises by the contraction of its intrinsic muscles. The contraction of these muscles and the compression of the palatine mucous membrane are what occasion the feeling; and I was at first astonished that, coming from so small an organ, it could appear so voluminous. Now the curious point is this--that no sooner had I learned by the eye its objective space-significance, than I found myself enabled mentally to feel it as a movement upwards of a body in the situation of the uvula. When I now have it, my fancy injects it, so to speak, with the image of the rising uvula; and it absorbs the image easily and naturally. In a word, a muscular contraction gave me a sensation whereof I was unable during forty years to interpret a motor meaning, of which two glances of the eye made me permanently the master. To my mind no further proof is needed of the fact that muscular contraction, merely as such, need not be perceived directly as so much motion through space.

Take again the contractions of the muscles which make the eyeball rotate. The feeling of these is supposed by many writers to play the chief part in our perceptions of extent. The space seen between two things means, according to these authors, nothing but the amount of contraction which is needed to carry the fovea from the first thing to the second. But close the eyes and note the contractions in themselves (even when coupled as they still are with the delicate surface sensations of the eyeball rolling under the lids), and we are surprised at finding how vague their space-import appears. Shut the eyes and roll them, and you can with no approach to accuracy tell the outer object which shall first be seen when you open them again. Moreover, if our eye-muscle-contractions had much to do with giving us our sense of seen extent, we ought to have a natural illusion of which we find no trace. Since the feeling in the muscles grows disproportionately intense as the eyeball is rolled into an extreme eccentric position, all places on the extreme margin of the field of view ought to appear farther from the centre than they really are, for the fovea cannot get to them without an amount of this feeling altogether in excess of the amount of actual rotation. When we turn to the muscles of the body at large we find the same vagueness. Goldscheider found that the minimal perceived rotation of a limb about a joint was no less when the movement was 'active' or produced by muscular contraction than when it was 'passively' impressed. The consciousness of active movement became so blunt when the joint (alone!) was made anæsthetic by faradization, that it became evident that the feeling of contraction could never be used for fine discrimination of extents. And that it was not used for coarse discriminations appeared clear to Goldscheider from certain other results which are too circumstantial for me to quote in detail. His general conclusion is that we feel our movements exclusively in our articular surfaces, and that our muscular contractions in all probability hardly occasion this sort of perception at all.

My conclusion is that the 'muscular sense' must fall back to the humble position from which Charles Bell raised it, and no longer figure in Psychology as the leading organ in space-perception which it has been so long 'cracked up' to be.

* * * * *

Before making a minuter study of Space as apprehended by the eye, we must turn to see what we can discover of space as known to the blind. But as we do so, let us cast a glance upon the results of the last pages, and ask ourselves once more whether the building up of orderly space-perceptions out of primitive incoherency requires any mental powers beyond those displayed in ordinary intellectual operations. I think it is obvious--granting the spacial quale to exist in the primitive sensations--that discrimination, association, addition, multiplication, and division, blending into generic images, substitution of similars, selective emphasis, and abstraction from uninteresting details, are quite capable of giving us all the space-perceptions we have so far studied, without the aid of any mysterious 'mental chemistry' or power of 'synthesis' to create elements absent from the original data of feeling. It cannot be too strongly urged in the face of mystical attempts, however learned, that there is not a landmark, not a length, not a point of the compass in real space which is not some one of our feelings, either experienced directly as a presentation or ideally suggested by another feeling which has come to serve as its sign. In degrading some sensations to the rank of signs and exalting others to that of realities signified, we smooth out the wrinkles of our first chaotic impressions and make a continuous order of what was a rather incoherent multiplicity. But the content of the order remains identical with that of the multiplicity--sensational both, through and through.

HOW THE BLIND PERCEIVE SPACE.

The blind man's construction of real space differs from that of the seeing man most obviously in the larger part which synthesis plays in it, and the relative subordination of analysis. The seeing baby's eyes take in the whole room at once, and discriminative attention must arise in him before single objects are visually discerned. The blind child, on the contrary, must form his mental image of the room by the addition, piece to piece, of parts which he learns to know successively. With our eyes we may apprehend instantly, in an enormous bird's-eye view, a landscape which the blind man is condemned to build up bit by bit after weeks perhaps of exploration. We are exactly in his predicament, however, for spaces which exceed our visual range. We think the ocean as a whole by multiplying mentally the impression we get at any moment when at sea. The distance between New York and San Francisco is computed in days' journeys; that from earth to sun is so many times the earth's diameter, etc.; and of longer distances still we may be said to have no adequate mental image whatever, but only numerical verbal symbols.

But the symbol will often give us the emotional effect of the perception. Such expressions as the abysmal vault of heaven, the endless expanse of ocean, etc., summarize many computations to the imagination, and give the sense of an enormous horizon. So it seems with the blind. They multiply mentally the amount of a distinctly felt freedom to move, and gain the immediate sense of a vaster freedom still. Thus it is that blind men are never without the consciousness of their horizon. They all enjoy travelling, especially with a companion who can describe to them the objects they pass. On the prairies they feel the great openness; in valleys they feel closed in; and one has told me that he thought few seeing people could enjoy the view from a mountain-top more than he. A blind person on entering a house or room immediately receives, from the reverberations of his voice and steps, an impression of its dimensions, and to a certain extent of its arrangement. The tympanic sense noticed on p. 140, supra, comes in to help here, and possibly other forms of tactile sensibility not yet understood. Mr. W. Hanks Levy, the blind author of 'Blindness and the Blind' (London), gives the following account of his powers of perception:

"Whether within a house or in the open air, whether walking or standing still, I can tell, although quite blind, when I am opposite an object, and can perceive whether it be tall or short, slender or bulky. I can also detect whether it be a solitary object or a continuous fence; whether it be a close fence or composed of open rails; and often whether it be a wooden fence, a brick or stone wall, or a quick-set hedge. I cannot usually perceive objects if much lower than my shoulder, but sometimes very low objects can be detected. This may depend on the nature of the objects, or on some abnormal state of the atmosphere. The currents of air can have nothing to do with this power, as the state of the wind does not directly affect it; the sense of hearing has nothing to do with it, as when snow lies thickly on the ground objects are more distinct, although the footfall cannot be heard. I seem to perceive objects through the skin of my face, and to have the impressions immediately transmitted to the brain. The only part of my body possessing this power is my face; this I have ascertained by suitable experiments. Stopping my ears does not interfere with it, but covering my face with a thick veil destroys it altogether. None of the five senses have anything to do with the existence of this power, and the circumstances above named induce me to call this unrecognized sense by the name of 'facial perception.'... When passing along a street I can distinguish shops from private houses, and even point out the doors and windows, etc., and this whether the doors be shut or open. When a window consists of one entire sheet of glass, it is more difficult to discover than one composed of a number of small panes. From this it would appear that glass is a bad conductor of sensation, or at any rate of the sensation specially connected with this sense. When objects below the face are perceived, the sensation seems to come in an oblique line from the object to the upper part of the face. While walking with a friend in Forest Lane, Stratford, I said, pointing to a fence which separated the road from a field, 'Those rails are not quite as high as my shoulder.' He looked at them, and said they were higher. We, however, measured, and found them about three inches lower than my shoulder. At the time of making this observation I was about four feet from the rails. Certainly in this instance facial perception was more accurate than sight. When the lower part of a fence is brickwork, and the upper part rails, the fact can be detected, and the line where the two meet easily perceived. Irregularities in height, and projections and indentations in walls, can also be discovered."

According to Mr. Levy, this power of seeing with the face is diminished by a fog, but not by ordinary darkness. At one time he could tell when a cloud obscured the horizon, but he has now lost that power, which he has known several persons to possess who are totally blind. These effects of aqueous vapor suggest immediately that fluctuations in the heat radiated by the objects may be the source of the perception. One blind gentleman, Mr. Kilburne, an instructor in the Perkins Institution in South Boston, who has the power spoken of in an unusual degree, proved, however, to have no more delicate a sense of temperature in his face than ordinary persons. He himself supposed that his ears had nothing to do with the faculty until a complete stoppage of them, not only with cotton but with putty on top of it, by abolishing the perception entirely, proved his first impression to be erroneous. Many blind men say immediately that their ears are concerned in the matter.

Sounds certainly play a far more prominent part in the mental life of the blind than in our own. In taking a walk through the country, the mutations of sound, far and near, constitute their chief delight. And to a great extent their imagination of distance and of objects moving from one distant spot to another seems to consist in thinking how a certain sonority would be modified by the change of place. It is unquestionable that the semi-circular-canal feelings play a great part in defining the points of the compass and the direction of distant spots, in the blind as in us. We start towards them by feelings of this sort; and so many directions, so many different-feeling starts.

The only point that offers any theoretic difficulty is the prolongation into space of the direction, after the start. We saw, ten pages back, that for extradition to occur beyond the skin, the portion of skin in question and the space beyond must form a common object for some other sensory surface. The eyes are for most of us this sensory surface; for the blind it can only be other parts of the skin, coupled or not with motion. But the mere gropings of the hands in every direction must end by surrounding the whole body with a sphere of felt space. And this sphere must become enlarged with every movement of locomotion, these movements gaining their space-values from the semi-circular-canal feelings which accompany them, and from the farther and farther parts of large fixed objects (such as the bed, the wainscoting, or a fence) which they bring within the grasp. It might be supposed that a knowledge of space acquired by so many successive discrete acts would always retain a somewhat jointed and so to speak, granulated character. When we who are gifted with sight think of a space too large to come into a single field of view, we are apt to imagine it as composite, and filled with more or less jerky stoppings and startings (think, for instance, of the space from here to San Francisco), or else we reduce the scale symbolically and imagine how much larger on a map the distance would look than others with whose totality we are familiar.

I am disposed to believe, after interrogating many blind persons, that the use of imaginary maps on a reduced scale is less frequent with them than with the rest of us. Possibly the extraordinary changeableness of the visual magnitudes of things makes this habit natural to us, while the fixity of tactile magnitudes keeps them from falling into it. (When the blind young man operated on by Dr. Franz was shown a portrait in a locket, he was vastly surprised that the face could be put into so small a compass: it would have seemed to him, he said, as impossible as to put a bushel into a pint.) Be this as it may, however, the space which each blind man feels to extend beyond his body is felt by him as one smooth continuum--all trace of those muscular startings and stoppings and reversals which presided over its formation having been eliminated from the memory. It seems, in other words, a generic image of the space-element common to all these experiences, with the unessential particularities of each left out. In truth, where in this space a start or a stop may have occurred was quite accidental. It may never occur just there again, and so the attention lets it drops altogether. Even as long a space as that traversed in a several-mile walk will not necessarily appear to a blind man's thought in the guise of a series of locomotor acts. Only where there is some distinct locomotor difficulty, such as a step to ascend, a difficult crossing, or a disappearance of the path, will distinct locomotor images constitute the idea. Elsewhere the space seems continuous, and its parts may even all seem coexistent; though, as a very intelligent blind friend once remarked to me, 'To think of such distances involves probably more mental wear and tear and brain-waste in the blind than in the seeing.' This seems to point to a greater element of successive addition and construction in the blind man's idea.

Our own visual explorations go on by means of innumerable stoppings and startings of the eyeballs. Yet these are all effaced from the final space-sphere of our visual imagination. They have neutralized each other. We can even distribute our attention to the right and left sides simultaneously, and think of those two quarters of space as coexistent. Does the smoothing out of the locomotor interruptions from the blind man's tactile space-sphere offer any greater paradox? Surely not. And it is curious to note that both in him and in us there is one particular locomotor feeling that is apt to assert itself obstinately to the last. We and he alike spontaneously imagine space as lying in front of us, for reasons too obvious to enumerate. If we think of the space behind us, we, as a rule, have to turn round mentally, and in doing so the front space vanishes. But in this, as in the other things of which we have been talking, individuals differ widely. Some, in imagining a room, can think of all its six surfaces at once. Others mentally turn round, or, at least, imagine the room in several successive and mutually exclusive acts (cf. p. 54, above).

* * * * *

Sir William Hamilton, and J. S. Mill after him, have quoted approvingly an opinion of Platner (an eighteenth-century philosopher) regarding the space-perceptions of the blind. Platner says:

"The attentive observation of a person born blind... has convinced me that the sense of touch by itself is altogether incompetent to afford us the representation of extension and space.... In fact, to those born blind, time serves instead of space. Vicinity and distance mean in their mouths nothing more than the shorter or longer time ... necessary to attain from some one feeling to some other."

After my own observation of blind people, I should hardly have considered this as anything but an eccentric opinion, worthy to pair off with that other belief that color is primitively seen without extent, had it not been for the remarkable Essay on Tactile and Visual Space by M. Ch. Dunan, which appeared in the Revue Philosophique for 1888. This author quotes three very competent witnesses, all officials in institutions for the blind [it does not appear from the text that more than one of them was blind himself], who say that blind people only live in time. M. Dunan himself does not share exactly this belief, but he insists that the blind man's and the seeing man's representation of space have absolutely naught in common, and that we are deceived into believing that what they mean by space is analogous to what we mean, by the fact that so many of them are but semi-blind and still think in visual terms, and from the farther fact that they all talk in visual terms just like ourselves. But on examining M. Dunan's reasons one finds that they all rest on the groundless logical assumption that the perception of a geometrical form which we get with our eyes, and that which a blind man gets with his fingers, must either be absolutely identical or absolutely unlike. They cannot be similar in diversity, "for they are simple notions, and it is of the essence of such to enter the mind or leave it all at once, so that one who has a simple notion at all, possesses it in all its completeness.... Therefore, since it is impossible that the blind should have of the forms in question ideas completely identical with our seeing ones, it follows that their ideas must be radically different from and wholly irreducible to our own." Hereupon M. Dunan has no difficulty in finding a blind man who still preserves a crude sensation of diffused light, and who says when questioned that this light has no extent. Having 'no extent' appears, however, on farther questioning, to signify merely not enveloping any particular tactile objects, nor being located within their outline; so that (allowing for latitude of expression) the result tallies perfectly with our own view. A relatively stagnant retinal sensation of diffused light, not varying when different objects are handled, would naturally remain an object quite apart. If the word 'extent' were habitually used to denote tactile extent, this sensation, having no tactile associates whatever, would naturally have 'extent' denied of it. And yet all the while it would be analogous to the tactile sensations in having the quality of bigness. Of course it would have no other tactile qualities, just as the tactile objects have no other optical qualities than bigness. All sorts of analogies obtain between the spheres of sensibility. Why are 'sweet' and 'soft' used so synonymously in most languages? and why are both these adjectives applied to objects of so many sensible kinds? Rough sounds, heavy smells, hard lights, cold colors, are other examples. Nor does it follow from such analogies as these that the sensations compared need be composite and have some of their parts identical. We saw in Chapter XIII that likeness and difference are an elementary relation, not to be resolved in every case into a mixture of absolute identity and absolute heterogeneity of content (cf. Vol. I, pp. 492-3).

I conclude, then, that although in its more superficial determinations the blind man's space is very different from our space, yet a deep analogy remains between the two. 'Big' and 'little,' 'far' and 'near,' are similar contents of consciousness in both of us. But the measure of the bigness and the farness is very different in him and in ourselves. He, for example, can have no notion of what we mean by objects appearing smaller as they move away, because he must always conceive of them as of their constant tactile size. Nor, whatever analogy the two extensions involve, should we expect that a blind man receiving sight for the first time should recognize his new-given optical objects by their familiar tactile names. Molyneux wrote to Locke:

"Suppose a man born blind, and now adult, and taught by his touch to distinguish between a cube and a sphere,... so as to tell, when he felt one and the other, which is the cube, which the sphere. Suppose then the cube and sphere placed on a table and the blind man to be made to see; query, whether by his sight, before he touched them, he could now distinguish and tell which is the globe, which the cube?"

This has remained in literature as 'Molyneux's query.' Molyneux answered 'No.' And Locke says:

"I agree with this thinking gentleman whom I am proud to call my friend, and am of opinion that the blind man at first sight would not be able to say which was the globe, which the cube, whilst he only saw them; though he could unerringly name them by his touch and certainly distinguish them by the difference of their figures felt."

This opinion has not lacked experimental confirmation. From Chesselden's case downwards, patients operated for congenital cataract have been unable to name at first the things they saw. "So, Puss, I shall know you another time," said Chesselden's patient, after catching the cat, looking at her steadfastly, and setting her down. Some of this incapacity is unquestionably due to general mental confusion at the new experience, and to the excessively unfavorable conditions for perception which an eye with its lens just extirpated affords. That the analogy of inner nature between the retinal and tactile sensations goes beyond mere extensity is proved by the cases where the patients were the most intelligent, as in the young man operated on by Dr. Franz, who named circular, triangular, and quadrangular figures at first sight.

VISUAL SPACE.

It is when we come to analyze minutely the conditions of visual perception that difficulties arise which have made psychologists appeal to new and quasi-mythical mental powers. But I firmly believe that even here exact investigation will yield the same verdict as in the cases studied hitherto. This subject will close our survey of the facts; and if it give the result I foretell, we shall be in the best of positions for a few final pages of critically historical review.

If a common person is asked how he is enabled to see things as they are, he will simply reply, by opening his eyes and looking. This innocent answer has, however, long since been impossible for science. There are various paradoxes and irregularities about what we appear to perceive under seemingly identical optical conditions, which immediately raise questions. To say nothing now of the time-honored conundrums of why we see upright with an inverted retinal picture, and why we do not see double; and to leave aside the whole field of color-contrasts and ambiguities, as not directly relevant to the space-problem,--it is certain that the same retinal image makes us see quite differently-sized and differently-shaped objects at different times, and it is equally certain that the same ocular movement varies in its perceptive import. It ought to be possible, were the act of perception completely and simply intelligible, to assign for every distinct judgment of size, shape, and position a distinct optical modification of some kind as its occasion. And the connection between the two ought to be so constant that, given the same modification, we should always have the same judgment. But if we study the facts closely we soon find no such constant connection between either judgment and retinal modification, or judgment and muscular modification, to exist. The judgment seems to result from the combination of retinal, muscular and intellectual factors with each other; and any one of them may occasionally overpower the rest in a way which seems to leave the matter subject to no simple law.

The scientific study of the subject, if we omit Descartes, began with Berkeley, and the particular perception he analyzed in his New Theory of Vision was that of distance or depth. Starting with the physical assumption that a difference in the distance of a point can make no difference in the nature of its retinal image, since "distance being a line directed endwise to the eye, it projects only one point in the fund of the eye--which point remains invariably the same, whether the distance be longer or shorter," he concluded that distance could not possibly be a visual sensation, but must be an intellectual 'suggestion' from 'custom' of some non-visual experience. According to Berkeley this experience was tactile. His whole treatment of the subject was excessively vague,--no shame to him, as a breaker of fresh ground,--but as it has been adopted and enthusiastically hugged in all its vagueness by nearly the whole line of British psychologists who have succeeded him, it will be well for us to begin our study of vision by refuting his notion that depth cannot possibly be perceived in terms of purely visual feeling.

The Third Dimension.

Berkeleyans unanimously assume that no retinal sensation can primitively be of volume; if it be of extension at all (which they are barely disposed to admit), it can be only of two-, not of three-, dimensional extension. At the beginning of the present chapter we denied this, and adduced facts to show that all objects of sensation are voluminous in three dimensions (cf. p. 136 ff.). It is impossible to lie on one's back on a hill, to let the empty abyss of blue fill one's whole visual field, and to sink deeper and deeper into the merely sensational mode of consciousness regarding it, without feeling that an indeterminate, palpitating, circling depth is as indefeasibly one of its attributes as its breadth. We may artificially exaggerate this sensation of depth. Rise and look from the hill-top at the distant view; represent to yourself as vividly as possible the distance of the uttermost horizon; and then with inverted head look at the same. There will be a startling increase in the perspective, a most sensible recession of the maximum distance; and as you raise the head you can actually see the horizon-line again draw near.

Mind, I say nothing as yet about our estimate of the 'real' amount of this depth or distance. I only want to confirm its existence as a natural and inevitable optical consort of the two other optical dimensions. The field of view is always a volume-unit. Whatever be supposed to be its absolute and 'real' size, the relative sizes of its dimensions are functions of each other. Indeed, it happens perhaps most often that the breadth- and height-feeling take their absolute measure from the depth-feeling. If we plunge our head into a wash-basin, the felt nearness of the bottom makes us feel the lateral expanse to be small. If, on the contrary, we are on a mountain-top, the distance of the horizon carries with it in our judgment a proportionate height and length in the mountain-chains that bound it to our view. But as aforesaid, let us not consider the question of absolute size now,--it must later be taken up in a thorough way. Let us confine ourselves to the way in which the three dimensions which are seen, get their values fixed relatively to each other.

Reid, in his Inquiry into the Human Mind, has a section 'Of the Geometry of Visibles,' in which he assumes to trace what the perceptions would be of a race of 'Idomenians' reduced to the sole sense of sight. Agreeing with Berkeley that sight alone can give no knowledge of the third dimension, he humorously deduces various ingenious absurdities in their interpretations of the material appearances before their eyes.

Now I firmly believe, on the contrary, that one of Reid's Idomenians would frame precisely the same conception of the external world that we do, if he had our intellectual powers. Even were his very eyeballs fixed and not movable like ours, that would only retard, not frustrate, his education. For the same object, by alternately covering in its lateral movements different parts of his retina, would determine the mutual equivalencies of the first two dimensions of the field of view; and by exciting the physiological cause of his perception of depth in various degrees, it would establish a scale of equivalency between the first two and the third.

First of all, one of the sensations given by the object is chosen to represent its 'real' size and shape, in accordance with the principles laid down on pp. 178 and 179. One sensation measures the 'thing' present, and the 'thing' then measures the other sensations. The peripheral parts of the retina are equated with the central by receiving the image of the same object. This needs no elucidation in case the object does not change its distance or its front. But suppose, to take a more complicated case, that the object is a stick, seen first in its whole length, and then rotated round one of its ends; let this fixed end be the one near the eye. In this movement the stick's image will grow progressively shorter; its farther end will appear less and less separated laterally from its fixed near end; soon it will be screened by the latter, and then reappear on the opposite side, and finally on that side resume its original length. Suppose this movement to become a familiar experience; the mind will presumably react upon it after its usual fashion (which is that of unifying all data which it is in any way possible to unify), and consider it the movement of a constant object rather than the transformation of a fluctuating one. Now, the sensation of depth which it receives during the experience is awakened more by the far than by the near end of the object. But how much depth? What shall measure its amount? Why, at the moment the far end is ready to be eclipsed, the difference of its distance from the near end's distance must be judged equal to the stick's whole length; but that length has already been judged equal to a certain optical sensation of breadth. Thus we find that given amounts of the visual depth-feeling become signs of fixed amounts of the visual breadth-feeling. The measurement of distance is, as Berkeley truly said, a result of suggestion and experience. But visual experience alone is adequate to produce it, and this he erroneously denied.

Suppose a colonel in front of his regiment at dress-parade, and suppose he walks at right angles towards the midmost man of the line. As he advances, and surveys the line in either direction, he looks more and more down it and less and less at it, until, when abreast of the midmost man, he feels the end men to be most distant; then when the line casts hardly any lateral image on his retina at all, what distance shall he judge to be that of the end men? Why, half the length of the regiment as it was originally seen, of course; but this length was a moment ago a retinal object spread out laterally before his sight. He has now merely equated a retinal depth-feeling with a retinal breadth-feeling. If the regiment moved, and the colonel stood still, the result would be the same. In such ways as these a creature endowed with eyes alone could hardly fail of measuring out all three dimensions of the space he inhabited. And we ourselves, I think, although we may often 'realize' distance in locomotor terms (as Berkeley says we must always do), yet do so no less often in terms of our retinal map, and always in this way the more spontaneously. Were this not so, the three visual dimensions could not possibly feel to us as homogeneous as they do, nor as commensurable inter se.

Let us then admit distance to be at least as genuinely optical a content of consciousness as either height or breadth. The question immediately returns, Can any of them be said in any strictness to be optical sensations? We have contended all along for the affirmative reply to this question, but must now cope with difficulties greater than any that have assailed us hitherto.

Helmholtz and Reid on Sensations.

A sensation is, as we have seen in Chapter XVII, the mental affection that follows most immediately upon the stimulation of the sense-tract. Its antecedent is directly physical, no psychic links, no acts of memory, inference, or association intervening. Accordingly, if we suppose the nexus between neural process in the sense-organ, on the one hand, and conscious affection, on the other, to be by nature uniform, the same process ought always to give the same sensation; and conversely, if what seems to be a sensation varies whilst the process in the sense-organ remains unchanged, the reason is presumably that it is really not a sensation but a higher mental product, whereof the variations depend on events occurring in the system of higher cerebral centres.

Now the size of the field of view varies enormously in all three dimensions, without our being able to assign with any definiteness the process in the visual tract on which the variation depends. We just saw how impossible such assignment was in the case where turning down the head produces the enlargement. In general, the maximum feeling of depth or distance seems to take the lead in determining the apparent magnitude of the whole field, and the two other dimensions seem to follow. If, to use the former instance, I look close into a wash-basin, the lateral extent of the field shrinks proportionately to its nearness. If I look from a mountain, the things seen are vast in height and breadth, in proportion to the farness of the horizon. But when we ask what changes in the eye determine how great this maximum feeling of depth or distance (which is undoubtedly felt as a unitary vastness) shall be, we find ourselves unable to point to any one of them as being its absolutely regular concomitant. Convergence, accommodation, double and disparate images, differences in the parallactic displacement when we move our head, faintness of tint, dimness of outline, and smallness of the retinal image of objects named and known, are all processes that have something to do with the perception of 'far' and of 'near'; but the effect of each and any one of them in determining such a perception at one moment may at another moment be reversed by the presence of some other sensible quality in the object, that makes us, evidently by reminding us of past experience, judge it to be at a different distance and of another shape. If we paint the inside of a pasteboard-mask like the outside, and look at it with one eye, the accommodation- and parallax-feelings are there, but fail to make us see it hollow, as it is. Our mental knowledge of the fact that human faces are always convex overpowers them, and we directly perceive the nose to be nearer to us than the cheek instead of farther of.

The other organic tokens of farness and nearness are proved by similar experiments (of which we shall ere long speak more in detail) to have an equally fluctuating import. They lose all their value whenever the collateral circumstances favor a strong intellectual conviction that the object presented to the gaze is improbable--cannot be either what or where they would make us perceive it to be.

Now the query immediately arises: Can the feelings of these processes in the eye, since they are so easily neutralized and reversed by intellectual suggestions, ever have been direct sensations of distance at all? Ought we not rather to assume, since the distances which we see in spite of them are conclusions from past experience, that the distances which we see by means of them are equally such conclusions? Ought we not, in short, to say unhesitatingly that distance must be an intellectual and not a sensible content of consciousness? and that each of these eye-feelings serves as a mere signal to awaken this content, our intellect being so framed that sometimes it notices one signal more readily and sometimes another?

Reid long ago (Inquiry, c. vi. sec. 17) said:

"It may be taken for a general rule that things which are produced by custom may be undone or changed by disuse or by contrary custom. On the other hand, it is a strong argument that an effect is not owing to custom, but to the constitution of nature, when a contrary custom is found neither to change nor to weaken it."

More briefly, a way of seeing things that can be unlearned was presumably learned, and only what we cannot unlearn is instinctive.

This seems to be Helmholtz's view, for he confirms Reid's maxim by saying in emphatic print:

"No elements in our perception can be sensational which may be overcome or reversed by factors of demonstrably experimental origin. Whatever can be overcome by suggestions of experience must be regarded as itself a product of experience and custom. If we follow this rule it will appear that only qualities are sensational, whilst almost all spatial attributes are results of habit and experience."

This passage of Helmholtz's has obtained, it seems to me, an almost deplorable celebrity. The reader will please observe its very radical import. Not only would he, and does he, for the reasons we have just been ourselves considering, deny distance to be an optical sensation; but, extending the same method of criticism to judgments of size, shape, and direction, and finding no single retinal or muscular process in the eyes to be indissolubly linked with any one of these, he goes so far as to say that all optical space-perceptions whatsoever must have an intellectual origin, and a content that no items of visual sensibility can account for.

As Wundt and others agree with Helmholtz here, and as their conclusions, if true, are irreconcilable with all the sensationalism which I have been teaching hitherto, it clearly devolves upon me to defend my position against this new attack. But as this chapter on Space is already so overgrown with episodes and details, I think it best to reserve the refutation of their general principle for the next chapter, and simply to assume at this point its untenability. This has of course an arrogant look; but if the reader will bear with me for not very many pages more, I shall hope to appease his mind. Meanwhile I affirm confidently that the same outer objects actually FEEL different to us according as our brain reacts on them in one way or another by making us perceive them as this or as that sort of thing. So true is this that one may well, with Stumpf, reverse Helmholtz's query, and ask: "What would become of our sense-perceptions in case experience were not able so to transform them?" Stumpf adds: "All wrong perceptions that depend on peculiarities in the organs are more or less perfectly corrected by the influence of imagination following the guidance of experience."

If, therefore, among the facts of optical space-perception (which we must now proceed to consider in more detail) we find instances of an identical organic eye-process, giving us different perceptions at different times, in consequence of different collateral circumstances suggesting different objective facts to our imagination, we must not hastily conclude, with the school of Helmholtz and Wundt, that the organic eye-process pure and simple, without the collateral circumstances, is incapable of giving us any sensation of a spatial kind at all. We must rather seek to discover by what means the circumstances can so have transformed a space-sensation, which, but for their presence, would probably have been felt in its natural purity. And I may as well say now in advance that we shall find the means to be nothing more or less than association--the suggestion to the mind of optical objects not actually present, but more habitually associated with the 'collateral circumstances' than the sensation which they now displace and being imagined now with a quasi-hallucinatory strength. But before this conclusion emerges, it will be necessary to have reviewed the most important facts of optical space-perception, in relation to the organic conditions on which they depend. Readers acquainted with German optics will excuse what is already familiar to them in the following section.

Let us begin the long and rather tedious inquiry by the most important case. Physiologists have long sought for a simple law by which to connect the seen direction and distance of objects with the retinal impressions they produce. Two principal theories have been held of this matter, the 'theory of identical points,' and the 'theory of projection,'--each incompatible with the other, and each beyond certain limits becoming inconsistent with the facts.

The Theory of Identical Points.

This theory starts from the truth that on both retinæ an impression on the upper half makes us perceive an object as below, on the lower half as above, the horizon; and on the right half an object to the left, on the left half one to the right, of the median line. Thus each quadrant of one retina corresponds as a whole to the similar quadrant of the other; and within two similar quadrants, al and ar for example, there should, if the correspondence were consistently carried out, be geometrically similar points which, if impressed at the same time by light emitted from the same object, should cause that object to appear in the same direction to either eye. Experiment verifies this surmise. If we look at the starry vault with parallel eyes, the stars all seem single; and the laws of perspective show that under the circumstances the parallel light-rays coming from each star must impinge on points within either retina which are geometrically similar to each other. The same result may be more artificially obtained. If we take two exactly similar pictures, smaller, or at least no larger, than those on an ordinary stereoscopic slide, and if we look at them as stereoscopic slides are looked at, that is, at one with each eye (a median partition confining the view of either eye to the picture opposite it), we shall see but one flat picture, all of whose parts appear sharp and single. Identical points being impressed, both eyes see their object in the same direction, and the two objects consequently coalesce into one.

The same thing may be shown in still another way. With fixed head converge the eyes upon some conspicuous objective point behind a pane of glass; then close either eye alternately and make a little ink-mark on the glass, 'covering' the object as seen by the eye which is momentarily open. On looking now with both eyes the ink-marks will seem single, and in the same direction as the objective point. Conversely, let the eyes converge on a single ink-spot on the glass, and then by alternate shutting of them let it be noted what objects behind the glass the spot covers to the right and left eye respectively. Now with both eyes open, both these objects and the spot will appear in the same place, one or other of the three becoming more distinct according to the fluctuations of retinal attention.

Now what is the direction of this common place? The only way of defining the direction of an object is by pointing to it. Most people, if asked to look at an object over the horizontal edge of a sheet of paper which conceals their hand and arm, and then to point their finger at it (raising the hand gradually so that at last a finger-tip will appear above the sheet of paper), are found to place the finger not between either eye and the object, but between the latter and the root of the nose, and this whether both eyes or either alone be used. Hering and Helmholtz express this by saying that we judge of the direction of objects as they would appear to an imaginary cyclopean eye, situated between our two real eyes, and with its optical axis bisecting the angle of convergence of the latter. Our two retinæ act, according to Hering, as if they were superposed in the place of this imaginary double-eye; we see by the corresponding points of each, situated far asunder as they really are, just as we should see if they were superposed and could both be excited together.

The judgment of objective singleness and that of identical direction seem to hang necessarily together. And that of identical direction seems to carry with it the necessity of a common origin, between the eyes or elsewhere, from which all the directions felt may seem to be estimated. This is why the cyclopean eye is really a fundamental part of the formulation of the theory of identical retinal points, and why Hering, the greatest champion of this theory, lays so much stress upon it.

It is an immediate consequence of the law of identical projection of images on geometrically similar points that images which fall upon geometrically DISPARATE points of the two retinæ should be projected in DISPARATE directions, and that their objects should consequently appear in TWO places, or LOOK DOUBLE. Take the parallel rays from a star falling upon two eyes which converge upon a near object, O, instead of being parallel, as in the previously instanced case. If SL and SR in Fig. 55 be the parallel rays, each of them will fall upon the nasal half of the retina which it strikes.

But the two nasal halves are disparate, geometrically symmetrical, not geometrically similar. The image on the left one will therefore appear as if lying in a direction leftward of the cyclopean eye's line of sight; the image of the right one will appear far to the right of the same direction. The star will, in short, be seen double,--'homonymously' double.

Conversely, if the star be looked at directly with parallel axes, O will be seen double, because its images will affect the outer or cheek halves of the two retinæ, instead of one outer and one nasal half. The position of the images will here be reversed from that of the previous case. The right eye's image will now appear to the left, the left eye's to the right--the double images will be 'heteronymous.'

The same reasoning and the same result ought to apply where the object's place with respect to the direction of the two optic axes is such as to make its images fall not on non-similar retinal halves, but on non-similar parts of similar halves. Here, of course, the directions of projection will be less widely disparate than in the other case, and the double images will appear to lie less widely apart.

Careful experiments made by many observers according to the so-called haploscopic method confirm this law, and show that corresponding points, of single visual direction, exist upon the two retinæ. For the detail of these one must consult the special treatises.

Note now an important consequence. If we take a stationary object and allow the eyes to vary their direction and convergence, a purely geometrical study will show that there will be some positions in which its two images impress corresponding retinal points, but more in which they impress disparate points. The former constitute the so-called horopter, and their discovery has been attended with great mathematical difficulty. Objects or parts of objects which lie in the eyes' horopter at any given time cannot appear double. Objects lying out of the horopter would seem, if the theory of identical points were strictly true, necessarily and always to appear double.

Here comes the first great conflict of the identity-theory with experience. Were the theory true, we ought all to have an intuitive knowledge of the horopter as the line of distinctest vision. Objects placed elsewhere ought to seem, if not actually double, at least blurred. And yet no living man makes any such distinction between the parts of his field of vision. To most of us the whole field appears single, and it is only by rare accident or by special education that we ever catch a glimpse of a double image. In 1838, Wheatstone, in his truly classical memoir on binocular vision and the stereoscope, showed that the disparateness of the points on which the two images of an object fall does not within certain limits affect its seen singleness at all, but rather the distance at which it shall appear. Wheatstone made an observation, moreover, which subsequently became the bone of much hot contention, in which he strove to show that not only might disparate images fuse, but images on corresponding or identical points might be seen double.

I am unfortunately prevented by the weakness of my own eyes from experimenting enough to form a decided personal opinion on the matter. It seems to me, however, that the balance of evidence is against the Wheatstonian interpretation, and that disparate points may fuse, without identical points for that reason ever giving double images. The two questions, "Can we see single with disparate points?" and "Can we see double with identical points?" although at the first blush they may appear, as to Helmholtz they appear, to be but two modes of expressing the same inquiry, are in reality distinct. The first may quite well be answered affirmatively and the second negatively.

Add to this that the experiment quoted from Helmholtz above by no means always succeeds, but that many individuals place their finger between the object and one of their eyes, oftenest the right; finally, observe that the identity-theory, with its Cyclopean starting point for all lines of direction, gives by itself no ground for the distance on any line at which an object shall appear, and has to be helped out in this respect by subsidiary hypotheses, which, in the hands of Hering and others, have become so complex as easily to fall a prey to critical attacks; and it will soon seem as if the law of identical seen directions by corresponding points, although a simple formula for expressing concisely many fundamental phenomena, is by no means an adequate account of the whole matter of retinal perception.

The Projection-Theory.

Does the theory of projection fare any better? This theory admits that each eye sees the object in a different direction from the other, along the line, namely, passing from the object through the middle of the pupil to the retina. A point directly fixated is thus seen on the optical axes of both eyes. There is only one point, however, which these two optical axes have in common, and that is the point to which they converge. Everything directly looked at is seen at this point, and is thus seen both single and at its proper distance. It is easy to show the incompatibility of this theory with the theory of identity. Take an objective point (like O in Fig. 50, when the star is looked at) casting its images R' and L' on geometrically dissimilar parts of the two retinæ and affecting the outer half of each eye. On the identity-theory it ought necessarily to appear double, whilst on the projection-theory there is no reason whatever why it should not appear single, provided only it be located by the judgment on each line of visible direction, neither nearer nor farther than its point of intersection with the other line.

Every point in the field of view ought, in truth, if the projection-theory were uniformly valid, to appear single, entirely irrespective of the varying positions of the eyes, for from every point of space two lines of visible direction pass to the two retinæ; and at the intersection of these lines, or just where the point is, there, according to the theory, it should appear. The objection to this theory is thus precisely the reverse of the objection to the identity-theory. If the latter ruled, we ought to see most things double all the time. If the projection-theory ruled, we ought never to see anything double. As a matter of fact we get too few double images for the identity-theory, and too many for the projection-theory.

The partisans of the projection-theory, beginning with Aguilonius, have always explained double images as the result of an erroneous judgment of the distance of the object, the images of the latter being projected by the imagination along the two lines of visible direction either nearer or farther than the point of intersection of the latter. A diagram will make this clear.

Let O be the point looked at, M an object farther, and N an object nearer, than it. Then M and N will send the lines of visible direction MM and NN to the two retinæ. If N be judged as far as O, it must necessarily lie where the two lines of visible direction NN intersect the plane of the arrow, or in two places, at N' and at N''. If M be judged as near as O, it must for the same reason form two images at M' and M''.

It is, as a matter of fact, true that we often misjudge the distance in the way alleged. If the reader will hold his forefingers, one beyond the other, in the median line, and fixate them alternately, he will see the one not looked at, double; and he will also notice that it appears nearer to the plane of the one looked at, whichever the latter may be, than it really is. Its changes of apparent size, as the convergence of the eyes alter, also prove the change of apparent distance. The distance at which the axes converge seems, in fact, to exert a sort of attraction upon objects situated elsewhere. Being the distance of which we are most acutely sensible, it invades, so to speak, the whole field of our perception. If two half-dollars be laid on the table an inch or two apart, and the eyes fixate steadily the point of a pen held in the median line at varying distances between the coins and the face, there will come a distance at which the pen stands between the left half-dollar and the right eye, and the right half-dollar and the left eye. The two half-dollars will then coalesce into one; and this one will show its apparent approach to the pen-point by seeming suddenly much reduced in size.

Yet, in spite of this tendency to inaccuracy, we are never actually mistaken about the half-dollar being behind the pen-point. It may not seem far enough off, but still it is farther than the point. In general it may be said that where the objects are known to us, no such illusion of distance occurs in any one as the theory would require. And in some observers, Hering for example, it seems hardly to occur at all. If I look into infinite distance and get my finger in double images, they do not seem infinitely far off. To make objects at different distances seem equidistant, careful precautions must be taken to have them alike in appearance, and to exclude all outward reasons for ascribing to the one a different location from that ascribed to the other. Thus Donders tries to prove the law of projection by taking two similar electric sparks, one behind the other on a dark ground, one seen double; or an iron rod placed so near to the eyes that its double images seem as broad as that of a fixated stove-pipe, the top and bottom of the objects being cut off by screens, so as to prevent all suggestions of perspective, etc. The three objects in each experiment seem in the same plane.

Add to this the impossibility, recognized by all observers, of ever seeing double with the fovea, and the fact that authorities as able as those quoted in the note on Wheatstone's observation deny that they can see double then with identical points, and we are forced to conclude that the projection-theory, like its predecessor, breaks down. Neither formulates exactly or exhaustively a law for all our perceptions.

Ambiguity of Retinal Impressions.

What does each theory try to do? To make of seen location a fixed function of retinal impression. Other facts may be brought forward to show how far from fixed are the perceptive functions of retinal impressions. We alluded a while ago to the extraordinary ambiguity of the retinal image as a revealer of magnitude. Produce an after-image of the sun and look at your finger-tip: it will be smaller than your nail. Project it on the table, and it will be as big as a strawberry; on the wall, as large as a plate; on yonder mountain, bigger than a house. And yet it is an unchanged retinal impression. Prepare a sheet with the figures shown in Fig. 57 strongly marked upon it, and get by direct fixation a distinct after-image of each.

Project the after-image of the cross upon the upper left-hand part of the wall, it will appear as in Fig. 58; on the upper right-hand it will appear as in Fig. 59. The circle similarly projected will be distorted into two different ellipses. If the two parallel lines be projected upon the ceiling or floor far in front, the farther ends will diverge; and if the three parallel lines be thrown on the same surfaces, the upper pair will seem farther apart than the lower.

Adding certain lines to others has the same distorting effect. In what is known as Zöllner's pattern (Fig. 60), the long parallels tip towards each other the moment we draw the short slanting lines over them yet their retinal images are the same they always were. A similar distortion of parallels appears in Fig 61.

Drawing a square inside the circle (Fig. 62) gives to the outline of the latter an indented appearance where the square's corners touch it. Drawing the radii inside of one of the right angles in the same figure makes it seem larger than the other. In Fig. 63, the retinal image of the space between the extreme dots is in all three lines the same, yet it seems much larger the moment it is filled up with other dots.

In the stereoscope certain pairs of lines which look single under ordinary circumstances immediately seem double when we add certain other lines to them.

Ambiguous Import of Eye-movements.

These facts show the indeterminateness of the space-import of various retinal impressions. Take now the eye's movements, and we find a similar vacillation. When we follow a moving object with our gaze, the motion is 'voluntary'; when our eyes oscillate to and fro after we have made ourselves dizzy by spinning around, it is 'reflex'; and when the eyeball is pushed with the finger, it is 'passive.' Now, in all three of these cases we get a feeling from the movement as it effects itself. But the objective perceptions to which the feeling assists us are by no means the same. In the first case we may see a stationary field of view with one moving object in it; in the second, the total field swimming more or less steadily in one direction; in the third, a sudden jump or twist of the same total field.

The feelings of convergence of the eyeballs permit of the same ambiguous interpretation. When objects are near we converge strongly upon them in order to see them; when far, we set our optic axes parallel. But the exact degree of convergence fails to be felt; or rather, being felt, fails to tell us the absolute distance of the object we are regarding. Wheatstone arranged his stereoscope in such a way that the size of the retinal images might change without the convergence altering; or conversely, the convergence might change without the retinal image altering. Under these circumstances, he says, the object seemed to approach or recede in the first case, without altering its size, in the second, to change its size without altering its distance--just the reverse of what might have been expected. Wheatstone adds, however, that 'fixing the attention' converted each of these perceptions into its opposite. The same perplexity occurs in looking through prismatic glasses, which alter the eyes' convergence. We cannot decide whether the object has come nearer, or grown larger, or both, or neither; and our judgment vacillates in the most surprising way. We may even make our eyes diverge, and the object will none the less appear at a finite distance. When we look through the stereoscope, the picture seems at no determinate distance. These and other facts have led Helmholtz to deny that the feeling of convergence has any very exact value as a distance-measurer.

With the feelings of accommodation it is very much the same. Donders has shown that the apparent magnifying power of spectacles of moderate convexity hardly depends at all upon their enlargement of the retinal image, but rather on the relaxation they permit of the muscle of accommodation. This suggests an object farther off, and consequently a much larger one, since its retinal size rather increases than diminishes. But in this case the same vacillation of judgment as in the previously mentioned case of convergence takes place. The recession made the object seem larger, but the apparent growth in size of the object now makes it look as if it came nearer instead of receding. The effect thus contradicts its own cause. Everyone is conscious, on first putting on a pair of spectacles, of a doubt whether the field of view draws near or retreats.

There is still another deception, occurring in persons who have had one eye-muscle suddenly paralyzed. This deception has led Wundt to affirm that the eyeball-feeling proper, the incoming sensation of effected rotation, tells us only of the direction of our eye-movements, but not of their whole extent. For this reason, and because not only Wundt, but many other authors, think the phenomena in these partial paralyses demonstrate the existence of a feeling of innervation, a feeling of the outgoing nervous current, opposed to every afferent sensation whatever, it seems proper to note the facts with a certain degree of detail.

Suppose a man wakes up some morning with the external rectus muscle of his right eye half paralyzed, what will be the result? He will be enabled only with great effort to rotate the eye so as to look at objects lying far off to the right. Something in the effort he makes will make him feel as if the object lay much farther to the right than it really is. If the left and sound eye be closed, and he be asked to touch rapidly with his finger an object situated towards his right, he will point the finger to the right of it. The current explanation of the 'something' in the effort which causes this deception is that it is the sensation of the outgoing discharge from the nervous centres, the 'feeling of innervation,' to use Wundt's expression, requisite for bringing the open eye with its weakened muscle to bear upon the object to be touched. If that object be situated 20 degrees to the right, the patient has now to innervate as powerfully to turn the eye those 20 degrees as formerly he did to turn the eye 30 degrees. He consequently believes as before that he has turned it 30 degrees; until, by a newly-acquired custom, he learns the altered spatial import of all the discharges his brain makes into his right abducens nerve. The 'feeling of innervation,' maintained to exist by this and other observations, plays an immense part in the space-theories of certain philosophers, especially Wundt. I shall elsewhere try to show that the observations by no means warrant the conclusions drawn from them, and that the feeling in question is probably a wholly fictitious entity. Meanwhile it suffices to point out that even those who set most store by it are compelled, by the readiness with which the translocation of the field of view becomes corrected and further errors avoided, to admit that the precise space-import of the supposed sensation of outgoing energy is as ambiguous and indeterminate as that of any other of the eye-feelings we have considered hitherto.

* * * * *

I have now given what no one will call an understatement of the facts and arguments by which it is sought to banish the credit of directly revealing space from each and every kind of eye-sensation taken by itself. The reader will confess that they make a very plausible show, and most likely wonder whether my own theory of the matter can rally from their damaging evidence. But the case is far from being hopeless; and the introduction of a discrimination hitherto unmade will, if I mistake not, easily vindicate the view adopted in these pages, whilst at the same time it makes ungrudging allowance for all the ambiguity and illusion on which so much stress is laid by the advocates of the intellectualist-theory.

The Choice of the Visual Reality.

We have native and fixed optical space-sensations; but experience leads us to select certain ones from among them to be the exclusive bearers of reality: the rest become mere signs and suggesters of these. The factor of selection, on which we have already laid so much stress, here as elsewhere is the solving word of the enigma. If Helmholtz, Wundt, and the rest, with an ambiguous retinal sensation before them, meaning now one size and distance, and now another, had not contented themselves with merely saying:--The size and distance are not this sensation, they are something beyond it which it merely calls up, and whose own birthplace is afar--in 'synthesis' (Wundt) or in 'experience' (Helmholtz) as the case may be; if they had gone on definitely to ask and definitely to answer the question, What are the size and distance in their proper selves? they would not only have escaped the present deplorable vagueness of their space-theories, but they would have seen that the objective spatial attributes 'signified' are simply and solely certain other optical sensations now absent, but which the present sensations suggest.

What, for example, is the slant-legged cross which we think we see on the wall when we project the rectangular after-image high up towards our right or left (Figs. 58 and 59)? Is it not in very sooth a retinal sensation itself? An imagined sensation, not a felt one, it is true, but none the less essentially and originally sensational or retinal for that,--the sensation, namely, which we should receive if a 'real' slant-legged cross stood on the wall in front of us and threw its image on our eye. That image is not the one our retina now holds. Our retina now holds the image which a cross of square shape throws when in front, but which a cross of the slant-legged pattern would throw, provided it were actually on the wall in the distant place at which we look. Call this actual retinal image the 'square' image. The square image is then one of the innumerable images the slant-legged cross can throw. Why should another one, and that an absent one, of those innumerable images be picked out to represent exclusively the slant-legged cross's 'true' shape? Why should that absent and imagined slant-legged image displace the present and felt square image from our mind? Why, when the objective cross gives us so many shapes, as it varies its position, should we think we feel the true shape only when the cross is directly in front? And when that question is answered, how can the absent and represented feeling of a slant-legged figure so successfully intrude itself into the place of a presented square one?

Before answering either question, let us be doubly sure about our facts, and see how true it is that in our dealings with objects we always do pick out one of the visual images they yield, to constitute the real form or size.

The matter of size has been already touched upon, so that no more need be said of it here. As regards shape, almost all the retinal shapes that objects throw are perspective 'distortions.' Square table-tops constantly present two acute and two obtuse angles; circles drawn on our wall-papers, our carpets, or on sheets of paper, usually show like ellipses; parallels approach as they recede; human bodies are foreshortened; and the transitions from one to another of these altering forms are infinite and continual. Out of the flux, however, one phase always stands prominent. It is the form the object has when we see it easiest and best: and that is when our eyes and the object both are in what may be called the normal position. In this position our head is upright and our optic axes either parallel or symmetrically convergent; the plane of the object is perpendicular to the visual plane; and if the object is one containing many lines it is turned so as to make them, as far as possible, either parallel or perpendicular to the visual plane. In this situation it is that we compare all shapes with each other; here every exact measurement and decision is made.

It is very easy to see why the normal situation should have this extraordinary pre-eminence. First, it is the position in which we easiest hold anything we are examining in our hands; second, it is a turning-point between all right- and all left-hand perspective views of a given object; third, it is the only position in which symmetrical figures seem symmetrical and equal angles seem equal; fourth, it is often that starting-point of movements from which the eye is least troubled by axial rotations, by which superposition of the retinal images of different lines and different parts of the same line is easiest produced, and consequently by which the eye can make the best comparative measurements in its sweeps. All these merits single the normal position out to be chosen. No other point of view offers so many æsthetic and practical advantages. Here we believe we see the object as it is; elsewhere, only as it seems. Experience and custom soon teach us, however, that the seeming appearance passes into the real one by continuous gradations. They teach us, moreover, that seeming and being may be strangely interchanged. Now a real circle may slide into a seeming ellipse; now an ellipse may, by sliding in the same direction, become a seeming circle; now a rectangular cross grows slant-legged; now a slant-legged one grows rectangular.

Almost any form in oblique vision may be thus a derivative of almost any other in 'primary' vision; and we must learn, when we get one of the former appearances, to translate it into the appropriate one of the latter class; we must learn of what optical 'reality' it is one of the optical signs. Having learned this, we do but obey that law of economy or simplification which dominates our whole psychic life, when we attend exclusively to the 'reality' and ignore as much as our consciousness will let us the 'sign' by which we came to apprehend it. The signs of each probable real thing being multiple and the thing itself one and fixed, we gain the same mental relief by abandoning the former for the latter that we do when we abandon mental images, with all their fluctuating characters, for the definite and unchangeable names which they suggest. The selection of the several 'normal' appearances from out of the jungle of our optical experiences, to serve as the real sights of which we shall think, is psychologically a parallel phenomenon to the habit of thinking in words, and has a like use. Both are substitutions of terms few and fixed for terms manifold and vague.

Sensations which we Ignore.

This service of sensations as mere signs, to be ignored when they have evoked the other sensations which are their significates, was noticed first by Berkeley and remarked in many passages, as the following:

"Signs, being little considered in themselves, or for their own sake, but only in their relative capacity and for the sake of those things whereof they are signs, it comes to pass that the mind overlooks them, so as to carry its attention immediately on to the things signified ... which in truth and strictness are not seen, but only suggested and apprehended by means of the proper objects of sight which alone are seen." (Divine Visual Language, § 12.)

Berkeley of course erred in supposing that the thing suggested was not even originally an object of sight, as the sign now is which calls it up. Reid expressed Berkeley's principle in yet clearer language:

"The visible appearances of objects are intended by nature only as signs or indications, and the mind passes instantly to the things signified, without making the least reflection upon the sign, or even perceiving that there is any such thing.... The mind has acquired a confirmed and inveterate habit of inattention to them (the signs). For they no sooner appear than, quick as lightning, the thing signified succeeds and engrosses all our regard. They have no name in language; and although we are conscious of them when they pass through the mind, yet their passage is so quick and so familiar that it is absolutely unheeded; nor do they leave any footsteps of themselves, either in the memory or imagination." (Inquiry, chap. v. §§ 2, 3.)

If we review the facts we shall find every grade of non-attention between the extreme form of overlooking mentioned by Reid (or forms even more extreme still) and complete conscious perception of the sensation present. Sometimes it is literally impossible to become aware of the latter. Sometimes a little artifice or effort easily leads us to discern it together, or in alternation, with the 'object' it reveals. Sometimes the present sensation is held to be the object or to reproduce its features in undistorted shape, and then, of course, it receives the mind's full glare.

The deepest inattention is to subjective optical sensations, strictly so called, or those which are not signs of outer objects at all. Helmholtz's treatment of these phenomena, muscæ volitantes, negative after-images, double images, etc., is very satisfactory. He says:

"We only attend with any ease and exactness to our sensations in so far forth as they can be utilized for the knowledge of outward things; and we are accustomed to neglect all those portions of them which have no significance as regards the external world. So much is this the case that for the most part special artifices and practice are required for the observation of these latter more subjective feelings. Although it might seem that nothing should be easier than to be conscious of one's own sensations, experience nevertheless shows that often enough either a special talent like that showed in eminent degree by Purkinje, or accident or theoretic speculation, are necessary conditions for the discovery of subjective phenomena. Thus, for example, the blind spot on the retina was discovered by Mariotte by the theoretic way; similarly by me the existence of 'summation'-tones in acoustics. In the majority of cases accident is what first led observers whose attention was especially exercised on subjective phenomena to discover this one or that; only where the subjective appearances are so intense that they interfere with the perception of objects are they noticed by all men alike. But if they have once been discovered it is for the most part easy for subsequent observers who place themselves in proper conditions and bend their attention in the right direction to perceive them. But in many cases--for example, in the phenomena of the blind spot, in the discrimination of over-tones and combination-tones from the ground-tone of musical sounds, etc.--such a strain of the attention is required, even with appropriate instrumental aids, that most persons fail. The very after-images of bright objects are by most men perceived only under exceptionally favorable conditions, and it takes steady practice to see the fainter images of this kind. It is a commonly recurring experience that persons smitten with some eye-disease which impairs vision suddenly remark for the first time the muscæ volitantes which all through life their vitreous humor has contained, but which they now firmly believe to have arisen since their malady; the truth being that the latter has only made them more observant of all their visual sensations. There are also cases where one eye has gradually grown blind, and the patient lived for an indefinite time without knowing it, until, through the accidental closure of the healthy eye alone, the blindness of the other was brought to attention.

"Most people, when first made aware of binocular double images, are uncommonly astonished that they should never have noticed them before, although all through their life they had been in the habit of seeing singly only those few objects which were about equally distant with the point of fixation, and the rest, those nearer and farther, which constitute the great majority, had always been double.

"We must then learn to turn our attention to our particular sensations, and we learn this commonly only for such sensations as are means of cognition of the outer world. Only so far as they serve this end have our sensations any importance for us in ordinary life. Subjective feelings are mostly interesting only to scientific investigators; were they remarked in the ordinary use of the senses, they could only cause disturbance. Whilst, therefore, we reach an extraordinary degree of firmness and security in objective observation, we not only do not reach this where subjective phenomena are concerned, but we actually attain in a high degree the faculty of overlooking these altogether, and keeping ourselves independent of their influence in judging of objects, even in cases where their strength might lead them easily to attract our attention." (Physiol. Optik, pp. 431-2.)

Even where the sensation is not merely subjective, as in the cases of which Helmholtz speaks, but is a sign of something outward, we are also liable, as Reid says, to overlook its intrinsic quality and attend exclusively to the image of the 'thing' it suggests. But here everyone can easily notice the sensation itself if he will. Usually we see a sheet of paper as uniformly white, although a part of it may be in shadow. But we can in an instant, if we please, notice the shadow as local color. A man walking towards us does not usually seem to alter his size; but we can, by setting our attention in a peculiar way make him appear to do so. The whole education of the artist consists in his learning to see the presented signs as well as the represented things. No matter what the field of view means, he sees it also as it feels--that is, as a collection of patches of color bounded by lines--the whole forming an optical diagram of whose intrinsic proportions one who is not an artist has hardly a conscious inkling. The ordinary man's attention passes over them to their import; the artist's turns back and dwells upon them for their own sake. 'Don't draw the thing as it is, but as it looks!' is the endless advice of every teacher to his pupil; forgetting that what it 'is' is what it would also 'look,' provided it were placed in what we have called the 'normal' situation for vision. In this situation the sensation as 'sign' and the sensation as 'object' coalesce into one, and there is no contrast between them.

Sensations which seem Suppressed.

But a great difficulty has been made of certain peculiar cases which we must now turn to consider. They are cases in which a present sensation, whose existence is supposed to be proved by its outward conditions being there, seems absolutely suppressed or changed by the image of the 'thing' it suggests.

This matter carries us back to what was said on p. 218. The passage there quoted from Helmholtz refers to these cases. He thinks they conclusively disprove the original and intrinsic spatiality of any of our retinal sensations; for if such a one, actually present, had an immanent and essential space-determination of its own, that might well be added to and overlaid or even momentarily eclipsed by suggestions of its signification, but how could it possibly be altered or completely suppressed thereby? Of actually present sensations, he says, being suppressed by suggestions of experience--

"We have not a single well-attested example. In all those illusions which are provoked by sensations in the absence of their usually exciting objects, the mistake never vanishes by the better understanding of the object really present, and by insight into the cause of deception. Phosphenes provoked by pressure on the eyeball, by traction on the entrance of the optic nerve, after-images, etc., remain projected into their apparent place in the field of vision, just as the image projected from a mirror's surface continues to be seen behind the mirror, although we know that to all these appearances no outward reality corresponds. True enough, we can remove our attention, and keep it removed, from sensations that have no reference to the outer world, those, e.g., of the weaker after-images, and of entoptic objects, etc.... But what would become of our perceptions at all if we had the power not only of ignoring, but of transforming into their opposites, any part of them that differed from that outward experience, the image of which, as that of a present reality, accompanies them in the mind?"

And again:

"On the analogy of all other experience, we should expect that the conquered feelings would persist to our perception, even if only in the shape of recognized illusions. But this is not the case. One does not see how the assumption of originally spatial sensations can explain our optical cognitions, when in the last resort those who believe in these very sensations find themselves obliged to assume that they are overcome by our better judgment, based on experience."

These words, coming from such a quarter, necessarily carry great weight. But the authority even of a Helmholtz ought not to shake one's critical composure. And the moment one abandons abstract generalities and comes to close quarters with the particulars, I think one easily sees that no such conclusions as those we have quoted follow from the latter. But profitably to conduct the discussion we must divide the alleged instances into groups.

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(a) With Helmholtz, color-perception is equally with space-perception an intellectual affair. The so-called simultaneous color-contrast, by which one color modifies another alongside of which it is said, is explained by him as an unconscious inference. In Chapter XVII we discussed the color-contrast problem; the principles which applied to its solution will prove also applicable to part of the present problem. In my opinion, Hering has definitively proved that, when one color is laid beside another, it modifies the sensation of the latter, not by virtue of any mere mental suggestion, as Helmholtz would have it, but by actually exciting a new nerve-process, to which the modified feeling of color immediately corresponds. The explanation is physiological, not psychological. The transformation of the original color by the inducing color is due to the disappearance of the physiological conditions under which the first color was produced, and to the induction, under the new conditions, of a genuine new sensation, with which the 'suggestions of experience' have naught to do.

That processes in the visual apparatus propagate themselves laterally, if one may so express it, is also shown by the phenomena of contrast which occur after looking upon motions of various kinds. Here are a few examples. If, over the rail of a moving vessel, we look at the water rushing along the side, and then transfer our gaze to the deck, a band of planks will appear to us, moving in the opposite direction to that in which, a moment previously, we had been seeing the water move, whilst on either side of this band another band of planks will move as the water did. Looking at a waterfall, or at the road from out of a car-window in a moving tram, produces the same illusion, which may be easily verified in the laboratory by a simple piece of apparatus. A board with a window five or six inches wide and of any convenient length is supported upright on two feet. On the back side of the board, above and below the window, are two rollers, one of which is provided with a crank. An endless band of any figured stuff is passed over these rollers (one of which can be so adjusted on its bearings as to keep the stuff always taut and not liable to slip), and the surface of the front board is also covered with stuff or paper of a nature to catch the eye. Turning the crank now sets the central band in continuous motion, whilst the margins of the field remain really at rest, but after a while appear moving in the contrary way. Stopping the crank results in an illusory appearance of motion in reverse directions all over the field.

A disk with an Archimedean spiral drawn upon it, whirled round on an ordinary rotating machine, produces still more startling effects.

"If the revolution is in the direction in which the spiral line approaches the centre of the disk the entire surface of the latter seems to expand during revolution and to contract after it has ceased; and vice versâ if the movement of revolution is in the opposite direction. If in the former case the eyes of the observers are turned from the rotating disk towards any familiar object--e.g. the face of a friend--the latter seems to contract or recede in a somewhat striking manner, and to expand or approach after the opposite motion of the spiral."

An elementary form of these motor illusions seems to be the one described by Helmholtz on pp. 568-571 of his Optik. The motion of anything in the field of vision along an acute angle towards a straight line sensibly distorts that line. Thus in Fig. 66: Let AB be a line drawn on paper, CDE the tracing made over this line by the point of a compass steadily followed by the eye, as it moves. As the compass-point passes from C to D, the line appears to move downwards; as it passes from D to E, the line appears to move upwards; at the same time the whole line seems to incline itself in the direction FG during the first half of the compass's movement; and in the direction HI during its last half; the change from one inclination to another being quite distinct as the compass-point passes over D.

Any line across which we draw a pencil-point appears to be animated by a rapid movement of its own towards the pencil-point. This apparent movement of both of two things in relative motion to each other, even when one of them is absolutely still, reminds us of the instances quoted from Vierordt on page 188, and seems to take us back to a primitive stage of perception, in which the discriminations we now make when we feel a movement have not yet been made. If we draw the point of a pencil through 'Zöllner's pattern' (Fig. 60, p. 232), and follow it with the eye, the whole figure becomes the scene of the most singular apparent unrest, of which Helmholtz has very carefully noted the conditions. The illusion of Zöllner's figure vanishes entirely, or almost so, with most people, if they steadily look at one point of it with an unmoving eye; and the same is the case with many other illusions.

Now all these facts taken together seem to show--vaguely it is true, but certainly--that present excitements and after-effects of former excitements may alter the result of processes occurring simultaneously at a distance from them in the retina or other portions of the apparatus for optical sensation. In the cases last considered, the moving eye, as it sweeps the fovea over certain parts of the figure, seems thereby to determine a modification in the feeling which the other parts confer, which modification is the figure's 'distortion.' It is true that this statement explains nothing. It only keeps the cases to which it applies from being explained spuriously. The spurious account of these illusions is that they are intellectual, not sensational, that they are secondary, not primary, mental facts. The distorted figure is said to be one which the mind is led to imagine, by falsely drawing an unconscious inference from certain premises of which it is not distinctly aware. And the imagined figure is supposed to be strong enough to suppress the perception of whatever real sensations there may be. But Helmholtz, Wundt, Delbœuf, Zöllner, and all the advocates of unconscious inference are at variance with each other when it comes to the question what these unconscious premises and inferences may be.

That small angles look proportionally larger than larger ones is, in brief, the fundamental illusion to which almost all authors would reduce the peculiarity of Fig. 67, as of Figs. 60, 61, 62 (p. 232). This peculiarity of small angles is by Wundt treated as the case of a filled space seeming larger than an empty one, as in Fig. 68; and this, according to both Delbœuf and Wundt, is owing to the fact that more muscular innervation is needed for the eye to traverse a filled space than an empty one, because the points and lines in the filled space inevitably arrest and constrain the eye, and this makes us feel as if it were doing more work, i.e. traversing a longer distance. When, however, we recollect that muscular movements are positively proved to have no share in the waterfall and revolving-spiral illusions, and that it is hard to see how Wundt's and Delbœuf's particular form of muscle-explanation can possibly apply to the compass-point illusion considered a moment ago, we must conclude that these writers have probably exaggerated, to say the least, the reach of their muscle-explanation in the case of the subdivided angles and lines. Never do we get such strong muscular feelings as when, against the course of nature, we oblige our eyes to be still; but fixing the eyes on one point of the figure, so far from making that part of the latter seem larger, dispels, in most persons, the illusion of these diagrams altogether.

As for Helmholtz, he invokes, to explain the enlargement of small angles, what he calls a 'law of contrast' between directions and distances of lines, analogous to that between colors and intensities of light. Lines cutting another line make the latter seem more inclined away from them than it really is. Moreover, clearly recognizable magnitudes appear greater than equal magnitudes which we but vaguely apprehend. But this is surely a sensationalistic law, a native function of our seeing-apparatus. Quite as little as the negative after-image of the revolving spiral could such contrast be deduced from any association of ideas or recall of past objects. The principle of contrast is criticised by Wundt, who says that by it small spaces ought to appear to us smaller, and not larger, than they really are. Helmholtz might have retorted (had not the retort been as fatal to the uniformity of his own principle as to Wundt's) that if the muscle-explanation were true, it ought not to give rise to just the opposite illusions in the skin. We saw on p. 141 that subdivided spaces appear shorter than empty ones upon the skin. To the instances there given add this: Divide a line on paper into equal halves, puncture the extremities, and make punctures all along one of the halves; then, with the finger-tip on the opposite side of the paper, follow the line of punctures; the empty half will seem much longer than the punctured half. This seems to bring things back to unanalyzable laws, by reason of which our feeling of size is determined differently in the skin and in the retina, even when the objective conditions are the same. Hering's explanation of Zöllner's figure is to be found in Hermann's Handb. d. Physiologie, iii. 1. p. 579. Lipps gives another reason why lines cutting another line make the latter seem to bend away from them more than is really the case. If, he says, we draw (Fig. 69) the line pm upon the line ab, and follow the latter with our eye, we shall, on reaching the point m, tend for a moment to slip off ab and to follow mp, without distinctly realizing that we are not still on the main line. This makes us feel as if the remainder mb of the main line were bent a little away from its original direction. The illusion is apparent in the shape of a seeming approach of the ends b, b, of the two main lines. This to my mind would be a more satisfactory explanation of this class of illusions than any of those given by previous authors, were it not again for what happens in the skin.

Considering all the circumstances, I feel justified in discarding his entire batch of illusions as irrelevant to our present inquiry. Whatever they may prove, they do not prove that our visual percepts of form and movement may not be sensations strictly so called. They much more probably fall into line with the phenomena of irradiation and of color-contrast, and with Vierordt's primitive illusions of movement. They show us, if anything, a realm of sensations in which our habitual experience has not yet made traces, and which persist in spite of our better knowledge, unsuggestive of those other space-sensations which we all the time know from extrinsic evidence to constitute the real space-determinations of the diagram. Very likely, if these sensations were as frequent and as practically important as they now are insignificant and rare, we should end by substituting their significates--the real space-values of the diagrams--for them. These latter we should then seem to see directly, and the illusions would disappear like that of the size of a tooth-socket when the tooth has been out a week.

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(b) Another batch of cases which we may discard is that of double images. A thoroughgoing anti-sensationalist ought to deny all native tendency to see double images when disparate retinal points are stimulated, because, he should say, most people never get them, but see all things single which experience has led them to believe to be single. "Can a doubleness, so easily neutralized by our knowledge, ever be a datum of sensation at all?" such an anti-sensationalist might ask.

To which the answer is that it is a datum of sensation, but a datum which, like many other data, must first be discriminated. As a rule, no sensible qualities are discriminated without a motive. And those that later we learn to discriminate were originally felt confused. As well pretend that a voice, or an odor, which we have learned to pick out, is no sensation now. One may easily acquire skill in discriminating double images, though, as Hering somewhere says, it is an art of which one cannot become master in one year or in two. For masters like Hering himself, or Le Conte, the ordinary stereoscopic diagrams are of little use. Instead of combining into one solid appearance, they simply cross each other with their doubled lines. Volkmann has shown a great variety of ways in which the addition of secondary lines, differing in the two fields, helps us to see the primary lines double. The effect is analogous to that shown in the cases which we despatched a moment ago, where given lines have their space-value changed by the addition of new lines, without our being able to say why, except that a certain mutual adhesion of the lines and modification of the resultant feeling takes place by psychophysiological laws. Thus, if in Fig. 70, l and r be crossed by an horizontal line at the same level, and viewed stereoscopically, they appear as a single pair of lines, s, in space. But if the horizontal be at different levels, as in l', r', three lines appear, as in s''.

Let us then say no more about double images. All that the facts prove is what Volkmann says, that, although there may be sets of retinal fibres so organized as to give an impression of two separate spots, yet the excitement of other retinal fibres may inhibit the effect of the first excitement, and prevent us from actually making the discrimination. Still farther retinal processes may, however, bring the doubleness to the eye of attention; and, once there, it is as genuine a sensation as any that our life affords.

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(c) These groups of illusions being eliminated, either as cases of defective discrimination, or as changes of one space-sensation into another when the total retinal process changes, there remain but two other groups to puzzle us. The first is that of the after-images distorted by projection on to oblique planes; the second relates to the instability of our judgments of relative distance and size by the eye, and includes especially what are known as pseudoscopic illusions.

The phenomena of the first group were described on page 232. A. W. Volkmann has studied them with his accustomed clearness and care. Even an imaginarily inclined wall, in a picture, will, if an after-image be thrown upon it, distort the shape thereof, and make us see a form of which our after-image would be the natural projection on the retina, were that form laid upon the wall. Thus a signboard is painted in perspective on a screen, and the eye, after steadily looking at a rectangular cross, is turned to the painted signboard. The after-image appears as an oblique-legged cross upon the signboard. It is the converse phenomenon of a perspective drawing like Fig. 71, in which really oblique-legged figures are seen as rectangular crosses.

The unstable judgments of relative distance and size were also mentioned on pp. 231-2. Whatever the size may be of the retinal image which an object makes, the object is seen as of its own normal size. A man moving towards us is not sensibly perceived to grow, for example; and my finger, of which a single joint may more than conceal him from my view, is nevertheless seen as a much smaller object than the man. As for distances, it is often possible to make the farther part of an object seem near and the nearer part far. A human profile in intaglio, looked at steadily with one eye, or even both, soon appears irresistibly as a bas-relief. The inside of a common pasteboard mask, painted like the outside, and viewed with one eye in a direct light, also looks convex instead of hollow. So strong is the illusion, after long fixation, that a friend who painted such a mask for me told me it soon became difficult to see how to apply the brush. Bend a visiting-card across the middle, so that its halves form an angle of 90º more or less; set it upright on the table, as in Fig. 72, and view it with one eye. You can make it appear either as if it opened towards you or away from you. In the former case, the angle ab lies upon the table, b being nearer to you than a; in the latter case ab seems vertical to the table--as indeed it really is--with a nearer to you than b. Again, look, with either one or two eyes, at the opening of a wine-glass or tumbler (Fig. 73), held either above or below the eye's level. The retinal image of the opening is an oval, but we can see the oval in either of two ways,--as if it were the perspective view of a circle whose edge b were farther from us than its edge a (in which case we should seem to be looking down on the circle), or as if its edge a were the more distant edge (in which case we should be looking up at it through the b side of the glass). As the manner of seeing the edge changes, the glass itself alters its form in space and looks straight or seems bent towards or from the eye, according as the latter is placed beneath or above it.

Plane diagrams also can be conceived as solids, and that in more than one way. Figs. 74, 75, 76, for example, are ambiguous perspective projections, and may each of them remind us of two different natural objects. Whichever of these objects we conceive clearly at the moment of looking at the figure, we seem to see in all its solidity before us. A little practice will enable us to flap the figures, so to speak, backwards and forwards from one object to the other at will. We need only attend to one of the angles represented, and imagine it either solid or hollow--pulled towards us out of the plane of the paper, or pushed back behind the same--and the whole figure obeys the cue and is instantaneously transformed beneath our gaze.

The peculiarity of all these cases is the ambiguity of the perception to which the fixed retinal impression gives rise. With our retina excited in exactly the same way, whether by after-image, mask or diagram, we see now this object and now that, as if the retinal image per se had no essential space-import. Surely if form and length were originally retinal sensations, retinal rectangles ought not to become acute or obtuse, and lines ought not to alter their relative lengths as they do. If relief were an optical feeling, it ought not to flap to and fro, with every optical condition unchanged. Here, if anywhere, the deniers of space-sensation ought to be able to make their final stand.

It must be confessed that their plea is plausible at first sight. But it is one thing to throw out retinal sensibility altogether as a space-yielding function the moment we find an ambiguity in its deliverances, and another thing to examine candidly the conditions which may have brought the ambiguity about. The former way is cheap, wholesale, shallow; the latter difficult and complicated, but full of instruction in the end. Let us try it for ourselves.

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In the case of the diagrams 72, 73, 74, 75, 76, the real object, lines meeting or crossing each other on a plane, is replaced by an imagined solid which we describe as seen. Really it is not seen but only so vividly conceived as to approach a vision of reality. We feel all the while, however, that the solid suggested is not solidly there. The reason why one solid may seem more easily suggested than another, and why it is easier in general to perceive the diagram solid than flat, seems due to probability. Those lines have countless times in our past experience been drawn on our retina by solids for once that we have seen them flat on paper. And hundreds of times we have looked down upon the upper surface of parallelopipeds, stairs and glasses, for once that we have looked upwards at their bottom--hence we see the solids easiest as if from above.

Habit or probability seems also to govern the illusion of the intaglio profile, and of the hollow mask. We have never seen a human face except in relief--hence the case with which the present sensation is overpowered. Hence, too, the obstinacy with which human faces and forms, and other extremely familiar convex objects, refuse to appear hollow when viewed through Wheatstone's pseudoscope. Our perception seems wedded to certain total ways of seeing certain objects. The moment the object is suggested at all, it takes possession of the mind in the fulness of its stereotyped habitual form. This explains the suddenness of the transformations when the perceptions change. The object shoots back and forth completely from this to that familiar thing, and doubtful, indeterminate, and composite things are excluded, apparently because we are unused to their existence.

When we turn from the diagrams to the actual folded visiting-card and to the real glass, the imagined form seems fully as real as the correct one. The card flaps over; the glass rim tilts this way or that, as if some inward spring suddenly became released in our eye. In these changes the actual retinal image receives different complements from the mind. But the remarkable thing is that the complement and the image combine so completely that the twain are one flesh, as it were, and cannot be discriminated in the result. If the complement be, as we have called it (on pp. 237-8), a set of imaginary absent eye-sensations, they seem no whit less vividly there than the sensation which the eye now receives from without.

The case of the after-images distorted by projection upon an oblique plane is even more strange, for the imagined perspective figure, lying in the plane, seems less to combine with the one a moment previously seen by the eye than to suppress it and take its place. The point needing explanation, then, in all this, is how it comes to pass that, when imagined sensations are usually so inferior in vivacity to real ones, they should in these few experiences prove to be almost or quite their match.

The mystery is solved when we note the class to which all these experiences belong. They are 'perceptions' of definite 'things,' definitely situated in tridimensional space. The mind uniformly uses its sensations to identify things by. The sensation is invariably apperceived by the idea, name, or 'normal' aspect (p. 238) of the thing. The peculiarity of the optical signs of things is their extraordinary mutability. A 'thing' which we follow with the eye, never doubting of its physical identity, will change its retinal image incessantly. A cross, a ring, waved about in the air, will pass through every conceivable angular and elliptical form. All the while, however, as we look at them, we hold fast to the perception of their 'real' shape, by mentally combining the pictures momentarily received with the notion of peculiar positions in space. It is not the cross and ring pure and simple which we perceive, but the cross so held, the ring so held. From the day of our birth we have sought every hour of our lives to correct the apparent form of things, and translate it into the real form by keeping note of the way they are placed or held. In no other class of sensations does this incessant correction occur. What wonder, then, that the notion 'so placed' should invincibly exert its habitual corrective effect, even when the object with which it combines is only an after-image, and make us perceive the latter under a changed but more 'real' form? The 'real' form is also a sensation conjured up by memory; but it is one so probable, so habitually conjured up when we have just this combination of optical experiences, that it partakes of the invincible freshness of reality, and seems to break through that law which elsewhere condemns reproductive processes to being so much fainter than sensations.

Once more, these cases form an extreme. Somewhere, in the list of our imaginations of absent feelings, there must be found the vividest of all. These optical reproductions of real form are the vividest of all. It is foolish to reason from cases lower in the scale, to prove that the scale can contain no such extreme cases as these; and particularly foolish since we can definitely see why these imaginations ought to be more vivid than any others, whenever they recall the forms of habitual and probable things. These latter, by incessantly repeated presence and reproduction, will plough deep grooves in the nervous system. There will be developed, to correspond to them, paths of least resistance, of unstable equilibrium, liable to become active in their totality when any point is touched off. Even when the objective stimulus is imperfect, we shall still see the full convexity of a human face, the correct inclination of an angle or sweep of a curve, or the distance of two lines. Our mind will be like a polyhedron, whose facets are the attitudes of perception in which it can most easily rest. These are worn upon it by habitual objects, and from one of these it can pass only by tumbling over into another.

Hering has well accounted for the sensationally vivid character of these habitually reproduced forms. He says, after reminding us that every visual sensation is correlated to a physical process in the nervous apparatus:

"If this psycho-physical process is aroused, as usually happens, by light-rays impinging on the retina, its form depends not only on the nature of these rays, but on the constitution of the entire nervous apparatus which is connected with the organ of vision, and on the state in which it finds itself. The same stimulus may excite widely different sensations according to this state.

"The constitution of the nervous apparatus depends naturally in part upon innate predisposition; but the ensemble of effects wrought by stimuli upon it in the course of life, whether these come through the eyes or from elsewhere, is a co-factor of its development. To express it otherwise, involuntary and voluntary experience and exercise assist in determining the material structure of the nervous organ of vision, and hence the ways in which it may react on a retinal image as an outward stimulus. That experience and exercise should be possible at all in vision is a consequence of the reproductive power, or memory, of its nerve-substance. Every particular activity of the organ makes it more suited to a repetition of the same; ever slighter touches are required to make the repetition occur. The organ habituates itself to the repeated activity....

"Suppose now that, in the first experience of a complex sensation produced by a particular retinal image, certain portions were made the special objects of attention. In a repetition of the sensible experience it will happen that notwithstanding the identity of the outward stimulus these portions will be more easily and strongly reproduced; and when this happens a hundred times the inequality with which the various constituents of the complex sensation appeal to consciousness grows ever greater.

"Now in the present state of our knowledge we cannot assert that in both the first and the last occurrence of the retinal image in question the same pure sensation is provoked, but that the mind interprets it differently the last time in consequence of experience; for the only given things we know are on the one hand the retinal image which is both times the same, and on the other the mental percept which is both times different; of a third thing, such as a pure sensation, interpolated between image and percept, we know nothing. We ought, therefore, if we wish to avoid hypotheses, simply to say that the nervous apparatus reacts the last time differently from the first, and gives us in consequence a different group of sensations.

"But not only by repetition of the same retinal image, but by that of similar ones, will the law obtain. Portions of the image common to the successive experiences will awaken, as it were, a stronger echo in the nervous apparatus than other portions. Hence it results that reproduction is usually elective: the more strongly reverberating parts of the picture yield stronger feelings than the rest. This may result in the latter being quite overlooked and, as it were, eliminated from perception. It may even come to pass that instead of these parts eliminated by election a feeling of entirely different elements comes to consciousness-elements not objectively contained in the stimulus. A group of sensations, namely, for which a strong tendency to reproduction has become, by frequent repetition, ingrained in the nervous system will easily revive as a whole when, not its whole retinal image, but only an essential part thereof, returns. In this case we get some sensations to which no adequate stimulus exists in the retinal image, and which owe their being solely to the reproductive power of the nervous apparatus. This is complementary (ergänzende) reproduction.

"Thus a few points and disconnected strokes are sufficient to make us see a human face, and without specially directed attention we fail to note that we see much that really is not drawn on the paper. Attention will show that the outlines were deficient in spots where we thought them complete.... The portions of the percept supplied by complementary reproduction depend, however, just as much as its other portions, on the reaction of the nervous apparatus upon the retinal image, indirect though this reaction may, in the case of the supplied portions, be. And so long as they are present, we have a perfect right to call them sensations, for they differ in no wise from such sensations as correspond to an actual stimulus in the retina. Often, however, they are not persistent; many of them may be expelled by more close observation, but this is not proved to be the case with all.... In vision with one eye ... the distribution of parts within the third dimension is essentially the work of this complementary reproduction, i.e. of former experience.... When a certain way of localizing a particular group of sensations has become with us a second nature, our better knowledge, our judgment, our logic, are of no avail.... Things actually diverse may give similar or almost identical retinal images; e.g., an object extended in three dimensions, and its flat perspective picture. In such cases it often depends on small accidents, and especially on our will, whether the one or the other group of sensations shall be excited.... We can see a relief hollow, as a mould, or vice versâ; for a relief illuminated from the left can look just like its mould illuminated from the right. Reflecting upon this, one may infer from the direction of the shadows that one has a relief before one, and the idea of the relief will guide the nerve-processes into the right path, so that the feeling of the relief is suddenly aroused.... Whenever the retinal image is of such a nature that two diverse modes of reaction on the part of the nervous apparatus are, so to speak, equally, or nearly equally, imminent, it must depend on small accidents whether the one or the other reaction is realized. In these cases our previous knowledge often has a decisive effect, and helps the correct perception to victory. The bare idea of the right object is itself a feeble reproduction which with the help of the proper retinal picture develops into clear and lively sensation. But if there be not already in the nervous apparatus a disposition to the production of that percept which our judgment tells us is right, our knowledge strives in vain to conjure up the feeling of it; we then know that we see something to which no reality corresponds, but we see it all the same."

Note that no object not probable, no object which we are not incessantly practised in reproducing, can acquire this vividness in imagination. Objective corners are ever changing their angles to the eyes, spaces their apparent size, lines their distance. But by no transmutation of position in space does an objective straight line appear bent, and only in one position out of an infinity does a broken line look straight. Accordingly, it is impossible by projecting the after-image of a straight line upon two surfaces which make a solid angle with each other to give the line itself a sensible 'kink.' Look with it at the corner of your room: the after-image, which may overlap all three surfaces of the corner, still continues straight. Volkmann constructed a complicated surface of projection like that drawn in Fig. 77, but he found it impossible so to throw a straight after-image upon it as to alter its visible form.

One of the situations in which we oftenest see things is spread out on the ground before us. We are incessantly drilled in making allowance for this perspective, and reducing things to their real form in spite of optical foreshortening. Hence if the preceding explanations are true, we ought to find this habit inveterate. The lower half of the retina, which habitually sees the farther half of things spread out on the ground, ought to have acquired a habit of enlarging its pictures by imagination, so as to make them more than equal to those which fall on the upper retinal surface; and this habit ought to be hard to escape from, even when both halves of the object are equidistant from the eye, as in a vertical line on paper. Delbœuf has found, accordingly, that if we try to bisect such a line we place the point of division about of its length too high.

Similarly, a square cross, or a square, drawn on paper, should look higher than it is broad. And that this is actually the case, the reader may verify by a glance at Fig. 78. For analogous reasons the upper and lower halves of the letter S, or of the figure 8, hardly seem to differ. But when turned upside down, the upper half looks much the larger.

Hering has tried to explain our exaggeration of small angles in the same way. We have more to do with right angles than with any others: right angles, in fact, have an altogether unique sort of interest for the human mind. Nature almost never begets them, but we think space by means of them and put them everywhere. Consequently obtuse and acute ones, liable always to be the images of right ones foreshortened, particularly easily revive right ones in memory. It is hard to look at such figures as a, b, c, in Fig. 79, without seeing them in perspective, as approximations, at least, to foreshortened rectangular forms.

At the same time the genuine sensational form of the lines before us can, in all the cases of distortion by suggested perspective, be felt correctly by a mind able to abstract from the notion of perspective altogether. Individuals differ in this abstracting power. Artistic training improves it, so that after a little while errors in vertical bisection, in estimating height relatively to breadth, etc., become impossible. In other words, we learn to take the optical sensation before us pure.

We may then sum up our study of illusions by saying that they in no wise undermine our view that every spatial determination of things is originally given in the shape of a sensation of the eyes. They only show how very potent certain imagined sensations of the eyes may become.

These sensations, so far as they bring definite forms to the mind, appear to be retinal exclusively. The movements of the eyeballs play a great part in educating our perception, it is true; but they have nothing to do with constituting any one feeling of form. Their function is limited to exciting the various feelings of form, by tracing retinal streaks; and to comparing them, and measuring them off against each other, by applying different parts of the retinal surface to the same objective thing. Helmholtz's analysis of the facts of our 'measurement of the field of view' is, bating a lapse or two, masterly, and seems to prove that the movements of the eye have had some part in bringing our sense of retinal equivalencies about--equivalencies, mind, of different retinal forms and sizes, not forms and sizes themselves. Superposition is the way in which the eye-movements accomplish this result. An object traces the line AB on a peripheral tract of the retina. Quickly we move the eye so that the same object traces the line ab on a central tract. Forthwith, to our mind, AB and ab are judged equivalent. But, as Helmholtz admits, the equivalence-judgment is independent of the way in which we may feel the form and length of the several retinal pictures themselves:

"The retina is like a pair of compasses, whose points we apply in succession to the ends of several lines to see whether they agree or not in length. All we need know meanwhile about the compasses is that the distance of their points remains unchanged. What that distance is, and what is the shape of the compasses, is a matter of no account."

Measurement implies a stuff to measure. Retinal sensations give the stuff; objective things form the yardstick; motion does the measuring operation; which can, of course, be well performed only where it is possible to make the same object fall on many retinal tracts. This is practically impossible where the tracts make a wide angle with each other. But there are certain directions in the field of view, certain retinal lines, along which it is particularly easy to make the image of an object slide. The object then becomes a 'ruler' for these lines, as Helmholtz puts it, making them seem straight throughout if the object looked straight to us in that part of them at which it was most distinctly seen.

But all this need of superposition shows how devoid of exact space-import the feelings of movement are per se. As we compare the space-value of two retinal tracts by superposing them successively upon the same objective line, so we also have to compare the space-value of objective angles and lines by superposing them on the same retinal tract. Neither procedure would be required if our eye-movements were apprehended immediately, by pure muscular feeling or innervation, for example, as distinct lengths and directions in space. To compare retinal tracts, it would then suffice simply to notice how it feels to move any image over them. And two objective lines could be compared as well by moving different retinal tracts along them as by laying them along the same. It would be as easy to compare non-parallel figures as it now is to judge of those which are parallel. Those which it took the same amount of movement to traverse would be equal, in whatever direction the movement occurred.

GENERAL SUMMARY.

With this we may end our long and, I fear to many readers, tediously minute survey. The facts of vision form a jungle of intricacy; and those who penetrate deeply into physiological optics will be more struck by our omissions than by our abundance of detail. But for students who may have lost sight of the forest for the trees, I will recapitulate briefly the points of our whole argument from the beginning, and then proceed to a short historical survey, which will set them in relief.

All our sensations are positively and inexplicably extensive wholes.

The sensations contributing to space-perception seem exclusively to be the surface of skin, retina, and joints. 'Muscular' feelings play no appreciable part in the generation of our feelings of form, direction, etc.

The total bigness of a cutaneous or retinal feeling soon becomes subdivided by discriminative attention.

Movements assist this discrimination by reason of the peculiarly exciting quality of the sensations which stimuli moving over surfaces arouse.

Subdivisions, once discriminated, acquire definite relations of position towards each other within the total space. These 'relations' are themselves feelings of the subdivisions that intervene. When these subdivisions are not the seat of stimuli, the relations are only reproduced in imaginary form.

The various sense-spaces are, in the first instance, incoherent with each other; and primitively both they and their subdivisions are but vaguely comparable in point of bulk and form.

The education of our space-perception consists largely of two processes--reducing the various sense-feelings to a common measure, and adding them together into the single all-including space of the real world.

Both the measuring and the adding are performed by the aid of things.

The imagined aggregate of positions occupied by all the actual or possible, moving or stationary, things which we know, is our notion of 'real' space--a very incomplete and vague conception in all minds.

The measuring of our space-feelings against each other mainly comes about through the successive arousal of different ones by the same thing, by our selection of certain ones as feelings of its real size and shape, and by the degradation of others to the status of being merely signs of these.

For the successive application of the same thing to different space-giving surfaces motion is indispensable, and hence plays a great part in our space-education, especially in that of the eye. Abstractly considered, the motion of the object over the sensitive surface would educate us quite as well as that of the surface over the object. But the self-mobility of the organ carrying the surface accelerates immensely the result.

In completely educated space-perception, the present sensation is usually just what Helmholtz (Physiol. Optik, p. 797) calls it, 'a sign, the interpretation of whose meaning is left to the understanding.' But the understanding is exclusively reproductive and never productive in the process; and its function is limited to the recall of previous space-sensations with which the present one has been associated and which may be judged more real than it.

Finally, this reproduction may in the case of certain visual forms be as vivid, or almost so, as actual sensation is.

The third dimension forms an original element of all our space-sensations. In the eye it is subdivided by various discriminations. The more distant subdivisions are often shut out altogether, and, in being suppressed, have the effect of diminishing the absolute space-value of the total field of view.

HISTORICAL.

Let us now close with a brief historical survey. The first achievement of note in the study of space-perception was Berkeley's theory of vision. This undertook to establish two points, first that distance was not a visual but a tactile form of consciousness, suggested by visual signs; secondly, that there is no one quality or 'idea' common to the sensations of touch and sight, such that prior to experience one might possibly anticipate from the look of an object anything about its felt size, shape, or position, or from the touch of it anything about its look.

In other words, that primitively chaotic or semi-chaotic condition of our various sense-spaces which we have demonstrated, was established for good by Berkeley; and he bequeathed to psychology the problem of describing the manner in which the deliverances are harmonized so as all to refer to one and the same extended world.

His disciples in Great Britain have solved this problem after Berkeley's own fashion, and to a great extent as we have done ourselves, by the ideas of the various senses suggesting each other in consequence of Association. But, either because they were intoxicated with the principle of association, or because in the number of details they lost their general bearings, they have forgotten, as a rule, to state under what sensible form the primitive spatial experiences are found which later became associated with so many other sensible signs. Heedless of their master Locke's precept, that the mind can frame unto itself no one new simple idea, they seem for the most part to be trying to explain the extensive quality itself, account for it, and evolve it, by the mere association together of feelings which originally possessed it not. They first evaporate the nature of extension by making it tantamount to mere 'coexistence,' and then they explain coexistence as being the same thing as succession, provided it be an extremely rapid or a reversible succession. Space-perception thus emerges without being anywhere postulated. The only things postulated are unextended feelings and time. Says Thomas Brown (lecture xxiii.): "I am inclined to reverse exactly the process commonly supposed; and instead of deriving the measure of time from extension, to derive the knowledge and original measure of extension from time." Brown and both the Mills think that retinal sensations, colors, in their primitive condition, are felt with no extension and that the latter merely becomes inseparably associated with them. John Mill says: "Whatever may be the retinal impression conveyed by a line which bounds two colors, I see no ground for thinking that by the eye alone we could acquire the conception of what we now mean when we say that one of the colors is outside [beside] the other."

Whence does the extension come which gets so inseparably associated with these non-extended colored sensations? From the 'sweep and movements' of the eye--from muscular feelings. But, as Prof. Bain says, if movement-feelings give us any property of things, "it would seem to be not space, but time." And John Mill says that "the idea of space is, at bottom, one of time." Space, then, is not to be found in any elementary sensation, but, in Bain's words, "as a quality, it has no other origin and no other meaning than the association of these different [non-spatial] motor and sensitive effects."

This phrase is mystical-sounding enough to one who understands association as producing nothing, but only as knitting together things already produced in separate ways. The truth is that the English Associationist school, in trying to show how much their principle can accomplish, have altogether overshot the mark and espoused a kind of theory in respect to space-perception which the general tenor of their philosophy should lead them to abhor. Really there are but three possible kinds of theory concerning space. Either (1) there is no spatial quality of sensation at all, and space is a mere symbol of succession; or (2) there is an extensive quality given immediately in certain particular sensations; or, finally, (3) there is a quality produced out of the inward resources of the mind, to envelop sensations which, as given originally, are not spatial, but which, on being cast into the spatial form, become united and orderly. This last is the Kantian view. Stumpf admirably designates it as the 'psychic stimulus' theory, the crude sensations being considered as goads to the mind to put forth its slumbering power.

Brown, the Mills, and Bain, amid these possibilities, seem to have gone astray like lost sheep. With the 'mental chemistry' of which the Mills speak--precisely the same thing as the 'psychical synthesis' of Wundt, which, as we shall soon see, is a principle expressly intended to do what Association can never perform--they hold the third view, but again in other places imply the first. And, between the impossibility of getting from mere association anything not contained in the sensations associated and the dislike to allow spontaneous mental productivity, they flounder in a dismal dilemma. Mr. Sully joins them there in what I must call a vague and vacillating way. Mr. Spencer of course is bound to pretend to 'evolve' all mental qualities out of antecedents different from themselves, so that we need perhaps not wonder at his refusal to accord the spatial quality to any of the several elementary sensations out of which our space-perception grows. Thus (Psychology, ii. 168, 172, 218):

"No idea of extension can arise from a simultaneous excitation" of a multitude of nerve-terminations like those of the skin or the retina, since this would imply a "knowledge of their relative positions"--that is, "a pre-existent idea of a special extension, which is absurd." "No relation between successive states of consciousness gives in itself any idea of extension." "The muscular sensations accompanying motion are quite distinct from the notions of space and time associated with them."

Mr. Spencer none the less inveighs vociferously against the Kantian position that space is produced by the mind's own resources. And yet he nowhere denies space to be a specific affection of consciousness different from time!

Such incoherency is pitiful. The fact is that, at bottom, all these authors are really 'psychical stimulists,' or Kantists. The space they speak of is a super-sensational mental product. This position appears to me thoroughly mythological. But let us see how it is held by those who know more definitely what they mean. Schopenhauer expresses the Kantian view with more vigor and clearness than anyone else. He says:

"A man must be forsaken by all the gods to dream that the world we see outside of us, filling space in its three dimensions, moving down the inexorable stream of time, governed at each step by Causality's invariable law,--but in all this only following rules which we may prescribe for it in advance of all experience,--to dream, I say, that such a world should stand there outside of us, quite objectively real with no complicity of ours, and thereupon by a subsequent act, through the instrumentality of mere sensation, that it should enter our head and reconstruct a duplicate of itself as it was outside. For what a poverty-stricken thing is this mere sensation! Even in the noblest organs of sense it is nothing more than a local and specific feeling, susceptible within its kind of a few variations, but always strictly subjective and containing in itself nothing objective, nothing resembling a perception. For sensation of every sort is and remains a process in the organism itself. As such it is limited to the territory inside the skin and can never, accordingly, per se contain anything that lies outside the skin or outside ourselves.... Only when the Understanding ... is roused to activity and brings its sole and only form, the law of Causality, into play, only then does the mighty transformation take place which makes out of subjective sensation objective intuition. The Understanding, namely, grasps by means of its innate, a priori, ante-experiential form, the given sensation of the body as an effect which as such must necessarily have a cause. At the same time the Understanding summons to its aid the form of the outer sense which similarly lies already preformed in the intellect (or brain), and which is Space, in order to locate that cause outside of the organism.... In this process the Understanding, as I shall soon show, takes note of the most minute peculiarities of the given sensation in order to construct in the outer space a cause which shall completely account for them. This operation of the Understanding is, however, not one that takes place discursively, reflectively, in abstracto, by means of words and concepts; but is intuitive and immediate.... Thus the Understanding must first create the objective world; never can the latter, already complete in se, simply promenade into our heads through the senses and organic apertures. For the senses yield us nothing further than the raw material which must be first elaborated into the objective conception of an orderly physical world-system by means of the aforesaid simple forms of Space, Time, and Causality.... Let me show the great chasm between sensation and perception by showing how raw the material is out of which the fair structure is upreared. Only two senses serve objective perception: touch and sight. They alone furnish the data on the basis whereof the Understanding, by the process indicated, erects the objective world.... These data in themselves are still no perception; that is the Understanding's work. If I press with my hand against the table, the sensation I receive has no analogy with the idea of the firm cohesion of the parts of this mass: only when my Understanding passes from the sensation to its cause does it create for itself a body with the properties of solidity, impenetrability, and hardness. When in the dark I lay my hand on a surface, or grasp a ball of three inches diameter, in either case the same parts of the hand receive the impression: but out of the different contraction of the hand in the two cases my Understanding constructs the form of the body whose contact caused the feeling, and confirms its construction by leading me to move my hand over the body. If one born blind handles a cubical body, the sensations of his hand are quite uniform on all sides and in all directions,--only the corners press upon a smaller part of his skin. In these sensations, as such, there is nothing whatever analogous to a cube. But from the felt resistance his Understanding infers immediately and intuitively a cause thereof, which now presents itself as a solid body; and from the movements of exploration which the arms made whilst the feelings of the hands remained constant he constructs, in the space known to him a priori, the body's cubical shape. Did he not bring with him ready-made the idea of a cause and of a space, with the laws thereof, there never could arise, out of those successive feelings in his hand, the image of a cube. If we let a string run through our closed hand, we immediately construct as the cause of the friction and its duration in such an attitude of the hand, a long cylindrical body moving uniformly in one direction. But never out of the pure sensation in the hand could the idea of movement, that is, of change of position in space by means of time, arise: such a content can never lie in sensation, nor come out of it. Our Intellect, antecedently to all experience, must bear in itself the intuitions of Space and Time, and therewithal of the possibility of motion, and no less the idea of Causality, to pass from the empirically given feeling to its cause, and to construct the latter as a so moving body of the designated shape. For how great is the abyss between the mere sensation in the hand and the ideas of causality, materiality, and movement through Space, occurring in Time! The feeling in the hand, even with different contacts and positions, is something far too uniform and poor in content for it to be possible to construct out of it the idea of Space with its three dimensions, of the action of bodies on each other, with the properties of extension, impenetrability, cohesion, shape, hardness, softness, rest, and motion--in short, the foundations of the objective world. This is only possible through Space, Time, and Causality ... being preformed in the Intellect itself,... from whence it again follows that the perception of the external world is essentially an intellectual process, a work of the Understanding, to which sensation furnishes merely the occasion, and the data to be interpreted in each particular case."

I call this view mythological, because I am conscious of no such Kantian machine-shop in my mind, and feel no call to disparage the powers of poor sensation in this merciless way. I have no introspective experience of mentally producing or creating space. My space-intuitions occur not in two times but in one. There is not one moment of passive inextensive sensation, succeeded by another of active extensive perception, but the form I see is as immediately felt as the color which fills it out. That the higher parts of the mind come in, who can deny? They add and subtract, they compare and measure, they reproduce and abstract. They inweave the space-sensations with intellectual relations; but these relations are the same when they obtain between the elements of the space-system as when they obtain between any of the other elements of which the world is made.

The essence of the Kantian contention is that there are not spaces, but Space--one infinite continuous Unit--and that our knowledge of this cannot be a piecemeal sensational affair, produced by summation and abstraction. To which the obvious reply is that, if any known thing bears on its front the appearance of piecemeal construction and abstraction, it is this very notion of the infinite unitary space of the world. It is a notion, if ever there was one; and no intuition. Most of us apprehend it in the barest symbolic abridgment: and if perchance we ever do try to make it more adequate, we just add one image of sensible extension to another until we are tired. Most of us are obliged to turn round and drop the thought of the space in front of us when we think of that behind. And the space represented as near to us seems more minutely subdivisible than that we think of as lying far away.

* * * * *

The other prominent German writers on space are also 'psychical stimulists.' Herbart, whose influence has been widest, says 'the resting eye sees no space,' and ascribes visual extension to the influence of movements combining with the non-spatial retinal feelings so as to form gradated series of the latter. A given sensation of such a series reproduces the idea of its associates in regular order, and its idea is similarly reproduced by any one of them with the order reversed. Out of the fusion of these two contrasted reproductions comes the form of space--Heaven knows how.

The obvious objection is that mere serial order is a genus, and space-order a very peculiar species of that genus; and that, if the terms of reversible series became by that fact coexistent terms in space, the musical scale, the degrees of warmth and cold, and all other ideally graded series ought to appear to us in the shape of extended corporeal aggregates,--which they notoriously do not, though we may of course symbolize their order by a spatial scheme. W. Volkmann von Volkmar, the Herbartian, takes the bull here by the horns, and says the musical scale is spatially extended, though he admits that its space does not belong to the real world. I am unacquainted with any other Herbartian so bold.

* * * * *

To Lotze we owe the much-used term 'local sign.' He insisted that space could not emigrate directly into the mind from without, but must be reconstructed by the soul; and he seemed to think that the first reconstructions of it by the soul must be super-sensational. But why sensations themselves might not be the soul's original spatial reconstructive acts Lotze fails to explain.

* * * * *

Wundt has all his life devoted himself to the elaboration of a space-theory, of which the neatest and most final expression is to be found in his Logik (ii. 457-60). He says:

"In the eye, space-perception has certain constant peculiarities which prove that no single optical sensation by itself possesses the extensive form, but that everywhere in our perception of space heterogeneous feelings combine. If we simply suppose that luminous sensations per se feel extensive, our supposition is shattered by that influence of movement in vision which is so clearly to be traced in many normal errors in the measurement of the field of view. If we assume, on the other hand, that the movements and their feelings are alone possessed of the extensive quality, we make an unjustified hypothesis, for the phenomena compel us, it is true, to accord an influence to movement, but give us no right to call the retinal sensations indifferent, for there are no visual ideas without retinal sensations. If then we wish rigorously to express the given facts, we can ascribe a spatial constitution only to combinations of retinal sensations with those of movement."

Thus Wundt, dividing theories into 'nativistic' and 'genetic,' calls his own a genetic theory. To distinguish it from other theories of the same class, he names it a 'theory of complex local signs.'

"It supposes two systems of local signs, whose relations--taking the eye as an example--we may think as ... the measuring of the manifold local-sign system of the retina by the simple local-sign system of the movements. In its psychological nature this is a process of associative synthesis: it consists in the fusion of both groups of sensations into a product, whose elementary components are no longer separable from each other in idea. In melting wholly away into the product which they create they become consciously undistinguishable, and the mind apprehends only their resultant, the intuition of space. Thus there obtains a certain analogy between this psychic synthesis and that chemical synthesis which out of simple bodies generates a compound that appears to our immediate perception as a homogeneous whole with new properties."

Now let no modest reader think that if this sounds obscure to him it is because he does not know the full context; and that if a wise professor like Wundt can talk so fluently and plausibly about 'combination' and 'psychic synthesis,' it must surely be because those words convey a so much greater fulness of positive meaning to the scholarly than to the unlearned mind. Really it is quite the reverse; all the virtue of the phrase lies in its mere sound and skin. Learning does but make one the more sensible of its inward unintelligibility. Wundt's 'theory' is the flimsiest thing in the world. It starts by an untrue assumption, and then corrects it by an unmeaning phrase. Retinal sensations are spatial; and were they not, no amount of 'synthesis' with equally spaceless motor sensations could intelligibly make them so. Wundt's theory is, in short, but an avowal of impotence, and an appeal to the inscrutable powers of the soul. It confesses that we cannot analyze the constitution or give the genesis of the spatial quality in consciousness. But at the same time it says the antecedents thereof are psychical and not cerebral facts. In calling the quality in question a sensational quality, our own account equally disclaimed ability to analyze it, but said its antecedents were cerebral, not psychical--in other words, that it was a first psychical thing. This is merely a question of probable fact, which the reader may decide.

* * * * *

And now what shall be said of Helmholtz? Can I find fault with a book which, on the whole, I imagine to be one of the four or five greatest monuments of human genius in the scientific line? If truth impels I must fain try, and take the risks. It seems to me that Helmholtz's genius moves most securely when it keeps close to particular facts. At any rate, it shows least strong in purely speculative passages, which in the Optics, in spite of many beauties, seem to me fundamentally vacillating and obscure. The 'empiristic' view which Helmholtz defends is that the space-determinations we perceive are in every case products of a process of unconscious inference. The inference is similar to one from induction or analogy. We always see that form before us which habitually would have caused the sensation we now have. But the latter sensation can never be intrinsically spatial, or its intrinsic space-determinations would never be overcome as they are so often by the 'illusory' space-determinations it so often suggests. Since the illusory determination can be traced to a suggestion of Experience, the 'real' one must also be such a suggestion: so that all space intuitions are due solely to Experience. The only psychic activity required for this is the association of ideas.

But how, it may be asked, can association produce a space-quality not in the things associated? How can we by induction or analogy infer what we do not already generically know? Can 'suggestions of experience' reproduce elements which no particular experience originally contained? This is the point by which Helmholtz's 'empiristic' theory, as a theory, must be judged. No theory is worthy of the name which leaves such a point obscure.

Well, Helmholtz does so leave it. At one time he seems to fall back on inscrutable powers of the soul, and to range himself with the 'psychical stimulists.' He speaks of Kant as having made the essential step in the matter in distinguishing the content of experience from that form--space, course--which is given it by the peculiar faculties of the mind. But elsewhere, again, speaking of sensationalistic theories which would connect spatially determinate feelings directly with certain neural events, he says it is better to assume only such simple psychic activities as we know to exist, and gives the association of ideas as an instance of what he means. Later, he reinforces this remark by confessing that he does not see how any neural process can give rise without antecedent experience to a ready-made (fertige) perception of space. And, finally, in a single momentous sentence, he speaks of sensations of touch as if they might be the original material of our space-percepts--which thus, from the optical point of view, 'may be assumed as given.'

Of course the eye-man has a right to fall back on the skin-man for help at a pinch. But doesn't this mean that he is a mere eye-man and not a complete psychologist? In other words, Helmholtz's Optics and the 'empiristic theory' therein professed must not be understood as attempts at answering the general question of how space-consciousness enters the mind. They simply deny that it enters with the first optical sensations. Our own account has affirmed stoutly that it enters then; but no more than Helmholtz have we pretended to show why. Who calls a thing a first sensation admits he has no theory of its production. Helmholtz, though all the while without an articulate theory, makes the world think he has one. He beautifully traces the immense part which reproductive processes play in our vision of space, and never--except in that one pitiful little sentence about touch--does he tell us just what it is they reproduce. He limits himself to denying that they reproduce originals of a visual sort. And so difficult is the subject, and so magically do catch-words work on the popular-scientist ear, that most likely, had he written 'physiological' instead of 'nativistic,' and 'spiritualistic' instead of 'empiristic' (which synonyms Hering suggests), numbers of his present empirical evolutionary followers would fail to find in his teaching anything worthy of praise. But since he wrote otherwise, they hurrah for him as a sort of second Locke, dealing another death-blow at the old bugaboo of 'innate ideas.' His 'nativistic' adversary Hering they probably imagine--Heaven save the mark!--to be a scholastic in modern disguise.

* * * * *

After Wundt and Helmholtz, the most important anti-sensationalist space-philosopher in Germany is Professor Lipps, whose deduction of space from an order of non-spatial differences, continuous yet separate, is a wonderful piece of subtlety and logic. And yet he has to confess that continuous differences form in the first instance only a logical series, which need not appear spatial, and that wherever it does so appear, this must be accounted a 'fact,' due merely 'to the nature of the soul.'

Lipps, and almost all the anti-sensationalist theorists except Helmholtz, seem guilty of that confusion which Mr. Shadworth Hodgson has done so much to clear away, viz., the confounding the analysis of an idea with the means of its production. Lipps, for example, finds that every space we think of can be broken up into positions, and concludes that in some undefined way the several positions must have pre-existed in thought before the aggregate space could have appeared to perception. Similarly Mr. Spencer, defining extension as an 'aggregate of relations of coexistent position,' says "every cognition of magnitude is a cognition of relations of position," and "no idea of extension can arise from the simultaneous excitation" of many nerves "unless there is a knowledge of their relative positions." Just so Prof. Bain insists that the very meaning of space is scope for movement, and that therefore distance and magnitude can be no original attributes of the eye's sensibility. Similarly because movement is analyzable into positions occupied at successive moments by the mover, philosophers (e.g. Schopenhauer, as quoted above) have repeatedly denied the possibility of its being an immediate sensation. We have, however, seen that it is the most immediate of all our space-sensations. Because it can only occur in a definite direction the impossibility of perceiving it without perceiving its direction has been decreed--a decree which the simplest experiment overthrows. It is a case of what I have called the 'psychologist's fallacy': mere acquaintance with space is treated as tantamount to every sort of knowledge about it, the conditions of the latter are demanded of the former state of mind, and all sorts of mythological processes are brought in to help. As well might one say that because the world consists of all its parts, therefore we can only apprehend it at all by having unconsciously summed these up in our head. It is the old idea of our actual knowledge being drawn out from a pre-existent potentiality, an idea which, whatever worth it may metaphysically possess, does no good in psychology.

My own sensationalistic account has derived most aid and comfort from the writings of Hering, A. W. Volkmann, Stumpf, Le Conte, and Schön. All these authors allow ample scope to that Experience which Berkeley's genius saw to be a present factor in all our visual acts. But they give Experience some grist to grind, which the soi-distant 'empiristic' school forgets to do. Stumpf seems to me the most philosophical and profound of all these writers; and I owe him much. I should doubtless have owed almost as much to Mr. James Ward, had his article on Psychology in the Encyclopædia Britannica appeared before my own thoughts were written down. The literature of the question is in all languages very voluminous. I content myself with referring to the bibliography in Helmholtz's and Aubert's works on Physiological Optics for the visual part of the subject, and with naming in a note the ablest works in the English tongue which have treated of the subject in a general way.

* * * * *

Reprinted, with considerable revision, from 'Mind' for 1887.

Prof. Jastrow has found that invariably we tend to underestimate the amount of our skin which may be stimulated by contact with an object when we express it in terms of visual space; that is, when asked to mark on paper the extent of skin affected, we always draw it much too small. This shows that the eye gets as much space feeling from the smaller line as the skin gets from the larger one. Cf. Jastrow: Mind, xi. 546-7; American Journal of Psychology, iii. 53.

Amongst sounds the graver ones seem the most extensive. Stumpf gives three reasons for this: 1) association with bigger causes; 2) wider reverberation of the hand and body when grave notes are sung; 3) audibility at a greater distance. He thinks that these three reasons dispense us from supposing an immanent extensity in the sensation of sound as such. See his remarks in the Tonpsychologie, i. 207-211.

Encyclopædia Britannica, 9th Edition, article Psychology, pp. 46, 58.

Philosophical Transactions (1841).

Hermann's Handb. d. Physiol., Bd. iii. 1, §. 575.

Loc. cit. §. 572.

Elemente der Psychophysik, ii. 475-6.

See Foster's Text-book of Physiology, bk. iii. c. vi. § 2.

Fechner, who was ignorant of the but lately discovered function of the semi-circular canals, gives a different explanation of the organic seat of these feelings. They are probably highly composite. With me, actual movements in the eyes play a considerable part in them, though I am hardly conscious of the peculiar feelings in the scalp which Fechner goes on to describe thus: "The feeling of strained attention in the different sense-organs seems to be only a muscular one produced in using these various organs by setting in motion, by a sort of reflex action, the set of muscles which belong to them. One can ask, then, with what particular muscular contraction the sense of strained attention in the effort to recall something is associated? On this question my own feeling gives me a decided answer; it comes to me distinctly not as a sensation of tension in the inside of the head, but as a feeling of strain and contraction in the scalp, with a pressure from outwards in over the whole cranium, undoubtedly caused by a contraction of the muscles of the scalp. This harmonizes very well with the expressions, sich den Kopf zerbrechen, den Kopf zusammennehmen. In a former illness, when I could not endure the slightest effort after continuous thought, and had no theoretical bias on this question, the muscles of the scalp, especially those of the back-head, assumed a fairly morbid degree of sensibility whenever I tried to think." (Elem. der Psychophysik, ii, 490-91.)

That the sensation in question is one of tactile rather than of acoustic sensibility would seem proved by the fact that a medical friend of the writer, both of whose membranæ tympani are quite normal, but one of whose ears is almost totally deaf, feels the presence and withdrawal of objects as well at one ear as at the other.

The skin seems to obey a different law from the eye here. If a given retinal tract be excited, first by a series of points, and next by the two extreme points, with the interval between them unexcited, this interval will seem considerably less in the second case than it seemed in the first. In the skin the unexcited interval feels the larger. The reader may easily verify the facts in this case by taking a visiting-card, cutting one edge of it into a saw-tooth pattern, and from the opposite edge cutting out all but the two corners, and then comparing the feelings aroused by the two edges when held against the skin.

Classen, Physiologie des Gesichtssinnes, p. 114; see also A. Riehl, Der Philosophische Kriticismus, ii. p. 149.

It is worth while at this point to call attention with some emphasis to the fact that, though the anatomical condition of the feeling resembles the feeling itself, such resemblance cannot be taken by our understanding to explain why the feeling should be just what it is. We hear it untiringly reiterated by materialists and spiritualists alike that we can see no possible inward reason why a certain brain-process should produce the feeling of redness and another of anger: the one process is no more red than the other is angry, and the coupling of process and feeling is, as far as our understanding goes, a juxtaposition pure and simple. But in the matter of spatial feeling, where the retinal patch that produces a triangle in the mind is itself a triangle, etc., it looks at first sight as if the sensation might be a direct cognition of its own neural condition. Were this true, however, our sensation should be one of multitude rather than of continuous extent; for the condition is number of optical nerve-termini, and even this is only a remote condition and not an immediate condition. The immediate condition of the feeling is not the process in the retina, but the process in the brain; and the process in the brain may, for aught we know, be as unlike a triangle,--nay, it probably is so,--as it is unlike redness or rage. It is simply a coincidence that in the case of space one of the organic conditions, viz., the triangle impressed on the skin or the retina, should lead to a representation in the mind of the subject observed similar to that which it produces in the psychological observer. In no other kind of case is the coincidence found. Even should we admit that we cognize triangles in space because of our immediate cognition of the triangular shape of our excited group of nerve-tips, the matter would hardly be more transparent, for the mystery would still remain, why are we so much better cognizant of triangles on our finger-tips than on the nerve-tips of our back, on our eye than on our ear, and on any of these parts than in our brain? Thos. Brown very rightly rejects the notion of explaining the shape of the space perceived by the shape of the 'nervous expansion affected.' "If this alone were necessary, we should have square inches and half inches, and various other forms, rectilinear and curvilinear, of fragrance and sound." (Lectures, XXII.)

Musical tones, e.g., have an order of quality independent either of their space- or time-order. Music comes from the time-order of the notes upsetting their quality-order. In general, if a b c d e f g h i j k, etc., stand for an arrangement of feelings in the order of their quality, they may assume any space-order or time-order, as d e f a h g, etc., and still the order of quality will remain fixed and unchanged.

The whole science of geometry may be said to owe its being to the exorbitant interest which the human mind takes in lines. We cut space up in every direction in order to manufacture them.

Kant was, I believe, the first to call attention to this last order of facts. After pointing out that two opposite spherical triangles, two gloves of a pair, two spirals wound in contrary directions, have identical inward determinations, that is, have their parts defined with relation to each other by the same law, and so must be conceived as identical, he showed that the impossibility of their mutual superposition obliges us to assign to each figure of a symmetrical pair a peculiar difference of its own which can only consist in an outward determination or relation of its parts, no longer to each other, but to the whole of an objectively outlying space with its points of the compass given absolutely. This inconceivable difference is perceived only "through the relation to right and left, which is a matter of immediate intuition." In these last words (welches unmittelbar auf Anschauung geht--Prolegomena, § 12) Kant expresses all that we have meant by speaking of up and down, right and left, as sensations. He is wrong, however, in invoking relation to extrinsic total space as essential to the existence of these contrasts in figures. Relation to our own body is enough.

In the eyes of many it will have seemed strange to call a relation a mere line, and a line a mere sensation. We may easily learn a great deal about any relation, say that between two points: we may divide the line which joins these, and distinguish it, and classify it, and find out its relations by drawing or representing new lines, and so on. But all this further industry has naught to do with our acquaintance with the relation itself, in its first intention. So cognized, the relation is the line and nothing more. It would indeed be fair to call it something less; and in fact it is easy to understand how most of us come to feel as if the line were a much grosser thing than the relation. The line is broad or narrow, blue or red, made by this object or by that alternately, in the course of our experience; it is therefore independent of any one of these accidents; and so, from viewing it as no one of such sensible qualities, we may end by thinking of it as something which cannot be defined except as the negation of all sensible quality whatever, and which needs to be put into the sensations by a mysterious act of 'relating thought.'

Another reason why we get to feel as if a space-relation must be something other than the mere feeling of a line or angle is that between two positions we can potentially make any number of lines and angles, or find, to suit our purposes, endlessly numerous relations. The sense of this indefinite potentiality cleaves to our words when we speak in a general way of 'relations of place,' and misleads us into supposing that not even any single one of them can be exhaustively equated by a single angle or a single line.

This often happens when the warm and cold points, or the round and pointed ones, are applied to the skin within the limits of a single 'Empfindungskreis.'

Vierordt, Grundriss der Physiologie, 5te Auflage (1877), pp. 326, 436.

Vorlesungen üb. Menschen- u. Thierseele (Leipzig, 1863), i. 214. See also Ladd's Physiological Psychology, pp. 396-8, and compare the account by G. Stanley Hall (Mind, x. 571) of the sensations produced by moving a blunt point lightly over the skin. Points of cutting pain, quivering, thrilling, whirling, tickling, scratching, and acceleration, alternated with each other along the surface.

Of the anatomical and physiological conditions of these facts we know as yet but little, and that little need not here be discussed. Two principal hypotheses have been invoked in the case of the retina. Wundt (Menschen- u. Thierseele, i. 214) called attention to the changes of color-sensibility which the retina displays as the image of the colored object passes from the fovea to the periphery. The color alters and becomes darker, and the change is more rapid in certain directions than in others. This alteration in general, however, is one of which, as such, we are wholly unconscious. We see the sky as bright blue all over, the modifications of the blue sensation being interpreted by us, not as differences in the objective color, but as distinctions in its locality. Lotze (Medizinische Psychologie, 333, 355), on the other hand, has pointed out the peculiar tendency which each particular point of the retina has to call forth that movement of the eyeball which will carry the image of the exciting object from the point in question to the fovea. With each separate tendency to movement (as with each actual movement) we may suppose a peculiar modification of sensibility to be conjoined. This modification would constitute the peculiar local tingeing of the image by each point. See also Sully's Psychology, pp. 118-121. Prof. B. Erdman has quite lately (Vierteljahrsschrift f. wiss. Phil., x. 324-9) denied the existence of all evidence for such immanent qualia of feeling characterizing each locality. Acute as his remarks are, they quite fail to convince me. On the skin the qualia are evident, I should say. Where, as on the retina, they are less so (Kries and Auerbach), this may well be a mere difficulty of discrimination not yet educated to the analysis.

1852, p. 331.

Maybe the localization of intracranial pain is itself due to such association as this of local signs with each other, rather than to their qualitative similarity in neighboring parts (supra, p. 19); though it is conceivable that association and similarity itself should here have one and the same neural basis. If we suppose the sensory nerves from those parts of the body beneath any patch of skin to terminate in the same sensorial brain-tract as those from the skin itself, and if the excitement of any one fibre tends to irradiate through the whole of that tract, the feelings of all fibres going to that tract would presumably both have a similar intrinsic quality, and at the same time tend each to arouse the other. Since the same nerve-trunk in most cases supplies the skin and the parts beneath, the anatomical hypothesis presents nothing improbable.

Unless, indeed, the foot happen to be spontaneously tingling or something of the sort at the moment. The whole surface of the body is always in a state of semi-conscious irritation which needs only the emphasis of attention, or of some accidental inward irritation, to become strong at any point.

It is true that the inside of the forearm, though its discriminative sensibility is often less than that of the outside, usually rises very prominently into consciousness when the latter is touched. Its æsthetic sensibility to contact is a good deal finer. We enjoy stroking it from the extensor to the flexor surface around the ulnar side more than in the reverse direction. Pronating movements give rise to contacts in this order, and are frequently indulged in when the back of the forearm feels an object against it.

These facts were first noticed by Wundt: see his Beiträge, p. 140, 202. See also Lamansky, Pflüger's Archiv, xi. 418.

So far all has been plain sailing, but our course begins to be so tortuous when we descend into minuter detail that I will treat of the more precise determination of locality in a long note. When P recalls an ideal line leading to the fovea the line is felt in its entirety and but vaguely; whilst P, which we supposed to be a single star of actual light, stands out in strong distinction from it. The ground of the distinction between P and the ideal line which it terminates is manifest--P being vivid while the line is faint; but why should P hold the particular position it does, at the end of the line, rather than anywhere else--for example, in its middle? That seems something not at all manifest.

To clear up our thoughts about this latter mystery, let us take the case of an actual line of light, none of whose parts is ideal. The feeling of the line is produced, as we know, when a multitude of retinal points are excited together, each of which when excited separately would give rise to one of the feelings called local signs. Each of these signs is the feeling of a small space. From their simultaneous arousal we might well suppose a feeling of larger space to result. But why is it necessary that in this larger spaciousness the sign a should appear always at one end of the line, z at the other, and m in the middle? For though the line be a unitary streak of light, its several constituent points can nevertheless break out from it, and become alive, each for itself, under the selective eye of attention.

The uncritical reader, giving his first careless glance at the subject, will say that there is no mystery in this, and that 'of course' local signs must appear alongside of each other, each in its own place;--there is no other way possible. But the more philosophic student, whose business it is to discover difficulties quite as much as to get rid of them, will reflect that it is conceivable that the partial factors might fuse into a larger space, and yet not each be located within it any more than a voice is located in a chorus. He will wonder how, after combining into the line, the points can become severally alive again: the separate puffs of a 'sirene' no longer strike the ear after they have fused into a certain pitch of sound. He will recall the fact that when, after looking at things with one eye closed, we double, by opening the other eye, the number of retinal points affected, the new retinal sensations do not as a rule appear alongside of the old ones and additional to them, but merely make the old ones seem larger and nearer. Why should the affection of new points on the same retina have so different a result? In fact, he will see no sort of logical connection between (1) the original separate local signs, (2) the line as a unit, (3) the line with the points discriminated in it, and (4) the various nerve-processes which subserve all these different things. He will suspect our local sign of being a very slippery and ambiguous sort of creature. Positionless at first, it no sooner appears in the midst of a gang of companions than it is found maintaining the strictest position of its own, and assigning place to each of its associates. How is this possible? Must we accept what we rejected a while ago as absurd, and admit the points each to have position in se? Or must we suspect that our whole construction has been fallacious, and that we have tried to conjure up, out of association, qualities which the associates never contained?

There is no doubt a real difficulty here; and the shortest way of dealing with it would be to confess it insoluble and ultimate. Even if position be not an intrinsic character of any one of those sensations we have called local signs, we must still admit that there is something about every one of them that stands for the potentiality of position, and is the ground why the local sign, when it gets placed at all, gets placed here rather than there. If this 'something' be interpreted as a physiological something, as a mere nerve-process, it is easy to say in a blank way that when it is excited alone, it is an 'ultimate fact' (1) that a positionless spot will appear; that when it is excited together with other similar processes, but without the process of discriminative attention, it is another 'ultimate fact' (2) that a unitary line will come; and that the final 'ultimate fact' (3) is that, when the nerve-process is excited in combination with that other process which subserves the feeling of attention, what results will be the line with the local sign inside of it determined to a particular place. Thus we should escape the responsibility of explaining, by falling back on the everlasting inscrutability of the psycho-neural nexus. The moment we call the ground of localization physiological, we need only point out how, in those cases in which localization occurs, the physiological process differs from those in which it does not, to have done all we can possibly do in the matter. This would be unexceptionable logic, and with it we might let the matter drop, satisfied that there was no self-contradiction in it, but only the universal psychological puzzle of how a new mode of consciousness emerges whenever a fundamentally new mode of nervous action occurs.

But, blameless as such tactics would logically be on our part, let us see whether we cannot push our theoretic insight a little farther. It seems to me we can. We cannot, it is true, give a reason why the line we feel when process (2) awakens should have its own peculiar shape; nor can we explain the essence of the process of discriminative attention. But we can see why, if the brute facts be admitted that a line may have one of its parts singled out by attention at all, and that that part may appear in relation to other parts at all, the relation must be in the line itself,--for the line and the parts are the only things supposed to be in consciousness. And we can furthermore suggest a reason why parts appearing thus in relation to each other in a line should fall into an immutable order, and each within that order keep its characteristic place.

If a lot of such local signs all have any quality which evenly augments as we pass from one to the other, we can arrange them in an ideal serial order, in which any one local sign must lie below those with more, above those with less, of the quality in question. It must divide the series into two parts,--unless indeed it have a maximum or minimum of the quality, when it either begins or ends it.

Such an ideal series of local signs in the mind is, however, not yet identical with the feeling of a line in space. Touch a dozen points on the skin successively, and there seems no necessary reason why the notion of a definite line should emerge, even though we be strongly aware of a gradation of quality among the touches. We may of course symbolically arrange them in a line in our thought, but we can always distinguish between a line symbolically thought and a line directly felt.

But note now the peculiarity of the nerve-processes of all these local signs: though they may give no line when excited successively, when excited together they do give the actual sensation of a line in space. The sum of them is the neural process of that line; the sum of their feelings is the feeling of that line; and if we begin to single out particular points from the line, and notice them by their rank, it is impossible to see how this rank can appear except as an actual fixed space-position sensibly felt as a bit of the total line. The scale itself appearing as a line, rank in it must appear as a definite part of the line. If the seven notes of an octave, when heard together, appeared to the sense of hearing as an outspread line of sound--which it is needless to say they do not--why then no one note could be discriminated without being localized, according to its pitch, in the line, either as one of its extremities or as some part between.

But not alone the gradation of their quality arranges the local-sign feelings in a scale. Our movements arrange them also in a time-scale. Whenever a stimulus passes from point a of the skin or retina to point f, it awakens the local-sign feelings in the perfectly definite time-order abcdef. It cannot excite f until cde have been successively aroused. The feeling c sometimes is preceded by ab, sometimes followed by ba, according to the movement's direction; the result of it all being that we never feel either a, c, or f, without there clinging to it faint reverberations of the various time-orders of transition in which, throughout past experience, it has been aroused. To the local sign a there clings the tinge or tone, the penumbra or fringe, of the transition bcd. To f, to c, there cling quite different tones. Once admit the principle that a feeling may be tinged by the reproductive consciousness of an habitual transition, even when the transition is not made, and it seems entirely natural to admit that, if the transition be habitually in the order abcdef, and if a, c, and f be felt separately at all, a will be felt with an essential earliness, f with an essential lateness, and that c will fall between. Thus those psychologists who set little store by local signs and great store by movements in explaining space-perception, would have a perfectly definite time-order, due to motion, by which to account for the definite order of positions that appears when sensitive spots are excited all at once. Without, however, the preliminary admission of the 'ultimate fact' that this collective excitement shall feel like a line and nothing else, it can never be explained why the new order should needs be an order of positions, and not of merely ideal serial rank. We shall hereafter have any amount of opportunity to observe how thoroughgoing is the participation of motion in all our spatial measurements. Whether the local signs have their respective qualities evenly graduated or not, the feelings of transition must be set down as among the veræ causæ in localization. But the gradation of the local signs is hardly to be doubted; so we may believe ourselves really to possess two sets of reasons for localizing any point we may happen to distinguish from out the midst of any line or any larger space.

M. Binet (Revue Philosophique, Sept. 1880, page 291) says we judge them locally different as soon as their sensations differ enough for us to distinguish them as qualitatively different when successively excited. This is not strictly true. Skin-sensations, different enough to be discriminated when successive, may still fuse locally if excited both at once.

It may, however, be said that even in the tongue there is a determination of bitter flavors to the back and of acids to the front edge of the organ. Spices likewise affect its sides and front, and a taste like that of alum localizes itself, by its styptic effect on the portion of mucous membrane, which it immediately touches, more sharply than roast pork, for example, which stimulates all parts alike. The pork, therefore, tastes more spacious than the alum or the pepper. In the nose, too, certain smells, of which vinegar may be taken as the type, seem less spatially extended than heavy, suffocating odors, like musk. The reason of this appears to be that the former inhibit inspiration by their sharpness, whilst the latter are drawn into the lungs, and thus excite an objectively larger surface. The ascription of height and depth to certain notes seems due, not to any localization of the sounds, but to the fact that a feeling of vibration in the chest and tension in the gullet accompanies the singing of a bass note, whilst, when we sing high, the palatine mucous membrane is drawn upon by the muscles which move the larynx, and awakens a feeling in the roof of the mouth.

The only real objection to the law of partial stimulation laid down in the text is one that might be drawn from the organ of hearing; for, according to modern theories, the cochlea may have its separate nerve-termini exclusively excited by sounds of differing pitch, and yet the sounds seem all to fill a common space, and not necessarily to be arranged alongside of each other. At most the high note is felt as a thinner, brighter streak against a darker background. In an article on Space, published in the Journal of Speculative Philosophy for January, 1879, I ventured to suggest that possibly the auditory nerve termini might be "excited all at once by sounds of any pitch, as the whole retina would be by every luminous point if there were no dioptric apparatus affixed." And I added: "Notwithstanding the brilliant conjectures of the last few years which assign different acoustic end-organs to different rates of air-wave, we are still greatly in the dark about the subject; and I, for my part, would much more confidently reject a theory of hearing which violated the principles advanced in this article than give up those principles for the sake of any hypothesis hitherto published about either organs of Corti or basilar membrane." Professor Rutherford's theory of hearing, advanced at the meeting of the British Association for 1886, already furnishes an alternative view which would make hearing present no exception to the space-theory I defend and which, whether destined to be proved true or false, ought, at any rate to make us feel that the Helmholtzian theory is probably not the last word in the physiology of hearing. Stepano, ff. (Hermann und Schwalbe's Jahresbericht, xv. 404, Literature 1886) reports a case in which more than the upper half of one cochlea was lost without any such deafness to deep notes on that side as Helmholtz's theory would require.

Donaldson, in Mind, x. 399, 577; Goldscheider, in Archiv f. (Anat. u.) Physiologie; Blix, in Zeitschrift für Biologie. A good résumé may be found in Ladd's Physiol. Psychology, part ii. chap. iv. §§ 21-23.

I tried on nine or ten people, making numerous observations on each, what difference it made in the discrimination of two points to have them alike or unlike. The points chosen were (1) two large needle-heads, (2) two screw-heads, and (3) a needle-head and a screw-head. The distance of the screw-heads was measured from their centres. I found that when the points gave diverse qualities of feeling (as in 3), this facilitated the discrimination, but much less strongly than I expected. The difference, in fact, would often not be perceptible twenty times running. When, however, one of the points was endowed with a rotary movement, the other remaining still, the doubleness of the points became much more evident than before. To observe this I took an ordinary pair of compasses with one point blunt, and the movable leg replaced by a metallic rod which could, at any moment, be made to rotate in situ by a dentist's drilling-machine, to which it was attached. The compass had then its points applied to the skin at such a distance apart as to be felt as one impression. Suddenly rotating the drill-apparatus then almost always made them seem as two.

This is only another example of what I call 'the psychologist's fallacy'--thinking that the mind he is studying must necessarily be conscious of the object after the fashion in which the psychologist himself is conscious of it.

Sitzb. der. k. Akad. Wien, Bd. lxxii., Abth. 8 (1875).

Zeitschrift für Biologie, xii. 226 (1876).

Vierteljahrsch. für wiss. Philos., ii. 377.

Exner tries to show that the structure of the faceted eye of articulates adapts it for perceiving motions almost exclusively.

Schneider tries to explain why a sensory surface is so much more excited when its impression moves. It has long since been noticed how much more acute is discrimination of successive than of simultaneous differences. But in the case of a moving impression, say on the retina, we have a summation of both sorts of difference; whereof the natural effect must be to produce the most perfect discrimination of all.

In the left-hand figure let the dark spot B move, for example, from right to left. At the outset there is the simultaneous contrast of black and white in B and A. When the motion has occurred so that the right-hand figure is produced, the same contrast remains, the black and the white having changed places. But in addition to it there is a double successive contrast, first in A, which, a moment ago white, has now become black; and second in B, which, a moment ago black, has now become white. If we make each single feeling of contrast = 1 (a supposition far too favorable to the state of rest), the sum of contrasts in the case of motion will be 3, as against 1 in the state of rest. That is, our attention will be called by a treble force to the difference of color, provided the color begin to move.--(Cf. also Fleischl, Physiologische Optische Notizen, 2te Mittheilung, Wiener Sitzungsberichte, 1882.)

Brown, Bain, J. S. Mill, and in a modified manner Wundt, Helmholtz, Sully, etc.

M. Ch. Dunan, in his forcibly written essay 'l'Espace Visuel et l'Espace Tactile' in the Revue Philosophique for 1888, endeavors to prove that surfaces alone give no perception of extent, by citing the way in which the blind go to work to gain an idea of an object's shape. If surfaces were the percipient organ, he says, "both the seeing and the blind ought to gain an exact idea of the size (and shape) of an object by merely laying their hand flat upon it (provided of course that it were smaller than the hand), and this because of their direct appreciation of the amount of tactile surface affected, and with no recourse to the muscular sense.... But the fact is that a person born blind never proceeds in this way to measure objective surfaces. The only means which he has of getting at the size of a body is that of running his finger along the lines by which it is bounded. For instance, if you put into the hands of one born blind a book whose dimensions are unknown to him, he will begin by resting it against his chest so as to hold it horizontal; then, bringing his two hands together at the middle of the edge opposite to the one against his body, he will draw them asunder till they reach the ends of the edge in question; and then, and not till then, will he be able to say what the length of the object is" (vol. xxv. p. 148). I think that anyone who will try to appreciate the size and shape of an object by simply 'laying his hand flat upon it' will find that the great obstacle is that he feels the contours so imperfectly. The moment, however, the hands move, the contours are emphatically and distinctly felt. All perception of shape and size is perception of contours, and first of all these must be made sharp. Motion does this; and the impulse to move our organs in perception is primarily due to the craving which we feel to get our surface-sensations sharp. When it comes to the naming and measuring of objects in terms of some common standard we shall see presently how movements help also; but no more in this case than the other do they help, because the quality of extension itself is contributed by the 'muscular sense.'

Fechner describes (Psychophysik, i. 132) a 'method of equivalents' for measuring the sensibility of the skin. Two compasses are used, one on the part A, another on the part B, of the surface. The points on B must be adjusted so that their distance apart appears equal to that between the points on A. With the place A constant, the second pair of points must be varied a great deal for every change in the place B, though for the same A and B the relation of the two compasses is remarkably constant, and continues unaltered for months, provided but few experiments are made on each day. If, however, we practise daily their difference grows less, in accordance with the law given in the text.

Prof. Jastrow gives as the result of his experiments this general conclusion (Am. Journal of Psychology, iii. 53): "The space-perceptions of disparate senses are themselves disparate, and whatever harmony there is amongst them we are warranted in regarding as the result of experience. The spacial notions of one deprived of the sense of sight and reduced to the use of the other space-senses must indeed be different from our own." But he continues: "The existence of the striking disparities between our visual and our other space-perceptions without confusing us, and, indeed, without usually being noticed, can only be explained by the tendency to interpret all dimensions into their visual equivalents." But this author gives no reasons for saying 'visual' rather than 'tactile;' and I must continue to think that probabilities point the other way so far as what we call real magnitudes are concerned.

Cf. Lipps on 'Complication,' Grundtatsachen, etc., p. 579.

Ventriloquism shows this very prettily. The ventriloquist talks without moving his lips, and at the same time draws our attention to a doll, a box, or some other object. We forthwith locate the voice within this object. On the stage an actor ignorant of music sometimes has to sing, or play on the guitar or violin. He goes through the motions before our eyes, whilst in the orchestra or elsewhere the music is performed. But because as we listen we see the actor, it is almost impossible not to hear the music as if coming from where he sits or stands.

Cf. Shand, in Mind, xiii. 340.

See, e.g., Bain's Senses and Intellect, pp. 366-7, 371.

When, for example, a baby looks at its own moving hand, it sees one object at the same time that it feels another. Both interest its attention, and it locates them together. But the felt object's size is the more constant size, just as the felt object is, on the whole, the more interesting and important object; and so the retinal sensations become regarded as its signs and have their 'real space-values' interpreted in tangible terms.

The incoherence of the different primordial sense-spaces inter se is often made a pretext for denying to the primitive bodily feelings any spatial quality at all. Nothing is commoner than to hear it said: "Babies have originally no spatial perception; for when a baby's toe aches he does not place the pain in the toe. He makes no definite movements of defence, and may be vaccinated without being held." The facts are true enough; but the interpretation is all wrong. What really happens is that the baby does not place his 'toe' in the pain; for he knows nothing of his 'toe' as yet. He has not attended to it as a visual object; he has not handled it with his fingers; nor have its normal organic sensations or contacts yet become interesting enough to be discriminated from the whole massive feeling of the foot, or even of the leg to which it belongs. In short, the toe is neither a member of the babe's optical space, of his hand-movement space, nor an independent member of his leg-and-foot space. It has actually no mental existence yet save as this little pain-space. What wonder, then, if the pain seem a little space-world all by itself? But let the pain once associate itself with these other space-worlds, and its space will become part of their space. Let the baby feel the nurse stroking the limb and awakening the pain every time her finger passes towards the toe; let him look on and see her finger on the toe every time the pain shoots up; let him handle his foot himself and get the pain whenever the toe comes into his fingers or his mouth; let moving the leg exacerbate the pain,--and all is changed. The space of the pain becomes identified with that part of each of the other spaces which gets felt when it awakens; and by their identity with it these parts are identified with each other, and grow systematically connected as members of a larger extensive whole.

'Pourquoi les Sensations visuelles sont elles étendues?' in Revue Philosophique, iv. 167.--As the proofs of this chapter are being corrected, I receive the third 'Heft' of Münsterberg's Beiträge zur Experimentellen Psychologie, in which that vigorous young psychologist reaffirms (if I understand him after so hasty a glance) more radically than ever the doctrine that muscular sensation proper is our one means of measuring extension. Unable to reopen the discussion here, I am in duty bound to call the attention of the reader to Herr M.'s work.

Even if the figure be drawn on a board instead of in the air, the variations of contact on the finger's surface will be much simpler than the peculiarities of the traced figure itself.

See for example Duchenne, Electrisation localisée, pp. 727, 770, Leyden; Virchow's Archiv, Bd. xlvii. (1869).

E.g., Eulenburg, Lehrb. d. Nervenkrankheiten (Berlin), 1878, i. 3.

'Ueber den Kraftsinn,' Virchow's Archiv, Bd. lxxvii. 134.

Archiv f. (Anat. u) Physiologie (1889), pp. 369, 540.

Direction in its 'first intention,' of course; direction with which so far we merely become acquainted, and about which we know nothing save perhaps its difference from another direction a moment ago experienced in the same way!

I have said hardly anything about associations with visual space in the foregoing account, because I wished to represent a process which the blind and the seeing man might equally share. It is to be noticed that the space suggested to the imagination when the joint moves, and projected to the distance of the finger-tip, is not represented as any specific skin-tract. What the seeing man imagines is a visible path; what the blind man imagines is rather a generic image, an abstraction from many skin-spaces whose local signs have neutralized each other, and left nothing but their common vastness behind. We shall see as we go on that this generic abstraction of space-magnitude from the various local peculiarities of feeling which accompanied it when it was for the first time felt, occurs on a considerable scale in the acquired perceptions of blind as well as of seeing men.

The ideal enlargement of a system of sensations by the mind is nothing exceptional. Vision is full of it; and in the manual arts, where a workman gets a tool larger than the one he is accustomed to and has suddenly to adapt all his movements to its scale, or where he has to execute a familiar set of movements in an unnatural position of body; where a piano-player meets an instrument with unusually broad or narrow keys; where a man has to alter the size of his handwriting--we see how promptly the mind multiplies once for all, as it were, the whole series of its operations by a constant factor, and has not to trouble itself after that with further adjustment of the details.

Pflüger's Archiv, xlv. 65.

Untersuchungen im Gebiete der Optik, Leipzig (1863), p. 188.

Problems of Life and Mind, prob. vi. chap. iv. § 45.

Volkmann, op. cit. p. 189. Compare also what Hering says of the inability in his own case to make after-images seem to move when he rolls his closed eyes in their sockets; and of the insignificance of his feelings of convergence for the sense of distance (Beiträge zur Physiologie, 1881-2, pp. 31, 141). Helmholtz also allows to the muscles of convergence a very feeble share in producing our sense of the third dimension (Physiologische Optik, 649-59).

Compare Lipps, Psychologische Studien (1885), p. 18, and the other arguments given on pp. 12 to 27. The most plausible reasons for contractions of the eyeball-muscles being admitted as original contributors to the perception of extent, are those of Wundt, Physiologische Psychologie, ii. 96-100. They are drawn from certain constant errors in our estimate of lines and angles; which, however, are susceptible, all of them, of different interpretations (see some of them further on).--Just as my MS. goes to the printer, Herr Münsterberg's Beiträge zur experimentellen Psychologie, Heft 2, comes into my hands with experiments on the measurement of space recorded in it, which, in the author's view, prove the feeling of muscular strain to be a principal factor in our vision of extent. As Münsterberg worked three hours a day for a year and a half at comparing the length of lines, seen with his eyes in different positions; and as he carefully averaged and 'percented' 20,000 observations, his conclusion must be listened to with great respect. Briefly it is this, that "our judgments of size depend on a comparison of the intensity of the feelings of movement which arise in our eyeball-muscles as we glance over the distance, and which fuse with the sensations of light" (p. 142). The facts upon which the conclusion is based are certain constant errors which Münsterberg found according as the standard or given interval was to the right or the left of the interval to be marked off as equal to it, or as it was above or below it, or stood in some more complicated relation still. He admits that he cannot explain all the errors in detail, and that we "stand before results which seem surprising and not to be unravelled, because we cannot analyze the elements which enter into the complex sensation which we receive." But he has no doubt whatever of the general fact "that the movements of the eyes and the sense of their position when fixed exert so decisive an influence on our estimate of the spaces seen, that the errors cannot possibly be explained by anything else than the movement-feelings and their reproductions in the memory" (pp. 166, 167). It is presumptuous to doubt a man's opinion when you haven't had his experience; and yet there are a number of points which make me feel like suspending judgment in regard to Herr M.'s dictum. He found, for example, a constant tendency to underestimate intervals lying to the right, and to overestimate intervals lying to the left. He ingeniously explains this as a result of the habit of reading, which trains us to move our eyes easily along straight lines from left to right, whereas in looking from right to left we move them in curved lines across the page. As we measure intervals as straight lines, it costs more muscular effort to measure from right to left than the other way, and an interval lying to the left seems to us consequently longer than it really is. Now I have been a reader for more years than Herr Münsterberg; and yet with me there is a strongly pronounced error the other way. It is the rightward-lying interval which to me seems longer than it really is. Moreover, Herr M. wears concave spectacles, and looked through them with his head fixed. May it not be that some of the errors were due to distortion of the retinal image, as the eye looked no longer through the centre but through the margin of the glass? In short, with all the presumptions which we have seen against muscular contraction being definitely felt as length, I think that there may be explanations of Herr M.'s results which have escaped even his sagacity; and I call for a suspension of judgment until they shall have been confirmed by other observers. I do not myself doubt that our feeling of seen extent may be altered by concomitant muscular feelings. In Chapter XVII (pp. 28-30) we saw many examples of similar alterations, interferences with, or exaltations of, the sensory effect of one nerve-process by another. I do not see why currents from the muscles or eyelids, coming in at the same time with a retinal impression, might not make the latter seem bigger, in the same way that a greater intensity in the retinal stimulation makes it seem bigger; or in the way that a greater extent of surface excited makes the color of the surface seem stronger, or if it be a skin-surface, makes its heat seem greater; or in the way that the coldness of the dollar on the forehead (in Weber's old experiments) made the dollar seem heavier. But this is a physiological way; and the bigness gained is that of the retinal image after all. If I understand Münsterberg's meaning, it is quite different from this: the bigness belongs to the muscular feelings, as such, and is merely associated with those of the retina. This is what I deny.

Archiv f. (Anat. u.) Physiol. (1889), p. 543.

Ibid. p. 496.

Ibid. p. 497. Goldscheider thinks that our muscles do not even give us the feeling of resistance, that being also due to the articular surfaces; whilst weight is due to the tendons. Ibid. p. 541.

"Whilst the memories which we seeing folks preserve of a man all centre round a certain exterior form composed of his image, his height, his gait, in the blind all these memories are referred to something quite different, namely, the sound of his voice." (Dunan, Rev. Phil., xxv. 357.)

Vol. xxv. pp. 357-8.

P. 135.

Essay conc. Hum. Und., bk. ii. chap. ix. § 8.

Philosophical Transactions, 1841. In T. K. Abbot's Sight and Touch there is a good discussion of these cases. Obviously, positive cases are of more importance than negative. An under-witted peasant, Noé M., whose case is described by Dr. Dufour of Lausanne (Guerison d'un Aveugle né; 1876) is much made of by MM. Naville and Dunan; but it seems to me only to show how little some people can deal with new experiences in which others find themselves quickly at home. This man could not even tell whether one of his first objects of sight moved or stood still (p. 9).

What may be the physiological process connected with this increased sensation of depth is hard to discover. It seems to have nothing to do with the parts of the retina affected, since the mere inversion of the picture (by mirrors, reflecting prisms, etc.), without inverting the head, does not seem to bring it about; nothing with sympathetic axial rotation of the eyes, which might enhance the perspective through exaggerated disparity of the two retinal images (see J. J. Müller, 'Raddrehung u. Tiefendimension,' Leipzig Acad. Berichte, 1875, page 124), for one-eyed persons get it as strongly as those with two eyes. I cannot find it to be connected with any alteration in the pupil or with any ascertainable strain in the muscles of the eye, sympathizing with those of the body. The exaggeration of distance is even greater when we throw the head over backwards and contract our superior recti in getting the view, than when we bend forward and contract the inferior recti. Making the eyes diverge slightly by weak prismatic glasses has no such effect. To me, and to all whom I have asked to repeat the observation, the result is so marked that I do not well understand how such an observer as Helmholtz, who has carefully examined vision with inverted head, can have overlooked it. (See his Phys. Optik, pp. 488, 723, 728, 772.) I cannot help thinking that anyone who can explain the exaggeration of the depth-sensation in this case will at the same time throw much light on its normal constitution.

"In Froriep's Notizen (1838, July), No. 133, is to be found a detailed account, with a picture, of an Esthonian girl, Eva Lauk, then fourteen years old, born with neither arms nor legs, which concludes with the following words: 'According to the mother, her intellect developed quite as fast as that of her brother and sisters; in particular, she came as quickly to a right judgment of the size and distance of visible objects, although, of course, she had no use of hands.'" (Schopenhauer, Welt als Wille, ii. 44.)

Physiol. Optik, p. 438. Helmholtz's reservation of 'qualities' is inconsistent. Our judgments of light and color vary as much as our judgments of size, shape, and place, and ought by parity of reasoning to be called intellectual products and not sensations. In other places he does treat color as if it were an intellectual product.

It is needless at this point to consider what Helmholtz's views of the nature of the intellectual space-yielding process may be. He vacillates--we shall later see how.

Op. cit. p. 214.

Before embarking on this new topic it will be well to shelve, once for all, the problem of what is the physiological process that underlies the distance-feeling. Since one-eyed people have it, and are inferior to the two-eyed only in measuring its gradations, it can have no exclusive connection with the double and disparate images produced by binocular parallax. Since people with closed eyes, looking at an after-image, do not usually see it draw near or recede with varying convergence, it cannot be simply constituted by the convergence-feeling. For the same reason it would appear non-identical with the feeling of accommodation. The differences of apparent parallactic movement between far and near objects as we move our head cannot constitute the distance-sensation, for such differences may be easily reproduced experimentally (in the movements of visible spots against a background) without engendering any illusion of perspective. Finally, it is obvious that visible faintness, dimness, and smallness are not per se the feeling of visible distance, however much in the case of well-known objects they may serve as signs to suggest it.

A certain maximum distance-value, however, being given to the field of view of the moment, whatever it be, the feelings that accompany the processes just enumerated become so many local signs of the gradation of distances within this maximum depth. They help us to subdivide and measure it. Itself, however, is felt as a unit, a total distance-value, determining the vastness of the whole field of view, which accordingly appears as an abyss of a certain volume. And the question still persists, what neural process is it that underlies the sense of this distance-value?

Hering, who has tried to explain the gradations within it by the interaction of certain native distance-values belonging to each point of the two retinæ, seems willing to admit that the absolute scale of the space-volume within which the natively fixed relative distances shall appear is not fixed, but determined each time by 'experience in the widest sense of the word' (Beiträge, p. 344). What he calls the Kernpunkt of this space-volume is the point we are momentarily fixating. The absolute scale of the whole volume depends on the absolute distance at which this Kernpunkt is judged to lie from the person of the looker. "By an alteration of the localization of the Kernpunkt, the inner relations of the seen space are nowise altered; this space in its totality is as a fixed unit, so to speak, displaced with respect to the self of the looker" (p. 345). But what constitutes the localization of the Kernpunkt itself at any given time, except 'Experience,' i.e., higher cerebral and intellectual processes, involving memory, Hering does not seek to define.

Stumpf, the other sensationalist writer who has best realized the difficulties of the problem, thinks that the primitive sensation of distance must have an immediate physical antecedent, either in the shape of "an organic alteration accompanying the process of accommodation, or else given directly in the specific energy of the optic nerve." In contrast with Hering, however, he thinks that it is the absolute distance of the spot fixated which is thus primitively, immediately, and physiologically given, and not the relative distances of other things about this spot. These, he thinks, are originally seen in what, broadly speaking, may be termed one plane with it. Whether the distance of this plane, considered as a phenomenon of our primitive sensibility, be an invariable datum, or susceptible of fluctuation, he does not, if I understand him rightly, undertake dogmatically to decide, but inclines to the former view. For him then, as for Hering, higher cerebral processes of association, under the name of 'Experience,' are the authors of fully one-half part of the distance-perceptions which we at any given time may have.

Hering's and Stumpf's theories are reported for the English reader by Mr. Sully (in Mind, iii. pp. 172-6). Mr. Abbott, in his Sight and Touch (pp. 96-8), gives a theory which is to me so obscure that I only refer the reader to its place, adding that it seems to make of distance a fixed function of retinal sensation as modified by focal adjustment. Besides these three authors I am ignorant of any, except Panum, who may have attempted to define distance as in any degree an immediate sensation. And with them the direct sensational share is reduced to a very small proportional part, in our completed distance-judgments.

Professor Lipps, in his singularly acute Psychologische Studien (p. 69 ff.), argues, as Ferrier, in his review of Berkeley (Philosophical Remains, ii. 330 ff.), had argued before him, that it is logically impossible we should perceive the distance of anything from the eye by sight; for a seen distance can only be between seen termini; and one of the termini, in the case of distance from the eye, is the eye itself, which is not seen. Similarly of the distance of two points behind each other: the near one hides the far one, no space is seen between them. For the space between two objects to be seen, both must appear beside each other, then the space in question will be visible. On no other condition is its visibility possible. The conclusion is that things can properly be seen only in what Lipps calls a surface, and that our knowledge of the third dimension must needs be conceptual, not sensational or visually intuitive.

But no arguments in the world can prove a feeling which actually exists to be impossible. The feeling of depth or distance, of farness or awayness, does actually exist as a fact of our visual sensibility. All that Professor Lipps's reasonings prove concerning it is that it is not linear in its character, or in its immediacy fully homogeneous and consubstantial with the feeling of literal distance between two seen termini; in short, that there are two sorts of optical sensation, each inexplicably due to a peculiar neural process. The neural process is easily discovered, in the case of lateral extension or spreadoutness, to be the number of retinal nerve-ends affected by the light; in the case of protension or mere farness it is more complicated and, as we have concluded, is still to seek. The two sensible qualities unite in the primitive visual bigness. The measurement of their various amounts against each other obeys the general laws of all such measurements. We discover their equivalencies by means of objects, apply the same units to both, and translate them into each other so habitually that at last they get to seem to us even quite similar in kind. This final appearance of homogeneity may perhaps be facilitated by the fact that in binocular vision two points situated on the prolongation of the optical axis of one of the eyes, so that the near one hides the far one, are by the other eye seen laterally apart. Each eye has in fact a foreshortened lateral view of the other's line of sight. In The London Times for Feb. 8, 1884, is an interesting letter by J. D. Dougal, who tries to explain by this reason why two-eyed rifle-shooting has such advantages over shooting with one eye closed.

Just so, a pair of spectacles held an inch or so from the eyes seem like one large median glass. The faculty of seeing stereoscopic slides single without an instrument is of the utmost utility to the student of physiological optics, and persons with strong eyes can easily acquire it. The only difficulty lies in dissociating the degree of accommodation from the degree of convergence which it usually accompanies. If the right picture is focussed by the right eye, the left by the left eye, the optic axes must either be parallel or converge upon an imaginary point some distance behind the plane of the pictures, according to the size and distance apart of the pictures. The accommodation, however, has to be made for the plane of the pictures itself, and a near accommodation with a far-off convergence is something which the ordinary use of our eyes never teaches us to effect.

These two observations prove the law of identical direction only for objects which excite the foveæ or lie in the line of direct looking. Observers skilled in indirect vision can, however, more or less easily verify the law for outlying retinal points.

This essay, published in the Philosophical Transactions, contains the germ of almost all the methods applied since to the study of optical perception. It seems a pity that England, leading off so brilliantly the modern epoch of this study, should so quickly have dropped out of the field. Almost all subsequent progress has been made in Germany, Holland, and, longo intervallo, America.

This is no place to report this controversy, but a few bibliographic references may not be inappropriate. Wheatstone's own experiment is in section 12 of his memoir. In favor of his interpretation see Helmholtz, Phys. Opt., pp. 737-9; Wundt, Physiol. Psychol., 2te Aufl. p. 144; Nagel, Sehen mit zwei Augen, pp. 78-82. Against Wheatstone see Volkmann, Arch. f. Ophth., v. 2-74, and Untersuchungen, p. 266; Hering, Beiträge zur Physiologie, 29-45, also in Hermann's Hdbch. d. Physiol., Bd. iii. 1 Th. p. 435; Aubert, Physiologie d. Netzhaut, p. 322; Schön, Archiv f. Ophthal., xxiv. 1. pp. 56-65; and Donders, ibid. xiii. 1. p. 15 and note.

When we see the finger the whole time, we usually put it in the line joining object and left eye if it be the left finger, joining object and right eye if it be the right finger. Microscopists, marksmen, or persons one of whose eyes is much better than the other, almost always refer directions to a single eye, as may be seen by the position of the shadow on their face when they point at a candle-flame.

Professor Joseph Le Conte, who believes strongly in the identity-theory, has embodied the latter in a pair of laws of the relation between positions seen single and double, near or far, on the one hand, and convergences and retinal impressions, on the other, which, though complicated, seems to me by far the best descriptive formulation yet made of the normal facts of vision. His account is easily accessible to the reader in his volume 'Sight' in the International Scientific Series, bk. ii. c. 8, so I say no more about it now, except that it does not solve any of the difficulties we are noting in the identity-theory, nor account for the other fluctuating perceptions of which we go on to treat.

Naturally it takes a smaller object at a less distance to cover by its image a constant amount of retinal surface.

Archiv f. Ophthal., Bd. xvii. Abth. 2, pp. 44-6 (1871).

A. W. Volkmann, Untersuchungen, p. 253.

Philosophical Transactions, 1852, p. 4.

Physiol. Optik, 649-664. Later this author is led to value convergence more highly. Arch. f. (Anat. u.) Physiol. (1878), p. 322.

Anomalies of Accommodation and Refraction (New Sydenham Soc. Transl., London, 1864), p. 155.

These strange contradictions have been called by Aubert 'secondary' deceptions of judgment. See Grundzüge d. Physiologischen Optik (Leipzig, 1876), pp. 601, 615, 627. One of the best examples of them is the small size of the moon as first seen through a telescope. It is larger and brighter, so we see its details more distinctly and judge it nearer. But because we judge it so much nearer we think it must have grown smaller. Cf. Charpentier in Jahresbericht, x. 430.

Revue Philosophique, iii. 9, p. 220.

See Chapter XXIV.

The only exception seems to be when we expressly wish to abstract from particulars, and to judge of the general 'effect.' Witness ladies trying on new dresses with their heads inclined and their eyes askance; or painters in the same attitude judging of the 'values' in their pictures.

The importance of Superposition will appear later on.

Physiol. Optik, p. 817.

Bowditch and Hall, in Journal of Physiology, vol. iii. p. 299. Helmholtz tries to explain this phenomenon by unconscious rotations of the eyeball. But movements of the eyeball can only explain such appearances of movements as are the same over the whole field. In the windowed board one part of the field seems to move in one way, another part in another. The same is true when we turn from the spiral to look at the wall--the centre of the field alone swells out or contracts, the margin does the reverse or remains at rest. Mach and Dvorak have beautifully proved the impossibility of eye-rotations in this case (Sitzungsber. d. Wiener Akad., Bd. lxi.). See also Bowditch and Hall's paper as above, p. 300.

Bulletins de l'Acad. de Belgique, xxi. 2; Revue Philosophique, vi. pp. 223-5; Physiologische Psychologie, 2te Aufl. p. 103. Compare Münsterberg's views, Beiträge, Heft 2, p. 174.

Physiol. Optik, pp. 562-71.

Physiol. Psych., pp. 107-8.

Grundtatsachen des Seelenlebens, pp. 526-30.

Cf. supra, vol. I. p. 515 ff.

See Archiv f. Ophthalm., v. 2, 1 (1859), where many more examples are given.

Untersuchungen, p. 250; see also p. 242.

I pass over certain difficulties about double images, drawn from the perceptions of a few squinters (e.g. by Schweigger, Klin. Untersuch über das Schielen, Berlin, 1881; by Javal, Annales d'Oculistique, lxxxv. p. 217), because the facts are exceptional at best and very difficult of interpretation. In favor of the sensationalistic or nativistic view of one such case, see the important paper by Von Kries, Archiv f. Ophthalm., xxiv. 4, p. 117.

Physiologische Untersuchungen im Gebiete der Optik, v.

Cf. E. Mach, Beiträge zur Analyse der Empfindungen, p. 87.

Cf. V. Egger, Revue Philos., xx. 488.

Loeb (Pflüger's Archiv, xl. 274) has proved that muscular changes of adaptation in the eye for near and far distance are what determine the form of the relief.

The strongest passage in Helmholtz's argument against sensations of space is relative to these fluctuations of seen relief: "Ought one not to conclude that if sensations of relief exist at all, they must be so faint and vague as to have no influence compared with that of past experience? Ought we not to believe that the perception of the third dimension may have arisen without them, since we now see it taking place as well against them as with them?" (Physiol. Optik, p. 817.)

Cf. E. Mach, Beiträge, etc., p. 90, and the preceding chapter of the present work, p. 86 ff.

I ought to say that I seem always able to see the cross rectangular at will. But this appears to come from an imperfect absorption of the rectangular after-image by the inclined plane at which the eyes look. The cross, with me, is apt to detach itself from this and then look square. I get the illusion better from the circle, whose after-image becomes in various ways elliptical on being projected upon the different surfaces of the room, and cannot then be easily made to look circular again.

In Chapter XVIII, p. 74, I gave a reason why imaginations ought not to be as vivid as sensations. It should be borne in mind that that reason does not apply to these complemental imaginings of the real shape of things actually before our eyes.

Hermann's Handb. der Physiologie, iii. 1. p. 565-71.

Bulletin de l'Académie de Belgique, 2me Série, xix. 2.

Wundt seeks to explain all these illusions by the relatively stronger 'feeling of innervation' needed to move the eyeballs upwards,--a careful study of the muscles concerned is taken to prove this,--and a consequently greater estimate of the distance traversed. It suffices to remark, however, with Lipps, that were the innervation all, a column of S's placed on top of each other should look each larger than the one below it, and a weathercock on a steeple gigantic, neither of which is the case. Only the halves of the same object look different in size, because the customary correction for foreshortening bears only on the relations of the parts of special things spread out before us. Cf. Wundt, Physiol. Psych., 2te Aufl. ii. 96-8; Th. Lipps, Grundtatsachen, etc., p. 535.

Hering would partly solve in this way the mystery of Figs. 60, 61, and 67. No doubt the explanation partly applies; but the strange cessation of the illusion when we fix the gaze fails to be accounted for thereby.

Helmholtz has sought (Physiol. Optik, p. 715) to explain the divergence of the apparent vertical meridians of the two retinæ, by the manner in which an identical line drawn on the ground before us in the median plane will throw its images on the two eyes respectively. The matter is too technical for description here; the unlearned reader may be referred for it to J. Le Conte's Sight in the Internat. Scient. Series, p. 198 ff. But, for the benefit of those to whom verbum sat, I cannot help saying that it seems to me that the exactness of the relation of the two meridians--whether divergent or not, for their divergence differs in individuals and often in one individual at diverse times--precludes its being due to the mere habitual falling-off of the image of one objective line on both. Le Conte, e.g., measures their position down to a sixth of a degree, others to tenths. This indicates an organic identity in the sensations of the two retinæ, which the experience of median perspective horizontals may roughly have agreed with, but hardly can have engendered. Wundt explains the divergence as usual, by the Innervationsgefühl (op. cit.. ii. 99 ff.).

Physiol. Optik, p. 547.

"We can with a short ruler draw a line as long as we please on a plane surface by first drawing one as long as the ruler permits, and then sliding the ruler somewhat along the drawn line and drawing again, etc. If the ruler is exactly straight, we get in this way a straight line. If it is somewhat curved we get a circle. Now, instead of the sliding ruler we use in the field of sight the central spot of distinctest vision impressed with a linear sensation of sight, which at times may be intensified till it becomes an after-image. We follow, in looking, the direction of this line, and in so doing we slide the line along itself and get a prolongation of its length. On a plane surface we can carry on this procedure on any sort of a straight or curved ruler, but in the field of vision there is for each direction and movement of the eye only one sort of line which it is possible for us to slide along in its own direction continually." These are what Helmholtz calls the 'circles of direction' of the visual field--lines which he has studied with his usual care. Cf. Physiol. Optik, p. 548 ff.

Cf. Hering in Hermann's Handb. der Physiol., iii. 1, pp. 558-4.

This shrinkage and expansion of the absolute space-value of the total optical sensation remains to my mind the most obscure part of the whole subject. It is a real optical sensation, seeming introspectively to have nothing to do with locomotor or other suggestions. It is easy to say that 'the Intellect produces it,' but what does that mean? The investigator who will throw light on this one point will probably clear up other difficulties as well.

Examination of Hamilton, 3d ed. p. 283.

Senses and Intellect, 3d ed. p. 183.

Exam. of Hamilton, 3d ed. p. 283.

Senses and Intellect, p. 372.

Vierfache Wurzel des Satzes vom zureichenden Grunde, pp. 52-7.

Psychol. als Wissenschaft, § 111.

Psychol. als Wissenschaft, § 113.

Lehrbuch d. Psychol., 2te Auflage, Bd. ii. p. 66. Volkmann's fifth chapter contains a really precious collection of historical notices concerning space-perception theories.

Why talk of 'genetic theories'? when we have in the next breath to write as Wundt does: "If then we must regard the intuition of space as a product that simply emerges from the conditions of our mental and physical organization, nothing need stand in the way of our designating it as one of the a priori functions with which consciousness is endowed." (Logik, ii. 460.)

P. 430.

Pp. 430, 449.

P. 428.

P. 442.

Pp. 442, 818.

P. 798. Cf. also Popular Scientific Lectures, pp. 301-3.

P. 456; see also 428, 441.

P. 797.

P. 812.

Bottom of page 797.

In fact, to borrow a simile from Prof. G. E. Müller (Theorie der sinnl. Aufmerksamkeit, p. 38), the various senses bear in the Helmholtzian philosophy of perception the same relation to the 'object' perceived by their means that a troop of jolly drinkers bear to the landlord's bill, when no one has any money, but each hopes that one of the rest will pay.

Grundtatsachen des Seelenlebens (1883), pp. 480, 591-2. Psychologische Studien (1885), p. 14.

Psychology, ii. p. 174.

Ibid. p. 168.

Senses and Intellect, 3d ed. pp. 366-75.

Cf. Hall and Donaldson in Mind, x. 559.

As other examples of the confusion, take Mr. Sully: "The fallacious assumption that there can be an idea of distance in general, apart from particular distances" (Mind, iii. p. 177); and Wundt: "An indefinite localization, which waits for experience to give it its reference to real space, stands in contradiction with the very idea of localization, which means the reference to a determinate point of space" (Physiol. Psych., 1te Aufl. p. 480).

G. Berkeley: Essay towards a new Theory of Vision; Samuel Bailey: A Review of Berkeley's Theory of Vision (1842); J. S. Mill's Review of Bailey, in his Dissertations and Disquisitions, vol. ii; Jas. Ferrier: Review of Bailey, in 'Philosophical Remains,' vol. ii; A. Bain: Senses and Intellect, 'Intellect,' chap. i; H. Spencer: Principles of Psychology, pt. vi. chaps. xiv, xvi; J. S. Mill: Examination of Hamilton, chap. xiii (the best statement of the so-called English empiricist position); T. K. Abbott: Sight and Touch, 1861 (the first English book to go at all minutely into facts; Mr. Abbott maintaining retinal sensations to be originally of space in three dimensions); A. C. Fraser: Review of Abbott, in North British Review for Aug. 1864; another review in Macmillan's Magazine, Aug. 1866; J. Sully: Outlines of Psychology, chap. vi; J. Ward: Encyclop. Britannica, 9th Ed., article 'Psychology,' pp. 53-5; J. E. Walter: The Perception of Space and Matter (1879)--I may also refer to a discussion between Prof. G. Groom Robertson, Mr. J. Ward, and the present writer, in Mind, vol. xiii.--The present chapter is only the filling out with detail of an article entitled 'The Spatial Quale,' which appeared in the Journal of Speculative Philosophy for January 1879 (xiii. 64).