Classics in the History of Psychology
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Christopher D. Green
York University, Toronto, Ontario
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The Principles of Psychology
THE PERCEPTION OF SPACE. 
THE FEELING OF CRUDE EXTENSITY.
IN the sensations of hearing, touch, sight, and pain we are accustomed to distinguish from among the other elements the element of voluminousness. We call the reverberations of a thunderstorm more voluminous than the squeaking of a slate-pencil; the entrance into a warm bath gives our skin a more massive feeling than the prick of a pin; a little neuralgic pain, fine as a cobweb, in the face, seems less extensive than the heavy soreness of a boil or the vast discomfort of a colic or a lumbago; and a solitary star looks smaller than the noonday sky. In the sensation of dizziness or subjective motion, which recent investigation has proved to be connected with stimulation of the semi-circular canals of the ear, the spatial character is very prominent. Whether the 'muscular sense' directly yields us knowledge of space is still a matter of litigation among psychologists. Whilst some go so far as to ascribe our entire cognition of extension to its exclusive aid, others deny to it all extensive quality whatever. Under these circumstances we shall do better to adjourn its consideration; admitting, however, that it seems at first sight as if we felt something decidedly more voluminous when we contract our thigh-muscles than when we twitch an eyelid or some small muscle in the face. It seems, moreover, as if this difference lay in the feeling of the thigh-muscles themselves.
In the sensations of smell and taste this element of varying vastness seems less prominent but not altogether absent. Some tastes and smells appear less extensive than complex flavors, like that of roast meat or plum pudding, on the one hand, or heavy odors like musk or tuberose, on [p. 135] the other. The epithet sharp given to the acid class would seem to show that to the popular mind there is something narrow and, as it were, streaky, in the impression they make, other flavors and odors being bigger and rounder. The sensations derived from the inward organs are also distinctly more or less voluminous. Repletion and emptiness, suffocation, palpitation, headache, are examples of this, and certainly not less spatial is the consciousness we have of our general bodily condition in nausea, fever, heavy drowsiness, and fatigue. Our entire cubic content seems then sensibly manifest to us as such, and feels much larger than any local pulsation, pressure, or discomfort. Skin and retina are, however, the organs in which the space-element plays the most active part. Not only does the maximal vastness yielded by the retina surpass that yielded by any other organ, but the intricacy with which our attention can subdivide this vastness and perceive it to be composed of lesser portions simultaneously coexisting along-side of each other is without a parallel elsewhere.  The ear gives a greater vastness than the skin, but is considerably less able to subdivide it. 
Now my first thesis is that this element, discernible in each and every sensation, though more developed in some than in others, is the original sensation of space, out of which all the exact knowledge about space that we afterwards come to have is woven by processes of discrimination, association, and selection. 'Extensity,' as Mr. James Ward calls it  on this view, becomes an element in each sensation just as intensity is. The latter every one will admit to be a distinguishable though not separable ingredient of the sensible quality. In like manner extensity, being an entirely peculiar kind of feeling indescribable except in terms of itself, and inseparable in actual experience from some sensational quality which it must accompany, can itself receive no other name than that of sensational element.
It must now be noted that the vastness hitherto spoken of is as great in one direction as in another. Its dimensions are so vague that in it there is no question as yet of surface as opposed to depth; 'volume' being the best short name for the sensation in question. Sensations of different orders are roughly comparable, inter se, with respect to their volumes. This shows that the spatial quality in each is identical wherever found, for different qualitative elements, e.g. warmth and odor, are incommensurate. Persons born blind are reported surprised at the largeness with which objects appear to them when their sight is restored. Franz says of his patient cured of cataract: "He saw everything much larger than he had supposed from the idea obtained by his sense of touch. Moving, and especially living, objects appeared very large."  Loud sounds have a certain enormousness of feeling. It is impossible to conceive of the explosion of a cannon as fining a small space. In general, sounds seem to occupy all the room between us and their source; and in the case of certain ones, the cricket's song, the whistling of the wind, the roaring of the surf, or a distant railway train, to have no definite starting point.
In the sphere of vision we have facts of the same order. 'Glowing' bodies, as Hering says, give us a perception "which seems roomy (raumhaft) in comparison with that of strictly surface color. A glowing iron looks luminous through and through, and so does a flame."  A luminous fog, a band of sunshine, affect us in the same way. As Hering urges: [p. 137]
" We must distinguish roomy from superficial, as well as distinctly from indistinctly bounded, sensations. The dark which with closed eyes one sees before one is, for example, a roomy sensation. We do not see a black surface like a wall in front of us, but a space fined with darkness, and even when we succeed in seeing this darkness as terminated by a black wall there still remains in front of this wall the dark space. The same thing happens when we find ourselves with open eyes in an absolutely dark room. This sensation of darkness is also vaguely bounded. An example of a distinctly bounded roomy sensation is that of a clear and colored fluid seen in a glass; the yellow of the wine is seen not, only on the bounding surface of the glass; the yellow sensation fins the whole interior of the glass. By day the so-called empty space between us and objects seen appears very different from what it is by night. The increasing darkness settles not only upon the things but also between us and the things. so as at last to cover them completely and fin the space alone. If I look into a dark box I find it fined with darkness, and this is seen not merely as the dark-colored sides or walls of the box. A shady corner in an otherwise well-lighted room is full of a darkness which is not only on the walls and floor but between them in the space they include. Every sensation is there where I experience it, and if I have it at once at every point of a certain roomy space, it is then a voluminous sensation. A cube of transparent green glass gives us a spatial sensation; an opaque cube painted green, on the contrary, only sensations of surface." 
There are certain quasi-motor sensations in the head when we change the direction of the attention, which equally seem to involve three dimensions. If with closed eyes we think of the top of the house and then of the cellar, of the distance in front of us and then of that behind us, of space far to the right and then far to the left, we have something far stronger than an idea, -- an actual feeling, namely, as if something in the head moved into another direction. Fechner was, I believe, the first to publish any remarks on these feelings. He writes as follows:
"When we transfer the attention from objects of one sense to those of another we have an indescribable feeling (though at the same time one perfectly determinate and reproducible at pleasure) of altered direction, or differently localized tension (Spannung). We feel a strain forward in the eyes, one directed sideways in the ears, increasing with the degree of our attention, and changing according as we look at an object carefully, or listen to something attentively ; wherefore we speak of straining the attention. The difference is most plainly felt when [p. 138] the attention vibrates rapidly between eye and ear. This feeling localizes itself with most decided difference in regard to the various sense-organs according as we wish to discriminate a thing delicately by touch, taste, or smell.
"But now I have, when I try to vividly recall a picture of memory or fancy, a feeling perfectly analogous to that which I experience when I seek to grasp a thing keenly by eye or ear; and this analogous feeling is very differently localized. While in sharpest possible attention to real objects (as well as to after-images) the strain is plainly forwards, and, when the attention changes from one sense to another, only alters its direction between the sense-organs, leaving the rest of the head free from strain, the case is different in memory or fancy; for here the feeling withdraws entirely from the external sense-organs, and seems rather to take refuge in that part of the head which the brain fins. If I wish, for example, to recall a place or person, it will arise before me with vividness, not according as I strain my attention forwards, but rather in proportion as I, so to speak, retract it backwards." 
It appears probable that the feelings which Fechner describes are in part constituted by imaginary semi-circular canal sensations.  These undoubtedly convey the most delicate perception of change in direction; and when, as here, the changes are not perceived as taking place in the external world, they occupy a vague internal space located within the head.  [p. 139]
In the skin itself there is a vague form of projection into the third dimension to which Hering has called attention.
" Heat is not felt only against the cutaneous surface, but when communicated through the air may appear extending more or less out from the surface into the third dimension of surrounding space ... We can determine in the dark the place of a radiant body by moving the hand to and fro, and attending to the fluctuation of our feeling of warmth. The feeling itself, however; is not projected fully into the spot at which we localize the hot body, but always remains in the neighborhood of the hand."
The interior of one's mouth-cavity feels larger when explored by the tongue than when looked at. The crater of a, newly-extracted tooth, and the movements of a loose tooth in its socket, feel quite monstrous. A midge buzzing against the drum of the ear will often seem as big as a butterfly. The spatial sensibility of the tympanic membrane has hitherto been very little studied, though the subject will well repay much trouble. If we approach it by introducing into the outer ear some small object like the tip of a rolled-up tissue-paper lamplighter, we are surprised at the large radiating sensation which its presence gives us, end at the sense of clearness and openness which comes when it is removed. It is immaterial to inquire whether the far-reaching sensation here be due to actual irradiation upon distant nerves or not. We are considering now, not the objective causes of the spatial feeling, but its subjective varieties, and the experiment shows that the same object gives more of it to the inner than to the outer cuticle of the ear. The pressure of the air in the tympanic cavity upon the membrane gives an astonishingly large sensation. We increase the pressure by holding our nostrils and closing our mouth and forcing air through our Eustachian tubes by an expiratory effort; and we can diminish it by either inspiring or swallowing under the same conditions of closed mouth and nose. In either case me get a large round tridimensional sensation inside of the head, which seems as if it must come from the affection of an organ much larger than the tympanic membrane, whose surface hardly exceeds that of one's little-finger-nail. [p. 140]
The tympanic membrane is furthermore able to render sensible differences in the pressure of the external atmosphere, too slight to be, felt either as noise or in this more violent way. If the reader will sit with closed eyes and let a friend approximate some solid object, like a large book, noiselessly to his face, he min immediately become aware of the object's presence and position -- likewise of its departure. A friend of the writer, making the experiment for the first time, discriminated unhesitatingly between the three degrees of solidity of a board, a lattice-frame, and a sieve, held close to his ear. Now as this sensation is never used by ordinary persons as a means of perception, we may fairly assume that its felt quality, in those whose attention is called to it for the first time, belongs to it quâ sensation, and owes nothing to educational suggestions. But this felt quality is most distinctly and unmistakably one of vague spatial vastness in three dimensions -- quite as much so as is the felt quality of the retinal sensation when we lie on our back and fin the entire held of vision with the empty blue sky. When an object is brought near the ear we immediately feel shut in, contracted; when the object is removed, we suddenly feel as if a transparency, clearness, openness, had been made outside of us. And the feeling will, by any one who will take the pains to observe it, be acknowledged to involve the third dimension in a vague, unmeasured state. 
The reader will have noticed, in this enumeration of facts, that voluminousness of the feeling seems to bear very little relation to the size of the organ that yields it. The ear and eye are comparatively minute organs, yet they give us feelings of great volume. The same lack of exact proportion between size of feeling and size of organ affected obtains within the limits of particular sensory organs. An object appears smaller on the lateral portions of the retina than it does on the fovea, as may be easily verified by holding the [p. 141] two forefingers parallel and a couple of inches apart, and transferring the gaze of one eye from one to the other. Then the finger not directly looked at will appear to shrink, and this whatever be the direction of the fingers. On the tongue a crumb, or the calibre of a small tube, appears larger than between the fingers. If two points kept equidistant (blunted compass- or scissors-points, for example) be drawn across the skin so as really to describe a pair of parallel lines, the lines will appear farther apart in some spots than in others. If, for example, me draw them horizontally across the face, so that the mouth falls between them, the person experimented upon will feel as if they began to diverge near the mouth and to include it in a well- marked ellipse. In like manner, if we keep the compass-
points one or two centimetres apart, and draw them down the forearm over the wrist and palm, finally drawing one along one finger, the other along its neighbor, the appearance will be that of a single line, soon. breaking into two, which become more widely separated below the wrist, to contract again in the palm, and finally diverge rapidly again towards the finger-tips. The dotted lines in Figs. 51 and 52 represent the true path of the compass-points; the full lines their apparent path. The same length of skin, moreover, will convey a more extensive sensation according to the manlier of stimulation. If the edge of a card be pressed against the skis, the distance between its extremities will seem shorter than that between two compass-tips touching the same terminal points.  
In the eye, intensity of nerve-stimulation seems to increase
the volume of the feeling as well as its brilliancy. If we raise and lower the gas alternately, the whole room and all the objects in it seem alternately to enlarge and contract. If we cover half a page of small print with a gray glass, the print seen through the glass appears decidedly smaller than that seen outside of it, and the darker the glass the greater the difference. When a circumscribed opacity in front of the retina, keeps off part of the light from the portion which it covers, objects projected on that portion may seem but half as large as when their image falls outside of it.  The inverse effect seems produced by certain drugs and anæsthetics. Morphine, atropine, daturine, and cold blunt the sensibility of the skin, so that distances upon it seem less. Haschish produces strange perversions of the general sensibility. Under its influence one's body may seem either enormously enlarged or strangely contracted. Sometimes a single member will alter its proportion to the rest; or one's back, for instance, will appear entirely absent, as if one mere hollow behind. Objects comparatively near will recede to a vast distance, a short street assume to the eye an immeasurable perspective. Ether and chloroform [p. 143] occasionally produce not wholly dissimilar results. Panum, the German physiologist, relates that when, as a, boy, he was etherized for neuralgia, the objects in the room grew extremely small and distant, before his held of vision dark-hued over and the roaring in his ears began. He also mentions that a friend of his in church, struggling in vain to keep awake, saw the preacher grow smaller and smaller and more and more distant. I myself on one occasion observed the same recession of objects during the beginning of chloroformization. In various cerebral diseases we find analogous disturbances.
Can we assign the physiological conditions which make the elementary sensible largeness of one sensation vary so much from that of another? Only imperfectly. One factor in the result undoubtedly is the number of nerve-terminations simultaneously excited by the outward agent that awakens the sensation. When many skin-nerves are warmed, or much retinal surface illuminated, our feeling is larger than when a lesser nervous surface is excited. The single sensation yielded by two compass-points, although it seems simple, is yet felt to be much bigger and blunter than that yielded by one. The touch of a single point may always be recognized by its quality of sharpness. This page looks much smaller to the reader if he closes one eye than if both eyes are open. So does the moon, which latter fact shows that the phenomenon has nothing to do with parallax. The celebrated boy couched for the cataract by Cheselden thought, after his first eye was operated, "all things he saw extremely large," but being couched of his second eye, said "that objects at first appeared large to this eye, but not so large as they did at first to the other; and looking upon the same object with both eyes, he thought it looked about twice as large as with the first couched eye only, but not double, that we can anyways discover."
The greater extensiveness that the feeling of certain parts of the same surface has over other parts, and that one order of surface has over another (retina over skin, for example), may also to a certain extent be explained by the operation of the same factor. It is an anatomical fact that the most spatially sensitive surfaces (retina, tongue, finger- [p. 144] tips, etc.) are supplied by nerve-trunks of unusual thickness, which must supply to every unit of surface-area an unusually large number of terminal fibres. But the variations of felt extension obey probably only a very rough law of numerical proportion to the number of fibres, A sound is not twice as voluminous to two ears as to one; and the above-cited variations of feeling, when the same surface is excited under different conditions, show that the feeling is a resultant of several factors of which the anatomical one is only the principal. Many ingenious hypotheses have been brought forward to assign the co-operating factors where different conditions give conflicting amounts of felt space, Later we shall analyze some of these cases in detail, but it must be confessed here in advance that many of them resist analysis altogether.  [p. 145]
THE PERCEPTION OF SPATIAL ORDER.
So far, all we have established or sought to establish is the existence of the vague form or quale of spatiality as an inseparable element bound up with the other peculiarities of each and every one of our sensations. The numerous examples we have adduced of the variations of this extensive element have only been meant to make clear its strictly sensational character. In very few of them will the reader have been able to explain the variation by an added intellectual element, such as the suggestion of a recollected experience. In almost all it has seemed to be the immediate psychic effect of a peculiar sort of nerve-process excited; and all the nerve-processes in question agree in yielding what space they do yield, to the mind, in the shape of a simple total vastness, in which, primitively at least, no order of parts or of subdivisions reigns.
Let no one be surprised at this notion of a space without order. There may be a space without order just as there may be an order without space.  And the primitive perceptions of space are certainly of an unordered kind. The order which the spaces first perceived potentially include must, before being distinctly apprehended by the mind, be woven into those spaces by a rather complicated set of intellectual acts. The primordial largenesses which the sensations yield must be measured and subdivided by consciousness, and added together, before they can form by their synthesis what we know as the real Space of the objective world. In these operations, imagination, association, attention, and selection play a decisive part; and although they nowhere add any new material to the space-data of sense, they so shuffle and manipulate these data and hide [p. 146] present ones behind imagined ones that it is no wonder if some authors have gone so far as to think that the sense-data have no spatial worth at all, and that the intellect, since it makes the subdivisions, also gives the spatial quality to them out of resources of its own.
As for ourselves, having found that all our sensations (however as yet unconnected and undiscriminated) are of extensive objects, our next problem is: How do we ARRANGE these at first chaotically given spaces into the one regular and orderly world of space which we now know?
To begin with, there is no reason to suppose that the several sense-spaces of which a sentient creature may become conscious, each fined with its own peculiar content, should tend, simply because they are many, to enter into any definite spatial intercourse with each other, or lie in any particular order of positions. Even in ourselves we can recognize this. Different feelings may coexist in us without assuming any particular spatial order. The sound of the brook near which I write, the odor of the cedars, the comfort with which my breakfast has fined me, and my interest in this paragraph, all lie distinct in my consciousness, but in no sense outside or alongside of each other. Their spaces are interfused and at most fin the same vaguely objective world. Even where the qualities are far less disparate, we may have something similar. If me take our subjective and corporeal sensations alone, there are moments when, as we lie or sit motionless, we find it very difficult to feel distinctly the length of our back or the direction of our feet from our shoulders. By a strong effort we can succeed in dispersing our attention impartially over our whole person, and then we feel the real shape of our body in a sort of unitary way. But in general a few parts are strongly emphasized to consciousness and the rest sink out of notice; and it is then remarkable how vague and ambiguous our perception of their relative order of location is. Obviously, the orderly arrangement of a multitude of sense-spaces in consciousness, something more than their mere separate existence is required. What is this further condition?
If a number of sensible extents are to be perceived alongside [p. 147] of each other and in definite order they must appear as parts in a vaster sensible extent which can enter the mind simply and ad at once. I think it will be seen that the difficulty of estimating correctly the form of one's body by pure feeling arises from the fact that it is very hard to feel its totality as a unit at all. The trouble is similar to that of thinking forwards and backwards simultaneously. When conscious of our head we tend to grow unconscious of our feet, and there enters thus an element of time-succession into our perception of ourselves which transforms the latter from an act of intuition to one of construction. This element of constructiveness is present in a still higher degree, and carries with it the same consequences, when we deal with objective spaces too great to be grasped by a single look. The relative positions of the shops in a town, separated by many tortuous streets, have to be thus constructed from data apprehended in succession, and the result is a greater or less degree of vagueness.
That a sensation be discriminated as part from out of a, larger enveloping space is then the condition sine quâ non of its being apprehended in a definite spatial order. The problem of ordering our feelings in space is then, in the first instance, a problem of discrimination, but not of discrimination pure and simple; for then not only coexistent sights but consistent sounds would necessarily assume web order, which they notoriously do not. Whatever is discriminated will appear as a small space within a larger space, it is true, but this is but the very rudiment of order. For the location of it within that space to become precise, other conditions still must supervene; and the best way to study what they are will be to pause for a little and analyze what the expression 'spatial order' means.
Spatial order is an abstract term. The concrete perceptions which it covers are figures, directions, positions, magnitudes, and distances. To single out any one of these things from a total vastness is partially to introduce order into the vastness. To subdivide the vastness into a multitude of these things is to apprehend it in a completely orderly way. Now what are these things severally? To [p. 148] begin with, no one can for an instant hesitate to say that some of them are qualities of sensation, just as the total vastness is in which they lie. Take figure: a square, a circle, and a triangle appear in the best instance to the eye simply as three different kinds elf impressions, each so peculiar that we should recognize it if it were to return. When Nunnery's patient had his cataracts removed, and a cube and a sphere were presented to his notice, he could at once perceive a difference in their shapes; and though he could not say which was the cube and which the sphere, he saw they were not of the same figure. So of lines: if we can notice lines at all in our field of vision, it is inconceivable that a vertical one should not affect us differently from an horizontal one, and should not be recognized as affecting us similarly when presented again, although we might not yet know the name 'vertical,' or any of its connotations, beyond this peculiar affection of our sensibility. So of angles: an obtuse one affects our feeling immediately in a different way from an acute one. Distance-apart, too, is a simple sensation -- the sensation of a line joining the two distant points: lengthen the line, you alter the feeling and with it the distance felt.
But with distance and direction we pass to the category of space-relations, and are immediately confronted by an opinion which makes of all relations something tote coelo different from all facts of feeling or imagination whatsoever. A relation, for the Platonizing school in psychology, is an energy of pure thought, and, as such, is quite incommensurable with the data of sensibility between which it may be perceived to obtain. We may consequently imagine a disciple of this school to say to us at this point: "Suppose you have made a, separate specific sensation of each line and each angle, what boots it? You have still the order of directions and of distances to account for; you have still the relative magnitudes of all these felt figures to state; you have their respective positions to define before you can be said to have brought order into your space. And not one of these de- [p. 149] terminations can be effected except through an act of relating thought, so that your attempt to give an account of space in terms of pure sensibility breaks down almost at the very outset. Position, for example, can never be a sensation, for it has nothing intrinsic about it; it can only obtain between a spot, line, or other figure and extraneous coordinates, and can never be an element of the sensible datum, the line or the spot, in itself. Let us then confess that Thought alone can unlock the riddle of space, and that Thought is an adorable but unfathomable mystery. Such a method of dealing with the problem has the merit of shortness. Let us, however, be in no such hurry, but see whether we cannot get a little deeper by patiently considering what these space-relations are.
'Relation' is a very slippery word. It has so many different concrete meanings that the use of it as an abstract universal may easily introduce bewilderment into our thought. We must therefore be careful to avoid ambiguity by making sure, wherever we have to employ it, what its precise meaning is in that particular sphere of application. At present we have to do with space-relations, and no others. Most 'relations' are feelings of an entirely different order from the terms they relate. The relation of similarity, e.g., may equally obtain between jasmine and tuberose, or between Mr. Browning's verses and Mr. Story's; it is itself neither odorous nor poetical, and those may well be pardoned who have denied to it all sensational content whatever. But just as, in the field of quantity, the relation between two numbers is another number, so in the field of space the relations are facts of the same order with the facts they relate. If these latter be catches in the circle of vision, the former are certain other patches between them. When we speak of the relation of direction of two points toward each other, we mean simply the sensation of the line that joins the two points together. The line is the relation; feel it and you feel the relation, see it and you see the relation; nor call you in any conceivable way think the latter except by imagining the former (however vaguely), or describe or indicate the one except by pointing to the other. And the moment you have imagined the line, the relation stands [p. 150] before you in all its completeness, with nothing further to be done. Just so the relation of direction between two lines is identical with the peculiar sensation of shape of the space enclosed between them. This is commonly called an angular relation.
If these relations are sensations, no less so are the relations of position. The relation of position between the top and bottom points of a vertical line is that line, and nothing else. The relations of position between a point and a horizontal line below it are potentially numerous. There is one more important than the rest, called its distance. This is the sensation, ideal or actual, of a perpendicular drawn from the point to the line.  Two lines, one from each extremity of the horizontal to the point, give us a peculiar sensation of triangularity. This feeling may be said to constitute the locus of all the relations of position of the elements in question. Rightness and leftness, upness and downness, are again pure sensations differing specifically from each other, and generically from everything else. Like all sensations, they can only be indicated, not described. If we take a cube and label one side top, another bottom, a third front, and a fourth back; there remains no form of words by which we can describe to another person which of the remaining sides is right and which left. We can only point and say here is right and there is left, just as we should say this is red and that blue. Of two points seen beside each other at all, one is always affected by one of these feelings, and the other by the opposite; the same is true of the extremities of any line.  [p. 151]
Thus it appears indubitable that all space-relations except those of magnitude are nothing more or less than pure sensational objects. But magnitude appears to outstep this narrow sphere. We hare relations of muchness and littleness between times, numbers, intensities, and qualities, as well as spaces. It is impossible, then, that such relations should form a particular kind of simply spatial feeling. This we must admit: the relation of quantity is generic and occurs in many categories of consciousness, whilst the other relations we have considered are specific and occur in space alone. When our attention passes from a shorter line to a longer, from a smaller spot to a larger, from a, feebler light to a stronger, from a paler blue to a richer, from a march tune to a galop, the transition is accompanied in the synthetic field of consciousness by a peculiar feeling of difference which is what we call the sensation of more, -- more length, more expense, more light, more blue, more motion. This transitional sensation of more must Be identical with itself under all these different accompaniments, or me should not give it the same name in every case. We get it when we pass from a short vertical line to a long horizontal one, from a small square to a large circle, as well as when we pass between those figures whose shapes are congruous. But when the shapes are congruous our consciousness of the relation is a good deal more distinct, and it is most distinct of all when, in the exercise of our analytic attention, we notice, first, a part, and then the whole, of a single line or shape. Then the more of the whole actually sticks out, as a separate piece of space, and is so envisaged. The same exact sensation of it is given when we are able to superpose one line or figure on another. This indispensable condition of exact measurement of the more has led some to think that the feeling itself arose in every case from original experiences of superposition. This is [p. 152] probably not an absolutely true opinion, but for our present purpose that is immaterial. So far as the subdivisions of a, sense-space are to be measured exactly against each other, objective forms occupying one subdivision must directly or indirectly be superposed upon the other, and the mind must get the immediate feeling of an outstanding plus. And even where we only feel one subdivision to be vaguely larger or less, the mind must pass rapidly between it and the other subdivision, and receive the immediate sensible shock of the more.
We seem thus to have accounted for all space-relations, and made them clear to our understanding. They are nothing but sensations of particular lines, particular angles, particular forms of transition, or (in the case of a distinct more) of particular outstanding portions of space after two figures have been superposed. These relation-sensations may actually be produced as such, as when a geometer draws new lines across a figure with his pencil to demonstrate the relations of its parts, or they may be ideal representations of lines, not really drawn. But in either case their entrance into the mind is equivalent to a more detailed subdivision, cognizance, and measurement of the space considered. The bringing of sub-divisions to consciousness constitutes, then, the entire process by which we pass from our first vague feeling of a total vastness to a cognition of the vastness in detail. The more numerous the subdivisions are, the more elaborate and perfect the cognition becomes. But inasmuch as all the sub-divisions are themselves sensations, and even the feeling of 'more' or 'less' is, where not itself a figure, at least a sensation of transition between two sensations of figure, it follows, for aught we can as yet see to the contrary, that all spatial knowledge is sensational at bottom, and that, as the sensations lie together in the unity of consciousness, no new material element whatever comes to them from a supra-sensible source.  [p. 153]
The bringing of subdivisions to consciousness! This, then, is our next topic. They may be brought to consciousness under three aspects in respect of their locality, in respect of their size, in respect of their shape.
The Meaning of Localization.
Confining ourselves to the problem of locality for the present, let us begin with the simple case of a sensitive surface, only two points of which receive stimulation from without. How, first, are these two points felt as alongside of each other with an interval of space between them? We must be conscious of two things for this: of the duality of the excited points, and of the extensiveness of the unexcited interval. The duality alone, although a necessary, is not a sufficient condition of the spatial separation. We may, for instance, discern two sounds in the same place, sweet and sour in the same lemonade, warm and cold, round and pointed contact in the same place on the skin, etc.  In all discrimination the recognition of the duality of two feelings by the mind is the easier the more strongly the feelings are [p. 154] contrasted in quality. If our two excited points awaken identical qualities of sensation, they must, perforce, appear to the mind as one; and, not distinguished at all, they are, a fortiori, not localized apart. Spots four centimetres distant on the back have no qualitative contrast at all, and fuse into a single sensation. Points less than three thousandths of a millimetre apart awaken on the retina sensations so contrasted that we apprehend them immediately as two. Now these unlikenesses which arise so slowly when we pass from one point to another in the back, so much faster on the tongue and finger-tips, but with such inconceivable rapidity on the retina, what are they? Can we discover anything about their intrinsic nature?
The most natural and immediate answer to make is that they are unlikeness of place pure and simple. In the words of the German physiologist  to who psychophysics owes much:
" The sensations are from the outset (von vornherein) localized. ... Every sensation as such is from the very beginning affected with the spatial quality, so that this quality is nothing like an external attribute coming to the sensation from a higher faculty, but must be regarded as something immanently residing in the sensation itself."
And yet the moment we reflect on this answer an insuperable logical difficulty seems to present itself. No single quail of sensation can, by itself, amount to a consciousness of position. Suppose no feeling but that of a single point ever to be awakened. Could that possibly be the feeling of any special whereness or thereness? Certainly not. Only when a second point is felt to arise can the first one acquire a determination of up, down, right or left, and these determinations are all relative to that second point. Each point, so far as it is placed, is then only by virtue of what it is not, namely, by virtue of another point. This is as much as to say that position has nothing intrinsic about it; and that, although a feeling of absolute bigness may, a feeling of place cannot, possibly form an immanent element in any single isolated sensation. The very writer we have quoted has given heed to this objection, for he continues (p. 335) by saying that the [p. 155] sensations thus originally localized "are only so in themselves, but not in the representation of consciousness, which is not yet present .... They are, in the first instance, devoid of all mutual relations with each other." But such a localization of the sensation 'in itself' would seem to mean nothing more than the susceptibility or potentiality of being distinctly localized when the time came and other conditions became fulfilled. Can we now discover anything about such susceptibility in itself before it has borne its ulterior fruits in the developed consciousness?
To begin with, every sensation of the skin and every visceral sensation seems to derive from its topographic seat a peculiar shade of feeling, which it would not have in another place. And this feeling per se seems quite another thing from the perception of the place. Says Wundt: 
"If with the finger we touch first the cheek and then the palm, exerting each time precisely the same pressure, the sensation shows notwithstanding a distinctly marked difference in the two cases. Similarly, when we compare the palm with the back of the hand, the nape of the neck with its anterior surface, the breast with the back; in short, any two distant parts of the skin with each other. and moreover, we easily remark, by attentively observing, that spots even tolerably close together differ in respect of the quality of their feeling. If we pass from one point of our cutaneous surface to another, we find a perfectly gradual and continuous alteration in our feeling, notwithstanding the objective nature of the contact has remained the same. Even the sensations of corresponding points on opposite sides of the body, though similar, are not identical. If, for instance, we touch first the back of one hand and then of the other, we remark a qualitative unlikeness of sensation. It must not be thought that such differences are mere matters of imagination, and that we take the sensations to be different because we represent each of them to ourselves as occupying a different place. With sufficient sharpening of the attention, we may, confining ourselves to the quality of the feelings alone, entirely abstract from their locality, and yet notice the differences quite as markedly." [p. 156]
Whether these local contrasts shade into each other with absolutely continuous gradations, we cannot say. But we know (continues Wundt) that
"they change, when we pass from one point of the skin to its neighbor, with very different degrees of rapidity. On delicately-feeling parts, used principally for touching, such as the finger-tips, the difference of sensation between two closely approximate points is already strongly pronounced; whilst in parts of lesser delicacy, as the arm, the back, the legs, the disparities of sensation are observable only between distant spots."
The internal organs, too, have their specific qualia of sensation. An inflammation of the kidney is different from one of the liver; pains in joints and muscular insertions are distinguished. Pain in the dental nerves is wholly unlike the pain of a burn. But very important and curious similarities prevail throughout these differences. Internal pains, whose seat we cannot see, and have no means of knowing unless the character of the pain itself reveal it, are felt where they belong. Diseases of the stomach, kidney, liver, rectum, prostate, etc., of the bones, of the brain and its membranes, are referred to their proper position. Nerve-pains describe the length of the nerve. Such localizations as those of vertical, frontal, or occipital headache of intracranial origin force us to conclude that parts which are neighbors, whether inner or outer, may possess by mere virtue of that fact a common peculiarity of feeling, a respect in which their sensations agree, and which serves as a token of their proximity. These local colorings are, moreover, so strong that we cognize them as the same, throughout all contrasts of sensible quality in the accompanying perception. Cold and heat are wide as the poles asunder; yet if both fall on the cheek, there mixes with them something that makes them in that respect identical; just as, contrariwise, despite the identity of cold with itself wherever found, when we get it first on the palm and then on the cheek, some difference comes, which keeps the two experiences for ever asunder."  [p.157]
And now let us revert to the query propounded a, moment since: Can these differences of mere quality in feeling, varying according to locality yet having each sensibly and intrinsically and by itself nothing to do with position, constitute the 'susceptibilities' we mentioned, the conditions of being perceived in position, of the localities to which they belong? The numbers on a row of houses, the initial letters of a set of words, have no intrinsic kinship with points of space, and yet they are the conditions of our knowledge of where any house is in the row, or any word in the dictionary. Can the modifications of feeling in question be tags or labels of this kind which in no wise originally reveal the position of the spot to which they are attached, but guide us to it by what Berkeley would call a 'customary tie'? Many authors have unhesitatingly replied in the affirmative; Lotze, who in his Medzinische Psychologie  first described the sensations in this way, designating them, thus conceived, as local-signs. This term has obtained wide currency in Germany, and in speaking of the 'LOCAL-SIGN THEORY' hereafter, I shall always mean the theory which denies that there can be in a sensation any element of actual locality, of inherent spatial order, any tone as [p. 158] it were which cries to us immediately and without further ado, 'I am here,' or 'I am there.' If, as may well be the case, we by this time and ourselves tempted to accept the Local-sign theory in a general way, we have to clear up several farther matters. If a sign is to lead us to the thing it means, we must have some other source of knowledge of that thing. Either the thing has been given in a previous experience of which the sign also formed part-they are associated ; or it is what Reid calls a 'natural' sign, that is, a feeling which, the first time it enters the mind, evokes from the native powers thereof a cognition of the thing that hitherto had lain dormant. In both cases, however, the sign is one thing, and the thing another. In the instance that now concerns us, the sign is a quality of feeling and the thing is a position. Now we have seen that the position of a point is not only revealed, but created, by the existence of other points to which it stands in determinate relations. If the sign can by any machinery which it sets in motion evoke consciousness either of the other points, or of the relations, or of both, it would seem to fulfil its function, and reveal to us the position we seek.
But such a machinery is already familiar to us. It is neither more nor less than the law of habit in the nervous system. When any point of the sensitive surface has been frequently excited simultaneously with, or immediately before or after, other points, and afterwards comes to be excited alone, there will be A tendency for its perceptive nerve-centre to irradiate into the nerve-centres of the other points. Subjectively considered, this is the same as if we said that the peculiar feeling of the first point SUGGESTS the feeling of the entire region with whose stimulation its own excitement has been habitually ASSOCIATED.
Take the case of the stomach. When the epigastrium is heavily pressed, when certain muscles contract, etc., the stomach is squeezed, and its peculiar local sign awakes in consciousness simultaneously with the local signs of the other squeezed parts. There is also a sensation of total vastness aroused by the combined irritation, and somewhere in this the stomach-feeling seems to lie. Suppose that later a pain arises in the stomach from some non-mechani- [p. 159] cal cause. It will be tinged by the gastric local sign, and the nerve-centre supporting this latter feeling will excite the centre supporting the dermal and muscular feelings habitually associated with it when the excitement was mechanical. From the combination the same peculiar vastness will again arise. In a word, 'something' in the stomach-sensation 'reminds' us of a total space, of which the diaphragmatic and epigastric sensations also form a part, or, to express it more briefly still, suggests the neighborhood of these latter organs. 
Revert to the case of two excited points on a surface with an unexcited space between them. The general result of previous experience has been that when either point was impressed by an outward object, the same object also touched the immediately neighboring parts. Each point, together with its local sign, is thus associated with a circle of surrounding points, the association fading in strength as the circle grows larger. Each will revive its own circle; but when both are excited together, the strongest revival will be that due to the combined irradiation. Now the tract joining the two excited points is the only part common to the two circles. And the feelings of this whole tract will therefore awaken with considerable vividness in the imagination when its extremities are touched by an outward irritant. The mind receives with the impression of the two distinct points the vague idea of a line. The twoness of the points comes from the contrast of their local signs: the line comes from the associations into which experience has wrought these latter. If no ideal line arises me have duality without sense of interval; if the line be excited actually rather [p. 160] than ideally, we have the interval given with its ends, in the form of a single extended object felt. E. H. Weber, in the famous article in which he laid the foundations of all our accurate knowledge of these subjects, laid it down as the logical requisite for the perception of two separated points, that the mind should, along with its consciousness of them, become aware of an unexcited interval as such I have only tried to show how the known laws of experience may cause this requisite to be fulfilled. Of course, if the local signs of the entire region offer but little qualitative contrast inter se, the line suggested will be but dimly defined or discriminated in length or direction from other possible lines in its neighborhood. This is what happens in the back, where consciousness can sunder two spots, whilst only vaguely apprehending their distance and direction apart.
The relation of position of the two points is the suggested interval or line. Turn now to the simplest case, that of a single excited spot. How can it suggest its position? Not by recalling any particular line unless experience have constantly been in the habit of marking or tracing some one line from it towards some one neighboring point. Now on the back, belly, viscera, etc., no such tracing habitually occurs. The consequence is that the only suggestion is that of the whole neighboring circle; i.e., the spot simply recalls the general region in which it happens to lie. By a process of successive construction, it is quite true that we can also get the feeling of distance between the spot and some other particular spot. Attention, by reinforcing the local sign of one part of the circle, can awaken a new circle round this part, and so de proche en proche we may slide our feeling down from our cheek, say, to our foot. But when we first touched our cheek we had no consciousness of the foot at all.  In the extremities, the lips, the tongue and other mobile parts, the case is different. We there have an instinctive tendency, when a, part of lesser discriminative [p.161] sensibility is touched, to move the member so that the touching object glides along it to the place where sensibility is greatest. If a body touches our hand we move the hand over it tin the finger-tips are able to explore it. If the sole of our foot touches anything we bring it towards the toes, and so forth. There thus arise lines of habitual passage from all points of a member to its sensitive tip. These are the lines most readily recalled when any point is touched, and their recall is identical with the consciousness of the distance of the touched point from the 'tip.' I think anyone must be aware when he touches a point of his hand or wrist that it is the relation to the finger-tips of which he is usually most conscious. Points on the fore-arm suggest either the finger-tips or the elbow (the latter being a spot of greater sensibility  ). In the foot it is the toes, and so on. A point can only be cognized in its relations to the entire body at once by awakening a visual image of the whole body. Such awakening is even more obviously than the previously considered cases a matter of pure association.
This leads us to the eye. On the retina the fovea and the yellow spot about it form a focus of exquisite sensibility, towards which every impression falling on an outlying portion of the field is moved by an instinctive action of the muscles of the eyeball. Few persons, until their attention is called to the fact, are aware how almost impossible it is to keep a conspicuous visible abject in the margin of the field of view. The moment volition is relaxed we find that without our knowing it our eyes have turned so as to bring it to the centre. This is why most persons are unable to keep the eyes steadily converged upon a point in space with nothing in it. The objects against the walls of the room [p. 162] invincibly attract the foveæ to themselves. If we contemplate a blank wall or sheet of paper, we always observe in a moment that we are directly looking at some speck upon it which, unnoticed at first, ended by 'catching our eye.' Thus whenever an image falling on the point P of the retina excites attention, it more habitually moves from that point towards the fovea than in any one other direction. The line traced thus by the image is not always a straight line. When the direction of the point from the fovea is neither vertical nor horizontal but oblique, the line traced is often a curve, with its concavity directed upwards if the direction is upwards, downwards if the direction is downwards. This may be verified by anyone who will take the trouble to make a simple experiment with a luminous body like a candle-flame in a dark enclosure, or a star. Gazing first at some point remote from the source of light, let the eye be suddenly turned full upon the latter. The luminous image will necessarily fall in succession upon a continuous series of points, reaching from the one first affected to the fovea. But by virtue of the slowness with which retinal excitements die away, the entire series of points will for an instant be visible as an after-image, displaying the above peculiarity of form according to its situation.  These radiating lines are neither regular nor invariable in the same person, nor, probably, equally curved in different individuals. We are incessantly drawing them between the fovea and every point of the held of view. Objects remain in their peripheral indistinctness only so long as they are unnoticed. The moment we attend to them they grow distinct through one of these motions -- which leads to the idea prevalent among uninstructed persons that we see distinctly all parts of the field of view at once. The result of this incessant tracing of radii is that whenever a local sign P is awakened by a spot of light falling upon it, it recalls forthwith, even though the eyeball be unmoved, the local signs of all the other points which lie between P and the fovea. It recalls them in imaginary form, just as the normal reflex movement would recall them in vivid form; and with their recall is given a consciousness more or less [p. 163] faint of the whole line on which they lie. In other words, no ray of light can fall on any retinal spot without the local sign of that spot revealing to us, by recalling the line of its most habitual associates, its direction and distance from the centre of the held. The fovea acts thus as the origin of a system of polar co-ordinates, in relation to which each and every retinal point has through an incessantly-repeated process of association its distance and direction determined. Were P alone illumined and all the rest of the field dark we should still, even with motionless eyes, know whether P lay high or low, right or left, through the ideal streak, different from all other streaks, which P alone has the power of awakening."  [p. 164]
And with this we can close the first great division of our subject. We have shown that, within the range of [p. 165] every sense, experience takes ab initio the spatial form. We have also shown that in the cases of the retina and skin [p. 166] every sensible total may be subdivided by discriminative attention into sensible parts, which are also spaces, and into relations between the parts, these being sensible spaces too. Furthermore, we have seen (in a foot-note) that different parts, once discriminated, necessarily fall into a determinate order, both by reason of definite gradations in their quality, and by reason of the fixed order of time-succession in which movements arouse them. But in all this nothing has been said of the comparative measurement of one sensible space-total against another, or of the way in which, by summing our divers simple sensible space-experiences together, we end by constructing what we regard as the unitary, continuous, and infinite objective space of the real world. To this more difficult inquiry we next pass.
THE CONSTRUCTION OF 'REAL' SPACE.
The problem breaks into two subordinate problems.
(1) How is the subdivision and measurement of the several sensorial spaces completely effected? and
(2) How do their mutual addition and fusion and reduction to the same scale, in a word, how does their synthesis, occur?
I think that, as in the investigation just finished, we found ourselves able to get along without invoking any data but those that pure sensibility on the one hand, and the ordinary intellectual powers of discrimination and recollec- [p. 167] tion on the other, were able to yield; so here we shall emerge from our more complicated quest with the conviction that all the facts can be accounted for on the supposition that no other mental forces have been at work save those we find everywhere else in psychology: sensibility, namely, for the data; and discrimination, association, memory, and choice for the rearrangements and combinations which they undergo.
1. The Subdivision of the Original Sense-spaces.
How are spatial subdivisions brought to consciousness ? in other words, How does spatial discrimination occur? The general subject of discrimination has been treated in a previous chapter. Here we need only inquire what are the conditions that make spatial discrimination so much finer in sight than in touch, and in touch than in hearing, smell, or taste.
The first great condition is, that different points of the surface shall differ in the quality of their immanent sensibility, that is, that each shall carry its special local-sign. If the skin felt everywhere exactly alike, a foot-bath could be distinguished from a total immersion, as being smaller, but never distinguished from a wet face. The local-signs are indispensable; two points which have the same local-sign will always be felt as the same point. We do not judge them two unless we have discerned their sensations to be different.  Granted none but homogeneous irritants, that organ would then distinguish the greatest multiplicity of irritants -- would count most stars or compass-points, or best compare the size of two wet surfaces -- whose local sensibility was the least even. A skin whose sensibility shaded rapidly off from a focus, like the apex of a boil, would be better than a homogeneous integument for spatial perception. The retina, with its exquisitely sensitive fovea, has this peculiarity, and undoubtedly owes to it a great part [p. 168] of the minuteness with which we are able to subdivide the total bigness of the sensation it yields. On its periphery the local differences do not shade off very rapidly, and we can count there fewer subdivisions.
But these local differences of feeling, so long as the surface is unexcited from without, are almost null. I cannot feel them by a pure mental act of attention unless they belong to quite distinct parts of the body, as the nose and the lip, the finger-tip and the ear; their contrast needs the reinforcement of outward excitement to be felt. In the spatial muchness of a colic -- or, to call it by the more spacious-sounding vernacular, of a 'bellyache' -- one can with difficulty distinguish the north-east from the south-west corner, but can do so much more easily if, by pressing one's finger against the former region, one is able to make the pain there more intense.
The local differences require then, an adventitious sensation, superinduced upon them, to awaken the attention. After the attention has once been awakened in this way, it may continue to be conscious of the unaided difference; lust as a sail on the horizon may be too faint for us to notice until someone's finger, placed against the spot, has pointed it out to us, but may then remain visible after the finger has been withdrawn. But all this is true only on condition that separate points of the surface may be exclusively stimulated. If the whole surface at once be excited from without, and homogeneously, as, for example, by immersing the body in salt water, local discrimination is not furthered. The local signs, it is true, all awaken at once; but in such multitude that no one of them, with its specific quality, stands out in contrast with the rest. If, however, a single extremity be immersed, the contrast between the wet and dry parts is strong, and, at the surface of the water especially, the local-signs attract the attention, giving the feeling of a ring surrounding the member. Similarly, two or three wet spots separated by dry spots, or two or three hard points against the skin, will help to break up our consciousness of the latter's bigness. In eases of this sort, where points receiving an identical kind of excitement are, nevertheless, felt to be locally distinct, and the objective irritants are also [p. 169] judged multiple, -- e.g., compass-points on skin or stars on retina, -- the ordinary explanation is no doubt just, and we judge the outward causes to be multiple because we have discerned the local feelings of their sensations to be different.
Capacity for partial stimulation is thus the second condition favoring discrimination. A sensitive surface which has to be excited in all its parts at once can yield nothing but a sense of undivided largeness. This appears to be the case with the olfactory, and to all intents and purposes with the gustatory, surfaces. Of many tastes and flavors, even simultaneously presented, each affects the totality of its respective organ, each appears with the whole vastness given by that organ, and appears interpenetrated by the rest.  [p. 170]
I should have been wining some years ago to name with- out hesitation a third condition of discrimination-saying it would be most developed in that organ which is susceptible of the most various qualities of feeling. The retina is un- questionably such an organ. The colors and shades it perceives are infinitely more numerous than the diversities of skin-sensation. And it can feel at once white and black, whilst the ear can in nowise so feel sound and silence. But the late researches of Donaldson, Blix, and Goldscheider,  on specific points for heat, cold, pressure, and pain in the skin; the older ones of Czermak (repeated later by Klug in Ludwig's laboratory), showing that a hot and a cold compass-point are no more easily discriminated as two than two of equal temperature; and some unpublished experiments of my own -- all disincline me to make much of this condition now.  There is, however, one quality of sensa- [p. 171] tion which is particularly exciting, and that is the feeling of motion over any of our surfaces. The erection of this into a separate elementary quality of sensibility is one of the most recent of psychological achievements, and is worthy of detaining us a while at this point.
The Sensation of Motion over Surfaces.
The feeling of motion has generally been assumed by physiologists to be impossible until the positions of terminus ad quem and terminus ad quem are severally cognized, and the successive occupancies of these positions by the moving body are perceived to be separated by a distinct interval of time.  As a matter of fact, however, we cognize only the very slowest motions in this way. Seeing the hand of a clock at XII and afterwards at VI, we judge that it has moved through the interval. Seeing the sun now in the east and again in the west, I infer it to have passed over my head. But we can only infer that which we already generically know in some more direct fashion, and it is experimentally certain that we have the feeling of motion given us as a direct and simple sensation. Czermak long ago pointed out the difference between seeing the motion of the second-hand of a watch, when we look directly at it, and noticing the fact of its having altered its position when we fix our gaze upon some other point of the dial-plate. In the first case we have a specific quality of sensation which is absent in the second. If the reader will find a portion of his skin -- the arm, for example -- where a pair of compass-points an inch apart are felt as one impression, and if he will then trace lines a tenth of an inch long on that spot with a pencil-point, he will be distinctly aware of the point's motion and vaguely aware of the direction of the motion. The perception of the motion here is certainly not derived from a pre-existing knowledge that its starting and ending points are separate positions in space, because positions in space ten times wider apart fail to be discriminated as such [p. 172] when excited by the dividers. It is the same with the retina. One's fingers when cast upon its peripheral portions cannot be counted -- that is to say, the five retinal tracts which they occupy are not distinctly apprehended by the mind as five separate positions in space -- and yet the slightest movement of the fingers is most vividly perceived as movement and nothing else. It is thus certain that our sense of movement, being so much more delicate than our sense of position, cannot possibly be derived from it. A curious observation by Exner  completes the proof that movement in a primitive form of sensibility, by showing it to be much more delicate than our sense of succession in time. This very able physiologist caused two electric sparks to appear in rapid succession, one beside the other. The observer had to state whether the right-hand one or the left-hand one appeared first. When the interval was reduced to as short a time as 0.044" the discrimination of temporal order in the sparks became impossible. But Exner found that if the sparks were brought so close together in space that their irradiation-circles overlapped, the eye then felt their flashing as if it were the motion of a single spark from the point occupied by the first to the point occupied by the second, and the time-interval might then be made as small as 0.015" before the mind began to be in doubt as to whether the apparent motion started from the right or from the left. On the skin similar experiments gave similar results.
Vierordt, at almost the same time,  called attention to certain persistent illusions, amongst which are these: If another person gently trace a line across our wrist or finger, the latter being stationary, it will feel to us as if the member were moving in the opposite direction to the tracing point. If, on the contrary, we move our limb across a fixed point, it will be seen as if the point were moving as well. If the reader will touch his forehead with his forefinger kept motionless, and then rotate the head so that the skin of the forehead passes beneath the finger's tip, he will have [p. 173] an irresistible sensation of the latter being itself in motion in the opposite direction to the head. So in abducting the fingers from each other; some may move and the rest be still still, but the still ones will feel as if they were actively separating from the rest. These illusions, according to Vierordt, are survivals of a primitive form of perception, when motion was felt as such, but ascribed to the whole content of consciousness, and not yet distinguished as belonging exclusively to one of its parts. When our perception is fully developed we go beyond the mere relative motion of thing and Bound, and can ascribe absolute motion to one of these components of our total object, and absolute rest to another. When, in vision for example, the whole background moves together, we think that it is ourselves or our eyes which are moving; and any object in the foregound which may move relatively to the background is judged by us to be still. But primitively this discrimination cannot be perfectly made. The sensation of the motion spreads over all that we see and infects it. Any relative motion of object and retina both makes the object seem to move, and makes us feel ourselves in motion. Even now when our whole object moves we still get giddy; and we still see an apparent motion of the entire held of view, whenever we suddenly jerk our head and eyes or shake them quickly to and fro. Pushing our eyeballs gives the same illusion. We know in all these cases what really happens, but the conditions are unusual, so our primitive sensation persists unchecked. So it does when clouds float by the moon. We know the moon is still; but we see it move even faster than the clouds. Even when we slowly move our eyes the primitive sensation persists under the victorious conception. If we notice closely the experience, we find that any object towards which we look appears moving to meet our eye. But the most valuable contribution to the subject is the paper of G. H. Schneider,  who takes up the matter zoologically, and shows by examples from every branch of the animal kingdom that movement is the quality by which animals most easily attract each other's attention. The in- [p. 174] stinct of shamming death 'is no shamming of death at all, but rather a paralysis through fear, which saves the insect, crustacean, or other creature from being noticed at all by his enemy. It is paralleled in the human race by the breath-holding stillness of the boy playing 'I spy,' to whom the seeker is near; and its obverse side is shown in our involuntary waving of arms, jumping up and down, and so forth, when we wish to attract someone's attention at a distance. Creatures 'stalking' their prey and creatures hiding from their pursuers alike show how immobility diminishes conspicuity. In the woods, if we are quiet, the squirrels and birds will actually touch us. Flies will light on stuffed birds and stationary frogs.  On the other hand, the tremendous shock of feeling the thing we are sitting on begin to move, the exaggerated start it gives us to have an insect unexpectedly pass over our skin, or a cat noiselessly come and snuffle about our hand, the excessive reflex effects of tickling, etc., show how exciting the sensation of motion is per se. A kitten cannot help pursuing a moving ball. Impressions too faint to be cognized at all are immediately felt if they move. A fly sitting is unnoticed, -- we feel it the moment it crawls. A shadow may be too faint to be perceived. As soon as it moves, however, we see it. Schneider found that a shadow, with distinct outline, and directly fixated, could still be perceived when moving, although its objective strength might be but half as great as that of a stationary shadow so faint as just to disappear. With a blurred shadow in indirect vision the difference in favor of motion was much greater -- namely, 13.3:40.7. If me hold a finger between our closed eyelid and the sunshine we shall not notice its presence. The moment we move it to and fro, however, we discern it. Such visual perception as this reproduces the conditions of sight among the radiates.  [p. 175]
Enough has now been said to show that in the education of spatial discrimination the motions of impressions across sensory surfaces must have been the principal agent in breaking up our consciousness of the surfaces into a consciousness of their parts. Even to-day the main function of the peripheral regions of our retina is that of sentinels, which, when beams of light move over them, cry 'Who goes there ?' and call the fovea to the spot. Most parts of the skin do but perform the same of office for the finger-tips. Of course finger-tips and fovea leave some power of direct perception to marginal retina and skin respectively. But it is worthy of note that such perception is best developed on the skin of the most movable parts (the labors of Vierordt and his pupils have well shown this); and that in the blind, whose skin is exceptionally discriminative, it seems to have become so through the inveterate habit which most of them possess of twitching and moving it under whatever object may touch them, so as to become better acquainted with the con- formation of the same. Czermak was the first to notice this. It may be easily verified. Of course movement of surface under object is (for purposes of stimulation) equivalent to movement of object over surface. In exploring the shapes and [p. 176] sizes of things by either eye or skin the movements of these organs are incessant and unrestrainable. Every such movement draws the points and lines of the object across the surface, imprints them a hundred times more sharply, and drives them home to the attention. The immense part thus played by movements in our perceptive activity is held by many psychologists  to prove that the muscles are themselves the space-perceiving organ. Not surface-sensibility, but 'the muscular sense,' is for these writers the original and only revealer of objective extension. But they have all failed to notice with what peculiar intensity muscular contractions call surface-sensibilities into play, and that the mere discrimination of impressions (quite apart from any question of measuring the space between them) largely depends on the mobility of the surface upon which they fall.  [p. 177]
2. The Measurement of the sense-spaces against each other.
What precedes is all we can say in answer to the problem of discrimination. Turn now to that of measurement of the several spaces against each other, that being the first step in our constructing out of our diverse space-experiences the one space we believe in as that of the real world.
The first thing that seems evident is that we have no immediate power of comparing together with any accuracy the extents revealed by different sensations. Our mouth-cavity feels indeed to itself smaller, and to the tongue larger, than it feels to the finger or eye, our tympanic membrane feels larger than our finger-tip, our lips feel larger then a surface equal to them on our thigh. So much comparison is immediate; but it is vague; and for anything exact; we must resort to other help.
The great agent in comparing the extent felt by one sensory surface with that felt by another, is superposition-superposition of one surface upon another, and superposition of one outer thing upon many surfaces. Thus are exact equivalencies and common measures introduced, and the way prepared for numerical results.
Could we not superpose one part of our skin upon another, or one object on both parts, we should hardly succeed in coming to that knowledge of our own form which we possess. The original differences of bigness of our different parts would remain vaguely operative, and we should have no certainty as to how much lip was equivalent to so much forehead, how much finger to so much back.
But with the power of exploring one part of the surface by another we get a direct perception of cutaneous equivalencies. The primitive differences of bigness are over-powered when we feel by an immediate sensation that a certain length of thigh-surface is in contact with the entire palm and fingers. And when a motion of the opposite finger-tips draws a line first along this same length of thigh and [p. 178] then along the whole of the hand in question, we get a new manner of measurement, less direct but confirming the equivalencies established by the first. In these ways, by superpositions of parts and by tracing lines on different parts by identical movements, a person deprived of sight can soon learn to reduce all the dimensions of his body to a homogeneous scale. By applying the same methods to objects of his own size or smaller, he can with equal ease make himself acquainted with their extension stated in terms derived from his own bulk, palms, feet, cubits, spans, paces, fathoms (armspreads), etc. In these reductions it is to be noticed that when the resident sensations of largeness of two opposed surfaces conflict, one of the sensations is chosen as the true standard and the other treated as illusory. Thus an empty tooth-socket is believed to be really smaller than the finger-tip which it will not admit, although it may feel larger; and in general it may be said that the hand, as the almost exclusive organ of palpation, gives its own magnitude to the other parts, instead of having its size determined by them. In general, it is, as Fechner says, the extent felt by the more sensitive part to which the other extents are reduced. 
But even though exploration of one surface by another were impossible, we could always measure our various surfaces against each other by applying the same extended object first to one and then to another. We should of course have the alternative of supposing that the object itself waxed and waned as it glided from one place to another (cf. above, p. 141); but the principle of simplifying as much as possible our world would soon drive us out of that assumption into the easier one that objects as a rule [p. 179] keep their sizes, and that most of our sensations are affected by errors for which a constant allowance must be made.
In the retina there is no reason to suppose that the bignesses of two impressions (lines or blotches) falling on different regions are primitively felt to stand in any exact mutual ratio. It is only when the impressions come from the same object that we judge their sizes to be the same. And this, too, only when the relation of the object to the eye is believed to be on the whole unchanged. When the object by moving changes its relations to the eye the sensation excited by its image even on the same retinal region becomes so fluctuating that we end by ascribing no absolute import whatever to the retinal space-feeling which at any moment we may receive. So complete does this overlooking of retinal magnitude become that it is next to impossible to compare the visual magnitudes of objects at different distances without making the experiment of superposition. We cannot say beforehand how much of a distant house or tree our finger will cover. The various answers to the familiar question, How large is the moon? -- answers which vary from a cartwheel to a wafer -- illustrate this most strikingly. The hardest part of the training of a young draughtsman is his learning to feel directly the retinal (i.e. primitively sensible) magnitudes which the different objects in the held of view subtend. To do this he must recover what Ruskin calls the 'innocence of the eye' -- that is, a sort of childish perception of stains of color merely as such, without consciousness of what they mean. With the rest of us this innocence is lost. Out of all the visual magnitudes of each known object we have selected one as the REAL one to think of, and degraded all the others to serve as its signs. This 'real' magnitude is determined by aesthetic and practical interests. It is that which we get when the object is at the distance most propitious for exact visual discrimination of its details. This is the distance at which we hold anything we are examining. Farther than this we see it too smell, nearer too large. And the larger and the smaller feeling vanish in the act of suggesting this one, their more important meaning. As I look along the dining- [p. 180] table I overlook the fact that the farther plates and glasses feel so much smaller than my own, for I know that they are all equal in size; and the feeling of them, which is a present sensation, is eclipsed in the share of the knowledge, which is a, merely imagined one.
If the inconsistencies of sight-spaces inter se can thus be reduced, of course there can be no difficulty in equating sight-spaces with spaces given to touch. In this equation it is probably the touch-feeling which prevails as real and the sight which serves as sign -- a reduction made necessary not only by the far greater constancy of felt over seen magnitudes, but by the greater practical interest which the sense of touch possesses for our lives. As a rule, things only benefit or harm us by coming into direct contact with our skin: sight is only a sort of anticipatory touch; the letter is, in Mr.Spencer's phrase, the 'mother-tongue of thought,' and the handmaid's idiom must be translated into the language of the mistress before it can speak clearly to the mind. 
Later on we shall see that the feelings excited in the joints when a limb moves are used as signs of the path traversed by the extremity. But of this more anon. As for the equating of sound-, smell-, and taste-volumes with those yielded by the more discriminative senses, they are too vague to need any remark. It may be observed of pain, however, that its size has to be reduced to that of the normal tactile size of the organ which is its seat. A finger with a felon on it, and the pulses of the arteries therein, both 'feel' larger than we believe they really 'are.' [p. 181]
It will have been noticed in the account given that when two sensorial sense-impressions, believed to come from the same object, differ, then THE ONE MOST INTERESTING, practically or æsthetically, Is JUDGED TO BE THE TRUE ONE. This law of interest holds throughout -- though a permanent interest, like that of touch, may resist a strong but fleeting one like that of pain, as in the case just given of the felon.
3. The Summation of the Sense-spaces.
Now for the next step in our construction of real space: How are the various sense-spaces added together into a consolidated and unitary continuum? For they are, in man at all events, incoherent at the start.
Here again the first fact that appears is that primitively our space-experiences form a chaos, out of which we have no immediate faculty for extricating them. Objects of different sense-organs, experienced together, do not in the first instance appear either inside or alongside or far outside of each other, neither spatially continuous nor discontinuous, in any definite sense of these words. The same thing is almost as true of objects felt by different parts of the same organ before discrimination has done its finished work. The most we can say is that all our space-experiences together form an objective total and that this objective total is vast.
Even now the space inside our mouth, which is so intimately known and accurately measured by its inhabitant the tongue, can hardly be said to have its internal directions and dimensions known in any exact relation to those of the larger world outside. It forms almost a little world by itself. Again, when the dentist excavates a small cavity in one of our teeth, we feel the hard point of his instrument scraping, in distinctly differing directions, a surface which seems to our sensibility vaguely larger than the subsequent use of the mirror tells us it 'really' is. And though the directions of the scraping differ so completely inter se, not one of them can be identified with the particular direction in the outer world to which it corresponds. The space of the tooth-sensibility is thus really a little world by itself, which can only become congruent with the outer space- [p. 182] world by farther experiences which shall alter its bulk, identify its directions, fuse its margins, and finally embed it as a definite part within a definite whole. And even though every joint's rotations should be felt to vary inter se as so many differences of direction in a common room; even though the same were true of diverse tracings on the skin, and of diverse tracings on the retina respectively, it would still not follow that feelings of direction, on these different surfaces, are intuitively comparable among each other, or with the other directions yielded by the feelings of the semi-circular canals. It would not follow that we should immediately judge the relations of them all to each other in one space-world.
If with the arms in an unnatural attitude we 'feel' things, we are perplexed about their shape, size, and position. Let the reader lie on his back with his arms stretched above his head, and it will astonish him to find how in able he is to recognize the geometrical relations of objects placed within reach of his hands. But the geometrical relations here spoken of are nothing but identities recognized between the directions and sizes perceived in this way and those perceived in the more usual ways. The two ways do not fit each other intuitively.
How lax the connection between the system of visual and the system of tactile directions is in man, appears from the facility with which microscopists learn to reverse the movements of their hand in manipulating things on the stage of the instrument. To move the slide to the seen left they must draw it to the felt right. But in a very few days the habit becomes a second nature. So in tying our cravat, shaving before a mirror, etc., the right and left sides are inverted, and the directions of our hand movements are the opposite of what they seen. Yet this never annoys us. Only when by accident we try to tie the cravat of another person do we learn that there are two ways of combining sight and touch perceptions. Let any one try for the first time to write or draw while looking at the image of his hand and paper in a mirror, and he will be utterly bewildered. But a very short training will teach him to undo in this respect the associations of his previous lifetime. [p. 183]
Prisms show this in an even more striking way. If the eyes be armed with spectacles containing slightly prismatic glasses with their bases turned, for example, towards the right, every object looked at will be apparently translocated to the left; and the hand put forth to grasp ally which object will make the mistake of passing beyond it on the left side. But less than an hour of practice in wearing such spectacles rectifies the judgment so that no more mistakes are made. In fact the new-formed associations are already so strong, that when the prisms are first laid aside again the opposite error is committed, the habits of a lifetime violated, and the hand now passed to the right of every object which it seeks to touch.
The primitive chaos thus subsists to a great degree through life so far as our immediate sensibility goes. We feel our various objects and their bignesses, together or in succession; but so soon as it is a question of the order and relations of many of them at once our intuitive apprehension remains to the very end most vague and incomplete. Whilst we are attending to one, or at most to two or three objects, all the others lapse, and the most we feel of them is that they still linger on the outskirts and can be caught again by turning in a certain way. Nevertheless throughout all this confusion we conceive of a world spread out in a perfectly fixed and orderly fashion, and we believe in its existence. The question is: How do this conception and this belief arise? How is the chaos smoothed and straightened out?
Mainly by two operations: Some of the experiences are apprehended to exist out- and alongside of each other, and others are apprehended to interpenetrate each other, and to occupy the same room. In this way what was incoherent and irrelative ends by being coherent and definitely related ; nor is it hard to trace the principles, by which the mind is guided in this arrangement of its perceptions, in detail.
In the first place, following the great intellectual law of economy, we simplify, unify, and identify as much as we possibly can. Whatever sensible data can be attended to together we locate together. Their several extents seem one extent. The place at which each appears is held to be the same with the place [p. 184] at which the others appear. They become, in short, so many properties of ONE AND THE SAME REAL THING. This is the first and great commandment, the fundamental 'act' by which our world gets spatially arranged.
In this coalescence in a 'thing,' one of the coalescing sensations is held to be the thing, the other sensations are taken for its more or less accidental properties, or modes of appearance.  The sensation chosen to be the thing essentially is the most constant and practically important of the lot; most often it is hardness or weight. But the hardness or weight is never without tactile bulk; and as we can always see something in our hand when me feel something there, we can always see something there when we essence of the 'thing.' Frequently a shape so figures, sometimes a, temperature, a taste, etc.; but for the most part temperature, smell, sound, color, or whatever other phenomena may vividly impress us simultaneously with the bulk felt or seen, figure among the accidents. Smell and sound impress us, it is true, when we neither see nor touch the thing; but they are strongest when we see or touch, so we locate the source of these properties within the touched or seen space, whilst their properties themselves we regard as overflowing in a weakened form into the spaces fined by other-things. In all this, it will be observed, the sense-data whose spaces coalesce into one are yield by different sense-organs. Such data have no tendency to displace each other from consciousness, but can be attended to together all at once. Often indeed they vary concomitantly and reach a maximum together. We may be sure, therefore, that the general rule of our mind is to locate IN each other all sensations which are associated in simultaneous experience, and do not interfere with each other's perception.  [p. 185]
Different impressions on the same sense-organ do interfere with each other's perception, and cannot well be attended to at once. Hence we do not locate them in each other's spaces, but arrange them in a serial order of exteriority, each alongside of the rest, in a space larger than that which any one sensation brings. This larger space, however, is an object of conception rather than of direct intuition, and bears all the marks of being constructed piecemeal by the mind. The blind man forms it out of tactile, locomotor, and auditory experiences, the seeing men out of visual ones almost exclusively. As the visual construction is the easiest to understand, let us consider that first.
Every single visual sensation or 'field of view' is limited. To get a new field of view for our object the old one must disappear. But the disappearance may be only partial. Let the first field of view be A B C. If we carry our attention to the limit C, it ceases to be the limit, and becomes the centre of the field, and beyond it appear fresh parts where there were none before:  A B C changes, in short, to C D E. But although the parts A B are lost to sight, yet their image abides in the memory; and if we think of our first object A B C as having existed or as still existing at all, we must think of it as it was originally presented, namely, as spread out from C in one direction just as C D E is spread out in another. A B and D E can never coalesce in one place (as they could were they objects of different senses) because they call never be perceived at once: we must lose one to see the other. So (the letters standing now for 'things') we get to conceive of the successive fields of things after the analogy of the several things which we perceive in a single field. They must be out- and along-side of each other, and we conceive that their juxtaposed spaces must make a larger space. A B C + C D E must, in short, be imagined to exist in the form of A B C D E or not imagined at all.
We can usually recover anything lost from sight by moving our attention and our eyes back in its direction; and [p. 186] through these constant changes every field of seen things comes at last to be thought of as always having a fringe of other things possible to be seen spreading in all directions round about it. Meanwhile the movements concomitantly with which the various fields alternate are also felt and remembered; and gradually (through association) this and that movement come in our thought to suggest this or that extent of fresh objects introduced. Gradually, too, since the objects vary indefinitely in kind, we abstract from their several natures and think separately of their mere extents, of which extents the various movements remain as the only constant introducers and associates. More and more, therefore, do we think of movement and seen extent as mutually involving? each other, until at last (with Bain and J. S. Mill) we may get to regard them as synonymous, and say, "What is the meaning of the word extent, unless it be possible movement?"  We forget in this conclusion that (whatever intrinsic extensiveness the movements may appear endowed with), that seen spreadoutness which is the pattern of the abstract extensiveness which we imagine came to us originally from the retinal sensation.
The muscular sensations of the eyeball signify this sort of visible spreadoutness, just as this visible spreadoutness may come in later experience to signify the 'real' bulks, distances, lengths and breadths known to touch and locomotion.  To the very end, however in us seeing men, the quality, the nature, the sort of thing we mean by extensiveness, would seem to be the sort of feeling which our retinal stimulations bring.
In one deprived of sight the principles by which the notion of real space is constructed are the same. Skin-feelings take in him the place of retinal feelings in giving [p. 187] the quality of lateral spreadoutness, as our attention passes from one extent of them to another, awakened by an object sliding along. Usually the moving object is our hand; and feelings of movement in our joints invariably accompany the feelings in the skin. But the feeling of the skin is what the blind man means by his skin; so the size of the skin-feelings stands as the absolute or real size, and the size of the joint-feelings becomes a sign of these. Suppose, for example, a blind baby with (to make the description shorter) a blister on his toe, exploring his leg with his finger-tip and feeling a pain shoot up sharply the instant the blister is touched. The experiment gives him four different kinds of sensation -- two of them protracted, two sudden. The first pair are the movement-feeling in the joints of the upper limb, and the movement-feeling on the skin of the leg and foot. These, attended to together, have their extents identified as one objective space -- the hand moves through the same space in which the leg lies. The second pair of objects are the pain in the blister, and the peculiar feeling the blister gives to the finger. Their spaces also fuse; and as each marks the end of a peculiar movement-series (arm moved, leg stroked), the movement-spaces are emphatically identified with each other at that end. Were there other small blisters distributed down the leg, there would be a number of these emphatic points; the movement-spaces would be identified, not only as totals, but point for point.  [p. 188]
Just so with space beyond the body's limits. Continuing the joint-feeling beyond the toe, the baby hits another object which he can still think of when he brings his back to its blister again. That object at the end of that joint feeling means a new place for him, and the more such objects multiply in his experience the wider does the space of his conception grow. If, wandering through the woods to-day by a new path, I find myself suddenly in a glad which affects my senses exactly as did another I reached last week at the end of different walk, I believe the two identical affection to present the same persisting glade, and infer that I have attained it by two differing roads. The case in whit differs when shorter movements are concerned. If, moving first one arm and then another, the blind child gets the same kind of sensation upon the hand, and gets it again as often as he repeats either process, he judges that he has touched the same object by both motions, and concludes that the motions terminate in a common place. From place to place marked in this way he moves, and adding the places moved through, one to another, he builds up his notion of the extent of the outer world. The seeing man's process is identical; only his units, which may be successive bird's-eye view, are much larger than in the case of the blind. [p. 189]
FEELINGS IN JOINTS AND FEELINGS IN MUSCLES
1. Feelings of Movement in Joints
I have been led to speak of feelings which arise in joints. As these feeling have too much neglecting Psychology hitherto, in entering now somewhat minutely in the interest of the reader, which under the rather dry abstractions of the previous pages may presumably have flagged.
When by simply flexing my right forefinger on its metacarpal joint, I trace with its tip an inch on the palm of my left hand, is my feeling of the size of the inch purely and simply a feeling in the skin of the palm, or have the muscular contractions of the right hand and forearm anything to do with it? In the preceding pages I have constantly assumed spatial sensibility to be an affair of surfaces. At first starting, the consideration of the 'muscular sense' as a space-measurer was postponed to a later stage. Many writers, of whom the foremost was Thomas Brown, in his Lectures on the Philosophy of the Human Mind, and of whom the latest is no less a Psychologist than Prof. Delboeuf,  hold that the consciousness of active muscular motion, aware of its own amount, is the fons et origo of all spatial measurement. It would seem to follow, if this theory were true, that two skin-feelings, one of a large patch, one of small one, possess their difference of spatiality, not as an immediate element, but solely by virtue of the fact that the large, to get its points successively excited, demands more muscular contraction than the small one does. Fixed associations with the several amounts of muscular contractions required in this particular experience would thus ex- [p. 190] plain the apparent sizes of the skin-patches, which sizes would consequently not be primitive data but derivative results.
It seems to me that no evidence of the muscular measurements in question exists; but that all the facts may be explained by surface-sensibility, provided we take that of the joint-surfaces also into account. The most striking argument, and the most obvious one, which an upholder of the muscular theory is likely to produce is undoubtedly this fact: if, with closed eyes, we trace figures in the air with the extended forefinger (the motions may occur from the metacarpal-, the wrist-, the elbow-, or the shoulder-joint indifferently), what we are conscious of in each case, and indeed most acutely conscious of, is the geometric path described by the finger-tip. Its angles, its subdivisions, are all as distinctly felt as if seen by the eye; and yet the surface of the finger-tip receives no impression at all.  But with each variation of the figure, the muscular contractions vary, and so do the feelings which these yield. Are not these latter the sensible data that make us aware of the lengths and directions we discern in the traced line?
Should we be tempted to object to this supposition of the advocate of perception by muscular feelings, that we have learned the spatial significance of the feelings by reiterated experiences of seeing what figure is drawn when each special muscular grouping is felt, so that in the last resort the muscular space feelings would be derived from retinal-surface feelings, our opponent might immediately hush us by pointing to the fact that in persons born blind the phenomenon in question is even more perfect than in ourselves. If we suggest that the blind may have originally traced the figures on the cutaneous surface of cheek, thigh, or palm, and may now remember the specific figure which each present movement formerly caused the skin-surface to perceive, he may reply that the delicacy of the motor percep- [p. 191] tion far exceeds that of most of the cutaneous surfaces; that, in fact, we can feel a figure traced only in its differentials, so to speak, -- a figure which we merely start to trace by our finger-tip, a figure which, traced in the same way on our finger-tip by the hand of another, is almost if not wholly unrecognizable.
The champion of the muscular sense seems likely to be triumphant until we invoke the articular cartilages, as internal surfaces whose sensibility is called in play by every movement we make, however delicate the latter may be.
To establish the part they play in our geometrizing, it is necessary to review a, few facts. It has long been known by medical practitioners that, in patients with cutaneous anæsthesia of a limb, whose muscles also are insensible to the thrill of the faradic current, a very accurate sense of the way in which the limb may be flexed or extended by the hand of another may be preserved.  On the other hand, we may have this sense of movement impaired when the tactile sensibility is well preserved. That the pretended feeling of outgoing innervation can play in these cases no part, is obvious from the fact that the movements by which the limb changes its position are passive ones, imprinted on it by the experimenting physician. The writers who have sought a rationale of the matter have consequently been driven by way of exclusion to assume the articular surfaces to be the seat of the perception in question. 
That the joint-surfaces are sensitive appears evident from the fact that in inflammation they become the seat of excruciating pains, and from the perception by everyone who lifts weights or presses against resistance, that every increase of the force opposing him betrays itself to his consciousness principally by the starting-out of new feelings or the increase of old ones, in or about the joints. If the structure and mode of mutual application of two articular surfaces be taken into account, it will appear that, granting the surfaces to be sensitive, no more favorable mechanical [p. 192] conditions could be possible for the delicate calling of the sensibility into play than are realized in the minutely graduated rotations and firmly resisted variations of pressure involved in every act of extension or flexion. Nevertheless it is a greet pity that we have as yet no direct testimony, no expressions from patients with healthy joints accidentally laid open, of the impressions they experience when the cartilage is pressed or rubbed.
The first approach to direct evidence, so far as I know is contained in the paper of Lewinski,  published in 1879. This observer had a patient the inner half of whose leg was anæsthetic. When this patient stood up, he had a curious illusion about the position of his limb, which disappeared the moment he lay down again: he thought himself knock-kneed. If, as Lewinski says, we assume the inner half of the joint to share the insensibility of the corresponding part of the skin, then he ought to feel, when the joint-surfaces pressed against each other in the act of standing, the outer half of the joint most strongly. But this is the feeling he would also get whenever it was by any chance sought to force his leg into a knock-kneed attitude. Lewinski was led by this case to examine the feet of certain ataxic patients with imperfect sense of position. He found in every instance that when the toes were flexed and drawn upon at the same time (the joint-surfaces drawn asunder) all sense of the amount of flexion disappeared. On the contrary, when he pressed a toe whilst flexing it, the patient's appreciation of the amount of flexion was much improved, evidently because the artificial increase of articular pressure made up for the pathological insensibility of the parts.
Since Lewinski's paper an important experimental research by A. Goldscheider  has appeared, which completely establishes our point. This patient observer caused his fingers, arms, and legs to be passively rotated upon their various joints in a mechanical apparatus which registered both the velocity of movement impressed and the amount [p. 193] of angular rotation. No active muscular contraction took place. The minimal felt amounts of rotation were in all cases surprisingly small, being much less than a single angular degree in all the joints except those of the fingers. Such displacements as these, the author says (p. 490), can hardly be detected by the eye. The point of application of the force which rotated the limb made no difference in the result. Rotations round the hip-joint, for example, were as delicately felt when the leg was hung by the heel as when it was hung by the thigh whilst the movements were performed. Anæsthesia of the skin produced by induction-currents also had no disturbing effect on the perception, nor did the various degrees of pressure of the moving force upon the skin affect it. It became, in fact, all the more distinct in proportion as the concomitant pressure-feelings were eliminated by artificial anæsthesia. When the joints themselves, however, were made artificially anæsthetic the perception of the movement grew obtuse and the angular rotations had to be much increased before they were perceptible. All these facts prove according to Herr Goldscheider, that the joint surfaces and these alone are the starting point of the impressions by which the movements of our members are immediately perceived.
Applying this result, which seems invulnerable, to the case of the tracing finger-tip, we see that our perception of the latter gives no countenance to the theory of the muscular sense. We indubitably localize the finger-tip at the successive points of its path by means of the sensations which we receive from our joints. But if this is so, it may be asked, why do we feel the figure to be traced, not within the joint itself, but in such an altogether different place? And why do we feel it so much larger than it really is?
I will answer these questions by asking another: Why do we move our joists at all? Surely to gain something more valuable than the insipid joint-feelings themselves. And these more interesting feelings are in the main produced upon the skin of the moving part, or of some other part over which it passes, or upon the eye. With movements of the fingers we explore the configuration of all real objects with which we have to deal, our own body as well as [p. 194] foreign things. Nothing that interests us is located in the joint; everything that interests us either is some part of our skin, or is something that we see as we handle it. The cutaneously felt and the seen extents come thus to figure as the important things for us to concern ourselves with. Every time the joint moves, even though we neither see, nor feel cutaneously, the reminiscence of skin-events and sights which formerly coincided with that extent of movement, ideally awaken as the movement's import, and the mind drops the present sign to attend to the import alone. The joint-sensation itself, as such, does not disappear in the process. A little attention easily detects it, with all its fine peculiarities, hidden beneath its vaster suggestions; so that really the mind has two space-perceptions before it, congruent in form but different in scale and place, either of which exclusively it may notice, or both at once, -- the joint-space which it feels and the real space which it means.
The joint-spaces serve so admirably as signs because of their capacity for parallel variation to all the peculiarities of external motion. There is not a direction in the real world nor a ratio of distance which cannot be matched by some direction or extent of joint-rotation. Joint-feelings, like all feelings, are roomy. Specific ones are contrasted inter se as different directions are contrasted within the same extent. If I extend my arm straight out at the shoulder, the rotation of the shoulder-joint will give me one feeling of movement; if then I sweep the arm forward, the same joint will give me another feeling of movement. Both these movements are felt to happen in space and differ in specific quality. Why shall not the specificness of the quality just consist in the feeling of a peculiar direction?  Why may not the several joint-feelings be so many perceptions of movement in so many different directions? That we cannot explain why they should is no presumption that they do not, for we never can explain why any sense-organ should awaken the sensation it does. [p. 195]
But if the joint-feelings are directions and extents, standing in relation to each other, the task of association in interpreting their import in eye- or skin-terms is a good deal simplified. Let the movement bc, of a certain joint, derive its absolute space-value from the cutaneous feeling it is always capable of engendering; then the longer movement abcd of the same joint will be judged to have a greater space-value, even though it may never have wholly merged with a skin-experience. So of differences of direction: so much joint-difference = so much skin-difference; therefore, more joint-difference = more skin-difference. In fact, the joint-feeling can frequently serve as a map on a reduced scale, of a reality which the imagination can identify at its pleasure with this or that sensible extension simultaneously known in some other way.
When the joint-feeling in itself acquires an emotional interest, -- which happens whenever the joint is inflamed and painful, -- the secondary suggestions fail to arise, and the movement is felt where it is, and in its intrinsic scale of magnitude. 
The localization of the joint-feeling in a space simultaneously known otherwise (i.e. to eye or skin), is what is commonly called the extradition or eccentric projection of the feeling. In the preceding 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, [p. 196] and with its place as thus known, the place which the joint- feeling fins 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 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 tile sine guâ non of the joint-feeling's projection to the farther end of it. When it is fined 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 fin 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 [p. 197] 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 [p. 198] 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 sensation 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. Volkman 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 belong to that class of general sensations which tell us of our inner states, but not of outer relations ; it does not belong among the sense-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 [p. 199] 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 down- ward 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 tile 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. [p. 200]
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 standing how vague their space- import appears. Shut the eyes and roll them, and you call 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 and 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 [p. 201] muscles of the body at large we find the same vagueness. Goldscheider found that the minimal perceived rotation of size depend on a comparison of [p. 202] 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 qualia 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-percep- [p. 203] tions 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 [p. 204] 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, anti 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. On the prairies the 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. Hank 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 dis- [p. 205] cover 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 brick-work, 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, call 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 determining the points of the com- [p. 206] pass 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 fined 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 mall operated on by Dr. Franz was [p. 207] 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 mans 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 side 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 [p. 208] 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 it 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 [p. 209] 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. Bough 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 [p. 210] determinations the blind man's space is very different from 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 tile patients were the most intelligent, as in the young man operated on by Dr Franz, [p. 211] who named circular, triangular, and quadrangular figures at first sight. 
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 banal 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 [p. 212] study the facts closely we soon and 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 call 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 if.). It is impossible to lie on one's back on a hill, to let tile empty abyss of blue 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 [p. 213] 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 held 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 [p. 214] 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 tile 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 held 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 [p. 215] 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 given amounts of the visual depth-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 mall 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 lie 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 near end of the object. [p. 216] 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 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 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 [p. 217] 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 ally 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 ape 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 me see in spite of them are conclusions from past experience, that the distances which we [p. 218] 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 owning to custom, but to the constitution of nature, when a contrary custom is found neither 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 he 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 [p. 219] 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 [p. 220] 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.  [p. 221] Let us begin the long and rather tedious inquiry by the most important case. Physiologists have long sought for [p.222] 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 each 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 [p. 223] 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. I 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- [p. 224] 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 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 lest 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 pro- [p. 225] 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, 0, 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 effect 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 [p. 226] 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 ail 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 [p. 227] 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 shell 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 [p. 228] 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. 
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 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 direc- [p. 229] tion, 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. diagram will make this clear. [p. 230]
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 held 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 inclusion 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. [p. 231] 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 foveæ, 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 impressions. 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 [p. 232] 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 well, it min 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 (Pig. 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 Pig 61. Drawing a square inside the circle (Fig. 52) gives to the outline of the latter an indented appearance where the square's corners touch it. Drawing the radii of one [p. 233]
[p. 234] 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 worst case we may see a stationary field of view with one moving object in it; in the second, the total held swimming more or less steadily in one direction in the third, a sudden lump or twist of the same total held.
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 But the objective total same [p. 235] 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. He 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 definite 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. [p. 236] 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 different 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 [p. 237] 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 one 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 [p. 238] 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 well 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 [p. 239] 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 aesthetic 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 [p. 240] 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 appearance, 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, me 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 sig- [p. 241] nified, 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 [p. 242] 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 tile outer world. Only so far as they serve this end hale 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 dryness 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 lend 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 [p. 243] which impairs 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 held of view means, he sees it also as it feels -- that is, as a collection of patches of color bounded by lines -- the whole terming 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 sensation, 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 held of vision, just as the image projected from [p. 244] 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 ?" 
"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 and 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 probably to conduct the discussion we must divide the alleged instances into groups.
(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 [p. 245] 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 [p. 246] 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 train, 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 [p. 247] 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 eve, 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 [p. 248] 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 seen, 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, Delboeuf, 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, 89 of Figs. 60, 61, 62 (pp. 232, 233). This peculiarity of small angles is by Wundt treated as the case of a fined space seeming larger than an empty one, as in Fig. 68; and this, according [p. 249] to both Delboeuf and Wundt is owing to the fact that more muscular innervation is needed for the eye to traverse a filled space than so 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 recol-
lect that muscular movements are positively proved to have no share in the waterfall and revolving-spirals illusions. and that it is hard to see how Wundt's and Delboeuf'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 [p. 250] 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. I, p. 579. Lipps  gives another reason [p. 251] 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 dare, we should end by substituting their significates -- the real space-values of the diagrams -- for them. These latter me should then seem to [p. 252] see directly, and the illusions would disappear like that of the side of a tooth-socket when the tooth has been out a week.
(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 skin 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 [p.253] fields, helps us to see the primary lines double. The effect is analogous to that shown in the cases which we despatched [sic] 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 psychophysiologica1 laws. Thus, if in Fig. 66, l and r be crossed by an horizontal line at the same level, and viewed stereoscopically, they appear as a single pair of lines, l, 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. 
(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. [p. 254]
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 illu- [p. 255] sion, 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 90° 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 [p. 256] 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 am-
biguous perspective projections, and may each of them remind us of two different natural objects. Whichever of these [p. 257] 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 end 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. In the case of the diagrams 72, 73, 74, 75, 76, the real object, lines meeting or crossing each other on a plane, is [p. 258] 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 generally 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; tile glass rim tilts this may or that, as if some inward spring suddenly became released in our eye. In these changes the actual retinal image receives different comments from the mind. But the remarkable thing is that the complement [p. 259] 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 reel 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 trans- [p. 260] 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 forms 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, [p. 261] after reminding us that every visual sensation is correlated to a physical process in the nervous apparatus: "If this psychophysical 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 open thing 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 it 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 [p. 262] 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 hat 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 disposi- [p. 263] tion 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. [p. 264]
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. Delboeuf has found, accordingly, that if we try to bisect such a line we place the point of division about 1/16 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, as [upside-down "S" and "8"] the upper half looks much the larger.  [p. 265]
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 bi-section, in estimating height relatively to breadth, etc., become impossible. In other words, we learn to take the optical sensation before us pure.  [p. 266]
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."  [p. 267]
Measurement implies a stuff to measure. Retinal sensations give the stuff; objective things form the yard-stick; 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 im possible where the tracts make a wide angle with each other. But there are certain directions in the held of view, certain retinal lines, along which it is particularly easy to make the image of an object slide. The object then be- comes 'ruler' for these lines, as Helmholtz; puts it,  making them seem straight throughout if the object looked straight to us in that pert 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 super- posing them successively upon the same objective line, so we also hare 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 com- [p. 268] pare 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.
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 [p. 269] 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 pert 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 effort of diminishing the absolute space-value of the total field of view.  [p. 270]
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 plurality 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 [p. 271] 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 Min 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 then 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 [p. 272] 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! [p. 273]
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, fining 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 drat 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 [p. 274] great chasm between sensation and perception by showing how raw the material is out of which the fair structure is upreared [sic]. 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 band 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 [p. 275] 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 fins 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.' Herbert, whose influence has been widest, says 'the resting eye sees no space,'  and ascribes [p. 276] visual extension to the influence of movements combining with the non-spatial retinal feelings so as to form graduated 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 heterogene- [p. 277] ous 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 [p. 278] 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 analyse 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 analyse 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 sole- [p. 279] ly 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 he 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 gent 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 means that he is a mere eye-man and not a complete psychologist ? In other words, Helmholtz's Optics and the 'empiristic theory' there professed are not to be understood as attempts at answering the general question of how space-consciousness enters the mind. They simply deny that it enters with the [p. 280] 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 thing 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 whenever 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. [p. 281] 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, there- [p. 282] fore 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, Leconte, 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.
 Encyclopæia Britannica, 9th Edition, article Psychology, pp. 46, 53.
 Philosophical Transactions (1841).
 Hermann's Handb. d. Physiol., Ed. iii. 1, S. 575.
 Loc. Cit. S. 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 whet 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 other 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 lend 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 tire 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 and, 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. Menschenu. Thierseele (Leipzig, 1883), i. 214. see also Ladd's Physiological Psychology, pp. 396-8, and compare the account by Cf. 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. Wunt (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. 1 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 world 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 fore-arm, 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 fore-arm feels an object against it.
 These facts were first noticed by Wundt: see his Beiträge, p. 140, 208. 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 render, 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, we will see no sort of logical connection between (l) 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. We 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' (l) 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 psyche-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 then 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 points, 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 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 n 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 stores 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 time 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 bow 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 slum 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 fatter 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 fin 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 tile 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
 Donaldsan, 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. &§ &§ 21-93.
 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 screwhead. 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 drilling 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, Ed. LXXII., Abth. 3 (1875).
 Zeitschrift für Biologie, xii. 226 (1876).
 Vierteljahrsch. für wiss. Philos., n. 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 dark; 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 rear), 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 Anger 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 in the middle of the edge opposite to the one against his body, he will draw them asunder tin they reach the ends of the edge in question: and then, and not tin 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 'lying 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 Ant 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 tile sensibility of the skin. Two compasses are used, one on the part A. another on the part R, 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 with out 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 pains seems 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 on the toe every time the pain shoots up; let him handle his foot himself and get the 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.
 Pourqoi les Sensation 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 locslisée, pp. 727, 770; Leyden; Virchow's Archiv, Ed. xlvii. (1869).
 E.g., Eulenbug, Lehrb. d. Nervenkrankheiten (Berlin), 1878, i. 3.
 'Ueber den Kraftsinn,' Virchow's archiv, Ed. 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 it 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 men 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 Cebiete 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, 1861-2, pp. 31, 141). Helmholtz also allows to the muscles of convergence a very feeble share in 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 corrections of the eyeball-muscles being admitted as original contributors to the perception of extent, are those of Wundt, Physiologische Psychologie, ii. 98-100. 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 care fully averaged and 'percented ' 20,000 observations, his conclusion must be listened to with great respect. Briefly it is this, that "our judgments 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 tire 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 tile 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 P 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. 28-80) 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. 542.
 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, no. 357-8.
 Classics editor's note: James' Insertion.
 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 Laussnne (Guerison d'un Aveuge-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 some 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 au observer Its Helmboltz, who has carefully examined vision with inverted head, can have overlooked it. (See his Phys. Optik, pp. 433, 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 Estonian 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 Wine, ii. 44)
 Physiol. Optik. P. 438. Helmholtz's reservation of 'qualities' 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 be 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 must 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 piece, adding that it seems to make of distance a fixed fluctuation 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, 11. 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 pretension 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 first 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 same distance behind the plane of the pictures, according to tile 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 held. 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 Anfl. p. 144; Nagel, Sehen mit zwei Augen, pp. 78-82. Against Wheatstone see Volkmann. arch. f. Ophth., v. 2-74, and Untersuchungen, p. 286; Hering, Beiträge zur Physiologie, 29-45, also in Hermann's Hdbch. d Physiol., Ed. iii. 1 Th. p. 435; Aubert, Physiologie d. Netzhsut, 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 huger, 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 R 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. 3, 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 small object at a less distance to cover by its image a constant amount of retinal surface.
 Archiv f. Ophthal., Bd. xvii. Abth. 2, pp. 44-8 (1871).
 A. W. Volkmann, Untersuchungen, p. 253.
 Philosophical Transactions, 1859, g. 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 held seems to move in one way, another part in another. The same is true when we torn from the spiral to look at the wall -- the centre of the field alone swells onto 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 ( Sitzunger d. Wiener Aksd., Bd. ixr.). See also Bowditch and Hall's paper as a above, p. 300.
 Bulletins de l'Acsd. de Belgique, xxi. 2; Revue philosophique, vi. 823-6; Physiologische Psycbologie, 2te Aufl. p. 103. Compare Münsterberg's views, Beiträge, Heft 2, p. 174.
 Physiol. Optik, pp. 662-71.
 Physiol. Psych., pp. 107-8.
 Grundtatsachen des Seelenlebens, pp. 526-30.
 Cf. supra, 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 shout double images, drawn from the perceptions of a few squinters (e.g. by Schweigger, Klin. Untersuch über dos Schielen. Berlin, 1881; by Javal. annales d'Oculistique, ixxxv. 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 i. Ophthalm., xxiv. 4, p. 117.
 Physiologische Untersuchungen im Gebiete der Optik, v.
 Ct. 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. 94 and the preceding chapter of the present work, p. 88 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 1'Académie de Belgique, 2me Série, xix.
 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 weather-cock 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. Of. Wundt, Physiol. Psych., 2te Aufl. ii. 968; Th. Lipps, (frundtatsschen, etc., p. 535.
 Hering would pertly solve in this way the mystery of Figs. 60, 61, and 87. No doubt the explanation pertly 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 verbatum 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 individuals 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 tin it becomes an after-image. We follow, in looking, the direction of this line, and in so doing we slide the line dong 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 held 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' on the visual held -- lines which he has studied with his usual care. Cf. Physiol. Optik, p. 648 ff.
 Cf. Hering in Hermann's Handb. der Physiol., iii. 1, pp. 553-4.
 This shrinkage and expansion of the absolute space-value of the 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
 Classics editor's note: James' Insertion.
 Examination of Hamilton, 3d ed, p. 283.
 Senses and Intellect, 3d ed. p. 183.
 Exam. of Hamilton. 3d ed, p. 283.
 Classics editor's note: James' Insertion
 Senses and Intellect, p. 372.
 Vierfsche Wurzel des Satzes vom zureichenden Grunde, pp. 52-7.
 Psychol. sis Wissenschaft, &§ 111.
 Psychol. als Wissenschaft, &§ 113.
 Lehrbuch d. Psychol., 2te Audage, Ed. 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. 450, 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 bin, when no one has any money, but each hopes that one of the rest will pay.
 Grundtatsachen des Seelenlebens (l883), pp. 480, 591-2. Psychologische Studien (1885), p. 14.
 Psychology, ii. p. 174.
 Ibid. p. 168.
 Senses and Intellect, 3d ed, pp. 368-75.
 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. 1; 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. 1884; another review in Macmillan's Magazine, Bug. 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).