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Classics Editor's note: Wundt's translator, Hubbard, uses "spacial" instead of the more common "spatial", and "empirism" for "empiricism" throughout. We have maintained the original spellings. We have also inserted the text's original page numbers in square brackets. The page numbers found in round brackets are Wundt's own references to other portions of the book.
II. PSYCHICAL COMPOUNDS
§ 10. SPACIAL IDEAS
1. Spacial and temporal ideas are immediately distinguished from intensive ideas by the fact that their parts are united, not in an arbitrarily variable, but in a definitely fixed order, so that when the order is thought of as changed the idea itself changes. Ideas with such a fixed arrangement are called in general extensive ideas.
Of the possible forms of extensive ideas, spacial ideas are distinguished by the fact that the fixed arrangement of the parts of a spacial compound holds only for the relation of the parts to one another, not for their relation to the ideating subject. This latter relation may be thought of as indefinitely varied. The objective independence of spacial compounds from the ideating subject is called the movability and torsibility of spacial compounds. The number of directions in which such movement and torsion may take place; is limited. They may all be reduced to three dimensions, in each of which it is possible to advance in two opposite directions. The number of directions in which the parts of a single compound may be arranged as well as the number in which various compounds may be arranged with reference to one another, is the same as the maximal number of directions in which movement and torsion are possible. This is what we call the three-dimensional character of space. A [p. 103] single spacial idea may, accordingly, be defined as a three dimensional compound whose parts are fixed in their location with regard to one another, but capable of indefinite variation in their location with regard to the ideating subject. This definition neglects, of course, the frequent changes in the arrangement of the parts, which occur in reality. When these changes take place, they are to be regarded as transitions from one idea to another. This three-dimensional arrangement of spacial ideas must of necessity include one-dimensional and two-dimensional arrangements as special cases. In such cases, however, the wanting dimensions must always be added in thought as soon as the relation of the idea to the ideating subject is taken into account.
2. This relation to the ideating subject, which is really present in all spacial ideas, renders it from the first psychologically impossible that the arrangement of the elements in such an idea should be an original attribute of the elements themselves, analagous to the intensity or quality of sensations; it requires rather that this arrangement should result from the bringing together of these elements, and should arise from some new psychical conditions that come with this coexistence. If this is not admitted, it becomes necessary not only to attribute a spacial quality to every single sensation, but also to postulate for every sensation, however limited, a simultaneous idea of the whole of three-dimensional space in its location with regard to the ideating subject. This would lead to the acceptance of an a priori space-perception prior to all concrete sensations, which is not only contradictory to all our experiences as to the conditions for the rise and development of psychical compounds in general, but also contradictory to all our experiences as to the influences that affect spacial ideas in particular.
3. All spacial ideas are arrangements either of tactical [p. 104] or of visual sensations. Indirectly, through of connection of other sensations with either tactual or visual ideas, the spacial relation may be carried over to other sensations. In the cases of touch and sight, it is obvious that the extended surface of the peripheral sense-organs, and their equipment with organs of movement, which render possible a varying location of the impressions in regard to the ideating subject, are both favorable conditions for an extensive, spacial arrangement of the sensations. The tactual sense is the earlier of the two here in question, for it appears earlier in the development of organisms and shows the structural relations in much coarser, but for that reason in many respects much plainer, form than the more delicately organized visual organ does. Still, it is to be noted that where vision is present, the spacial ideas from touch are greatly influenced by those from sight.
A. SPACIAL TOUCH-IDEAS.
4. The simplest possible touch-idea is a single, approximiately punctiform impression on the skin. If such an impression is presented even when the eyes are turned away, there arises a definite idea of the place touched. Introspection shows that this idea, which is called the localization of the stimulus, under the normal condition where vision is present is not immediate, as we should expect it to be if the spacial quality were an original attribute of sensations, but that it depends upon a secondary, generally very obscure, visial idea of the region touched. Localization is, therefore, more exact near bounding lines of the touch-organs than on the uniform intervening surfaces, since these bounding lines are more prominent in the visual images. The arousal of a visual idea through the tactual impression, even when the eyes are turned away, is possible because every point of the organ of touch [p. 105] gives to the touch-sensation a peculiar qualitative coloring, which is independent of the quality of the external impression and is probably due to the character of the structure of the skin, which varies from point to point and is never exactly the same in two separate regions.
This local coloring is called the local sign of the sensation. It varies in different regions of the skin at very different rates: rapidly on the tip of the tongue, on the ends of the fingers, and on the lips; slowly on the broader surfaces of the limbs and trunk. A measure for the rate of this variation may be obtained by applying two impressions near each other to any region of the skin. So long as the distance of the impressions is less than that of distinguishable local signs they are perceived as a single one, but so soon as they pass this limit they are perceived as specially separate. The smallest, just noticeable distance between two impressions is called the space-threshold for touch. It varies from one or two millimetres (tips of tongue and fingers) to sixty-eight millimetres (back, upper arm, and leg). On the pressure-spots (p. 47), when the stimuli are favorably applied, still shorter distances can be perceived. Then, too, the threshold is dependent on the condition of the tactual organ and on practice. As a result of the first, for example, the threshold is smaller for children than for adults, since the differences in structure that condition the local signs, are obviously more crowded together. As a result of practice, the threshold is smaller in the case of the blind than of those who have vision, especially at the ends of the fingers, which are most used for touching.
5. The influence of visual ideas of the regions touched, where vision is present, as just described, teaches that the localization of tactual impressions and the spacial arrangement of a number of such impressions is not due to an original spacial quality of cutaneous points or to any [p. 106] primary space-forming function of the tactual organ. On the contrary, it presupposes spacial ideas of sight, which can be made use of, however, only because the various parts of the tactual organ have certain qualitative attributes, local signs, which arouse the visual image of the part touched. There is no reason for attributing an immediate spacial relation to the local signs themselves; it is obviously enough that they act as qualitative signals to arouse the appropriate visual images. This connection with vision depends upon the frequent union of the two. The steeliness of localization will, therefore, be aided by all the influences that increase either the clearness of the visual images or the qualitative differences in local signs.
We may describe the formation of spacial ideas in this case as the arrangement of tactical stimuli in visual images are already present. The whole process is a consequence of the constant connection of these images with the qualitative local signs of the stimuli. The union of the local signs and the visual images of the corresponding region may, then, be rewarded as an incomplete, but very constant, fusion. The fusion is incomplete because both visual image and tactual impression retain their independent character; but it is so constant that, when the state of the tactual organ remains the same, it seems invariable. This last fact explains the relative certainty of localization. The predominating elements of this fusion are the tactual sensations. For many persons the visual images are pushed so far into the background that they can not be perceived with any certainty, even with the greatest attention. The apprehension of space, in such cases, is perhaps an immediate function of tactual and motor sensations, as for the blind (v. inf. 6). As a rule, however, more careful observation shows that it is possible to recognize the position, and distance of the impressions only by attempting [p. 107] to make the indefinite visual image of the region touched more distinct.
6. The conditions that hold when vision is present, are essentially different from those found in cases of blindness, especially congenital or early acquired blindness. Blind persons retain for a long time memory images of familiar visual objects, so that the spacial ideas of touch always remain, to some extent, products of a fusion between tactual sensations and visual images. But these visual images can not be continually renewed, so that the persons in question come more and more to make use of movements. The sensations of movement that arise from the joints and muscles in passing from one tactual impression to another (p. 46), serve as a measure for the movement executed and, at the same time, as a measure for the distance between the two impressions. These sensations of movement, which in acquired blindness are additions to the gradually fading visual images and in part substitutes for them, are, in congenital blindness, the only means present from a the first for the formation of an idea of the relative position and distance of the single impressions. We observe in the latter case continual movements of the touch-organs, especially the fingers, over the object. Added to these movements are a more concentrated attention to tactual sensations and a greater practice in their discrimination. Still, the low grade of development of this sense, in comparison with sight, always shows itself in the fact that the apprehension of continuous lines and surfaces is much less perfect than that of approximately punctiform impressions arranged in various ways. The necessity of making a blind-alphabet of arbitrary figures formed by various combinations of raised points, is a striking proof of this. Thus, for example, in the ordinary alphabet (Braille's) one point represents A, two points in a horizontal line B, [p. 108] two points in a vertical line C, etc. With six points at most all the letters can be formed, but the points must be far enough apart to be perceived is separate with the end of the index finger. The way in which this alphabet is read is characteristic for the development of the space-ideas of the blind. As a rule the index fingers of both hands are used for this purpose. The right finger precedes and apprehends a group of points simultaneously (synthetic touch), the left finger follows somewhat more slowly and apprehends the single points successively (analytic touch). Both the synthetic and analytic impressions are united and referred to the same object. This method of procedure shows clearly that the spacial discrimination of tactual impressions is no more immediately given in this case than in the case where vision was present, but that here the improvements by means of which the finger that is used for analytic touch passes from point to point, play the same part as the accompanying visual ideas did in the normal cases with vision.
An idea of the extent and direction of these movements can arise only under the condition that every movement is accompanied by an inner tactual sensation (p. 46, 6). The assumption that these inner tactual sensations are immediately connected with an idea of the space passed through in the movement, would be highly improbable, for it would not only presuppose the existence of a connate perception of surrounding space and of the position of the subject in respect to the same (p. 103), but it would include another particular assumption. This is the assumption that inner and outer touch-sensations, although they are otherwise alike in quality and physiological substrata, still differ in that inner sensations give, along with the sensation, an image of the position of the subject and of the spacial arrangement of the immediate environment. This would really necessitate a return [p. 109] to the Platonic doctrine of the memory of innate ideas, for the sensations of movements arising from touch are here thought of as the mere external occasional causes for the revival of innate transcendental ideas of space.
7. Apart from its psychological improbability, such an hypothesis as that just mentioned can not be reconciled with the influence exercised by practice on the discrimination of local signs and of differences in movements. There is no other way except to attribute the rise of spacial ideas here, as in normal cases with vision (p. 106), to the combinations of the sensations themselves as presented in experience. These combinations consist in the fact that in passing from one outer tactual impression to another, any two sensations, a and b, with a certain difference in local signs, always have a corresponding inner touch-sensation, a, accompanying the movement; while two sensations, a and c, with a greater difference in local signs, have a more intense sensation of movement, g. For the blind there is always such a regular combination of inner and outer touch-sensations. From the strictly empirical point of view it can not be affirmed that either of these sensational systems, itself, brings the idea of spacial arrangement; we can only say that this arrangement results regularly from the combination of the two. On this basis the special ideas of the blind, arising, as they do, from external impressions, are defined as the product of the fusion of external tactual sensations and their qualitatively guided local signs, with internal tactual sensations, graded according to intensity. The external sensations with their attributes as determined by the external stimulus, are the predominating elements in this fusion. These push the local signs with their qualitative peculiarities, and the sensations of movement with their intensive attributes, so far into the background, that, like the overtones of a clang they [p. 110] can be perceived only when the attention is especially concentrated upon them. Spacial ideas from touch are, accordingly, due to a complete fusion. Their characteristic peculiarity, in contrast, for example, with intensive tonal fusions, is that the subordinate and supplementary elements are different in character, and at the same time related to one another according to definite laws. They are different, for the local signs form a pure qualitative system, while the inner touch-sensations which accompany the movements of the tactual organs, form a series of intensifies. They are related, for the motor energy used in passing through an interval between two points, increases with the extent of the interval, that, in proportion to the qualitative difference between the local signs, there must also be an increase in the intensity of the sensations of movement.
8. The spacial arrangement of tactual impressions is thus the product of a twofold fusion. First, the subordinate elements fuse, in that the various qualities of the local sign system, which is spread out in two dimensions, are related to one another according to the grades of intensity of the sensations of movement. Secondly, the tactual impressions as determined by the external stimuli, fuse with the product of the first union. Of course, the two processes do not take place successively, but in one and the same act, for the local signs and movements must both be aroused by the external stimuli. Still, the external sensations vary with the nature of the objective stimulus, while the local signs and internal tactual sensations are subjective elements, whose mutual relations always remain the same even when the external impressions vary. This is the psychological condition for the constancy of attributes which we ascribe to space itself, in contrast wich [sic] the great changeableness of the qualitative attributes of objects in space. [p. 111]
9. After the fusion between local signs and internal tactual sensations has once been effected, either one of these elements lay itself, though perhaps in a limited degree, is able to bring out a localization of the sensations, and even to arouse complex spacial ideas. In this way not only normal individuals with vision, but also the blind, even the congenitally blind, have an idea of the place touched, and can perceive as specially separate two impressions that are far enough apart, even when the touch-organs remain perfectly quiet. Of course, the congenitally blind can have no visual image of the region touched, but they have instead of this an idea of a movement of the part touched and, where several impressions are received, the idea of a movement from one to the other. The same fusion takes place in ideas thus formed as in the ordinary ones, where movements are really present, only here the one factor, the inner tactual sensation is merely a memory-image.
10. In the same way, we may have the reverse process. The real contents of experience may be a sum of inner tactual sensations which arise from the movement of some part of the body, while no noticeable external tactual sensations whatever are given, and yet these external sensations which accompany the movement may still be the basis of a spacial idea. This is regularly the case when we have pure ideas of our own movements. If, for example, we shut our eyes and then raise our arm, we have at every moment an idea of the position of the arm. To be sure, external tactual sensations that arise from the torsion and folding of the skin, play some part here too, but they are relatively unimportant in comparison with the internal sensations from the joints, tendons, and muscles.
It can be easily observed that where vision is present, this idea of position comes from an obscure visual image, of the [p. 112] limb with its surroundings, which is aroused even when the eyes are closed or turned away. This connection is so close that it may arise between the mere memory-image of the inner tactual sensation and the corresponding visual idea, as is observed in the case of paralytics, where sometimes the mere will to execute a certain movement arouses the idea of a movement really executed. Evidently the ideas of one's own movements depend, when vision is present, on incomplete fusions, just as the external spacial ideas of touch do, only here the internal sensations play the part that the outer sensations play in the former case. This leads to the assumption that the inner tactual sensations also have local signs, that is, the sensations in the various joints, tendons, and muscles show certain series of local differences. Introspection seems to confirm this view. If we move alternately the knee-joint, hip-joint, and shoulder-joint, or even the corresponding joints on the right and left sides, the quality of the sensation seems each time a little different, even if we neglect the connection with a visual image of the limb, which can never be entirely suppressed. Then, too, it is impossible to see how accompanying visual images could arise at all without such differences. That would require not only a connate idea of space in the mind, but also a connate knowledge of the position and movements of the limbs in space for every moment.
11. From the relations that exist in the normal cases with vision, we can understand the way in which the ideas of their own movements arise in the case of the congenitally blind. Here, instead of a fusion with a visual image, there must be a fusion of sensations of movement with the local signs. Outer tactual sensations also act is aids in this case. In fact, they are much more important here than when vision is present. The ideas of the blind as to their own move- [p. 113] ments are exceedingly uncertain so long as they are unaided by contact with external objects. When, however, they touch such objects, they have the advantage of greater practice with the external tactal sense and a keener attention for the same. The so-called "distance-sense of the blind" is a proof of this. It consists in the ability to perceive from some distance, without direct contact, a resisting object, as, for example, a neighboring wall. Now, it can be experimentally demonstrated that this distance-sense is made up of two factors: a very weak tactual stimulation of the forehead by the atmospheric resistance, and a change in the sound of the step. The latter acts as a signal to concentrate the attention enough so that the weak tactual stimulations can be perceived. The "distance-sense" disappears, accordingly, when the tactual stimulations are prevented by binding a cloth around the forehead or when the steps are rendered inaudible.
12. Besides our ideas of the position and movements of the various parts of our body, we have also an idea of the position and movement of our whole body. The former can never have anything but a relative significance; it is only when considered in connection with the latter that they become absolute. The organ of orientation for this general idea is the head. We always have a definite idea of the position of the head; the other organs are localized in our ideas, generally, indeed, very indefinitely, with reference to it, according to the particular complexes of inner and outer tactual sensations in each case. The specific organ of orientation in the head is the system of semicircular canals, to which are added as secondary aids the inner and outer tactual sensations resulting from the action of the muscles of the head. The function of these canals as an organ of orientation can be most easily understood by assuming that [p. 114] inner tactual sensations with especially marked differences in local signs, arise in them through the influence of the changing pressure of the fluid medium, which fills them. It is highly probable that dizziness, which comes from rapid rotation of the head, is due to the sensations caused by the violent movements of this fluid. This is in accord with the observations that partial derangements of the canals bring about constant illusions in localization, and complete derangement of the same is followed by an almost total suspension of the ability to localize.
12a. The antagonistic theories in regard to the psychical formation of spacial ideas, are generally called nativism and empirism. The nativistic theory seeks to derive localization in space from connate properties of the sense-organs and sense-centres, while the empiristic theory seeks to derive it from the influences of experience. This discrimination does not give proper expression to the actual opposition that exists, for the assumption of connate spacial ideas may be attacked without affirming that these ideas arise through experience. This is the case when, as above, space-perceptions are regarded as products of psychical fusions due both to the physiological properties of the organs of sense and of movement, and to the general laws for the rise of psychical compounds. Such processes of fusion and the arrangements of sense-impressions based upon them, are everywhere the substrata of our experience, but for this very reason it is inadmissible to call them "experience" itself. It is much more proper to point out the opposition that really exists, as that of nativistic and genetic, theories. It is to be noted that the widespread nativistic theories contain empirical elements, while, on the other hand, empirical theories contain nativistic elements, so that the difference is sometimes very small. Supporters of the nativistic view assume that the arrangement of impressions in space corresponds directly to the arrangement of sensitive points in the skin and retina. The special way in which the projection outward is effected, especially the ideas of the distance and magnitude of objects, and the reference of a plurality of specially [p. 115] separated impressions to a single object, are all regarded as dependent upon "attention", "will", or even "experience". Supporters of the empirical theory, on the other hand, generally presuppose space as given in some way or other, and then interpret each single idea as a localization in this space due to some empirical motive. In the theory of spacial ideas from sight, tactual space is generally regarded as this originally given space; in the theory of tactual ideas, original spacial qualities have sometimes been attributed to motor sensations. Thus, in the actual concrete theories empirism and nativism are very ill defined concepts. They agree in the use of the complex concepts of popular psychology, such as '"attentions", "will", and "experience", without any examination or analysis. In this respect they are different from the genetic theory, which seeks to show the elementary processes from which the ideas rise, by means of a psychological analysis of the ideas. In spite of their weaknesses, the nativistist and empiristic theories have served to set the psychological problem that exists here, clearly before us and to bring to light a great number of facts for its solution.
B. SPACIAL SIGHT-IDEAS.
13. The general properties of the touch-sense are repeated in the visual sense, but in a more highly organized form. Corresponding to the sensory surface of the outer skin, we have here the retina with its rods and cones arranged in rows and forming an extraordinarily fine mosaic of sensitive points. Corresponding to the movements of the tactual organs, we have the movements of both eyes in fixating objects and following their bounding lines. Still, while tactual impressions are perceived only through immediate contact with the objects, the refractive media in front of the retina throw inverted, reduced images upon it. These images are so small that space is allowed for a large number of simultaneous impressions, and the ability of light to traverse space makes it possible for both neighboring and distant objects to yield [p. 116] impressions. Vision thus becomes a distance-sense in a much higher degree than hearing. Light can be perceived from incomparably greater distances than sound. Furthermore, only visual ideas are directly localized at different distances from the subject; for auditory ideas this localization is always indirect, through the aid of visual ideas of space.
14. With regard to its spacial attributes, every visual idea may be resolved into two factors: 1) the location of the single elements in relation to one another, and 2) their location in relation to the ideating subject. Even the idea of one single point of light, contains both these factors, for we must always represent a point in some spacial environment, and also in some direction and at some distance from ourselves. These factors can be separated only through deliberate abstraction, never in reality, for the relation of any point in space to its environment, regularly determines its relation to the ideating subject. As a result of this dependence, the analysis of visual ideas may better start with the location of the elements in relation to one another, and then take up later the location of the compound in regard to the subject.
a. The Location of the Elements of a Visual Idea inRelation to One Another.
15. In the apprehension of the reciprocal relations between elements of a visual idea, the attributes of the tactual sense are all repeated, only in a much more highly organized form, and with a few modifications significant for the visual ideas. Here, too, we immediately connect with the simplest possible, approximately punctiform, impression the idea of its place in space; that is, we give it a certain definite position in relation to the parts of space about it. This localization is not effected, however, as in touch, by the [p. 117] direct reference of the impression to the corresponding point of the sense-organ itself, but we project it into a field of vision, which lies at some distance outside of the ideating subject. Here too we have a measure, as in the case of touch, for the accuracy of localization, in the distance at which two approximately punctiform impressions can be just distinguished as spacially different. The distance is not given in this case is a directly measurable linear extension on the sensory surface itself, but as the shortest perceptible interval between two points in the field of vision. The field of vision may be thought of as placed at any distance whatever from the subject, so that it is best to use as a measure for the fineness of localization, not a linear extension, but an angle, the angle formed by the intersection of the lines passing through the nodal point of the eye, from the points in the field of vision to the corresponding retinal points. This angle of vision remains constant so long as the size of the retinal image is unchanged, while the distance between the points in the field of vision increases in proportion to their distance from the subject. If an equivalent linear distance is sought in place of the angle of vision, it can be found in the diameter of the retinal image. This may be reckoned directly from the angle and the distance of the retina from the nodal point of the eye.
16. The measurements of the keenness of localization with the eye, made according to this principle, show that there is a great difference for different parts of the field of vision, just as was found for different regions of the tactual organs (p. 105). Still, the distances that measure the smallest perceptible intervals here are all very much smaller. Then, again, there are many regions of finer discrimination scattered over the tactual organ, but only one region of finest discrimination in the field of vision. This is the middle, which [p. 118] corresponds to the centre of the retina. From this region towards the periphery the fineness of localization diminishes ,very rapidly. The whole field of vision or the whole retinal surface, is, accordingly, analogous to a single tactual region, as, for example, that of the index finger, except that it very much surpasses the latter in fineness of localization, especially at the centre, where two impressions at a distance corresponding to 60" -- 90" in the angle of vision, are just distinguishable, while two degrees and a half toward the periphery, the smallest perceptible extension is 3' 30", and at eight degrees it increases to 1o.
In normal vision we turn the eye towards objects of which we wish to gain more accurate spacial ideas, in such a way that they lie in the middle of the field of vision, their images falling, accordingly, on the centre of the retina. We speak of such objects as seen directly, of all others, which lie in the eccentric parts of the field of vision, as seen indirectly. The centre of the region of direct vision is called the point of regard, or the fixation-point. The line that unites the centre of the retina with that of the field of vision is known as the line of regard.
If we reckon the distance on the retina that corresponds to the smallest angle of vision at which two points in the centre of the field of vision may be perceived as separate, it will be found to be .004 to .006 mm. This distance is equal to the diameter of a retinal cone, and since the cones are so close together in the centre of the retina that they are in direct contact, it may be concluded with probability that two impressions must fall upon at least two different retinal elements if they are to be perceived as separate in space. This view is supported by the fact that in the peripheral regions of the retina the rods and cones, which are the two forms of elements sensitive to light, are [p. 119] really separated by greater intervals. It may, then, be assumed that the keenness of vision, or the ability to distinguish two distinct points in the field of vision, is directly dependent on the proximity of the retinal elements to one another, for two impressions can be distinguished as specially different only when they act upon different elements.
16a. Because of this interrelation between the keenness of vision and the arrangement of retinal elements, it has often been concluded that every such element has from the first the property of localizing any stimulus that acts upon it, in that position in space which corresponds to its own projection in the field of vision. In this way the attempt has been made to reduce the property of the visual sense by virtue of which it represents its objects in an external field of vision at some distance from the subject, to a condate energy of the retinal elements or of their central connections in the visual centre in the brain. There are certain pathological disturbances of vision that seem at first sight to confirm this assumption. When some region of the retina is pushed out of place as a result of inflammation underneath, certain distortions in the images, the so-called metamor-phopsia, arise. The extent and direction of these distortions can be fully explained when it is assumed that the displaced retinal elements continue to localize their impressions as they did when in their normal positions. But it is obvious that these distortions of the images when, as in most cases, they appear as continually changing phenomena during the gradual formation and disappearance of the excretion, furnish us with no more evidence for a connate energy of localization in the retina than does the readily observed fact that distorted images of objects are seen when one looks through prismatic glasses. If, on the other hand, a stationary condition is gradually reached, the metamorphopsia disappear, and that, too, not only in cases where it may be assumed that the retinal elements return to their original position, but even in those cases where such a return is entirely improbable on account of the extent of the affection. In cases like the latter, the development of a new connection between the single retinal elements and their corresponding points in the field [p. 120] of vision, must be assumed. This conclusion is supported by observations made with normal eyes on the gradual adaptation to distorted images which are produced by external optical appliances. If a pair of prismatic glasses are worn before the eyes, marked and disturbing distortions of the images are the regular results. The straight bounding lines appear bent and the forms of the objects are thus distorted. These disturbances gradually disappear entirely if the glasses are worn some time. When the glasses are removed the distortions may appear in the opposite direction. All these phenomena can be understood if we presuppose that the spacial localizations of vision are not original, but acquired.
17. Besides the retinal sensations there are other psychical elements that always take part in the reciprocal spacial arrangement of light-impressions. The physiological properties of the dye point a priori to the sensations that accompany ocular movements, as such elements. These movements obviously play the same part in the estimation of distances in the field of vision as the tactual movements do in the estimation of tactual impressions. The grosser conditions of touch are, however, here reproduced in a much more delicate and highly developed form. The eye can be turned in all directions about its centre of rotation, which is fixed in its relation to the head, by means of a most admirably arranged system of six muscles. It is thus well suited to following continuously the bounding lines of objects or to passing each [p. 121] time in the shortest line from a given fixation-point to another. The movements in the directions which correspond to the position of the objects most frequently and closely observed, namely, downward and inward movements, are favored above the others by the arrangement of the muscles. Furthermore, the movements of the two eyes are so adapted to one another through the synergy of their innervation, that normally the two lines of regard are always turned upon the same fixation point. In this way a cooperation of the two eyes is made possible which not only permit a more perfect apprehension of the position of objects in relation to one another, but, more especially, furnishes the most essential means for the determination of the spacial relation of objects to the subject (24 seq).
18. The phenomena of vision teach that the idea of the relative distance of two points from each other is dependent on the motor energy of the eye employed in passing through this distance, just as the discrimination of two distinct points in the field of vision depends on the arrangement of the retinal elements. The motor energy becomes a component of the idea through its connection with a sensation which can be perceived, especially in extensive movements and by comparing ocular movements in various directions. Thus, for example, the upward movement of the eyes is clearly accompanied by more intense sensations than the downward movements; and the same is true of outward movements of one eye as compared with its inward movements.
The influence of sensations of movement on the localization are most apparent in the cases of disturbance arising from partial paralysis of single ocular muscles. These disturbances correspond exactly to the changes in the amount of energy required to move the eye. The general principle [p. 122] of such disorders is that the distance between two points seems greater when they lie in the direction of the more difficult movement. The more difficult movement has a correspondingly more intense motor sensation, which under normal conditions accompanies a more extensive movement. As a result, the distance passed through appears greater. Furthermore, the same illusion may appear for distances that lie in the same direction, bait have not been actually passed through, for the standard found during a, movement determines the motor impulse in the eye even when it is not moved.
19. Similar differences in the estimation of distances can be demonstrated for the normal eye. Although the ocular muscles are so arranged that their movements in various directions require about the same amount of exertion, still, this is not exactly so. The reasons are apparently closely connected with the adaptation of the eye to its functions. The neighboring objects of our immediate environment, on which the lines of regard must be converged, are the ones most often looked it. For this reason, the muscles of the eye have so adapted themselves that the movements for the convergence of the lines of regard are the easiest, particularly those directed downwards as compared with other possible movements of convergence. This general facilitation of convergence has been acquired by the addition of special auxiliary and compensatory muscles (superior and inferior oblique) to the muscles that move the eye upwards and downwards (superior and inferior recti). As a result of the greater complexity of muscular activity thus necessary for the upward and downward movements of the eyes, the exertion is greater in these directions than towards the two sides, where only the internal and external recti act. The relative case of downward movements of convergence shows itself partly in the differences in the intensity of sensations accom- [p. 123] panying the movements, as already remarked (p. 121), and partly in the fact that downward convergence is involuntarily too great and upward too small. There are certain constant optical illusions depending on the direction of the object in the field of vision, which correspond to these differences in the motor mechanism. They are of two kinds: illusions of direction, and those of magnitude.
Both eyes are subject to an illusion as to the Direction of vertical lines in the field of vision. Such a line whose upper end is inclined 1o -- 3o outward, appears vertical, and one really vertical, seems inclined inward. Since the illusion is in opposite directions for the two eyes, it disappears in binocular vision. it can obviously be explained by the fact just noted, that the downward movements of the eyes are connected with an involuntary increase, and the upward movements with a decrease, in the convergence. This deflection of the movement from the vertical is not noticed, but we refer it to the object as a deflection in the opposite direction. An equally regular illusion in magnitude appears when we compare distances extending in different directions in the field of vision. This, too, is very probably to be referred to the asymmetry in the arrangement of the muscles which arises from the adaptation of the eye to the ordinary position of objects in space. A vertical straight line is judged on the average 1/6 too long as compared with an equal horizontal line. A square, accordingly, appears as a rectangle whose base is shorter than its sides, and a square drawn by the eye is always too low. This illusion is explained when we remember that, as a result of the highly developed tendency to convergence, the muscular activity for upward and downward movements is much more complex than for inward [p. 124] and outward movements. The consequence is the same as in the case of partially paralyzed eyes, distances in the direction of the more difficult movement appear greater.
19a. Besides this difference between vertical and horizontal distances, which is most noticeable because it is so large, there are less marked differences between upward and downward, as well as between outward and inward distances. The upper half of a vertical line is overestimated on the average by 1/16 Of its length, and the outer half of a horizontal line by 1/40. The first way be due to a slight asymmetry in the arrangement of the upper and lower muscles, or it may be due to the involuntary convergence of the lines of regard in downward movement, or, finally, to a combination of both influences. The effect of convergence is due to the fact that it corresponds to an approach of the object, so that we are generally inclined to see the lower half of the line nearer. In accordance with certain conditions of association to be described later (§ 16, 9), when the angle of vision remains constant, whatever is judged as nearer is judged to be smaller, so that the lower half of a line seems shorter than the upper. This explanation by the perspective can not be applied to the greater illusion in the overestimation of vertical as compared with horizontal lines, for if it were applicable, the illusion would at most be about equal to that found in the comparison of the two halves of a vertical line, while in reality it is approximately three times as great. The fact that this greater illusion appears only when straight distances are compared, not in the case of objects bounded by curved lines, is also a proof against the explanation by perspective. A circle, for example, does not appear as an ellipse with a longer vertical axis, but as a real circle. The slight overestimation of the outer half of a horizontal line is also due most probably to the asymmetrical activity of the muscles, which arises from the relative ease of convergence-movements.
20. Added to these two illusions, which arise from the special structure of ocular muscles in their adaptation to the purposes of vision, there are certain other variable optical [p. 125] illusions that are due to certain attributes of all voluntary movements and have their analoga in the movements of the tactual organs. These illusions may also be divided into those of direction, and those of magnitude. The former follow the rule that acute angles are overestimated, obtuse underestimated, and that the direction of the intersecting lines varies correspondingly. For the illusions of magnitude we have the rule. forced or interrupted movements require more exertion than free and continuous ones. Any straight line that necessitates fixation is, accordingly, overestimated in comparison with an open distance marked off by two points, and a straight line interrupted by several dividing lines is overestimated in comparison with an uninterrupted line.
The tactual analogon of the illusion in angles is the tendency to overestimate small articular movements and to underestimate large ones. This comes under the general principle that a relatively greater expenditure of energy is required for a short movement than for a more extensive one, because it is more difficult to begin a movement than to continue it after it is already started. The tactual phenomenon analogous to the overestimation of interrupted lines, is that a distance estimated by a movement of one of the limbs always seems shorter when it is passed through in a single continuous movement than it does when the movement is several times interrupted. Here, too, the sensation corresponds to the expenditure of energy, which is, of course, greater for an interrupted than for a continuous movement. The overestimation of interrupted lines by the eye, takes place, as we can easily understand, only so long as no motives arise from the way in which the division is made, to hinder the movement of the eye over the interrupted line. Such a hindrance is present, for example, when the line is interrupted only once. This one point of division makes fixation [p. 126] necessary. If we compare such a line with a continuous one, we tend to estimate the first without any movement, with the point of division as a fixation-centre, while the second is apprehended by a movement of the eye. As a result the continuous line seems longer than the interrupted line.
21. All these phenomena point to the immediate dependence of the apprehension of spacial directions and magnitudes on ocular movements. As further evidence pointing in the same direction, we have the negative fact that the arrangement of the retinal elements, especially their proximity to one another, normally has no influence on the ideas of direction and magnitude. This is most strikingly evident in the fact that the distance between two points appears the same whether served in direct or indirect vision. Two points that are clearly distinguished in direct vision, may become one in the eccentric parts of the field of vision, but so soon as they are distinguished at all, they will appear just as far apart in one region as in the other. This independence of the proximity of the retinal elements, in our perception of magnitude, holds even for a part of the retina that is not sensitive to light at all -- for the blind spot, where the optic nerve comes into the eye. Objects whose images fall on the blind spot are not seen. The size of this spot is about 6o, and it is located 15o inward from the point of fixation. Images of considerable size, as, for example, that of a human face at a distance of six feet, may disappear entirely on it. Still, when points appear at the right and left or below and above this region, we localize them just as far from each other as we should in any other, uninterrupted part of the field of vision. The same fact is observed when some part of the retina becomes blind through pathological conditions. The resulting break in the field of vision shows itself only ill the fact that images falling on it are not seen, never [p. 127] through any changes in the localization of objects lying on opposite sides of the blind region. 
22. All these phenomena teach that the keenness of vision and the apprehension of directions and distances in the field of vision, are two different functions, which depend upon different conditions: the first depends on the proximity of the retinal elements to one another, the second on ocular movements. It follows directly that spacial ideas from sight can not be regarded as original and given immediately in the action of impressions of light with their spacial arrangement, any more than can the spacial ideas of touch. The spacial order is, here too, developed from the combination of certain sensational components which, taken separately, have no spacial attributes whatever. Other conditions also indicate that the sensational elements are related here in the same way as in the case of touch, and that the development of visual space under normal conditions runs entirely parallel to the development of space in congenital blindness, the only condition under which touch attains a similar independence. Retinal impressions correspond to impressions of contact, and ocular movements to touch-movements. Tactual impressions can gain spacial qualities only through the local coloring of the sensations connected with them -- the local signs and in like manner -- we must presuppose the same for retinal impressions.
22a. To be sure, a qualitative gradation of local signs on  the retina can not be demonstrated with the same evidentness as for the skin. Still, by the use of colors it can be established in general that for greater distances from the retinal centre the sensational quality gradually changes. The colors are not so saturated in indirect vision, and the color-tone also changes; for example, yellow appears orange. There is, indeed, in these properties of the retina no strict proof for the existence of pure local differences in the sensations, at least not in the fine gradations that must be assumed in the retinal centre, for example. Still, they show that local differences in sensations do exist, and this seems to justify the assumption of such even beyond the limits of demonstration. This is all the more justifiable because here, where the gradations are much finer, the tendency to translate sensational differences directly into local differences, which has already been noticed in the case of touch, will be much more apt to destroy their specifically qualitative character. As a confirmation of this view we have the fact that the clearly demonstrable sensational differences at greater distances from the retinal centre, can be observed only under favorable conditions of limited impressions, and disappears entirely when surfaces of uniform color are looked at. This disappearance of qualitative differences which are in themselves considerable, must be attributed in part at least to their relation to local differences. When, however, such relatively great differences disappear as a result of this relation, so that special methods are required for their demonstration, it can not be expected that very small differences will be demonstrable at all.
23. We assume, accordingly, qualitative local signs, which, judging from the data derived from the keenness of vision, are graded in the finest stages at the retinal centre and more slowly in the eccentric parts. The formation of visual space may then be described as a combination of this system of local signs arranged in two dimensions, with a system of intensive sensations of movement. For any two local signs a and b there will be a corresponding sensation of movement a arising from the movement through the distance a b and [p. 129] serving as a measure of the same. A longer distance a c will have a more intense sensation of movement, g. Just as the point of finest discrimination on the finger is the centre of reference, so in the same way the retinal centre is such a point of reference for the eye. In fact, this is from the laws of ocular movements more obvious for the eye than it is for the tactual organ. Any luminous point in the field of vision is a stimulus for the centre of occular innervation, and tends to turn the line of regard reflexively upon itself. This reflex relation of eccentric stimuli to the retinal centre is probably an essential condition for the development of the synergy of ocular movements mentioned above, and is, at the same time, an explanation of the great difficulty of observing objects in indirect vision. This difficulty is evidently due to the greater reflex impulse toward a point in indirect vision when the attention is concentrated upon it, than toward less favored points. As a result of the preeminent importance which the retinal centre has for ocular movements, the point of fixation necessarily becomes the centre of reference in the field of vision, and all distances in this field are brought under a unitary standard by being determined with reference to the fixation-point. The excitation of local sign is due to the action of external impressions, and both together cause the movement towards the retinal centre. The whole process of visual space-arrangement is thus due to the fusion of three different sensational elements: first, the sensational qualities depending upon the character of the external stimulus, second the qualitative local signs depending on the places where the stimuli act, and third, the intensive motor sensations determined by the relation of the stimulated points to the centre of the retina. The latter elements may either accompany actual movements -- this is the original case -- or, when the eye remains at rest, are [p. 130] mere motor impulses of a particular intensity. Because of the regular connection between qualitative local signs and intensive sensations of movement, they may both together be regarded as a single system of complex local signs. The spacial localization of a simple visual impression, is a product of a complete fusion of the sensation caused by the external stimulus with the two interconnected elements belonging to this system of complex local signs. The arrangement of a number of simple impressions in space consists in the combination of a great number of such fusions, which are graded in quality and intensity according to the elements of the system of local signs. The predominating elements in these fusions are the sensations due to the external stimulation. In comparison with these, the elements of the system of local signs are so obscure, even in their original quality and intensity, that for the immediate apprehension of objects they are entirely lost except as spacial qualities.
Connected with this complex process of fusion, which determines the order of the elements in the field of vision, is still another. This latter process, which takes place in the formation of every spacial idea, arises from the relation of the object seen to the subject. We pass now to the consideration of this second process.
b. The Location of Visual Ideas in Relation to theIdeating Subject.
24. The simplest case of a relation between an impression and the subject, that can appear in a visual idea, is evidently that in which the impression is reduced to a single point. If a single point of light is presented in the field of vision, both lines of regard are turned upon it as a result of the reflex impulse exerted by the stimulus (p. 129), in such [p. 131] a way that in both eyes the images fall upon the retinal centres. At the same time the organs of accommodation are adapted to the distance of the point. The point thus represented on the centres of both retinas is seen as single and as situated in a certain particular direction and at a certain particular distance from the ideating subject.
The subject is represented, as a rule, by a point that may be defined as the middle point of the straight line connecting the centres of rotation of the two eyes. We will call this the point of orientation for the field of vision, and the straight line drawn from it to the intersection of the two lines of regard, that is to the external fixation-point, the line of orientation. When a point in space is fixated, there is always a fairly exact idea of the direction of the line of orientation. This idea is produced by the inner tactual sensations connected with the position of the two eyes. Such sensations are very noticeable because of their intensity, when the eyes are rotated much out of the central position. They are just as perceptible for a single eye, so that localization in direction is as perfect in monocular as in binocular vision. In the former case, however, the line of orientation generally coincides with the line of regard. 
25. The idea of the distance of the objects from the subject, or of the absolute length of the line of orientation, is much more indefinite than that of its direction. We are always inclined to ideate this distance shorter than it really is, as may be shown by comparing it with a standard [p. 132] placed somewhere in the field of vision perpendicular to the line of orientation. In this way we find that the distance on the standard judged to be equal to the line of orientation, is always much shorter than the real length of this line. The difference between the two increases further away the point of fixation moves, that is, the longer the line of orientation becomes. The only sensational components that can produce this idea of distance, are those inner tactual sensations connected with the position of the two eyes, that arise particularly from the convergence of the lines of regard and give somewhat of a measure for the absolute extent of this convergence. In fact, it is possible to observe sensations when the convergence is changed; mainly from the inner angle of the eye when the degree of convergence is increased, from the outer, when it is decreased. The sum of all the sensations corresponding to a given position of convergence distinguishes it completely from all other positions.
26. It follows that an idea of a definite, absolute length of the line of orientation can be developed only through the influences of experience, where in addition to the sensational elements a great many associations also have a part. This explains why these ideas always remain indefinite and why they are sometimes aided, sometimes interfered with by other components of visual ideas, especially by the size of the retinal images of familiar objects. On the other hand, we have a relatively fine measure in the sensations of convergence for differences in the distances of objects seen, that is, for the relative changes which the length of the line of orientation undergoes when the fixation-point approaches or recedes. For positions in which the lines of regard are nearly parallel, changes in convergence may be perceived that correspond to an angle of vision of 60" or 70". When the convergence increases, this least perceptible change in convergence also [p. 133] increases considerably, but, in spite of that, the corresponding differences in the length of the line of orientation become smaller and smaller. Thus the purely intensive sensations which accompany movements of convergence, are translated directly into ideas of changes in the distance between the fixation-point and the point of orientation of the subject.
This translation of a certain particular sensational complex into an idea of distance, is not due to any connate energy, but to a particular psychical development, as is shown by a great number of experiences which point to such a development. Among these is the fact that the apprehension both of absolute distances and of differences in distance, is greatly improved by practice. Children are generally inclined to localize very distant objects in the immediate neighborhood: they grasp at the moon, at the slater on the tower, etc. In the same way, it has been observed that the congenitally blind are, immediately after an operation, entirely unable to distinguish near and far.
27. It is of importance for the development of this discrimination between far and near, that under the natural conditions of vision not mere isolated points are presented, but extended three-dimensional objects, or at least a number of points at different depths, to which we assign relatively different distances their respective lines of orientation.
Let us consider first the simplest case, where two points c and b are presented, lying at different depths, and connected by a straight line. A change in the fixation from a to b is always accompanied by a change in convergence, and brings about, first, the passage through a continuous series of retinal local signs corresponding to the line ab, and, secondly, a sensation of movement, [alp], corresponding to the difference in convergence between these two points. This gives us here, too, the elements of a spacial fusion. The [p. 134] product of this fusion is, however, peculiar in kind; it differs in both its components, in the successive series of local signs and in the concomitant sensations of movement, from the fusions that arise when a line in the field of vision is passed over (p. 128). In the latter case the changes in local signs and sensations of movement are alike for both eyes, while in changing the point of fixation from far to near or the reverse they are opposite in the two eyes. For when the right eye a rotation towards the left convergence gives it will produce a rotation towards the right in the left eye, and vice versa. The same must also hold for the movement of the retinal images: when the image of the point as it leaves the point of fixation, moves towards the right in the right eye, it moves towards the left in the left eye, and vice versa. The first takes place when the eyes turn from a nearer to a more distant point, the latter, when they move in the opposite direction. Such fusions arising from movements of convergence have, so far as their qualitative and intensive components are concerned, a composition analogous to that on which the arrangement of the elements in the field of vision with regard to one another depends; but the special way in which these elements are united is entirely different in the two cases.
28. Thus, the fusions between local signs and sensations of convergence form a system of complex local signs which is analogous to that deduced above (p. 130), but still peculiar in its composition. This system, differing in composition from the system of local signs in the field of vision, is supplementary to the latter in that it adds to the reciprocal relation between the objective elements a relation between the ideating subject and these elements. The relation to the subject divides into two ideational elements, characterized by peculiar sensational elements: the idea of direction and [p. 135] that of distance. Both refer primarily to the point of orientation in the head of the ideating subject, and are then secondarily applied to the relations of external objects in regard to one another. Thus, we come to assign to two points which lie at different distances along the line of orientation a direction and distance in relation to each other. All such ideas of spacial distance referring to various positions along the line of orientation, when taken together, are called ideas of depth, or when they are also ideas of particular single objects ideas of three dimensions.
29. An idea of depth arising in the way described varies according to objective and subjective conditions. The determination of the absolute distance of an isolated point in the field of vision, is always very uncertain. Even, the determination of the relative distance between two points a and b lying at different depths is generally certain only under the condition assumed above, that they are connected by a line along which the points of fixation for the two eyes can move in changing the convergence from a to b. We may call such lines which connect different points in space with one another lines of fixation. The principle may then be formulated: points in space are apprehended in their true relations only when they are connected by lines of fixation, along which the point of fixation may move. This principle is explicable on the ground that the condition of a regularly connected change in the local signs of the retina and in the accompanying sensations of convergence, that is, the condition for the rise of ideas of depth as we found before (p. 133), is obviously fulfilled only when impressions are presented which can arouse the appropriate local signs.
30. When the condition mentioned is not fulfilled, there arises either an imperfect and indefinite idea of the different relative distances of the two points from the subject, or else [p. 136] the two points seem to the equally distant -- a phenomenon which can appear only when one of the points is rigidly fixated. Under the latter condition still another charge, always arises in the idea; only the fixated point is seen as single, the other as double. The same thing happens while looking at objects when they are not connected with the binocular fixation-point by means of lines of fixation. Double images that arise in this way are uncrossed -- i.e., the right belongs to the right eye, the left to the left eye -- when the crossed fixated point is nearer than the observed object and crossed when the point is beyond the object.
Binocular localization in depth and binocular double images are, accordingly, phenomena directly interrelated; where the former is indefinite and imperfect, we have double images, and where, on the other hand, the latter are absent, the, localization in depth is definite and exact. The two phenomena stand in such a relation to the line of fixation that, when it is present, localization is aided and double images removed. Still, this rule is not without exception, for when a point is ridgidly fixated with both eyes, double images arise easily in spite of any lines of fixation that may be present. This is explained by the necessary conditions, for both of depth as mentioned above (p. 133). Just as the absence of lines of fixation results in the lack of the required succession of the local signs, so in a sigular manner the sensations of conference connected with movement, are absent in rigid fixation.
c. Relations between the Location of the Elements in regard to one another and the Location in Regard to the Subject.
31. When the field of vision is thought of as merely a location of impressions in relation to one another, we represent it to ourselves is a surface, and call the single ob- [p. 137] jects lying in this surface ideas of two dimensions, in contrast to the ideas of depth. But even an idea of two dimensions must always be related to the seeing subject in two ways. First, every point in the field of vision is seen ill a particular direction on the subjective line of orientation mentioned above (p. 131). Secondly, the whole field of vision is localized at some distance or other from the subject, though this distance may be very indefinite.
The location in a particular direction results in an erect ideational object corresponding to an inverted retinal image. This relation between the objective localization in direction and the retinal image is as necessary a result of ocular movements as the inversion of the image itself is a result of the optical properties of the eye. Our line of orientation in space is the external line of regard or, for binocular vision, the middle line resulting from the combined effects of movements of fixation. A direction upward on this line of orientation in external space corresponds to a direction downward in the space where the retinal image lies, behind the centre of ocular rotation, and vice versa. It follows that the retinal image must be inverted if we are to see the object erect.
32. The location at some distance or other, which is also never absent, brings about the result that all the points of the field of vision seem to be arranged on the surface of a concave hemisphere whose centre is the point of orientation, or, in monocular vision, the point of the eye's rotation. Now, small areas of a large curved surface appear plane, so that the two-dimensional ideas of single objects are as a rule plane; thus, for example, figures drawn upon t plane, as those of plane geometry. But as soon as some parts of the general field of vision separate from it in such a way that they are localized before or behind, that is in different planes, the idea of two dimensions gives place to one of three. [p. 138]
32 a. The fusions formed between qualitative local signs and sensations of convergence when we change from the fixation of a more distant point to a nearer, or the reverse, may be called complex local signs of depth. Such local signs form for every series of points lying before or behind the fixation-point, or for an extended body which is nothing but a series of such points, a regularly arranged system in which a stereometric form located at a particular distance is always unequivocally represented by a particular fusion. When one of two points lying at different distances is fixated, the other is characterized by the different position of its images in the two eyes, and by the correspondingly different direction of the complex local signs in the two cases. The same is true for connected series of points or extended bodies. When we look at a solid object, it throws images in the two eyes that are different from each other on account of the different relative position of the object with regard to the two eyes. We may designate the difference between the positions of certain point in the image in the two eyes as the binocularparallax. This parallax is zero for the point fixated and for those points which are equally distant on the line of orientation; for all other points it has some real positive or negative value accordingly, as they are more or less distant than the fixation-point. If we fixate solid objects with both eyes, only the point fixated, together with those points which are equidistant and in its neighborhood in the field of vision, will give rise to images corresponding in position in the two eyes. All points of the object located at different distances, give images varying in position and size. These differences in the images are just what produce the idea of the solidity of the object when the proper lines of fixation are present. For in the way above described, the angle of binocular parallax for the image of any point lying before or behind the point of fixation and connected with the same by a line of fixation, furnishes, according to its direction and magnitude, a measure for the relative distance of this point in depth through the complex local signs connected with the angle of parallax. This angle of parallax for a given objective depth, decreases proportionally to the distance of the solid object, so that the impression of solidity diminishes, the further of the objects are, and when the distance is so great that all angles of parallax [p. 139] disappear, the body will appear flat, unless the associations to be discussed later (§ 16, 9) produce an idea of depth.
33. The influence of binocular vision on the idea of depth may be investigated experimentally by means of a stereoscope. This instrument consists of two prisms with their angles of refraction turned toward each other in such a way that it renders possible a binocular combination of two plain drawings which correspond to the retinal images from a three-dimensional object. The influence of the various conditions that underlie the formation of ideas of depths, may, in this way, be studied much better than by looking at actual three-dimensional objects, for here we may vary the conditions at will.
To give a concrete illustration, it is observed that complex stereoscopic pictures generally require several movements of convergence back and forth before a clear plastic idea arises. Furthermore, the effect of the parallax appears in looking at stereoscopic pictures whose parts are movable in respect to each other. Such movements are accompanied by changes in the relief which answer exactly to the corresponding changes in binocular parallax. This parallax is dependent on the distance of the two eyes from each other, so that ideas of depth can be produced even in the case of objects too distant in reality to give a plastic effect, by combining in the stereoscope pictures taken from positions much further apart than the two eyes are. This is done, for example, in making stereoscopic photographs of landscapes. The result is that these photographs when combined do not look like real landscapes, but like plastic models regarded from a short distance.
34. In monocular vision all the conditions are absent which are connected with movements of convergence, and with binocular differences in the retinal images, and which may be [p. 140] artificially reproduced with the stereoscope. Still, not all the influences are wanting even here to produce a localization in the third dimension, although this localization is more imperfect.
The direct influence of movements of accomodation have in comparison with other conditions a relatively small, perhaps entirely insignificant influence. Still, like movements of convergence, they too are accompanied by sensations which can be clearly perceived in the else of greater changes of accommodation from distant to neighboring points. For smaller changes in depth these sensations are very uncertain. As a result the movement of a point in the direction of the line of regard, when it is looked at with only one eye, is generally not clearly observed until a change in the size of the retinal image appears.
35. For the development of monocular ideas of depth the influences which the components of the so-called perpective exercise, are of the greatest importance. These are the relative magnitude of the of vision, the trend of limiting lines, the direction of shadows, the change in colors due to atmospheric absorption, etc. All these influences, which act in exactly the same way in monocular and binocular vision, depend on associations of ideas, and will, therefore, be treated in a later chapter (§ 16).
35a. We have in general the same opposing theories for the explanation of visual ideas as for tactual ideas (p. 114). The empirical theory has sometimes committed the fallacy of limiting itself to optics and turning the real problem of space perception over to touch. In such cases it has tried to explain only how a localization of visual ideas can take place with the aid of experience, on the basis of already existing spacial ideas from touch. Such an interpretation is, however, not only self-contradictory, but it also conflicts with experience, which shows that normal persons with vision, visual space-perception determines tactual, not the reverse (p. 104). The fact of general development, that touch [p. 141] is the more primitive sense, can not be applied to the development of the individual. The chief evidences in support of nativistic theories are, first, the metamorphopsia after dislocation of retinal elements (p. 119) and, secondly, the position of the line of orientation (p. 131), which indicates united functioning of the two eyes from the first. It has been noted already (p. 120) that the metamorphopsia and other related phenomena prove the exact opposite as soon as the chances to which they are due become stationary. Furthermore, the fact that in long continued use of only one eye the line of orientation comes to coincide with the line of regard (p. 131), proves that the position of this line is not given from the first, but that it has arisen under the influence of the conditions of vision. Still another fact against nativistic and in favor of the genetic theory is the development in the child of the synergy of ocular movements under the influence of external stimuli and the organization of space-perceptions which apparently accompanies it. Here as in many other respects the development of most animals is different. In the latter cases the reflex connections of retinal impressions with movements of the eyes and head function perfectly immediately after birth. (v. inf. § 9, 2).
The genetic theory has gained the ascendency over older nativistic and empirical views primarily through the more thorough investigation of the phenomena of binocular vision. Nativism has difficulty with the question why we generally see objects single although they produce images in each of the two eyes. The effort is made to avoid the difficulty by assuming that two identical retinal points are connected with the same optic fibre which divides in the chiasma, and that in this way they represent in the sensorium only a single point. This doctrine of the "identitv of the two retinas" was, however, untenable as soon as the actual conditions of binocular vision in three-dimensions began to be investigated. Especially the invention of the stereoscope thus brought with it a new era for the genetic theory of vision.
 A process analogous to this elimination of the metamophopsia is sometimes observed in binocular vision when the disturbances arising from squinting are gradually overcome. When the squinting begins, the two lines of regard no longer meet in the field of vision, so that double images of objects arise. These may gradually disappear, however, if the condition of the eyes remains perfectly stationary; a new set of relations is developed for the retinal elements of the squinting eye.
 In this connection, we have the fact that the blind spot does not appear as a break in the field of vision, without sensational contents, but as a continuation of the general brightness and color of the whole field; for example, as white when we are looking at a white surface, as black when we look at a black one. This filling out of the blind spot is possible only through reproduced sensations, and is to be considered as one of the phenomena of association to be discussed later (§ 16).
 The habit of seeing with two eyes results in exceptions to this rule. Often when one eye is closed, the line of orientation remains the same as in binocular vision and does not coincide with the line of regard. In such cases the closed eye usually makes the corresponding movements of convergence upon a common fixation-point with the open eye.