Draw upon a piece of transparent celluloid the two pairs of vertical lines shown in Fig. 46. Let the distance between the left-hand members of the pairs be 64 mm.; this is the average interocular distance, or distance from centre to centre of the pupils when the eyes are directed straight forward to the horizon.1 Look steadily at some distant point, and bring up the transparent slide before the eyes, in such a way that the mid- dle points of the left-hand lines fall upon the foveas. These two lines are then imaged upon corresponding points, and are seen as one line. The right- hand lines are imaged upon disparate points; they are, however, 1 It would, perhaps, be better to say the 'conventional' than the 'aver- age ' interocular distance, since a distance of 64 mm., though commonly given as the average, is probably somewhat too high (Nagel's Hcuidbuch d. Physiol., iii., 1905, 292). It is best of all to make the measurement afresh in every in- dividual case (Titchener, Exper. Psychol., I., ii., 1 901, 245).
312 Spatial Perceptions seen as a single line, standing nearer to you than the other. The combination of disparate images gives the perception of depth. — Now, if you hold up two pencils before the eyes, that in the left hand at arm's length, that in the right a little to the right of the other, and a little nearer; and if you observe the pair of pencils first with the left and then with the right eye alone, you will find that the left-eye view is represented by the left-hand pair of lines in the figure and the right-eye view by the right-hand pair (binoc- ular parallax).
Draw upon another slide the pair of lines shown in Fig. 47. Look at a distant point, and bring up the slide in such a way that the middle points of the two lines are imaged on the foveas. You see a single line, the lower half of which stretches away, while the upper half inclines towards you. Set up a pencil in this position, and note the images formed in the two eyes.
Disparity of retinal images thus accounts for the fact that an object in external space is seen as solid. But the object is also seen as distant from oneself, as lying so many metres away: the point fixated is localised in the third Fig. 47. dimension, just as definitely as the points imaged on disparate retinal areas. How do we localise the fixation-point?
It is possible, of course, that we localise it, too, in terms of retinal disparity. What is now the point of fixation, imaged on corresponding retinal points, has been in the past, and will be in the future, a point that is imaged on disparate retinal points: that is to say, it has been and will be localised, by retinal disparity, in relation to other fixation- points. In time, then, every point in objective space will acquire what we may call a relative position in visual space; and it is a well-known law of psychology that the frequent occurrence of a relative character tends to transform it, for § 86. The Third Dimension 313 perception, into an absolute character; we speak in absolute terms of a heavy child, a light travelling bag, a strong voice, a good light, without any conscious reference or comparison. The transformation might be greatly assisted, in the case of visual space-perception, by associations derived from tactual space: what we can easily reach would be seen as absolutely near, and so on. Or again, it is possible that we localise the fixation-point by the help of secondary criteria. On the whole, however, it seems probable that absolute localisation is effected by way of muscular sensa- tions, the sensations aroused by movements of accommoda- tion and convergence.
The indirect or secondary aids to localisation in depth may be summed up as follows: linear perspective, the course of contour lines in the field of vision; aerial perspective, relative clearness of outline and distinctness of hue; the distribution of light and shade; interposition, the partial covering of far by nearer objects; apparent magnitude, —a criterion that is especially valuable in the case of familiar objects; movement of objects in the field of vision; and movement of our own head or body: if we fixate a near object, and move the head to one side, distant objects show a movement in the same direction; if we fixate a far object, and move the head as before, nearer objects show a movement in the opposite direction. No doubt all of these aids have had their share in the formation of our visual space-perceptions \ but it is questionable whether any one of them is essential.
A like question may be raised with regard to eye-movement: it is, in fact, a matter of keen controversy whether the movements of accommodation and convergence are constitutive factors in space-perception, or whether they are, like the movements of head and body, of merely secondary importance, — e.g., as aids to fixation. On the physiological side we have the fact that the two eyes form a single motor organ; they move together, automatically, under all the conditions of a possible fixation. If the fixation-point is very 314 Spatial Perceptions remote, and lies in the median plane, the lines of regard are parallel; and they remain thus parallel for remote fixation at any part of the field. If the fixation-point lies nearer, in the median plane, the lines of regard become symmetrically convergent; the eyes, which before were directed straight forward at the horizon, turn inward through equal angles. If the new fixation-point does not lie in the median plane, the lines of regard become asymmetrically convergent; in this case, either the two eyes turn inward, through unequal angles, or the one eye turns in while the other, through a smaller angle, turns out. These two types of convergence are maintained, again, for the fixation of points at any part — up, down, right, left — of the field of vision. In short, wherever the eyes can act together, for purposes of binocular vision, they do act together; and the one thing that they cannot do is to act separately against binocular vision; it is impossible, with normal eyes, for the lines of regard to diverge.
On the psychological side we have a long series of experimental studies, whose results are not easily harmonised. Psychological opinion is, in the main, unfavourable to the connection of the depth- perception with sensations of eye-movement; and it must be granted that our discrimination of distance is far more delicate than we should expect it to be, were it mediated solely by muscular sensa- tions. Nevertheless, it seems certain that these sensations can furnish the data for localisation. Recent experiments, carried out with all precautions, lead to the conclusion that in monocular vision the sensations of accommodation, and in binocular vision the sensations of convergence, give fairly accurate cues to the position of objects in external space. The sensations are not always discoverable by introspection; the perception of distance may come to conscious- ness directly. This, however, is not surprising; space is so familiar to us, and the cortical set or adjustment for the perception of space must be so entirely habitual, that the immediacy of the spatial attitude is only natural; the surprising thing is, rather, that the sensations in many cases are discoverable, that the peripheral cues do persist in consciousness. At the same time it must be remembered that sensations of movement, in vision as in touch, are only secondarily, by analogy, the source of our perception of the § 86. The Third Dimension 315 third dimension; they are, as we have put it, cues to this perception. They may get their spatial significance either from the relative depth-perception due to disparity of retinal images (if that is re- garded as primary), or by a more direct association with the tridi- mensional space of touch.
There is, as we have intimated above, a monocular perception of depth. One-eyed persons have no difficulty in finding their way about; and we ourselves, if we close one eye, suffer from no illusion as to the solidity of the objects around us. In all such cases, the observer can change his position with regard to sur- rounding objects; the objects themselves may change their positions, with regard to him and to one another; and various other secondary criteria of distance are still available. As direct cues to the perception of depth there are, first, the sensations of accommodation already mentioned; and secondly, within certain limits, — though this factor has been disputed, — the parallax of indirect vision: the relative position of the retinal images of objects seen by the same eye in indirect vision changes, if ac- commodation is changed, or if the eye or the object moves; and it is supposed that this shift of position may play a part, in monocular vision, similar to that played in binocular vision by the disparity of retinal images. But, whatever its resources may be, monocular localisation is normally very far from accurate. If a curtain ring is suspended in the median plane of the observer's body, and he is given a pencil and required, with one eye closed, to thrust the pencil through the ring, the pencil will pass at surprising distances before or behind it.1 All the direct criteria of depth-perception have a limited range of effectiveness. Accommodation can hardly come into account for objects more than 2 m. away, and the parallax of indirect vision is of appreciable importance only for objects that lie at arm's aYou may often see connoisseurs looking at a picture monocularly, through the curved hand. The hand serves as a tube, whose walls shut out dis- tracting impressions. The main advantage of monocular vision is that the plane of the picture is less evident to it than to binocular vision, so that the secondary indications of distance, upon which the artist must rely for his depth- values, have a better chance to produce their effect.
3 16 Spatial Perceptions length in the lower portion of the field of vision. Convergence, if experiments are to be trusted, becomes useless at a distance of 15 to 20 m. Retinal disparity may work, in theory, up to a dis- tance of some 2700 m. (p. 325): but in practice it is replaced, long before this point is reached, by the indirect or secondary criteria of the depth perception.
§ 87. The Stereoscope. — If the visual perception of depth is due to disparity of the retinal images formed by a single object, then the conditions of tridimensional vision can be synthetised, artificially reproduced, without our having recourse to more than two dimensions of objective space. For the two slightly different pictures taken by the two retinas are plane pictures, and not themselves solid facsimiles of the object. Suppose, then, that we make on paper two drawings of one and the same thing, — a figure of the thing as it looks to the right eye, and a figure of it as it looks to the left, — and that we present each drawing to its appropriate eye. The two drawings, reversals of the two retinal images of a single object seen in perspective, must combine to form the representation of such an object; that is, they must give us the illusion, or rather the synthesis, of the third^dimerjsion. They do, lin fact, combine in this manner; they show what is called stereoscopic relief. The experiment may be performed in a great variety of ways: there are, however, two instru- ments that have an especial importance, — Wheatstone's reflecting stereoscope and Brewster's refracting stereo- scope.
An early form of Wheatstone's stereoscope is shown in Fig. 48. Two plane mirrors, into which the two eyes look, are so adjusted that their backs form an angle of 90 °. The diagrams slip into grooves in two vertical panels, which move in and out on slides § Sy. The Stereoscope along two flat wooden arms. The arms themselves turn about a common centre, which lies in the projection of the line of junction of the mirrors. The rays reflected from the mirrors fall upon the eyes as if they came from a single solid object immediately in FlG. 48. Wheatstone's Reflecting Stereoscope. — C. Wheatsone, Phil. Trans, of the Royal Soc. of London, 1852, pt. i., 3.
front; or, in other words, the eyes see the combined (virtual) image of the two figures as if through and behind the mirrors.
The manipulation of the instrument is simple. The diagrams to be combined are slipped into the grooves. The arms are set in the same straight line, and theslides are pushed well out upon them, at equal distances from the mirrors. The panels are placed at an angle of 45 ° to the mir- rors. The observer sits, looking into the mirrors, and slowly moves the ends of the arms outwards, away from him, until the images combine. Seen for the first time, the stereoscopic effect is surprising in its tridimensional reality.1 Brewster's refracting stereoscope, although scientifically a less valu- able instrument, has by its cheapness and compactness driven the reflecting stereoscope out of general use. In its modern form, the stereoscope is furnished with a light wooden hood, fitting 1 It must be remembered that the use of mirrors involves a left-right con- version of the stereograms.
FIG. 49. Plan of Wheatstone's Stereoscope.
3iS Spatial Perceptions closely over forehead and nose, which serves to exclude lateral light.1 The eyes look at the stereograms through lenticular prisms (double convex semi-lenses): the prisms bring it about that, despite the convergence of the lines of regard, the stereograms are imaged on the retinas approximately as if the lines of regard were parallel; the rounding of the prism-surfaces renders the binocular image both larger and more distinct than it would otherwise be. The long bar, upon which the stereographic card slides, allows of the adjustment of the carrier for eyes of different focal lengths. The stereograms usually supplied with the instrument are paired photographs, taken by cameras whose lenses are — or should be — separated by the average interocular distance. If the cameras are set still farther apart, the binocular (enlarged, virtual) image shows an exaggeration of perspective, and the land- scape or building seen in relief has the' appearance of a model.
It might be supposed, at first thought, that the stereoscope would settle the con- troversy regarding eye-movement (p. 313). There are, however, various reasons why it cannot. For one thing, it does not permit of a rigorous control of the conditions of observation; the secondary criteria of dis- tance can never be entirely ruled out. Thus it is possible, in the Wheatstone stereoscope, to vary the degree of convergence while the magnitude of the retinal images remains unchanged (this by pushing the arms still farther out, after perspective vision has been attained, and then by bringing them back again into the same straight line), and to vary the size of the images while convergence remains unchanged (this by moving the slides in and out, nearer to and farther from the mirrors); but the chief result — in the first case, change of apparent magnitude of 1 The hood-stereoscope was devised by O. W. Holmes in 1S61.
FIG. 50. Plan of Brew- ster's Refracting Stereo- scope, old model. — D. Brewster, The Stereo- scope, its History, Theory and Construction, 1856.
§87. The Stereoscope the binocular image; and in the second, change of its apparent it £ distance — proves very clearly that the perception is largely de-(l ' termined by cortical set; the observer is influenced by his knowledge // of tridimensional space. For another thing, though we may exclude eye-movement proper, we can never exclude the motor disposi- tions of the eye; and these, on the eye-movement theory, may take the place of movements actually performed.
Figure 51 shows a simple instrument which embodies the princi- ple of three more special apparatus. It consists, besides rods and Fig, 51. Demonstrational Stereoscope, Telestereoscope and Pseudoscope.
clamps, of the hood of a refracting stereoscope (with the prisms removed), two hand-mirrors, and two pocket-mirrors. If stereo- grams are placed in clips at the back of the hand-mirrors, we have a Wheatstone stereoscope. If the instrument is set on a window- sill, with the hand-mirrors parallel to the pocket-mirrors and facing the landscape, we have Helmholtz' telestereoscope: the interocular distance is, to all intents, increased to the distance between the large mirrors, and the perception of depth is enhanced. Finally, if the left-hand small mirror and the right-hand large mirror are thrown down, and the remaining mirrors set, facing each other, at an angle of 450 to the median plane of the observer, we 320 Spatial Perceptions have Stratton's form of Mach's mirror pseudoscope: the left eye looks directly at its object, while the right eye sees the same ob- ject twice reflected; hence the right eye is, so to say, displaced to the left of the left eye, and the distance-relations of the object are inverted; near becomes far, and far, near.
Retinal Rivalry and Binocular Colour-mixture. — So far, we have used the stereoscope for the combination of disparate images of a single object. We may also employ it for the imaging of different objects upon corresponding retinal areas. What happens, if we present to the two eyes pictures of identical shape, size, and position, but of varied content?
By far the most frequent result is the phenomenon known as retinal rivalry. Cut a card to the size of a stereoscopic slide (refracting stereoscope), and paste on it, at the right distance apart, two i-cm. squares of red and green paper, the one crossed by vertical and the other by horizontal black lines. Try to com- bine the two images in the stereoscope. You will find that they oscillate: now the red and now the green will appear; now the one colour will seem to hang, like a translucent veil, before the other; now a patch of the one will give way to the other, which spreads gradually over the whole square. A steady binocular image is not obtained. Whether the one or the other image can be held by the attention (which, in this case, means the cortical set -underlying the observer's intention to see red or to see green, and the eye-movements aroused in the effort to hold, follow, or find a disappearing image) is a matter of dispute. It seems, I however, that long practice may overcome the rivalry; for ex- pert microscopists rarely close the unoccupied eye while they are observing.
Under certain conditions, the phenomenon of retinal rivalry is replaced by that of binocular lustre. Suppose that you are looking at a dead-finished surface, which is smooth over its whole extent, but is not quite even: then the one eye may be in the direction of the reflected light, so that to it the surface looks bright, while the other may not be in this direction, so that to it the surface looks dull, or shows the reflection of some coloured object. Such a surface, seen inordinary binocular vision, appears lustrous. If, I § 88. The Perception of Space: Locality 321 then, we place in the stereoscope two pictures of the same object, the one white and the other coloured, — still better, if the one is white and the other black, — we shall get the perception of sheen or lustre. The binocular image of Fig. 52 does, in fact, show a graphite-like polish, although, for most observers, traces of rivalry also persist. Lastly, the phe- nomenon of rivalry may be replaced by that of a binocular colour- mixture. The existence of this mixture has, again, been keenly disputed, but there can be no question of its occurrence. In the author's experience, the best way to secure it by aid of the stereoscope is to combine two small fields of dull and unsaturated colour. The paper squares must be pasted with extreme accuracy upon the cardboard slide; and the observation should be made with the images a little out of focus, so that the contours of the fields are blurred. Some observers, however, succeed most easily with identical contours of considerable complexity: trials may be made with differently coloured postage stamps. Where the mixture is attained, the re- sultant colour is the same as in ordinary colour-mixture, but its brightness is the mean of those of the combined colours. § 88. The Perception of Space: Locality. — Our visual perception of place or position is very highly organised; stimuli that are dis- tinguished as spatially different, in daylight vision, are also definitely FlG. 53. Hering's Binocular Colour Mixer. L, R, the two eyes; b, dark box; gg', coloured glasses (red and blue); pp, supporting plate of clear glass; sss, squares of white paper. — Her- mann's Hdbch. d. Physiol., Y 322 Spatial Perceptions placed in relation to one another.1 With the skin it is other- wise; the cutaneous perception of locality is less developed; and we are able, in the course of a single experiment, to bring out various modes and degrees of localisation. Suppose, for instance, that a pair of compasses, having delicately rounded points of hard rubber, is set down upon the skin of the fore- arm, with the points i mm. apart. We perceive, with eyes closed, a single, sharp pressure upon the forearm. Locali- sation may be effected in several ways: we may feel an im- pulse to move the hand of the opposite side towards the part touched, or we may have a visual picture of the arm and of the point resting upon it, or the pressure may touch off at once some form of words (" Halfway up the arm, in the middle"). The visual picture and the words are, of course, secondary criteria of cutaneous position, and the feel of the localising movement, though much more nearly primitive, is also, if we may trust the conclusions of § 85, in the last resort of secondary character. Here, then, is what we may call the absolute perception of cutaneous locality, the perception of the position of a single pressure. Now let us consider the relative perception: let the compass points be gradually separated, by small steps, and let us note the results. We get, first of all, a larger, blunt point; this gradually passes into a small surface of oval form: then comes a thickish line; then the perception of two sharp points, with a faint linear connection between them; 1 This statement is true as a first approximation to the facts. We ought, by rights, to take account of indirect as well as of direct vision, of vision of luminous points in the dark as well as of vision in the daylight, of pathologi- cal states of the retina, of the action of the ocular muscles in normal and abnormal conditions, of the position of the head. But if all the details were discussed, the psychology of space-perception would require a large book to itself!
§ 88. The Perception of Space: Locality 323 and then the two points stand out separate and distinct. But all this while there has been no perception of the direction in which the lines or points lie; not, perhaps, till the compass-points are 25 mm. apart, can the observer say ' longitudinal ' or ' transverse.' Our perception begins as that of an absolutely localised, undifferentiated, cutaneous expanse; the expanse presently shows relative spatial dif- ference, but a difference that cannot be expressed in terms of direction; next appears the indefinite perception of spatial duality, of two disconnected extents; and, finally, the relation of these extents becomes definite, and the perception of relative or directional position is complete.
The testing of the skin by means of the aesthesiometric com- passes is one of the oldest psychological experiments. E. H. Weber (p. 219) published in 1834 the results of an exploration of the entire bodily surface; he found that the perception of spatial difference is keenest for the tip of the tongue and fingers, dullest for the upper arm, thigh, and back. Weber supposed that he was thus measuring the space limen, the just noticeable magni- tude of cutaneous space. In fact, however, there is no necessary relation between spatial duality (difference of localisation) and spatial magnitude (extension, length of line between points). The discrimination of magnitudes, with or without the perception of direction, is a subject for special investigation. We discuss it in the following § 89.
If two juxtaposed pressure-spots (p. 146) are stimulated at one and the same moment, the pressure sensations blend, to give a single, stronger sensation; there is no spatial distinction. The determination of spatial duality by the simultaneous stimulation of pressure-spots is difficult, and the results are variable: they de- pend, not only on the tendency of the separate sensations to blend, but also on the intensity of the stimuli used, and especially on the general disposition (cortical set) of the observer. If, on the other hand, neighbouring spots are successively stimulated, at an interval of about 1 sec, their sensations are distinguished: the Spatial Perceptions difference is at first indefinite, — the pressures are different, and that is all; but after several repetitions of the observation it may become a difference of perceived position.
As regards simultaneous stimulation, the resting eye behaves in the same way as the skin. The cones have, at the fovea, an average diameter of 3 /x (1 ^ = 0.001 mm.). Points in space