V. THE PSYCHOLOGICAL LABORATORY IN EMERSON HALL
A monumental staircase leads from the first—the lecture-room—floor of Emerson Hall to the second, the library floor; at the two ends of its broad corridor smaller staircases lead to the third floor, the laboratory. Its general division of space is seen at a glance from the sketch of the ground plan (opposite page 1). Eighteen rooms of various sizes with outside windows form a circle around the central hall which is well lighted by large skylights; but at each end of the hall itself two large windowless spaces are cut off and each of these is divided into three dark rooms. We have thus twenty-four rooms, besides coat-room, toilet-rooms, etc. A further stair leads to the wide attic which is mainly a store-room for the institution.
In order that the laboratory should be adaptable to the most diverse purposes, the permanent differentiation of the rooms has been kept in narrow limits. It seemed unwise to give from the first every room to a special line of research, as the preponderance of special interests may frequently shift; there are years when perhaps studies in physiological and comparative psychology make the largest demand and others in which studies in æsthetical and educational psychology stand in the foreground. A thorough-going specialization, by which special rooms are reserved for tactual studies and others for chronoscope work or for kymograph researches, allows of course certain conveniences in the fixed arrangement of instruments and a certain elaboration of equipment that is built in, but it very much impairs the flexibility of the whole laboratory, and has thus not seemed advisable for an institution whose catholic attitude welcomes investigations as different as those contained in this volume.
To be sure certain constant requirements have demanded a special fitting up of one room as a workshop, one room for the more delicate instruments, one for the beginning course in experimental work, a lecture-room for the courses in comparative psychology, a photography-room, a battery-room, a sound-proof room, the chief animal rooms, and the dark rooms. We have seven light-proof rooms, finished in black, of which two have outside windows for heliostats; of the others, four can be used for optical research; the longest one contains the photometer. Six other rooms, including the lecture-room, may be darkened by opaque blinds. One contains a partition with door and a grooved window-frame fitted with screens in which openings of any desired size and shape may be cut. This window is opposite the main door of the room, and opposite this, across the central hall, some sixty feet away, is the door of another dark room; optical stimuli can thus be given from this window to a subject over seventy feet away.
Several rooms are fitted up with special reference to the investigation of the various forms of organic movement, animal behavior and intelligence. As one result of several investigations in animal psychology already pursued here, the laboratory has a considerable number of devices for testing and making statistical studies of the senses and intelligence, methods of learning and emotional reactions of animals.
Adequate provision is made for the keeping of animals in a large, well-lighted, and well-ventilated corner room. Instead of having aquaria built into the room, an aquarium-table eighteen feet long has been constructed to support moveable aquaria of various sizes. Whenever it is desirable for the purposes of an investigation, any of these aquaria may be moved to the research-room of the investigator or to such quarters as the special conditions of the experiment demand.
The vivarium-room contains, in addition to provisions for water-inhabiting animals, cages of a variety of forms and sizes. The largest of these cages, six and a half feet high, six feet wide, and four feet deep, may be used for birds, monkeys, or any of the medium-sized mammals. Cages for rabbits, guinea-pigs, and other small animals are arranged in frames which support four double compartments. Similarly, small cages suitable for mice, rats, and other small rodents are in supporting frames which carry four of the double cages, each of which is removeable and may be carried to the experimenting-room at the convenience of the experimenter.
In a large unheated room above the main laboratory are tanks for amphibians and reptiles. These tanks, since they can be kept at a low temperature during the winter, are very convenient and useful for frogs, tortoises, and similar hibernating animals.
In view of the prime importance of electricity to a modern psychological laboratory, a rather elaborate system of wiring has been designed and built in. The unit of this system is a small delivery-board six inches wide by eight inches high, which carries the following five circuits: a, a time-circuit for running magnetic signals; bb, two low-tension circuits for chronoscope, bells, signals, etc.; c, a high-tension alternating current (110 v. and 60 phases) for alt. current motors, to be used where great constancy of speed is desired; d, a high-tension direct current (110 v.) for dir. current motors, where it is desired to vary the speed continuously (by the introduction of resistance). Two such delivery-boards have been set on opposite walls of all except the smallest rooms, which have but one board. Circuits a and b are represented on the board by binding-posts, while the high-tension currents, c and d, appear as flush, protected sockets that take a double-pole plug.
Circuit a is a single circuit led from a time-pendulum permanently set in the battery-room, and carried once around the laboratory. It is connected with the a binding-posts of the individual delivery-boards in parallel. It follows that the time-circuit is alike for all the rooms at any one time; but in different hours the pendulum can be adjusted to give various impulse-rates. If an investigation requires some special rate of impulse, the special time-apparatus is set up in the investigator's room and current for it taken from one of the b pairs of posts.
Each b pair goes directly from the delivery-board to the battery-room and ends at a double-pole (telephone type) socket on a large switch-board. Thus every room has two or four direct and independent connections with the battery-room.
The c and d circuits do not come from the battery-room, but from their respective generators that are stationed outside of the building. They are of course connected at the delivery-boards in parallel.
The large switch-board in the battery-room consists of an upper and a lower part. The upper part bears the double-pole sockets from the b posts in all the rooms; the lower part carries some fifty pairs of single-pole sockets that are connected with the batteries stationed near by. These pairs are labelled, and some give a current from cells of the Leclanché type, others of a gravity type. The student has merely to choose the kind and number of cells that he needs, from the lower part, and connect them with one of the double-pole sockets of the upper part which runs to a b pair in his own room. By connecting two double-pole sockets with each other, the student can establish a circuit between any two rooms of the laboratory,—this for purposes of telephonic or other communication. Since every room has two, and most of the rooms have four of the b circuits, the greatest variety and elasticity of service is attained.
The large switch-board further carries a voltmetre and an ammetre, both of the Weston make, which are reached (electrically) from double-pole jacks (sockets) on the upper part of the board. Thus before connecting the current with his room, the student can in a moment measure its amount and intensity. These instruments are of the flushface type, and dead-beat.
All of the rooms are lighted by electricity, and the lighting system is independent of the delivery-boards. Nine of the rooms are provided with soapstone sinks, and six (not including the lavatories and service-room) with enamelled iron or porcelain sinks. All the sinks have two taps and each of these ends with a screw-thread so as to take a tip and rubber hose. The soapstone sinks were specially designed with soapstone drip-boards. This is probably the best material for a research-room, and the porcelain and enamel sinks were put only where a neater appearance was desired, or where chemicals were to be frequently used—as for instance in the battery and photographic rooms. Gas is not used for illumination, but six rooms are provided with jets for the smoking of drums, soldering, brazing, etc.
The instrument-room is equipped with large dust-proof cases for holding the more delicate and valuable instruments. The larger unused pieces are stored, out of sight but readily accessible, in an attic which has a clear floor-space of something more than half the total area of the laboratory. Dust-proof cases for demonstration and class-work material are provided in the lecture- and class-rooms.
The shop contains a wood-working bench with two vices, tool-racks, shelves, drawers, cupboards, and stock-racks, for the use of students; and a 9-in. lathe, circular saw, grinding- and buffing-machine, separate bench, vice, racks, and drawers for the use of the mechanic. The machinery is run by a 5 h.p. electric motor suspended from one of the outside brick walls, on brackets. One who selects the equipment of such a shop has to weigh carefully the respective merits of circular and band saws; the latter undoubtedly lends itself to a greater variety of uses, but it is also a far more dangerous machine to have running in a room to which students are to be given access. This latter consideration determined in the present case the choice of a circular saw. It is quite dangerous enough, and may be used only by, or under the supervision of, the mechanic.
It has been stated on competent authority that a truly sound-proof room cannot be built except under ground. This has not been attempted, but the laboratory contains one room (no. 17) which is virtually sound-proof. A double door separates it from the adjoining experimenter's room, and double doors also separate this from the main hall. The wall between these two rooms consists of two layers of plaster with special deadening material inserted between. Two small tubes, ordinarily stuffed with felt, connect these rooms. When the acoustical stimulus is a tuning-fork, it is placed in a distant room, connected with one of the b circuits of the sound-proof room, and then with a telephone receiver near the subject's ear.
The photographic-room contains the ordinary sink, red lights, shelves, etc. The indirect entrance is light-tight when the door is not closed, so that the experimenter may pass in and out even when developing is going on. This room, like all the others which have no window (except the sound-proof room), has forced ventilation.
The class-room is designed for the experimental training-courses. It has eight of the regular delivery-boards, ten tables, instrument-case, blackboard, and sink.
The lecture-room for specialized courses in comparative and experimental psychology seats eighty students. It is provided with two Bausch and Lomb electric projection-lanterns, horizontal and vertical microscope attachments, and attachment for the projection of opaque objects. On the lecturer's platform, besides the blackboard, projection-screen, and chart-racks (capable of holding twenty charts), is a large demonstration-table provided with a delivery-board, water, gas, sixteen chart-drawers, two other drawers, and three cupboards.
As has been said before, the general psychology course of the University is not given on the laboratory floor, but downstairs in the large lecture-hall with about 400 seats. A number of large demonstration instruments of the laboratory serve the special purpose of this course; this hall too has its own stereopticons.
Our instrumentarium is, of course, in first line, the collection of apparatus bought and constructed through the fourteen years of work. Yet with the new expansion of the institute a considerable number of psychological, physical, and physiological well-tested instruments has been added. Especially in the departments of kymographic, chronoscopic, and optical apparatus the equipment presents a satisfactory completeness; its total value may be estimated to represent about twelve thousand dollars. Yet the place of the laboratory which we appreciate most highly is not the instrument-room but the workshop, in which every new experimental idea can find at once its technical shape and form. Whether those experimental ideas will be original and productive, whether their elaboration will be helpful for the progress of our young science, in short, whether the work in the new laboratory will fulfil the hopes with which we entered it, may be better decided as soon as a few further volumes of the Harvard Psychological Studies shall have followed the present one, which is still from cover to cover a product of Harvard's pre-Emerson-Hall period.
OPTICAL STUDIES
STEREOSCOPIC VISION AND THE DIFFERENCE OF RETINAL IMAGES
BY G. V. HAMILTON
The question which the Laboratory proposed to me for experimental enquiry was one which demanded a definite reply of yes or no. The positive answer seemed a necessary consequence of the traditional psycho-physiological theories, while a certain practical consideration seemed to suggest the negative solution. The question which seems to have been overlooked so far was this: According to the theory of stereoscopic vision two points of light which are seen by each of the two eyes under the same angle appear to lie in the same plane; as soon as the angle for the right eye is larger than that for the left, that is, as soon as the two stimulated retinal points in the right eye are more distant than the two retinal points stimulated in the left eye, the right light-point seems to be farther away than the left one. If we relate them to planes vertical on the ideal binocular fixation-line, the right point lies in a more distant plane. This principle, which, of course, controls all arrangements for stereoscopic effect, is deduced from experiences in which the fixation-line is vertical to the line that connects the nodal points of the two eyes; the plane in which the equally distant points lie is then parallel to the forehead. If, on the other hand, the eyes are turned to the side, that is, if the ideal fixation-line forms an acute angle with the line connecting the eyeballs, the two fixated light-points, which lie in a plane perpendicular to the fixation-line, cannot be seen by the two eyes under the same angle. Any object on my right side is somewhat nearer to my right eye than to my left, and therefore must throw a larger image on my right retina. The two light-points of a plane vertical to the fixation-line give thus with the eyes turned to the right two unequal pairs of retinal stimuli; and the difference of the retinal stimulations is evidently just the same as if the eyes were looking straight forward but the two lights were at different distances. If difference of retinal images really produces the conscious experience of seeing the lights in differently distant planes, vertical to the fixation-line, it follows that with the eyes turned to the right, lights which objectively lie in the same plane must appear subjectively to lie in different distances. The question arises whether the facts correspond to this conclusion. If we look with eyes turned sidewise towards a plane vertical to the direction of seeing, do the points of that plane remain in it for consciousness or do we see them in different planes? We see that practical considerations suggest a "No" to this question, because it would mean that everything which does not lie exactly in front of us must change its plastic form, and this the more strongly the more we see it on our right or our left, and this of course again the more strongly the nearer it is to the eyes, inasmuch as the relative difference of the retinal images must increase with the nearness of the object. If a short-sighted person fixates an object a few centimetres from the eyes strongly turned to the side, the distances in the retinal image of the one eye may be almost the double of those in the other. Under normal conditions the differences would be smaller, but yet everything would be necessarily distorted in its three-dimension shape as soon as it is seen in indirect vision or with sidewise fixation. On the other hand, if the objects keep their three-dimensional relations in spite of sidewise movements, it is evident that the accepted psycho-physiological theory of stereoscopic vision is incomplete and must be revised in a very essential way. The experiment had to decide. Of course the question might be approached experimentally in different ways. It would have been possible, for instance, to study the stereoscopic synthesis of two separate flat pictures seen with the eyeballs in different positions. But we preferred the simplest possible way, seeking the threshold of distance for two parallel vertical edges with eyes turned forward and to the side. We chose edges instead of hanging threads for the purpose of avoiding the possible influence of the apparent thickness of the threads on the judgment of distance. Of course, distance is here never distance from the one or the other eye, but from the centre of the line which connects the two nodal points of the eyes; the two vertical planes whose edges were to be compared stood always vertical on the ideal line of fixation which starts from that central point between the two eyeballs.
The apparatus used in these experiments consists of three parts, viz.:
(1) A plank 2.5 metres x 9.5 centimetres x 4 centimetres, set on edge and screwed to a table at either end.
(2) A head-rest 45 centimetres high, 35 centimetres broad and 15 centimetres deep. Attached to the centre of the lower strip of the frame is a concave trough for the chin. Another trough, shaped to fit over the vertex and with a strip of wood fastened to the front of it for the forehead, slides up or down within the frame. The attachment for the forehead can be moved and fixed at various positions antero-posteriorly. By means of these devices the head can be securely fixed in any position desired without discomfort to the subject.
In order to have the eyes always in the same plane and at a known distance from the apparatus at the other end of the plank, a hole was made in either side of the frame with its centre at a level of the eyes. Extending through the vertical diameter of each hole is a fine wire. Fitted into the inner portion of each hole is a cardboard tube 10 centimetres long: the inner end of each tube contains a vertical wire so arranged that the four wires all fall into a plane at right angles to the long direction of the plank. A mirror at the outer exit of either hole enables the experimenter to align the tips of the subject's corneæ with the wires.
Two parallel strips of wood are so attached to the "head-rest" end of the plank—one below and the other above it—that they can be rotated laterally upon the plank, with the bolt which secures them to it for a centre of rotation. Opposite this centre, and attached to the anterior surface of the upper parallel strip is a wire needle 25 centimetres long. By means of a quadricircular piece of cardboard attached to the plank at the end of the needle, the extent of rotation to the right or left can be read off in degrees. (The point midway between the two corneal tips when they are aligned with the wires is in the same axis of rotation as the head-rest.)
A vertical iron rod 50 centimetres long extends upwards from either end of the parallel strips, and upon these rods the frame of the head-rest can be moved up or down by means of thumb-screws upon which it rests.
(3) At the opposite end of the plank there is attached a flat board, 35 centimetres long and 30 centimetres wide. Attached to the edge of the board which faces the head-rest is a piece of black cardboard 40 centimetres long by 35 centimetres broad. In the centre of the cardboard is a rectangular aperture, 7 centimetres by 14 centimetres. On the upper surface of the board are two slots, one at either side. Sliding within each of these slots is a block of wood to which is attached an upright sheet of black-painted tin, 15 centimetres wide and 20 centimetres high. The surfaces of these tins lie in planes parallel to the plane of the four wires in the head-rest, when the latter is at right angles to the plank. When their surfaces are equidistant from the wires, the inner vertical edges of the tins are separated from each other by 3 centimetres. The sides of the slots, in which the blocks with their tins slide, are fitted with millimetre scales, thus enabling the experimenter to determine the distance of the edges from the corneæ. The point on the scale at which an edge was exactly 2 metres from the vertical plane of the wires was chosen as the "zero" point, and if this distance was decreased by moving an edge forward, the latter was said to stand at "minus" one, two, or more millimetres, as the case might be. Likewise, an edge was said to stand at "plus" the number of millimetres' distance beyond the zero point if it had been moved at a greater distance than 2 metres from the wires. A piece of ground glass attached to the distal end of apparatus enabled the experimenter to secure a uniform illumination, the room being darkened and the light coming from a 32-candle-power electric lamp set about a metre and a half behind and on a slightly lower level than the glass.
It was found that by shading the lamp itself and admitting a dim light to the room by means of drawing down only the ordinary thin window-shades, the edges could be made to seem almost isolated in space and to stand out in clear relief.
The subjects of the experiment were Messrs. Bell, Flexner, and Tait. Each subject determined the equality-point and the threshold for the normal primary position of the eyes, for the eyes in a lateral position of 15° and in a lateral position of 30°, both to the left and to the right.
Eyes at 0° means the following: that the most anterior part of the two corneæ lies in a plane parallel to and two metres' distance from the plane in which the two parallel edges lie at 0. Eyes at 30° to the left means that a line drawn in front of the two corneæ intersects such a line at an angle of 30°, the left eye being at the distal end of the line. In calculating the visual angles 7.4 mm. are added in order to compensate for the distance from the extreme anterior portion of the cornea to the nodal point of the eye.
The results for Mr. Tait are as follows:
The position of eyes 0°. The right edge was moved, at first from an evident + position to equality, then from equality to the - threshold, then from an evident - position to equality, then from equality to the + threshold. These four points were determined each fifteen times and the average taken. Then exactly the same fifteen sets of four determinations with the left edge moved. The averages of these 120 experiments are these: When the left edge is moved from + to =:-2.77, from = to -:-6.97, from - to =:+0.77, from = to +5.93. When the right edge is moved from + to =: +2.83, from = to -:-1.6, from - to =:+5.9, from = to +:+10.53. The first equality-point appears thus when the left edge is moved at -0.76, when the right edge is moved at +4.41, with a threshold of about 5 in either case. With the normal eye-position the edges must thus not be exactly in the same plane to appear equally distant; at a distance of 2000 mm. the left must be about 2 mm. nearer than the right to appear in the same plane, vertical to the line of regard.
If the position of the eyes is 15° to the left, we have the following results: When the left edge is moved from + to =:-4.17, from = to -:-8.5, from - to =:-1.33, from = to +:+1; when the right edge is moved from + to =:+4.17, from = to -:+1.17, from - to =:+4.5, from = to +:+8.67.
If the position of the eyes is 30° to the left, we find when the left edge is moved from + to =:-2.67, from = to -:-6.67, from - to =:+0.5, from = to +:+3.33. When the right edge is moved from + to =:+2.33, from = to -:-0.02, from - to =:+9., from = to +:+12.33.
If we take again the general averages, we have for the eye-position of 15° to the left an equality-point of -3.25 if the left edge is moved and judged and +4.63 if the right edge is moved and judged. That is, if the right edge stands at 2000 mm. the left edge must be moved to 1996.75, and if the left stands at 2000, the right must be moved to 2004.63. For the eye-position of 30° to the left, the equality-point lies at -1.49 if the left edge is moved and judged, and at +5.91 if the right edge is the variable. The threshold lies in all three cases, for eyes at 0°, at 15°, and at 30°, at about ±5 mm.; the position of the eyes has thus no influence on the threshold for the perception of distance in the direction of regard.
But the point essential for our investigation is of course not the threshold but the equality-point. To take the extremes of the eye-positions 0° and 30° we find the equality when the left edge is judged, at -0.76 for 0° and -1.49 for 30°, and when the right edge is moved, at +4.41 at 0° and +5.91 at 30°; the middle is thus +1.82 for 0° and +2.21 for 30°, that is a difference of less than 0.4 mm.
To understand this figure we must enter into the calculation of the angles. We have an eye-distance of 60 mm., a distance of the edges from the cornea 2000 mm., from the nodal points 2007.4 mm., the distance of each edge from the median line 15 mm., the distance of the two edges from each other thus 30 mm. as long as they are in the same plane. We have to determine the angle under which each eye sees the distance of the two edges. A simple trigonometric calculation gives the following figures: If both eyes are in normal position, at 0°, and both edges are in the same plane, 2000 mm. from the corneæ, the angle for each eye is 51' 22". If the left edge is now moved to +5, the left eye sees the distance of the edges at an angle of 51' 25", the right eye under 51' 10", the difference is thus 15"; if the left edge is at +10 mm., the left eye's angle is 51' 29", the right eye's angle 50' 59", the difference 30". If the left edge is moved to -5 mm., the left eye's angle is 51' 18", the right eye's angle 51' 33", the difference 15"; if the left edge is moved to -10 mm., the left eye's angle is 51' 14", the right eye's angle 51' 45", the difference 31". Now we saw that with normal eye-position when the left edge was moved the threshold was +5.93 and -6.97; a difference of 15" to 20" between the visual angles of the two eyes was thus amply sufficient to give a distinct experience of different distance. When the left eye's angle was about 15" smaller than the angle of the right eye, the difference of the retinal images gave a sure impression of the greater nearness of the left edge.
If we now bring the eyes into the position of 30°, the angles are of course different when both edges are in the same plane vertical to the direction of regard. If the two edges are in the same plane, the left eye's angle is 50' 59" and the right eye's angle 51' 45", the difference thus 46". If we move the left edge to +5, the left angle becomes 51' 1", the right angle 51' 34", the difference 33". If we move the left to +10, the left angle becomes 51' 4", the right 51' 24"; the difference is thus still 20", and we must move the left edge to +17 mm. to get an equal angle for the left and the right eye. If we move the left to -5, the difference becomes of course larger, the left eye sees under 50' 56", the right eye 51' 55", the difference 59"; and at -10, the left eye has the angle 50' 53", the right eye 52' 6", difference 1' 13". It is hardly necessary to state here the angles for the changes of the right edge or for an eye-position of 15°, inasmuch as the maximum differences bring out our case most clearly. With an eye-position of 15°, the edges at the same plane give angles of 51' 10" and 51'34", that is, a difference of 24"; if the left edge is moved to -5 mm. the difference becomes 38"; if it is moved to -10 mm. the difference is 54"; if the left edge is moved to +5 the difference decreases to 10" and at +10 mm. to 6".
We have thus the following fundamental result: If the eyes are in normal primary position, a movement of the left edge to ±6 mm. is constantly apperceived at threshold of distance and this corresponds to retinal images whose visual angles differ by about 17". A difference of 17" in the visual angles of the two eyes produces thus under the conditions of this experiment for this subject a strong stereoscopic effect when the eyes are in primary position. If the eyes are in the position of the head 30° to the left, the left eye thus much further from the edges than the right eye, the visual angle of the left image thus much smaller than that of the right image, we find the same equality-point with the same threshold. We saw that in this position the two visual angles would be equal if the left edge were moved to +17 mm.; instead of at +17, the equality-point—when the left edge is judged—lies at -1.49, that is, at a point at which the visual angle of the left eye is more than 46" smaller than the angle of the right eye. While in normal position a difference of the two retinal images of 17" constitutes a distinct threshold value; at a lateral position of the eyes of 30° the great difference of 46" becomes necessary to give the impression of equal plane, while a decrease of that difference to 30" gives a distinct feeling of greater distance. Equal retinal images produce for the lateral eyes thus the same effect which for the normal position very different images produce; and to get for the lateral eyes the effect which equal images produce for the normal position, the angles of the images must differ by 46".
The results for the second subject, Mr. Flexner, are practically the same. With the position of the eyes at 0°, when the left edge is judged and moved, we find the following averages: from + to =: +0.03, from = to -:-3.8, from - to =:-0.7, from = to +:+3.93; when the right edge is moved from + to =:-0.08, from = to -:-4.29, from - to =:+1.21, from = to +:+4.08. It is evident that the difference between right and left which existed for Mr. Tait does not enter into Mr. Flexner's results. The equality-point as average of 120 experiments lies for normal eye-position practically at zero, and the threshold is ±4 mm.; his sensibility for differences of retinal images is thus still finer than for Mr. Tait, as we saw that the threshold of ±4 mm. means a difference of visual angles of less than 15". If Mr. Flexner's head is turned 15° to the left, his left eye thus considerably farther away from the edges than the right eye, the results are these: If the left edge is moved and judged, we find from + to =:-0.02, from = to -:-3.17, from - to =:0, from = to +:+4.67; if the right edge is moved from + to =:-0.01, from = to -:-2.5, from - to =:-0.8, from = to +:+3.33. Experiments with lateral movement of 30° were not carried through, as the subject, accustomed to eye-glasses, became less accurate in the judgments; but the experiments with the position of 0° and of 15° are unequivocal. They show that the equality-point and the thresholds are exactly the same for 15´ as for 0°. For the lateral position of 15° again the average equality-point is exactly at 0° and the threshold at less than ±4 mm. We saw that for a lateral movement of 15° the difference of the angles at the equality-point is 24". We find thus for Mr. Flexner that with primary eye-position a difference of angles of less than 15" gives a distinct stereoscopic effect, while with a lateral position of the eyes a plane effect demands a difference of 24" for the two visual angles.
Experiments with Dr. Bell finally showed a rather strong fluctuation of judgments and the determination of the equality-point for normal eye-position has not only too large a middle variation to be a reliable basis, but is influenced by a constant tendency to underestimate the distance of the edge moved. Yet the general result is the same as with the other two subjects, that is, the equality-point is with him, too, practically the same for the eyes in normal and in lateral position.
The general conclusion from the results of all three subjects is thus evidently that the traditional physiological theory is untenable, the stereoscopic effect cannot be simply a function of the difference of the two retinal images. The same pair of unequal retinal images which gives a most striking stereoscopic effect for eyes in primary position, has no stereoscopic effect for eyes in lateral position and vice versa. The stereoscopic interpretation is thus the function of both the difference of the retinal images and the position of the eyeballs. Of course the two retinal images are in any case never felt as two pictures if they are not different enough to produce a double image. With the primary position of the eyes as long as the two different retinal views are sufficiently similar to allow a synthesis in a three-dimensional impression of our object, we perceive every point of the object not as double image but as one point of a given distance. The distance feeling of the normal stereoscopic vision demands thus itself more than the reference to the different retinal images, and the only factor which can explain the phenomena is the response of the eye-muscles which react on the double images by increase or decrease of convergence. The distance of a point in a stereoscopic image is determined by the impulse necessary for that particular act of convergence of the eyeballs by which the two retinal images on non-cor-responding points would be changed into images on corresponding points. The different retinal images are thus ever for the normal eye-position merely the stimuli for the production of that process which really determines the experience of distance, that is, the motor impulse to a change in convergence.
If thus the stereoscopic vision under normal conditions is ultimately dependent upon the central motor impulses, it is not surprising that a change in the psycho-physical conditions of movement produces a change in the resulting impulses. Such a change in the conditions is given indeed whenever the eyes are in a lateral position. Just as the same stimulus produces a different response when the arm or leg is in a flexed or an extended position, so the retinal double images stimulate different responses according to the particular position of the eyeballs. That pair of unequal retinal images that in primary eye-position produce in going from one end of the object to the other a strong increase of convergence and thus a feeling of greater nearness, may produce with the lateral eye-position no increase of convergence and thus a feeling of equal distance or even a decrease of convergence and thus a feeling of removal. The psycho-physical system upon which our three-dimensional visual perception depends is then much more complex than the usual theory teaches; it is not the retinal image of the double eye, but this image together with the whole distribution of contractions in the eye-muscles, which determines the stereoscopic vision: the same retinal images may give very different plastic perceptions for different positions of the eyeballs.
The experiments point thus to the same complex connection which Professor Münsterberg emphasized in his studies of the "Perception of distance."[1] I may quote the closing part of his article to bring out the intimate connection of the two problems. He reports his observations on the so-called verant and insists that the monocular verant almost as little as the ordinary binocular stereoscope can give the impression of normal distance of nature. Professor Münsterberg writes: "Whoever is able to separate seeing in three dimensions from seeing in natural distance cannot doubt that in both cases alike we reach the first end, the plastic interpretation, but are just as far removed from the other, the feeling of natural distance, as in the ordinary vision of pictures. The new instrument is thus in no way a real 'verant.'
"The question arises, Why is that so? If I bring my landscape picture on a transparent glass plate into such a distance from my one eye that every point of this transparent photograph covers for my resting eye exactly the corresponding point of the real landscape and yet accommodation is excluded, as, for instance, in the case of the short-sighted eye, or in the case of the normal eye with the verant lenses, then we have exactly the retinal images of the real view of nature and the same repose of the lens. Why are we, nevertheless, absolutely unable to substitute the near object for the far one? This problem exists in spite of all the theoretical assurances that the one ought to appear exactly like the other, and I think that it is not impossible to furnish an answer to it.
"If I am not mistaken, there is one point of difference between seeing the mere picture and seeing the far landscape, which has been neglected in the usual discussions. Every one knows, of course, that we see the picture and the landscape normally with the help of eye-movements. The eye moves from point to point; but psychologists have neglected the consideration that the relation between eye-movement and retinal image must be quite a different one for the landscape and for its photograph. Let us consider the simplest possible case, the case of the myopic eye without any lenses whatever, and without any need of accommodation for a picture as near to the eye as 10 cm. If I take a small landscape picture made with a camera whose distance from lens to plate is 10 cm., I have a splendid plastic view if I see it at a distance of about 10 cm. from my eye. I have before me just such a picture in which two mountain peaks are, in the photograph, 1 cm. distant from each other. If I now have my little picture at the distance of 10 cm. from the eye, these two mountain tops correspond in their distance of 1 cm. exactly to the retinal image which the two real mountains, which are ten miles away and one mile distant from each other, produce in my retina. The retinal image of the two mountain peaks in the photograph is thus for my resting eye indeed identical with that of real nature. Does that mean that I have to make the same eye-movement to go from the left to the right mountain in the landscape as in the picture? Of course, that would be so, the movement would be just as identical as the retinal images if the nodal point of the light-rays were identical with the rotation-point of the eyeball. But everybody knows that this is not at all the case. The light-rays cross in the lens. The angle of vision, and thus the size of the retinal image, are thus dependent upon the distance of the lens from the retina. But the movement of the eye is related to a rotation-point which lies about 13 mm. behind the cornea, roughly speaking 1 cm. behind the nodal point of the rays. This additional centimetre plays, of course, no rôle whatever, if I look at my mountains in the real landscape; following with my eyeball from the fixation-point of the left mountain to the fixation-point of the right mountain, I make a movement whose angle can be declared identical with the angle under which I saw the two mountains with the resting eye in the first position. This angle of vision was determined by the distance of the nodal point, which was in our case ten miles, while the angle of eye-movement was determined by the distance of the rotation-point, which would be ten miles plus one centimetre, and there is of course no possible difference for practical discrimination between these two distances.
"But the situation is completely changed if I turn to my little picture 10 cm. distant from my eye. The angle under which I see my two peaks is, of course, again the same under which I saw them in the real landscape. It is determined by the distance of the picture from the nodal point, which is in this case 10 cm. But the angle of the eye-movement necessary to fixate first the left and then the right peak is now a much smaller one because it is again determined by the distance from the rotation-point, and that is in this case 10 cm. plus 1 cm. With this short distance of the picture from the eye this one additional centimetre is not at all the negligible quantity which it was in addition to ten miles in the landscape. For the two real mountains the angle of the eye-movement had a tangent of one tenth; for the photograph mountains, in spite of their equal size of retinal image, the angle of necessary movement would of course have a tangent of one eleventh. Roughly speaking, we could say that the photograph, in order to produce the same eye-movement which the mountains in the landscape excited, would need a pictorial distance between the two photograph mountains of 11 mm. instead of 10 mm. Of course if the distance in the picture were made 11 mm. instead of 10, it would not cover any more the mountains of the landscape. The retinal image would thus be relatively too large and would not give us any longer the true landscape. On the other hand, if we tried to correct it by bringing the picture one centimetre nearer to the eye, then of course every retinal image would be enlarged by that necessary tenth, and yet there would be no help for the situation, as now again the eye-movement demanded by the retinal image would be relatively increased too.
"We can put it in this way: my real landscape demands a relation between retinal image and movement which my picture cannot produce under any circumstances whatever. That which would be needed to imitate the relations would be realized only if I had my retinal images from the picture at a distance of 10 cm., and at the same time the movements belonging to the same picture seen at a distance of 9 cm. That is of course unrealizable. We cannot see a picture without having our movements constantly controlled by the size of the real retinal images, as it is necessary that the distance seen in indirect vision is the distance covered by the fixation-point during the eye-movement. That demands, as we have seen, a different relation between retinal image and eye-movement for near and far, and no verant and no stereoscope can eliminate this factor. If a 10-mm. object in the photograph demands an 11-mm. movement to give the impression of real natural distance, then we have a condition which cannot be fulfilled.
"If we remember how extremely delicate is our normal sensitiveness for retinal distances and how the newer studies in stereoscopic vision have demonstrated an unsuspected delicacy of adjustment between retinal images and motor responses, it is evident that this so far always neglected relation must be an extremely important one. If we have one adjustment of central reaction in which a certain eye-movement corresponds to retinal images of one size, and another adjustment in which the same movements correspond to retinal images which are ten per cent larger, we can really not expect our judgment of distance to neglect the difference between these two systems of relations. Of course they represent two extreme cases. Every distance beyond 10 cm. demands its special adjustment up to the point where the distance becomes too large to be influenced by the distance from the nodal point to the rotation-point. We must thus presuppose a sliding scale of ever new adjustments for the different distances at which we see any object, and we have, in this relation, probably not the least important factor in the judgment of the third dimension for relatively near objects, and probably even more important than the irradiation circles which control the accommodation, as these circles must be the same for objects which lie before and behind the fixation-point. Of course the whole system of our localizing reactions becomes through these considerations more complex by far than the schematizations of the text-books propose. But physiological optics has shown at every point in its development that mere simplification has not always meant a deeper insight into the real relations."
It is evident that our studies in stereoscopic vision with lateral eye-position involve exactly the same principle and reaffirm completely Professor Münsterberg's theoretical views. In both cases, in the monocular of the verant as in the binocular of our experiments, the same retinal image has different psycho-physiological space-value on account of the different motor situation.