Harvard Psychological Studies, Volume 2

by Unknown

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.