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gence. But the experiments are so difficult that, while in every case the inclination of the horopteric line was proved, the exact angle could not be made out with certainty. It seemed to me about 7° for all degrees of convergence, and therefore for all distances. It certainly does not seem to increase with the degree of convergence, as maintained by Meissner.
Experiment 2.-I next adopted another and I think a better method. I used a plane and diagram covered with true verticals only, as in Fig. 80. I placed this,
instead of vertical as in previous experiments, inclined 7° with the vertical, and therefore in the supposed position of the horopter. Placing the face in a vertical position and the plane of vision horizontal—i. e., my eyes at the same height as the little circles—I combined these successively, and watched how the lines came together. I found that when the plane is inclined 7o all the lines, even the farthest apart—viz., 30 inches—came together perfectly parallel. I then tried the plane inclined 8°; the parallelism was still complete for all degrees of convergence. But when the plane was inclined go, the inclination of the lines in coming together successively was distinctly perceptible. I am sure, therefore, that the true inclination is about 70 or 8°.
Such are the phenomena ; now for the interpretation. It will be observed that when the planè represented by the diagram Fig. 80 is inclined to the visual-plane, all the vertical lines converge by perspective; the convergence increasing with the distance from the central line, as in Fig. 81, which represents such an inclined plane referred to a plane perpendicular to the visual plane.
By calculation and careful plotting, I find that at the distance of 15 inches the convergence of the first two lines, 6 inches apart, for a plane inclined 8°, is each about 1° 31', or to each other 3° 2' ; of the second pair, 12 inches apart, 3° 3' each, or 6° 6' to each other; of the third pair, 18 inches apart, 4° 35' each, or 9° 10' to each other; of the fourth pair, 24 inches apart, 6° 7' each, or 12° 14' to each other; of the fifth pair, 30 inches apart, 7° 40' each, or 15° 20' to each other. Therefore, an increasing rotation of the eyes outward is necessary to bring these together parallel. The distance of the point of sight measured from the line joining the optic centers varied from 44 inches in the first to 17 inch in the last case; but the inclination of the horopteric line was the same in every case. This is probably the most accurate means of determining by direct experiment both the horopter and the degree of rotation of the eyes for every degree of convergence of the optic axes.
Experiment 3.—I next tried the same experiment with the visual plane depressed 45°, but yet perfectly horizontal—i. e., with the chin lifted. In this position, on combining the vertical lines, I find that they retain perfectly their natural perspective convergence. On decreasing the inclination of the diagram the perspective convergence becomes less and less, until when the plane of the diagram is vertical the lines come together again parallel for all degrees of convergence, as already found in the previous experiment. I conclude therefore that in turning the visual plane downward the inclination of the horopteric line becomes less and less, until when the visual plane is depressed 45° it becomes perpendicular to that plane, and at the same time expands to a surface, but not to a plane as Meissner supposes.
In turning the visual plane upward, I find, especially for high degrees of convergence, that I must incline the plane of the diagram more than 8° (viz., about 10°) in order that the lines shall come together parallel. From this I conclude a higher degree of rotation of the eyes and a higher inclination of the horopteric line.
The points on which I do not confirm Meissner are: 1. The increasing inclination of the horopteric line with increasing nearness of the point of sight. I make it constant. 2. I think it probable also that Meissner is wrong in supposing that the horopter, when the visual plane is depressed 45°, is a plane. It is certainly a surface, but not a plane; for it is geometrically clear that points in a perpendicular plane to the right or left of the point of sight can not fall on corresponding points of the two retinæ (page 117). The horopter in this case is evidently a curved surface. I do not undertake to determine its nature by mathematical calculation, and the experimental investigation is unsatisfactory for the reason already given, viz., the extreme indistinctness of perception of points situated any considerable distance from the point of sight in any direction.
In regard to the horopter I consider the following points to be well established :
1. As a necessary consequence of the outward rotation of the eyes in convergence, for all distances in the primary visual plane the horopter is a line inclined to the visual plane, the lower end nearer the observer. But whether the inclination is constant, or increases or decreases with distance. I have not been able to determine with certainty. It is probably constant.
2. In depressing the visual plane, the inclination of the horopteric line becomes less and less, until when the visual plane is inclined 45° below the primary position the horopteric line becomes perpendicular to the visual plane, and at the same time expands into a surface. The exact nature of that surface I have not attempted to investigate, for reasons already explained ; but it is evidently a curved surface.
3. In elevating the visual plane, especially with strong convergence, the inclination of the horopteric line increases.
Finally, the question naturally occurs : Of what advantage is this outward rotation of the eyes, and the
Perhaps I ought to say in my own case and in those of several other persons with normal eyes.
consequent limitation of the horopter to a line? Or is it not rather a defect? Should the law of Listing be regarded as the ideal of ocular motion under all circumstances, and should the departure from this law in the case of convergence be regarded as abnormal? Or is there some useful purpose 'subserved by the rotation of the eyes on their optic axes ? I feel quite sure that there is a useful purpose subserved; for there are special muscles adapted to produce this rotation, and the action of these muscles is consensual with the adjustments, axial and focal, and with the contraction of the pupil. This purpose I explain as follows:
A general view of objects in a wide field is a necessary condition of animal life in its higher phases ; but an equal distinctness of all objects in this field would be fatal to that thoughtful attention which is necessary to the development of the higher faculties of the human mind. Therefore the human eye is so constructed and moved as to restrict as much as possible the conditions both of distinct vision and of single vision. Thus, as in monocular vision the more elaborate structure of the central spot restricts distinct vision to the visual line, and focal adjustment still further restricts it to a single point in that line, the point of sight, so also in binocular vision axial adjustment restricts single vision to the horopter, while rotation on the optic axes restricts the horopter to a single line.