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with each other, and the eyes be brought so near to any points a a, Fig. 71 (taking care that the visual plane shall be perpendicular to the plane of the diagram), that these shall unite beyond the plane of the diagram at the distance of 7 inches, the two lines will coincide perfectly. If then the diagram be turned upside down, and the lines be again united by squinting—the diagram being in this case a little farther off, so that the point of sight shall again be 7 inches—the coincidence of the lines will be again perfect. Fig. 72-in which R and L represent the right and left eyes respectively,
a A and a' H the lines to be combined in these two positions, and A the point of sight-will explain how the combination takes place. The line H A H is the horopteric line.
This experiment is difficult to make, but I am quite confident of the reliability of the results reached. I made many experiments with different degrees of inclination of the lines a H, a' H, and therefore with different degrees of convergence, and many calculations based on these experiments, to determine the inclination of the horopteric line for different degrees of convergence. 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. 73. I placed this, instead of vertical as in previous experiments, inclined
7°, 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 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 9°, the inclination of the lines in coming together successively
was distinctly perceptible. I am sure therefore that the true inclination is about 70 or 8o.
Such are the phenomena; now for the interpretation. It will be observed that when the plane represented by the diagram fig. 73 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. 74, 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 optic centers varied per
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. In this position, on combining the vertical lines, I find that they retain perfectly their natural spective 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.
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. 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 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