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quainted, attempts to determine the horopter directly by experiment. According to him, if a stretched thread be held in the median plane at right angles to the primary visual plane, about 6 to 8 inches distant, and the point of sight be directed on the middle, the thread will not appear single, but the two images will cross each other

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eye image, and I l' the left-eye image. Now, as the images are heteronymous at the upper end and homonymous at the lower end, it is evident that they will unite at some farther point above and some nearer point below. By inclining the thread in the manner indicated—i. e., by carrying the upper end farther and bringing the lower end nearer—the two images come together more and more, until at a certain angle of inclination, varying with the distance of the point of sight, they unite perfectly. The thread is now in the horopter.

Experiment.—I find that the best way to succeed with Meissner's experiment is as follows: Hold i stretched black thread.parallel with the surface of the glass of an open window, and within half an inch of it. Now, with the eyes in the primary position, look, not at the thread, but at some spot on the glass. It will be seen that the double images of the thread are not parallel, but make a small angle with each other, thus- Now bring the lower end nearer the ohserver very gradually. It will be seen that the double images become more and more nearly parallel, until at a certain angle of inclination the parallelism is perfect. I have made several experiments with a view to measuring the angle of inclination for different dis


tances of the point of sight. I find that for 8 inches the inclination is about 70 or 8°; for 4 inches, about 8° or go. It seems to increase as the point of sight is nearer. But of this increase subsequent experiments make me doubtful.

Meissner's results may be summarized thus :

1. With the eyes in the primary position and the point of sight at infinite distance, the horopter is a plane perpendicular to the median line of sight (plane of Aguilonius).

2. For every nearer point of sight in the primary plane, the horopter is not a surface at all, but a line inclined to the visual plane and dipping toward the observer, the inclination increasing with the nearness of the point of sight or degree of convergence.

3. In turning the plane of vision upward, the inclination of the horopteric line increases. In turning the plane of vision downward, the inclination of the horopteric line decreases, until it becomes zero at 45°, and the horopteric line expands into a plane passing through the point of sight and perpendicular to the median visual line.

Furthermore, Meissner attributes these results to a rotation of the eyes on the optic or visual axes outward ;

FIG. 77.

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so that the vertical lines of demarkation, CD, CD', Fig. 77, no longer coincide perfectly with the vertical meridians A B, A' B', nor the horizontal lines of demarkation G H, G' H' with the horizontal meridians EF, E' F', as they do when the eyes are parallel, but cross them at a small angle. With eyes parallel, the images of a vertical line will fall on the vertical lines of demarkation (for these then coincide with the vertical meridians) and be seen single. But if the eyes rotate outward in convergence, then the images of a vertical line will no longer fall on the vertical lines of deinarkation, and therefore will be seen double except at the point of sight. In order that the image of a line shall fall on the vertical lines of demarkation and be seen single, with the eyes in this rotated condition, the line must not be vertical, but inclined with the upper end farther away and the lower end nearer to the observer. It is evident also that under these circumstances the horopter can not be a surface, but is restricted to a line. This requires some explanation.

If the eyes be converged on a vertical line, and then rotated on their optic axes, as we have seen, the line will be doubled except at the point of sight. This doubling is the result of horizontal displacement of the two images in opposite directions at the two ends—the upper ends heteronymously, the lower ends homonymously. Now, since heteronymous images unite by carrying the object farther away and homonymous images by bringing it nearer, it is evident that if the line be inclined by carrying the upper end farther and bringing the lower end nearer, the two images will unite completely, and thus form a horopteric linė. But all points to the right or left of this horopteric line will also double by rotation of the eyes; but this doubling is by vertical displacement, as shown in Fig. 77. Now doubling by vertical displacement can not be remedied by increasing

Fig. 78.

or decreasing distance, because the eyes are separated horizontally. It is therefore irremediable. Hence no form of surface can satisfy the conditions of single vision right and left of the horopteric line. Hence, also, the restriction of the horopter to a line, and the inclination of that line on the plane of vision, are necessary consequences of the rotation of the eyes on their visual axes.

This rotation I have already proved in the most conclusive manner by experiments detailed in the last chapter.

It will be seen by reference to the preceding chapter that my results coincide perfectly with those of Meissner, although I was ignorant of Meissner's researches when I commenced my experiments many years ago

(1867). The end in view in the

and also the methods used, were different. Meissner was investigating the question of the horopter, and outward rotation of the eyes was the logical inference from the position of the horopter discovered by him. I was investigating the laws of convergent motion, and the nature of the horopter was a logical consequence of the outward rotation which I discovered. Meissner's method is, however, far less refined and exact than mine.

I have also proved the inclination of the horopteric line by direct

experiments by my method. Experiment 1.-If two lines, one black on white and the other white on black, be drawn with an inclination of 11° with the vertical, and therefore 21°

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with each other, and the eyes be brought so near to any points a a, Fig. 78 (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 squintingthe 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. 79—in which R and L represent the right and left eyes respectively,

Fig. 79.

RL, the two eyes; n, the nose; A, point of sight; H H, the horopteric line.

a H 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 conver

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