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gree of rotation increasing with the degree of convergence. To generalize this as a law of ocular motion I have found extremely difficult, because there are so few persons who are able to verify the results, on account of imperfect voluntary control of the ocular muscles, and especially the difficulty or even impossibility which most persons find in observing intelligently images which are not at the point of sight. Nevertheless, I have found several persons who by considerable practice have been able to confirm nearly all these experiments. I have also made observations directly on the eyes of other persons in the manner described in the fifth experiment, and noted the rotation of the iris in strong convergence. I think, therefore, I am justified in announcing the outward rotation of the eyes in convergence as a general law.
The Effect of Elevation and Depression of the Visual Plane on Rotation. The question next occurs, What is the effect, on this rotation, of elevation or depression of the visual plane? I have also made many experiments to determine this point.
Experiment 6.-In making experiments of this kind, all that is necessary is that the experimental plane shall be exactly perpendicular to the visual plane. This may be insured either by keeping the face in its former position and changing the inclination of the plane, or else, more conveniently, by fixing the plane in its vertical position and changing the inclination of the face. If we choose the latter method, then, for experiments with the visual plane elevated, the head or face is turned downward and the eyes look upward toward the brows upon the experimental plane -care being taken that the eyes in their new position shall be on a level with the center of the plane. By experiments of this kind I find that the outward rotation in convergence, especially in strong convergence, increases decidedly for the same degree of convergence with the elevation of the visual plane.
Experiment 7.-For experiments on rotation with the visual plane depressed, the face must be turned upward (taking care as before that the eyes in their new position are on a level with the center of the plane), and then the eyes look downward toward the point of the nose upon the experimental plane. In this case I find that for the same degree of convergence the rotation decreases steadily, until it becomes zero for all degrees of convergence when the visual plane is depressed 45° below its primary position—i. e., when the eyes look toward the point of the nose. Below this angle the rotation seems to be inverse—i. e., inward—although it is impossible to try this with strong convergence, because the nose is in the way.
Cause of the Rotation. It is probable that the rotation is produced by the action of the inferior oblique muscles. If so, we can understand why it increases with elevation of the visual plane, and decreases with its depression ; for in the first case the tension on these muscles would be increased, while in the latter case it would be decreased.
Previous Researches on this Subject.—At the time of my own researches in 1867 * the only writer who to my knowledge had made experiments on the rotation of the eyes on the visual axes in convergence was Meissner. Since that time I find that Hering and others have done so. The results Meissner arrives at are substantially the same as my own; but he arrives at them indirectly, while investigating the question of the horopter, and by methods far less exact than those employed by myself. My results, therefore, must be regarded as a confirmation and a demonstration of his. Meissner's method will be spoken of under the head of the horopter.
*“ American Journal of Sciences,” vol. xlvii, pp. 68 and 153, 1869. + “ Archives des Sciences,” tome iii, 1858, p. 160.
Laws of Parallel and of Convergent Motion Compared. -We will now formulate the laws of convergent motion, and at the same time contrast them with those of parallel motion.
1. When the eyes move in the primary plane in the same direction (parallel motion), there is no torsion; but when they move in that plane in opposite directions, as in convergence, they rotate outward.
2. When the visual plane is elevated and the eyes move in the same direction by parallel motion, then lateral motion to the right produces torsion to the right, and to the left, torsion to the left; but when, on the contrary, they move in opposite directions, as in convergence, then as the right eye moves to the left, i. e., toward the nose, it rotates to the right, and as the left eye moves toward the nose, i. e., to the right, it rotates to the left. If Listing's law operated at all in this case, as it acts in the opposite direction, it would tend to neutralize the effects of convergent rotation; but such is not the fact. On the contrary, as we have seen, the outward rotation increases with elevation of the visual plane.
3. When the visual plane is depressed, and the eyes. move from side to side by parallel motion, then lateral motion to the right is attended with torsion to the left, and motion to the left with torsion to the right. Also when the eyes move by convergent motion in opposite directions, they rotate in the same direction as in the
case of parallel motion ; but there is this great difference: that while in parallel motion the torsion increases with the angle of depression, in convergent motion rotation decreases to zero at 45°. If Listing's law operated at all in this case, it would coöperate with and increase the effect of convergent motion; but the very reverse is the fact, the rotation decreasing with the angle of depression.
4. We have already shown that the so-called torsion of parallel motion is not a true rotation on the optic axes, but only an apparent rotation, the result of reference to a new spatial meridian not parallel with the primary meridian. On the contrary, the rotation produced by convergent motion is a true rotation on the optic axes, as shown by the fact that one eye without change of position will rotate in sympathy with the convergent motion of the other eye (experiments 4 and 5).
It is evident, then, that when the eyes move in the same direction parallel to each other, as in ordinary vision of distant objects, then all their motions are governed by Listing's law; but when, on the contrary, they move in opposite directions, as in convergence, then the law of Listing is either greatly modified or else it is overborne, and another law reigns in its place.
If we look at any point, the two visual lines converge and meet at that point. Its two images therefore fall on corresponding points of the two retinæ, viz., on their central spots. A small object at this point of convergence is seen absolutely single. We have called this point “ the point of sight.” All objects beyond or on this side the point of sight are seen double—in the one case homonymously, in the other heteronymously --because their images do not fall on corresponding points of the two retinæ. But objects below or above, or to one side or the other side of the point of sight, may possibly be seen single also. The sum of all the points which are seen single while the point of sight remains unchanged is called the horopter.
Or it may be otherwise expressed thus: Each eye projects its own retinal images outward into space, and therefore has its own field of view crowded with its own images. When we look at any object, we bring the two external images of that object together, and superpose them at the point of sight. Now the point of sight, together with the images of all other objects or points which coalesce at that moment, lie in the horopter. The images of all objects lying in the horopter