its previous position L s through an angle of 90°, until its line of sight is Ls'. In other words, I run the point of sight or point of convergence from the distant point of the wall w along the line R s to the point a near the root of the nose. When I do so, I see the spectral image incline to the right, thus, indicating

(since the image is spectral) a rotation of the eye in the same direction. This experiment is very difficult, but it is conclusive.

Experiment 5.-I shut one eye, say the left, and look across the root of the nose at a distant object, as in Fig. 63. An assistant now observes attentively my iris, and notes with care the position of the radiating lines. Now, without changing at all the direction of the line of sight, I change the point of sight to an object or point very near the root of the nose, as in Fig. 63, by turning the optic axis of the shut eye through 90°. I again relax the convergence so as to make the optic axes parallel, and again converge upon the near point; and so on alternately. With every convergence the iris is seen to rotate like a wheel outward. I have subjected my eyes to the observation of five different persons, and they all made the same statement in regard to the direction of rotation.

There can be no longer any doubt that my eyes in convergence rotate on the optic axes outward, the degree 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.-The only writer who has to my knowledge made experiments on rotation of the eyes in convergence is Meissner.* The results he 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.

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

* "Archives des Sciences," tome iii, 1858, p. 160.

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 thẹ 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 it 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 refer

ence 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 wholly abrogated, or else overborne, and another law reigns in its place.

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