apparent rotation on the visual axis torsion. This is the more important, because there is a real rotation on the visual axis, which we shall speak of under the next head.*

SECTION 1.-LAWS OF CONVERGENT MOTION.

We have thus far confined ourselves to explanation of the laws which govern the eyes when they move in the same direction with axes parallel, as in looking from side to side or up and down. I have called this the law of parallel motion. We now come to speak of the laws which govern the eyes when they move in opposite directions, as in convergence. These I shall call the laws of convergent motion.

In convergence there is not merely an apparent rotation or torsion, but a real rotation of the eyes on the optic or visual axes; and since the motions are in opposite directions, the rotations are also opposite. But, except in very strong convergence, the rotation is small and difficult to observe, and therefore has been either overlooked or denied by many observers. As the existence or nonexistence of this rotation has an important bearing on the much-vexed question of the horopter, it is important that proof should be accumulated even to demonstration.

The first difficulty which meets us in experimenting on this subject is, that spectral images, which are such delicate indicators of ocular motion, are almost useless here. In parallel motion of the eyes these images follow every movement with the utmost exactness, but in convergent motion they do not. Suppose, for example, with the eyes parallel or nearly so, a spectral image is

* I am indebted to Mrs. Franklin for having drawn my attention to the fact that several writers, Volkmann, Donders, Aubert, etc., have perceived that the rotation of the eyes in Helmholtz's experiments is only apparent.

branded on the vertical meridians of both eyes. In convergence each eye may move through 45° or more, and yet the place of the spectral image remains the same, viz., directly in front. The eye also in extreme convergence may rotate on the optic axis 10°, but the vertical image remains still perfectly vertical. The reason of this is, that the two retinal images are on corresponding points, and therefore by the law of corresponding points their external representatives are indissolubly united. In moving the eyes in opposite directions, it is impossible that the images should move except by separating; but separation, either complete or partial, is impossible without violating the law of corresponding points—a law which is never violated under any circumstances whatsoever. Actual objects therefore, not spectral images, must be used in these experiments.

As the experiments about to be described are among the most difficult in the whole field of binocular vision, and as in many of them it is absolutely necessary that the primary visual plane should be perfectly horizontal, I must first define what we mean by the primary visual plane, and show how it may be made perfectly horizontal.

Take a thin plate, like a cardboard; place its edge on the root of the nose and the card at right angles to the line of the face, in such wise that the plane of the card shall cut through the center of the two pupils, and you can see only its edge. The card is then in the primary visual plane. Keeping the position of the card fixed in relation to the face, the face may be elevated or depressed, and the card will be also elevated or depressed, but will remain in the primary visual plane. But if the card be elevated or depressed so as to make a different angle with the line of the face, then the visual plane is elevated or depressed above or below the

primary position. When the head is erect and the line of the face vertical, the primary visual plane is horizontal. Suppose we wish now to look at a vertical wall in such wise that the primary

visual plane shall be perfectly horizontal. We first mark on the wall a horizontal line

n

FIG. 67.

exactly the height of the root of the nose. Standing then say 6 feet off, and shutting first one eye and then the other, we bring the image of the lowest part of the root of the nose directly across the line. The primary plane is then perfectly horizontal. In Fig. 67, n and n' are the curves of the outline of the root of the nose as seen by the right and left eye respectively, and n n' is the horizontal line on the wall. We are now prepared to make our experiments.

Experiment 1.-Prepare a plane 2 feet long and 1 foot wide. Dividing this by a middle line into two

equal squares, let one of the halves be painted black and the other white. Let the whole be covered with rectangular coördinates, vertical and horizontal, on the

black half the lines being white and on the white half black, as in Fig. 68. Near the middle of the two square halves, and at the crossing of a vertical and horizontal line, make two small circles, e c'. Set up this plane on c the table in a perfectly vertical position, and at a distance of 2 or 3 feet. Rest the chin on the table immediately in front of the plane, with a book or other support under the chin, so that the root of the nose shall be exactly the same height as the circles, which in this case is about 6 inches. Now, shutting alternately one eye and the other, bring the image of the lowest part of the root of the nose coincident with the horizontal line running through the circles. The primary plane is now perfectly horizontal, and therefore at right angles to the experimental plane. Now, finally, converge the eyes until the right eye looks directly at the left circle, and the left eye at the right circle, and of course the two circles combine. If one is practiced in such experiments, and observes closely, he will see that the vertical lines of the two squares (which can be readily distinguished, because those of the one are white and of the other black), as they approach and pass over one another successively, are not perfectly parallel, but make a small angle, thus- ; and also that the

angle increases as the convergence is pushed farther and farther so that lines even beyond the circles are brought successively together. Similarly also the horizontals cut each other at a small angle, but this fact is not so easy to observe as in the case of the verticals.

Such are the phenomena; now for the interpretation. It must be remembered that images of objects differ wholly from spectral images in this, viz.: that spectral images, being fixed impressions on the retina, follow

FIG. 69.

the motions of the eye with perfect exactness; while, images of objects being movable on the retina, their external representatives in convergence seem to move in a direction contrary to the motions of the eye (page 124). This is true of all motions, whether by transfer of the point of sight or by rotation about the optic axes. Now, in the above experiment, the images of the two squares with all their lines seem to rotate about the point of sight outward-i. e., the right-hand square to the right, and the left-hand square to the left. At first sight this might seem to indicate a contrary rotation of the eyes, viz., inward. But not so; for, observe, the field of view of the right eye is the left or black square, and the field of view of the left eye is the right or white square. The right-eye field turns to the left, showing a rotation of the right eye to the right; while the left-eye field turns to the right, showing a rotation of the left eye to the left. Thus the two eyes in convergence rotate outward. This

R

is shown in the diagram Fig. 69, in which e c' is the experimental plane. The arrows show the direction of rotation of the images of the plane and of the eyes.

Experiment 2.-When one becomes accustomed to experiments of this kind, he can make them in many ways. I find the following one of the easiest and most convenient: Measure the exact height of the root of the nose upon the sash of the open window, and mark it. Stand with head erect about 3 or 4 feet from the window. Using the cross-bars of the sash-frame as hori