black lines, both vertical and horizontal, crossing one another at small angle, as if the images of both eyes had rotated on

Or

the visual line in opposite directions. This angle of crossing increases as the plane of the diagram is brought nearer and decreases as the diagram is carried farther from the eyes. these different angles of crossing may be obtained without moving the diagram or the head, by converging the eyes more and more and causing the white and black vertical lines to pass successively over each other. This is more easily done if there are several small circles on each half, similarly situated but at different distances from each other. In this diagram, the lines being of different colors do not stereoscopically combine easily-they do not cling together as in the other case. Their approach toward or recession from one another and the angle which they make with one another may be marked with the utmost exactness. Nor is there any danger of confounding the two images. For since the eyes are crossed we know that the white lines belong to the right eye and the black lines to the left eye, we can therefore determine the direction in which each image rotates. I find always that the black lines or the image of the left eye rotates to the right and the white lines or the image of the right eye rotates to the left Now as the image always moves in a direction contrary to the motion of the eye (differing in this respect from spectra), this indicates a rotation of both eyes on the optic axes outward

To test this question still farther I constructed another diagram with the horizontal lines continuous across but the verticals not perfectly vertical, the upper ends of those of the right half inclining to the left and those of the left half to the right

by about 1° 20' (fig. 7). On bringing the circles together I found that at a certain distance of the diagram-but only at a

certain distance depending upon the interval between the circles-the verticals coalesced perfectly; the horizontals, however, as might be expected, still crossed at a small angle, and in the same direction as before, viz: the whites or right eye image thus and the blacks or left eye image thus

indicating in this case also rotation of each eye outward. Beyond the proper distance the verticals approach but do not attain parallelism; within the proper distance they cross in a direction contrary to that in the diagram. When the circles are ten inches apart, the proper distance is nearly three feet and the image therefore about seven inches from the eyes.

Helmholtz has a diagram similar in all respects to my own except turned upside down, in which, he states, both verticals and horizontals coincide perfectly when the circles are combined. Our own figure (fig. 7) turned upside down will answer for Prof. Helmholtz's. We quote his own words: "The horizontal lines are parts of the same straight line; the vertical lines are not perfectly vertical. The upper end of those of the right figure are inclined to the right and those of the left figure to the left by about 1 degrees." But his experience differs from our own in a most unaccountable manner. He says: "Now combine the two sides stereoscopically, either by squinting or by a stereoscope, and you will see that the white lines of the one coincide with the black lines of the other, as soon as the centers of both figures coincide, although the vertical lines of the two figures are not parallel to each other." He accounts for this, not by rotation of the eyes but by the

principle of the difference between real and apparent verticality. The ignorance of this principle he believes has vitiated the results of all previous observers. He illustrates this principle thus: "When you draw on paper a horizontal line, and another line crossing it exactly at right angles, the right superior angle will appear to your right eye too great and to your left eye too small; the other angles show corresponding deviations. To have an apparently right angle, you must make the vertical line incline by an angle of about 1 degrees for it to appear really vertical. We must distinguish therefore between the really vertical lines and the apparently vertical lines in the field of view." "Now look alternately with the right and the left eye at these figures (fig. 7 turned upside down). You will find that the angles of the right figure appear to the right eye equal to right angles, and those of the left figure so appear to the left eye; but the angles of the left figure appear to the right eye to deviate much from a right angle, as also do those of the right figure to the left eye." Prof. Helmholtz therefore believes that the perfect stereoscopic coincidence of the vertical lines of his diagram is the result of this principle. "Therefore," he says, "not the really vertical meridians of the two fields correspond as has been hitherto supposed, but the apparently vertical meridians. On the contrary, the horizontal meridians really correspond at least for normal eyes which are not fatigued."

On this principle Prof. Helmholtz builds his whole theory of the Horopter. But that this principle cannot account for the phenomena he observes I think can be proved. In the first place, I find that if there be any distinction between real and apparent verticality for my eyes, the difference is too small to be detected by the simple observation of lines drawn at right angles with each other. For my own eyes really vertical lines are also apparently vertical, and lines inclined 1 from verticality are not at all apparently vertical. I have tried several other normal eyes with the same result. But leaving this aside: in the second place, it is by no means indifferent whether the two halves be combined by a "stereoscope or by squinting." If they are combined by a stereoscope as stereoscopes are usually constructed, the right half is looked at by the right eye and the left half by the left eye, so that the point of sight and the plane of combination is beyond the diagram; coincidence in this case, therefore, would be a true illustration of Prof. Helmholtz's principle. But if they are combined by squinting, the eyes are crossed, and therefore the right eye is looking at the left half and the left eye at the right half of the diagram, and therefore in Prof. Helmholtz's own

words, the verticals should "deviate much from a right angle," viz: 2 degrees. I have tried many eyes and I have yet found none in which the coincidence of the verticals of Prof. Helmholtz's diagram was perfect when combined by means of a stereoscope, i. e., beyond the diagram; but I have found one person to whom the coincidence seemed to be perfect when the combination was made by squinting.

It is evident, then, that Prof. Helmholtz's principle cannot explain the stereoscopic coincidence by squinting in his own experiment. I myself believe that if the coincidence takes place only by squinting (as in the case mentioned above), it can only be explained by rotation of the eyes inward. It is true that in this case the horizontals ought to cross also; but Prof. Helmholtz himself admits that such is sometimes the fact, but attributes it to fatigue. "After keeping the eyes," he says, "a long time looking at a near object, as in reading or writing, I have found that the horizontal lines crossed each other; but they became parallel again when I had looked for some time at a distant object."

On reading Prof. Helmholtz's lecture and finding his results so different from my own, I immediately tried his figure by squinting, but found the verticals cross one another at an inclination much greater than in the diagram itself, while the horizontals also crossed but at a less angle. On turning the figure upside down, however, the verticals coincided perfectly when the proper distance was obtained, though the horizontals crossed as before. All these phenomena are easily explained by rotation of the eyes outward. To test the question still more thoroughly, I then constructed other diagrams in which both verticals and horizontals were inclined so as to make an angle of 14 degrees with the true vertical and the true horizontal (fig. 8) and therefore perfect squares with one another. At the proper distance, when the small circles were brought together, the coincidence of both verticals and horizontals seemed to be perfect. When the plane of the diagram was too near or too far, all the lines crossed, in the one case in one direction and in the other case in the other direction. I then constructed still other diagrams, in which the inclination of the lines with the true vertical and the true horizontal were 40 minutes, 2 degrees and 5 degrees. In all cases I brought the lines in coincidence, but of course by different degrees of convergence. In the last the optic convergence necessary was extreme, and the strain on the eyes considerable; but in the other cases there was not the slightest difficulty or strain. Recollecting, however, that Prof. Helmholtz supposed that the change of position of the horizontals might be the result of

fatigue, I tried repeatedly after long rest but always the phenomena were precisely the same. In the diagram in which the

inclination of the lines was five degrees I observed, however, that a greater degree of convergence was necessary to bring the horizontals in coincidence than to bring the verticals into coincidence. The difference in the distance of the diagram in the two cases was about two inches and the difference in the distance of the point of sight was about one-half inch. I cannot explain this except by supposing that the form of the optic globe was changed by the excessive action of the muscles.

I can conceive of no possible source of fallacy in these experiments. From long practice they have become almost as easy to me as any ordinary act of vision. They do not now fatigue my eyes in the slightest degree. I see the lines of the two images, which I bring together just as plainly as if they were black and white threads. While watching them I control their motions almost as perfectly as if I was sliding with my hands two frames with white and black threads stretched across them. There is not the shadow of a doubt, therefore, that in my own case the eyes in convergence rotate slightly outward, and that the amount of rotation increases with the degree of convergence.

I next proceeded to determine the amount of rotation for different distances of the point of sight. In the diagram in which the inclination of the lines was 5 degrees, the distance of the image was only 2 to 24 inches; for the lines inclined 2 degrees, the distance of the image was 4 inches; for lines inclined 1 degrees, the distance was 7 inches; and for 40 minutes, the distance was about 12 to 14 inches. I am able, by great strain, to obliterate or nearly obliterate the common field of view of the two eyes. In this case of course the eyes