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erty. Third, we treated of the still more wonderful correspondence of the two retince point for point, and of their spatial representatives point for point; and considered how by ocular motion the two images of the same object are made to fall on corresponding points of the two retinæ, and their spatial representatives are thereby made to coincide and become one; and how, finally, all the phenomena of binocular vision flow from this property.

We have therefore apparently covered the ground originally laid out. But there are still a number of questions on binocular vision, somewhat more abstruse and more disputed than the preceding, but of go high interest that they must not be wholly neglected. The remaining chapters will be devoted to these.

The conclusions reached on these points are almost wholly the result of my own investigations. They sometimes agree with those of other investigators and sometimes do not. They therefore rest on no higher authority than their own reasonableness. I bring them forward as an original contribution to the science of binocular vision, and invite the thoughtful reader to repeat the experiments and to verify or disprove the conclusions.

PART III.

ON SOME DISPUTED POINTS IN

BINOCULAR VISION.

CHAPTER I.

LAWS OF OCULAR MOTION.

SECTION 1.-LAWS OF PARALLEL MOTION.-LISTING'S LAW.

We have already (page 63) spoken of spectral images produced by strong impressions on the retina. It is evident that these, being the result of impressions branded upon the retina and remaining there for some time, must while they remain follow all the motions of the

eye with the greatest exactness. They are specially adapted, therefore, for detecting motions of the eyes, such as slight torsions or rotations on the optic axes, which could not be detected in any other way.

Experiment 1.Let the experimental room be darkened by closing the shutters, but allow light to enter through a vertical slit between the shutters of one window. Standing before the window with head erect, gaze steadily at the slit until a strong impression is branded in upon the vertical meridian of the retina. If we now turn about to the blank wall, we see a very distinct colored vertical spectral image of the slit. Placing now the eyes in the primary position—i. e., with face perpendicular and eyes looking horizontally -if, without changing the position of the head, we turn the eyes to the right or left horizontally, the image remains vertical. Also if we turn the eyes upward or downward by elevating or depressing the visual plane, the image remains vertical. But if, with the visual plane elevated extremely, say 40°, we cause the eyes to travel to the right or left, say also 40°, or if we turn the eyes from their original primary position obliquely upward and to one side to the same point, the image is no longer vertical, but leans decidedly to the same side; i. e., in going to the right, the image leans to the right, thus- ; in going to the left, it leans to the

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left, thus- If, on the contrary, the visual plane be depressed, then motion of the eyes to the right causes the image to lean to the left, thus- ; while motion

to the left causes it to lean to the right, thus- /.

Experiment 2.—If, instead of a vertical, we use a horizontal slit in the window, and thus obtain a horizontal image and throw it on the wall as before, then, if the image has been made with the eyes in the primary position, it will be seen on the wall perfectly horizontal. Furthermore, if the eyes travel right and left in the primary visual plane, or upward and downward by elevating or depressing the visual plane, the image retains its perfect horizontality. But if, with the visual plane elevated, we cause the point of sight

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to travel to the one side or the other, the image is seen to turn to the opposite side; i. e., when the eyes turn to the right, the image turns to the left, thus ; when they turn to the left, the image rotates to the right, thus

If the visual plane be depressed, then motion to the right causes the image to rotate to the right,

and motion to the left causes it to rotate to the left,

These rotations of the image depend wholly on the oblique position of the eyes, and it makes no difference how that oblique position is reached—whether by motion along rectangular coördinates, as in the experiments, or by oblique motion from the primary position. Furthermore, the amount of rotation of the image increases with the amount of elevation or depression of the visual plane, and the amount of lateral motion of the eyes.

Experiment 3.—The fact of rotation or torsion of the images, and the direction of that torsion, are easily determined by the somewhat rough methods detailed above; but if we desire to measure the amount of torsion, the wall or other experimental plane must be covered with rectangular coördinates, vertical and horizontal. By experimenting in this way, I find that for extreme oblique positions the torsion of the vertical image on the vertical lines of the experimental plane is about 15°, but the torsion of the horizontal image on the horizontal lines is only about 5o. The reason of this difference will be explained farther on.

Putting now all these results together, the following diagram (Fig. 62) gives the position of the vertical and horizontal images when projected on a vertical plane for all positions of the point of sight. Simple inspection of the diagram is sufficient to show that the inclination or torsion of the vertical image on the true verticals, and that of the horizontal image on the true horizontals, are in opposite directions. If torsion

FIG. 62.

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DIAGRAM SHOWING THE INCLINATION OF VERTICAL AND HORIZONTAL IMAGES

FOR ALL POSITIONS OF THE POINT OF SIGHT, WHEN PROJECTED ON VERTI-
CAL PLANE.

of the images show torsion of the eye, there must be a fallacy somewhere. The one or the other must be wrong; for when one indicates torsion to the right, the other indicates torsion to the left, and vice versa. To show this contradictory testimony more clearly, and thus to prove that there is a fallacy here, we make another experiment.

Experiment 4.—Make a rectangular cross-slit in the window, gaze steadily upon it until the spectral impres

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