vexed questions of binocular vision. Now while I believe the evidence is overwhelmingly in favor of the nativistic theory, i. e., the congenital existence of corresponding points, yet I feel perfectly confident that the existence of M. Pictet's images of illusion, from their very nature, cannot be proved; and that all the phenomena which he adduces as proof may be easily explained by the known laws of binocular vision. Passing over. therefore, the many interesting questions touched upon in M. Pictet's very suggestive paper, I will confine myself wholly to M. Pictet's illusive images; my sole object being to rescue the theory of binocular vision from the confusion into which it has been thrown by the introduction of this new idea.

M.

In order to account for single vision with two eyes, Muller supposed that the nerve fibers which terminate peripherally in identical points of the retina (corresponding fibers) are centrally fused into one fiber, or terminate centrally in one brain cell. Pictet admits that the nativistic theory is by no means depend ent on this assumption-the existence of corresponding or identical points as a congenital fact, by whatsoever structural contrivance effected, being all that is contemplated by this theoryyet all his reasonings are based upon, and all his experiments are intended to prove, an alliance between corresponding fibers equivalent to the fusion of Müller. For M. Pictet, corresponding fibers under all conceivable circumstances behave like, and therefore are substantially, a single bifurcating fiber. Assuming, then, an anatomical structure equivalent to fusion of corresponding fibers into one in the brain, M. Pictet proceeds to show that, by the well-known physiological law which refers all impressions on the nerve centers to the peripheral extremities of the nerve fibers, an impression made upon any point of one retina, being carried to the brain, would thence be necessarily referred back to both extremities of the bifurcating fiber, i. e., to corresponding points of both retina. Therefore, if luminous rays from an object impress the retina of one eye, the impression transmitted to the brain must be referred back equally to both eyes, producing two identical external images in the field of view; the one a true image produced by the luminous impression on the retina of one eye, the other an "image of illusion"-a subjective or spectral image reflected from the point of alliance within the brain to the retina of the other eye. According to M. Pictet, therefore, even when we shut one eye we still, in a certain sense, see objects with both eyes; for there is a true image belonging to the open eye and an illusive image to the closed eye. These two images are identical and seen at the same place. Stereoscopic effects are not observable in monocular vision only because these two images are perfectly identical and perfectly united.

It is easy to see, from the perfect identity and the inseparable union of the true and illusive images, how difficult, nay, even impossible and therefore futile, to attempt to prove the existence of the latter. Nevertheless, M. Pictet details several experiments which, he thinks, prove beyond doubt the existence of such illusive images in every act of vision. I wish to show that the phenomena of M. Pictet's experiments may be explained without resorting to illusive images. Before doing so, however, I find it necessary to state very concisely certain general principles of binocular vision which I shall use in their explanation, referring the reader to my previous papers for a fuller statement and proof. Throughout this paper I shall refer back to these principles by means of the numerals affixed.

1. The impressions produced by luminous retinal images are transmitted to the brain and, by a psychological law, are projected outward into the external world and seen there as external images. Each eye has its own field of view crowded with its own images. As these images are usually seen double, it will often be convenient to regard them not as objects but as external images, the signs of objects. Only when the two images formed by the same object are superposed do we see the object single and in its true position. This takes place when the luminous images fall on corresponding points. The two retinal images on corresponding points are seen externally as a single image or object. It is true this may be regarded as really a single image -the sign of the fusion of the nerve fibers. But since we can move about the two images of the same object, bring them near together, unite them partly or unite them wholly, as we please; and since, moreover, we can even take images of different objects and superpose them, and if they be similar, unite them so as to appear as one object, it is better, because it more easily explains visual phenomena, to regard single binocular vision as the result of the superposition of two images.

12. In binocular vision with the optic axis parallel, as in gazing at a distant object, the whole field of view and all objects in the field, including the visible parts of the face, are shifted by the right eye a half interocular space to the left, and by the left eye the same distance to the right, without altering the relative position of parts; so that the two eyes and their visual lines seem to unite to form a single binocular eye, and a single middle visual line along which the eye seems to look. Any line, rod or plane in the median line, as also the nose itself, is doubled heteronymously, and becomes two lines, rods or planes, parallel to each other, and separated by a space exactly equal to the interocular space. Between the two noses and between the two parallel lines, rods or planes, the combined eyes seem to look out along the combined visual lines upon the distant object.

Of course, by this shifting of the two fields all objects are similarly doubled.

Thus in binocular vision the two eyes seem actually to be superposed and corresponding points to coincide. This apparent combination of the eyes and their visual lines is the necessary result of the existence of corresponding points. Images on corresponding points are seen single; all objects in the two visual lines must impress corresponding points; therefore the visual lines themselves, if they were visible lines, would be seen single. This can take place only by combining to form a single middle visual line.

3. In turning the eyes in any direction without altering their convergence objects seem stationary, and the visual lines seem to move and sweep over them. But when we turn the two eyes in opposite directions, as in strong convergence, then the visual lines seem stationary (i. e., we seem to look in the same direction). and all objects or rather images seem to move in a direction contrary to the actual motion of the eye; the whole field of view of each eye with all its images rotates about the optic center in a direction contrary to the rotation of the eye. This is plainly seen by voluntarily and strongly converging the eyes upon an imaginary point near at hand, and at the same time watching the movements of the more distant images. The whole field of view of the right eye with all its images will be seen to rotate to the right and of the left eye to the left, i. e., homonymously. The images of all objects as they are swept successively by the visual lines of the two eyes are brought successively in front and superposed. If we could turn our eyes outward, the fields and their images would move heteronymously. This is seen to a limited extent in the act of falling to sleep.* Even with the two eyes turned outward, therefore, the two visual lines are united in front, and objects on the visual lines are brought in front and superposed. This is the necessary result of the properties of corresponding points; but I have also proved it by observations made upon persons whose eyes in a perfectly pas sive state turned slightly outward.*

Thus, there are two apparent movements of the visual fields accomplished by the eyes in binocular vision: 1st, a shifting of each field heteronymously a half interocular space; this is invol untary and habitual, and would of itself double all objects heteronymously; 2d, in ocular convergence, a rotation of each field about the optic center homonymously. The necessary consequences of these movements are: (a) that the two images of an object at the point of sight are superposed and the object is seen single; objects on this side the point of sight are doubled heteronymously, while objects beyond the point of sight are doubled

*The proof of this statement I hope to give shortly in a separate article.

homonymously; (b) that all objects (different objects) lying in the visual lines, whether on this side or beyond the point of sight, have two of their images (one of each) superposed; so that the two visual lines under all circumstances are combined to form a binocular visual line passing from the combined eyes, through the point of sight, and onward to infinite distance.

Let us now, in the light of these facts, examine M. Pictet's experiments. I will pass over for the present what he seems to regard as his crucial experiments, and take up first the general phenomena of double images, as a proper understanding of the nature of these will make all that follows clear.

If we hold up a finger before the eyes, and gaze at the wall on the opposite side of the room, two heteronymous images of the finger will be seen separated by a space nearly equal to the interocular space. As a question of geometry this is sufficiently explained by the different parallactic position of the finger as seen by the two eyes; as a question of binocular vision, by the shifting of the fields of view of the two eyes heteronymously as already explained (2).

But the images are transparent. M. Pictet lays much stress on this. It is, he says, "an essential point which we have not found in works on optical physiology" (p. 105). He explains it as follows: There is a part of the wall which sends no luminous rays to the right eye (viz: that covered by the righteye image); but this part impresses the left eye, and this impression is propagated to the right eye, and perceived by it at the same place as an illusive image. The finger, therefore, will appear transparent to the right eye because by means of an illusive image the wall is seen behind it. The same explanation of course applies to the left-eye image of the finger, which is transparent, according to M. Pictet, because the left eye sees the wall behind it by means of an illusive image propagated from the right eye. Now our explanation is entirely different; and we cannot but think that the transparency of double images have been so little noticed by writers only because their explanation seemed so obvious. Our explanation is as follows: We see every part of the wall because no part is concealed from both eyes. The images must seem transparent since they conceal nothing from the observer. M. Pictet would say the righteye image conceals nothing from the right eye, and the left-eye image nothing from the left eye, and therefore the parts covered by these images must be seen, by the corresponding eye, by means of illusive images; but we say, a part of the wall is concealed from the right eye (viz: that upon which the right-eye image falls), but this part is visible to the left eye; similarly, a part of the wall is concealed from the left eye, but this part is visible to the right. M. Pictet says, every part of the wall is

seen by each eye, either by true or by illusive images; we say, every part of the wall is seen, not by each eye, but by the binocular observer; not some parts by true and some by illusive images, but only by true images.

If instead of a finger we use a screen several inches wide (wider than the interocular space), then the double images will not entirely separate. They will slide over each other heteronymously through a space equal to the interocular space (2) The overlapping area will be opaque because it covers a portion of the wall concealed from both eyes; the rest will be transpar

1.

ent. The visual result is represented by fig. 1, in which SS is the right-eye image of the screen. S'S' the left-eye image, and S'S the overlapping area. These facts are more completely represented by my method in figs. 2 and 3, of which fig. 2 represents

the actual relation of parts, and fig. 3 the visual result. In fig. 2, R and L are the right and left eye respectively, n the nose,

m the median line, vv the visual lines, SS the screen. Fig. 3 will readily explain itself if the reader will call to mind that in all my figures representing visual results capitals represent combined images, small italics right-eye images, and dashed italics left-eye images. If now the optic axes be gradually converged, as already explained (3), these heteronymous images will slide over each other homonymously, making the opaque area larger and larger, and the transparent margins smaller and