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vision; but, on the contrary, they are seen at their real distance, though not in their natural position. Indeed, it is only by virtue of this fact that we have perception of binocular perspective. The diagram therefore, although it truly represents the parallactic position of the double images, does not represent truly their apparent distance. If, on the other hand, we attempt in the diagram to refer the double images to their real distance (observing the law of direction), then they unite and form one, which is equally untrue. Thus, if we represent truly the visual position, we misrepresent the visual distance; if, on the contrary, we try to represent the visual distance, we misrepresent the visual position. It is evident therefore that the usual diagrams, while they represent truly many important visual phenomena, wholly fail to represent truly many others, especially the facts of binocular perspective.
The falseness of the usual mode of representation becomes much more conspicuous if, instead of two or more objects, we substitute a continuous rod or line. In this case the absurdity of projecting the double images on the plane of sight is so evident that it is never attempted. The mode universally used for representing the visual result when a rod is placed in the median plane is shown in Figs. 90–93, of which Fig. 90 represents the actual position of the rod in the median plane, and the actual position of the visual lines when the eyes are fixed on the nearer end A; Fig. 91, the same when the eyes are fixed on the farther end B; and Figs. 92 and 93, the visual results in the two cases respectively. Now it will be observed that in both these figures representing visual results (Figs. 92 and 93) the image of the rod belonging to each eye is coincident with the visual line of the other eye, and therefore makes an angle with its own visual line equal to the visual angle R A L, R BL. But this is not true; for Figs. 90 and 91 show that it ought to make but half
that angle. If these figures therefore truly represent the position of the double images (as indeed they do), then they do not truly represent the position of the visual lines. The truth is, in natural vision the visual
lines are shifted, as well as the images of all objects not situated at the point of sight, and to the same degree, 80 that the position of such objects relative to the visual lines is perfectly maintained in the visual result.
It is evident then that figures constructed on the usual plan, while they give correctly the place and distance of objects seen single, fail utterly to give the place of double images. They are well adapted to express binocular combination of similar objects or similar figures on the plane of sight, but are wholly inadequate to the expression of the facts of binocular perspective, whether in natural objects or scenes or in stereoscopic pictures.
In an article published in January, 1871,* I proposed, therefore, a new and I am convinced a far truer mode of diagrammatic representation of the phenomena of binocular vision, applicable alike to all cases. satisfied that if this method had always been used, much of the confusion and many of the mistakes to be found in the writings on binocular vision would have been avoided. But it is evident that such a new and truer method must be founded upon some fundamental binocular phenomena usually overlooked. I must first therefore enforce these. They may be compendiously stated in the form of two fundamental laws. It will be best, however, before formulating them, to give some familiar experiments, and then to give the laws as an induction from the facts thus brought out.
Experiment 1.—If a single object, as for example a finger, be held before the eyes in the median plane, and the eyes be directed to a distant point so that their axes are parallel, the object will of course be seen double, the heteronymous images being separated from each other by a space exactly equal to the interocular space. Now, the nose is no excception to this law. The nose is always seen double and bounding the common field of view on either side.
* "American Journal of Science," Series III, vol. I, p. 33.
Experiment 2.-If two similar objects be placed before the eyes in the horizontal plane of sight, and separated by a space exactly equal to the interocular space, and the eyes be directed to a distant point so that their axes are parallel and the two visual lines shall pass through the two objects, then both objects will be doubled, the double images of each being separated by an interocular space; and therefore two of the four images-viz., the right-eye image of the right object, and the left-eye image of the left object—will combine to form a single binocular image in the middle; while the right-eye image of the left object will be seen to the left, and the left-eye image of the right object to the right. Thus there will be three images seen—a middle binocular image, and two monocular images, one on each side, that on the right side belonging to the left eye alone, and that on the left to the right eye alone. Now, the eyes themselves are no exception to this law. In binocular vision the eyes themselves seem each to double—two of the images combining to form a binocular eye in the middle (wil cyclopienne), while the other two are beyond the two images of the nose on either side, and therefore hidden from view. Each eye seems to itself to occupy a central position, while it sees (or would see if the nose were not in the way) its fellow on the other side of the double images of the nose.
In other words, in binocular vision, when the optic axes are parallel, as in gazing on a distant object, the whole field of view, with all its objects, including the parts of the face, is shifted by the right eye a half interocular spare to the left, and by the left eye a half interocular space to the right, without altering the relative position of parts. It is evident that, by this shifting in opposite directions, the two eyes with their visual lines are brought together in perfect coincidence, so that corresponding points in the two retina seem to be perfectly united.
The facts as thus far stated—both the actual condition of things as we know them, and the visual results as they seem to the binocular observer—are represented in the following diagrams. Fig. 94 shows the actual condition of things, and Fig. 95 the visual result, in the first experiment; Fig. 96 the actual condition of things, and Fig. 97 the binocular visual result, in the second experiment. To explain further : In Fig. 94, R and L are the right and left eyes ; N, the nose; A, the object