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case of convergence be regarded as abnormal? Or is there some useful purpose subserved by the rotation of the eyes on their optic axes? I feel quite sure that there is a useful purpose subserved; for there are special muscles adapted to produce this rotation, and the action of these muscles is consensual with the adjustments, axial and focal, and with the contraction of the pupil. This purpose I explain as follows:

A general view of objects in a wide field is a necessary condition of animal life in its higher phases; but an equal distinctness of all objects in this field would be fatal to that thoughtful attention which is necessary to the development of the higher faculties of the human mind. Therefore the human eye is so constructed and moved as to restrict as much as possible the conditions both of distinct vision and of single vision. Thus, as in monocular vision the more elaborate structure of the central spot restricts distinct vision to the visual line, and focal adjustment still further restricts it to a single point in that line, the point of sight, so also in binocular vision axial adjustment restricts single vision to the horopter, while rotation on the optic axes restricts the horopter to a single line.




FIG. 75.

In all that I have said thus far, I have made use of the ordinary mode of representing binocular visual phenomena. I have done so because I could thus make myself more easily understood. But it is evident on a little reflection that the usual diagrams do not in any case represent the real visual facts—i. e., the facts as they really seem to the binocular observer.

Thus, for example, if a, B, and c, Fig. 75, be three objects in the median plane, but at different distances, and the two eyes, R and L, be converged on B, as already explained, a and c will be both seen double the former heteronymously, the latter homonymously. It will be observed that in the diagram the double images of both a and care referred to the plane of sight P P. Now every one who has ever tried the experiment knows that the double images are not thus referred in natural vision ; but, on the con


trary, 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. 76–79, of which Fig. 76 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. 77, the same when the eyes are fixed on the farther end B; and Figs. 78 and 79, the visual results in the two cases respectively. Now it will be observed that in both these figures representing visual results (Figs. 78 and 79) 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 B L. But this is not true, for Figs. 76 and 77 show that it ought to make but half that angle. If

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these figures therefore truly represent the position of the double images (as indeed they do), then they do not represent the visual or apparent 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, so 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. I am 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

*“American Journal of Science,” Series III, vol. i, p. 83.

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