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of the lines connected by the primed vinculum. By this means the two visual lines vv are brought together and combined as the common visual line V, and two of the images of the objects b b are brought together and superposed at B; the median line is doubled and ro

FIG. 127.

FIG. 128.


tated heteronymously to the positions m m', carrying with them the double images of the median object A as a a'. The above diagram correctly represents the position and the distance of the double images a a', and the position of the combined image B, but can not represent the distance of the combined image, because there is no point of sight. For the point of sight is really the point of optic convergence or meeting of visual lines; in diagrams representing visual results, it is the point of crossing of the doubled median lines ; but this point, by both definitions, would be in this case behind the head. The diagram therefore correctly represents all the visual facts; for, there being in divergence

no point of sight, the distance of objects in the visual line is indeterminate as represented. It is impossible by the usual method to correctly represent any of the visual facts.

3. If the Law of Direction be opposed to the Law of Corresponding Points, the Latter will prevail.—These two most fundamental laws of vision are sometimes in discordance with each other. The reason of this may be thus explained: The law of direction is the fundamental law of monocular vision, as the law of corresponding points is of binocular vision. Now, for each eye, and therefore for the monocular observer, direction is determined by reference to the optic axis, but for the binocular observer by reference to the median line. On account of this difference of line of reference, while objects seen single are seen in their true positions, double images are always seen in positions different, and in some cases widely different, from the object which they represent. The difference may even amount to 45°. For example: The binocular field of view in my own case is 100° in a horizontal direction. By strong convergence I can nearly bring the double images of the root of my nose together, and thus obliterate the common field. I am sure therefore that I can make the optic axes of my two eyes cross each other at right angles. In such a case, of course, objects directly in front are doubled and their images separated 90° from each other, while objects lying to the right and left 90° from each other are brought to the front and their images superposed. Here the images are 45° from the true position of the objects which they represent. Thus, Fig. 129 represents the actual relation of things in this case, and Fig. 130 the visual result, showing that the positions of the objects M and a a are com

pletely reversed. It may indeed be said that the case of a a seen in front may be reconciled with the law of direction. For, if the combined images be referred to

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the point of optic convergence A, as indeed they often are, then each eye sees its own object in its true direction, but only mistakes its distance. To this I would

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answer that each eye does indeed give the true direction, as is quickly shown by shutting one of them, but the two eyes together do not. Each sees its own object in

the true direction, but the binocular observer sees their combination in a wrong direction. In the case of the double images m and m' of the object M, it is still more difficult to explain their apparent position by the law of direction.

A curious Corollary. It is seen that, under all circumstances, whatever be the position of the optic axes, objects in the visual lines are moved to the front and seen there. Now the same would be true if our eyes were turned directly outward right and left. There can be no doubt that if we could turn our eyes directly outward, or if our eyes, retaining their present organization and properties in regard to corresponding points, were transferred to the sides of the head with their axes straight right and left-i. e., making an angle of 180° with each other-images of objects in the direction of these axes, and therefore directly right and left, would be moved round 90° each, and combined and seen di

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rectly in front. This seems an extraordinary result, but it is a necessary consequence of the law of corresponding points. The retinal images of the two objects are on corresponding points, viz., on the central spots;

therefore, by the law of corresponding points, they must be seen as one. But where else can this take place but in front? The accompanying figures are a diagrammatic representation of these facts, Fig. 131 being the supposed condition of things, and Fig. 132 the visual result. After the frequent explanations of similar figures, a bare inspection will be sufficient.

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