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foreground and background are seen, are truly représented, no attempt is made to represent the double images of the foreground when the background is re. girded, or vice versa. It is impossible by this usual inethod to represent these double images without refer

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ring them to the same plane; but this would of course destroy the perspective, which it is the very object of the diagram to illustrate. The new method, on- the contrary, represents the true distance of the point of sight, and the true positions and distances of the double images, and therefore the true binocular perspective. In other words, it represents truly all the binocular visual phenomena. It will be best to preface this explanation by an additional experiment.

Experiment.If a rectangular card, like an ordinary stereoscopic card, or a letter envelope, be held before the face at any convenient distance while the eyes gaze on vacancy, i. e., with the optic axes parallel, the two

Fig. 126.

images of the card will be seen to slide over each other heteronymously, each a distance equal to a half interocular space, and therefore relatively to each other exactly an interocular space. If the card be longer than an interocular space, there will be a part where the two images will overlap.

This is represented in the accompanying diagrams, of which Fig. 127 represents the card when looked at, and Fig. 128 the visual result when the eyes are parallel. In this visual result c c is the right-eye im:ge of the card, c' d' the left-eye image, and dd the binocular overlapping. This overlapped part will be opaque, because nothing can be seen behind it by either eye. But right and left of this are two transparent spaces. That on the left belongs to the image of the right eye, but not to that of the left, and therefore the left eye sees objects beyond it. That on the right belongs to the left eye, but the right eye sees objects beyond it.

If two circles, a a, be drawn on the card, Fig. 127, an interocular space apart, they will unite into a lin

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ocular circle A in the center of the opaque part, Fig. 128, while two monocular circles a a' will occupy the transparent borders.

By the law of alternation spoken of on page 108, sometimes the right eye will prevail, the right-hand transparent border will disappear, and the whole righteye image cc will appear opaque. Then the left eye prevails, and the left-hand border will disappear, and the whole left-eye image c' d' will appear opaque. Sometimes both borders disappear, and only the binocular overlapping is seen. Sometimes the whole double image, including both borders, becomes opaqne. But the true normal binocular appearance or visual result is given in Fig. 128—i. e., opaque center and transparent borders, these borders being exactly equal to the interocular space.

We are now prepared to show how stereoscopic phenomena may be represented by our new method. In Fig. 129, c c represents a stereoscopic card in position; m s, the median screen, which cuts off the supernumerary monocular images; a a, identical points in the foreground of the pictures, and bb, in the background. The two eyes and the nose are represented as before by R, L, and n; and a R, a L, b R, L are ray-lines. Leaving out the dotted lines beyond the card, this diagram represents the actual condition of things. The dotted lines beyond the picture show the mode of representation usually adopted.

When the eyes are directed to a a, then a R, a I become visual lines, and a a are united and seen at the point of sight A. When the eyes are directed to b b, then b R, 6 L become visual lines, and b and b are united and seen single at the point of sight B.

The defect of this mode of representation is, that it takes no cognizance of the double images of b b when A is regarded, or of a a when B is regarded. The attempt to represent these would destroy the perspective.


By our new method, on the contrary, all the phenomena are represented. In Fig. 130 is shown the visual result when the eyes are fixed on the background; in Fig. 131, the visual result when the eyes are fixed

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on the foreground. In Fig. 130 we see that the nose n n' and the median screen ms m's are doubled heteronymously, and the space between the two is the common and only field of view (for the monocular fields are cut off by the screen). In the middle between these is the binocular eye E, looking straight forward. This is manifestly exactly what we see in the stereoscope. Again, we see that the two images of the card bare slidden over each other, in such wise that bb, Fig. 129, are brought together in the middle, united, and seen single in Fig. 130. But where? at what distance ? Evidently this can only be at the point of sight, which, as I have already explained, is, in diagrammatic representations of visual phenomena, where the common visual line and the two median lines meet one another at the point B, Fig. 130. Meanwhile a a, Fig. 129, will have crossed over and become heteronymous, and their double images a a', Fig. 130, will be seen just where their ray-lines E a and E a' cut the median planes, viz., at a a'. In Fig. 131, which is the visual result when the eyes are fixed on the foreground, the shifting or sliding of the two images of the card is not quite eo great as before. It is only enough to bring together the nearer points a a, Fig. 129, but not bb. These latter, therefore, are homonymously double. The united images of a a are seen single on the common visual line, and at the distance A where the double images of the median line cross each other; while b b are seen homonymously double, and at b b', the intersection of their ray-lines with the continuation of the median lines after crossing ; for homonymous images are always referred beyond the point of sight.

The mode of representing combinations with the naked eyes by squinting is similar. Of course the place of the combined picture will in this case be between the eyes and the card. I reproduce (Fig. 132), for the sake of comparison, the usual mode of representation from page 153. In order to make the perspective nat

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