Experiment 4.-Now try the same experiment by the use of the board, and the true mode of representation becomes manifest. On the median line, Fig. 106, place three pins, and draw dotted lines to each of them from the position of the eyes, which shall be the visible representatives of either visual lines or ray-lines. As in the experiment the eyes will look at B, let the dotted lines to B be stronger to represent visual lines;

then the others will represent only ray-lines. Now when this diagram is observed with the point of sight at B, Fig. 106, then the visual result-i. e., what we actually see on the board-will be Fig. 107. It is seen that the whole diagram Fig. 106 is rotated in opposite directions about the point of sight B to make the result, Fig. 107. But the real nature of the rotation is shown by comparing the result with the eyes parallel, Fig. 108, with the result with the eyes converged on B, Fig. 107.

With the eyes parallel, the whole diagram is simply doubled heteronymously by each eye shifting it half an interocular space in opposite directions. Now conver

FIG. 109.

ging the eyes slowly, the two images of Fig. 106 shown in Fig. 108 are seen to rotate on E until the points bb' and the dotted lines b E, b' E unite to form B E, Fig. 107. In doing so, cc' have approached, but not united; they are therefore still heteronymous, while a a' have met and passed each other, and become homonymously double.

Therefore Fig. 107 truly represents all the visual facts. It gives both the parallactic position of the points in relation to the observer, their relative position in regard to each other, and their relative distance. Or, if we leave out in the original diagram, as complicating the figure, all except the necessary median line and pins, as in Fig. 109, then the visual result is given in Fig. 110. Or, adding in the visual result only the visual line and the most necessary ray-lines, viz., those going to the binocular eye, we have Fig. 111. This last figure we shall hereafter use to represent the phenomena. of binocular perspective.

Application to Stereoscopic Phenomena.-We wish now to apply this new method of representation to the phenomena of the stereoscope. We reproduce here as Fig. 112 the diagram used on page 131. It is seen that while the different distances, A and B, at which the

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

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

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.

FIG. 112.

This is represented in the accompanying diagrams, of which Fig. 113 represents the card when looked at, and Fig. 114 the visual result when the eyes are parallel. In this visual result cc is the right-eye image of the card, c'e' 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. 113, an interocular space apart, they will unite into a bin

By the law of alternation spoken of on page 93, sometimes the right eye will prevail, the right-hand transparent border will disappear, and the whole right-eye image c c will appear opaque. Then the left eye prevails, and the left-hand border will disappear, and the whole left-eye image c'c' will appear opaque. Sometimes both borders disappear, and only the binocular overlapping is seen. Sometimes the whole double image, including both borders, becomes opaque. But the true normal binocular appearance or visual result is given in Fig. 114—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. 115, 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, b 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 L become visual lines, and a a are united and seen at the point of sight A. When the eyes are directed to bb, then b R, b 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 bb when A is regarded, or of a a when B is regarded. The attempt to represent these would destroy the perspective.