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opposite directions, the right carrying it to the position 1 A E, the left eye to the position n' A E, shown by

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FIG. 115.

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the unprimed and the primed vinculum respectively. The real nature of the rotation, however, is shown by comparing the appearance of the drawing when the eyes are parallel with its appearance when the eyes are converged on A. Fig. 115 represents the visual result when the same drawing is viewed with the eyes parallel. By comparing this figure with the visual result when the eyes converge on A (Fig. 114), it is seen that the two images of the whole drawing rotate on the optic center of the binocular eye E, until the pins a a' and the visual



lines v v' of Fig. 115 unite to form the binocular image A and the binocular visual line V of Fig. 114. If the eyes be converged very gradually, the slow approach of the points a a', carrying with them the dotted lines vu', as if turning on the center of the binocular eye E, can be distinctly seen.

Experiment 3.—If we again erase the dotted representatives of the visual lines and draw them converging and crossing at the nearer pin B, as in Fig. 116, then

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Fig. 117 gives the visual result. It is as if the whole diagram, Fig. 116, had been rotated on the point of sight B in two directions, viz., a right-handed rotation by the right eye and a left-handed rotation by the left eye. But what actually takes place is seen by first gazing at a distant object and comparing the visual result thus obtained, shown in Fig. 118, with that obtained by converging the eyes on B, shown in Fig. 117. It is seon that the double images of the whole diagram turn

on the center Euntil 6 V', Fig. 113, unite to form B, Fig. 117, and v E, v' E to form V E; and of course the other

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lines, a a', vu', cross over and become homonymous. When the eyes converge as in this last experiment, the points R and L on the experimental board, Fig. 110, must be a little less than an interocular space apart.

Let us now return to the original experiment with three points or objects in the median line given on page 248. We reproduce here the figure (Fig. 119) usually used to illustrate the visual result. We have already shown how impossible it is to represent all the visual results in this way. If we are bent on representing the parallactic position of the double images, then we must refer them all to the same plane, as in Fig. 119; but this is false. If, on the other hand, we try to place them at the distances at which we actually see them, observing the law of direction, then the double images unite, which is also false.

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. 120, 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. 120, then the visual resulti. e., what we actually see on the board—will be Fig. 121. It is seen that the whole diagram Fig. 120 is rotated in opposite directions about the point of sight B to make the result, Fig. 121. But the real nature of the rotation is shown by comparing the result with the eyes parallel, Fig. 122, with the result with the eyes "converged on B, Fig. 121.

Fig. 122.

With the eyes parallel, the whole diagram is simply doubled heteronymously by each eye shifting it half an interocular space in opposite directions. Now converging the eyes slowly, the two images of Fig. 120 shown in Fig. 122 are seen to rotaže on E until the points b b' and the dotted lines 7 E,W E unite to form B E, Fig. 121. 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. 121 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. 123, then the visual result is given in Fig. 124. 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. 125. This last figure we shall hereafter use tɔ 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. 126 the diagram used on page 150. It is seen that while the different distances, A and B, at which the

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