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board to fit over the bridge of the nose. Such a board is admirably fitted for all experiments on binocular perspective.

Experiment 1.-Draw a line through the middle of the board from the notch n, Fig. 96. This will be the visible representative of the median line; and as the median line is used in all the experiments, this may be made permanent. On this line place two pins at A and B. Draw also from the points L and R dotted lines

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parallel to the median line and to each other, as the visible representatives of the visual lines when the optic axes are parallel, as when looking at a distant object. Now fit the plane over the bridge of the nose, and place it in a horizontal position a little below the primary plane of vision, say half an inch or an inch, so that the whole surface is distinctly seen, and then look

beyond at a distant object. Leaving out the board in the representations, the actual position of the lines is shown in Fig. 97 and the visual result in Fig. 98. Remembering that in all our figures capitals represent combined or binocular images, simple italics right-eye images, and primed italics left-eye images, it will be seen that the whole board, with all the lines and objects on it and the parts of the face, has been shifted left and right by the two eyes, so that the nose and the median line are seen as two noses and two parallel lines with their pins, separated by a space exactly equal to the interocular space, and the two visual lines are brought together and united in the middle to form a common visual line V, as if coming from a single binocular

eye E. If two small circles be drawn or a pin be set at the end of the dotted visual lines in Fig. 97; these will be united in the result Fig. 98, at the end of the combined visual line V. There will also of course be seen to the extreme right and left monocular images of the dotted representatives of the visual lines, and of the circles or pins at their farther end. I have connected by vincula the images of the whole drawing, the primed vinculum being the image of the left eye, the other of the right.

Experiment 2.-If we now erase the parallel visual lines vv on the board, and draw them convergent on the pin A, so that Fig. 99 shall represent the actual condition, and then adjust the board again to the nose and look at the pin A, the visual result, or what we shall see, is given in Fig. 100. By comparing this result with the actual condition of things—i. e., by comparing Fig. 100 with Fig. 99-it would seem as if the whole drawing on the board, inclụding the eyes and nose, had been turned about the point of sight A by the two eyes in

opposite directions, the right carrying it to the position LA E, the left eye to the position r' A E, shown by the unprimed and the primed vinculum respectively.

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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. 101 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. 100), 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 vl of Fig. 101 unite to form the binocular image A and the binocular visual line V of Fig. 100. If the eyes be converged very gradually, the slow approach of the points a a', carrying with them the dotted lines v v', as if turning on the center of the binocular eye E, can be distinctly seen.

FIG. 101.

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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. 102, then Fig. 103 gives the visual result. It is as if the whole diagram, Fig. 102, 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. 104, with that obtained by converging the eyes on B, shown in Fig. 103. It is seen that the donble images of the whole diagram turn on the center E until 6 b', Fig. 104, unite to form B, Fig. 103, and v E, v' E to form VE; and of course the other lines, a a', vv', cross over and become homonymous. When the eyes converge as in this last experiment, the points R and L on the experimental board, Fig. 96, 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 213. We reproduce here the figure (Fig. 105) 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. 105; but this is false. If, on the other hand, we try to place

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them at the distances at which we actually see them, observing the law of direction, then the double images unite, which is also false.

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