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background B to foreground A, and we acquire a distinct perception of depth of space between these two points.

But, for those at all practiced in binocular experiments, by far the most perfect naked-eye combination is obtained by crossing the eyes ; i. e., by combining on the nearer instead of the farther side of the pictures. For this purpose, however, it is necessary that the mounting be reversed ; i. e., the right-hand picture must be put on the left side, and the left-hand picture on the right side of the card. By this reversal it is evident that identical points in the background of the two pictures are nearer together than identical points in the foreground.

If, now, holding such a card before us at any convenient distance, say 18 inches or 2 feet, we converge the optic axes so that the right eye shall look across directly toward the left picture, and the left eye

toward the right picture, then the two pictures will unite at the point of crossing of the optic axes (point of sight), and will be seen there in exquisite miniature, but with perfect perspective. The effect is really marvelously beautiful. For persons of slightly presbyopic eyes there will be no difficulty in getting the combined image perfectly clear. In normal eyes, as already explained (page 117), there must be dissociation between the axial and focal adjustments before the combined image is perfectly clear. For those who can not make this dissociation it may be necessary to use very slightly concave glasses. Again, if the observer is annoyed by the existence of the monocular uncombined images to the right and left, it will be best to use two side screens, as already explained (page 114), instead of the median screen used in combining beyond the plane of the picture.

Experiment.—I draw (Fig. 47) two projections of a skeleton truncated cone precisely like those represented on page 129, but reversed. It is seen, for example, that the centers of the small circles are in this case farther

Fig. 47.

apart than the centers of the large circles. If, now, holding these about 18 inches distant, I combine them by crossing the optic axes, the impression of a skeleton truncated cone with the smaller end toward me is as complete as possible. The singleness of the impression at first seems perfect, but by observing attentively the lines a and a' it will be seen that they unite only in points and not throughout—that they come together as a v, thus—V, or an inverted v—1, or an x-X, according to the distance of the point of sight. In other words, when by greater convergence the small circle is single, the larger circle is double; and when by less convergence the larger circle is single, then the smaller circle is double. And thus the eyes run the point of sight back and forth, uniting first the one and then the other, and in this way acquire a clear conception of depth of space between the smaller and larger circles.

These facts are illustrated by the diagram Fig. 48, in which, as before, R and L are the two eyes; n, the root of nose; P P, the plane of the pictures ; a and a', identical points of the foreground, and b and b' of the background; and scand sc', the two side-screens to cut off

monocular images. When Fig. 48.

the eyes are directed toward a and a', these unite and are seen at the point of sight as a single object A. When the eyes by less convergence are directed to b and ', then these are seen

single at the point of sight SSC

B. The point of sight runs X- A

back and forth from A to

B, and we thus acquire distinct perception of depth of space between.

Of course, any stereoscopic pictures may be combined in this way if we re

verse the mounting; and I am quite sure that any one who will try it will be delighted with the beautiful miniature effect and the perfection of the perspective.

Combination by the Use of the Stereoscope. The stereoscope is an instrument for facilitating binocular combinations beyond the plane of the pictures. By means of lenses also it supplements the lenses of the eyes, and thus makes on the retinæ perfect images of a near object, although the eyes are looking at a distant object, and are therefore unadjusted for a near one. The lenses also enlarge the images, acting like a perspective glass, and thus complete the illusion of a natural scene or object.

It is difficult to convince many persons that there is in the stereoscope any doubling of points in the foreground when the background is regarded, and vice versa. But such is really always the fact; and if we do not observe it, it is because we have not carefully analyzed our visual impressions. It is best observed in skeleton diagrams of geometrical figures, such as are commonly used to explain the principles of stereoscopy. In ordinary stereoscopic pictures it is also easily observed in those cases where points in the extreme foreground and background are in the same range; as, for example, when a column far in front is projected against a building. In such a case, when we look at the building the column is distinctly double, and vice versa. For myself, I never look at a stereoscopic card, whether in a sterescope or by naked-eye combination, without distinctly observing this doubling. For example: I now combine in a stereoscope the stereoscopic pictures of a skeleton polyhedron. The illusion of a polyhedral space inclosed by white lines is perfect. Now, when I look at the farther inclosing lines I see the nearer ones double, and vice versa. Moreover, I perceive that this doubling is absolutely necessary to the stereoscopic effect, for it is exactly like what would take place if I were looking at an actual skeleton polyhedron.


Inverse Perspective. I have heard a few persons declare that they saw no superiority of a stereoscope over an ordinary enlarging or perspective glass; that they saw just as well while looking through the stereoscope if they shut one eye as with both eyes open. Such persons evidently do not combine properly the two pictures, and they lose a real enjoyment. That the binocular is a real perspective, entirely different from other kinds, may be clearly demonstrated by the phenomena of inverse perspective now about to be described.

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If stereoscopic diagrams suitably mounted for viewing in a stereoscope be combined with the naked eye by squinting (crossing the optic axes), as in Fig. 48 (page 134), or if such diagrams properly mounted for

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