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combination by squinting be viewed in the stereoscope, the perspective is completely reversed, the background becoming the foreground, and vice versa. For example, Fig. 49 represents a stereoscopic card. When the two
pictures are combined with a stereoscope, the result is a jelly-mold with the small end toward the observer; but if the same be combined with the naked eye by squinting, we have now beautifully shown the same jelly-mold reversed, and we are looking into the hollow. If there should be other forms of perspective strongly marked in the pictures, these may even be overborne by the inverse binocular perspective. For example, in the stereoscopic picture Fig. 50, representing the interior of a bridgeway, the diminishing size of the arches and the converging lines, even without the stereoscope, at once by mathematical perspective suggest the interior of a long archway. This impression is greatly strengthened by viewing it in the stereoscope; for the binocular perspective and the mathematical perspective strengthen each other, and the illusion is complete. But if we combine these with the naked eyes by squinting, we see with perfect distinctness, not a long hollow archway, the small arch representing the farther end, but a short conical solid, with the small end toward the observer. Thus the binocular perspective entirely overbears the mathematical.
The cause of this reversal of the natural perspective is shown in the following diagrams. In Fig. 51 the mounting is reversed, as seen by the fact that the points b and B' in the background are nearer together than the points a and a' in the foreground. By combining these in a stereoscope, the background is seen nearer the observer at B, and the foreground thrown farther back to A. In Fig. 52 the pictures are mounted suitably for viewing in the stereoscope, but are combined by the naked eye. Here also the perspective is reversed, for the background is seen at a nearer point B, and the foreground at a farther point A.
This inverse perspective is easily brought out, not only in stereoscopic diagrams, but in nearly all stereoscopic pictures, even in those representing extensive and
complex views. In these, of course, when viewed in the stereoscope, the binocular is in harmony with other forms of perspective, and each enhances the effect of the other. But if we combine with the naked eyes by squinting, or if we reverse the mounting and view again with the stereoscope, there is in either case a complete discordance between the binocular and other forms of perspective. In some cases the ordinary perspective is too strong for the binocular, and the only result is a kind of confusion of the view ; but in others the binocular completely overbears all opposition and reverses the perspective, often producing the strangest effects.
For example, I now take up a stereoscopic card representing a building with extensive grounds in front. I view it in a stereoscope. The natural perspective comes out beautifully—the fine building in the background, the sloping lawn in the middle, and a piece of statuary and a fountain in the foreground. I now combine the same with the naked eyes by squinting. As soon as the combination is perfect and the vision distinct, the
house is seen in front, and through a space in the wall the statue and fountain are seen behind. Observing more closely, all the parts of the house, the slope of
the roof, and the slope of B
the lawn are also reversed. In Fig. 53, A and B show the natural and the inverted
perspective in section, and the arrows the direction in which the observer is looking. In the one case the roof and the lawn slope downward and toward the observer; in the other, downward and away from the observer. In the one case the building is a solid object; in the other it is an inverted shell, and we are looking at the interior of the shell.
In nearly all stereoscopic views I can thus invert the perspective by naked-eye combination. Almost the only exceptions are views looking up the streets of cities. Here the mathematical perspective is too strong to be overborne. Stereoscopic pictures of the full moon are quite common. If these be viewed in a stereoscope, we have the natural perspective, viz., the appearance of a globe; if combined with the naked eyes by squinting, we have a hollow hemisphere. If the mounting be
reversed, then the hollow is seen in the stereoscope and the solid globe with the naked eyes. We will give one more example. I have now a stereoscopic view of the city of Paris, but not looking up the streets. When viewed in the stereoscope, the perspective is natural and perfect; the large houses are in the foreground and below, and the others gradually smaller and higher, until the dimmest and smallest are on the uppermost part and form the distant background. I am looking on the upper surface of a receding rising plane full of houses. I now combine the same pictures with the naked eyes by squinting. As soon as the combined image comes out clear, I see the smallest and dimmest houses on the upper part of the scene, but nearest to
I am looking on the under side of a receding declining plane, on which the houses grow larger and larger in the distance, until they become largest at the lowest and farthest margin of the plane. If the mounting of the pictures be reversed, then the natural perspective will be seen with the naked eyes, and the inverse perspective just described will be seen in the stereoscope.
The extreme accuracy of our judgment of relative distance by binocular perspective is well shown by the combination, either by the naked eyes or by the stereoscope, of apparently identical figures on a flat plane. For example, in combining with the naked eyes the figures of a regularly figured wall-paper or tessellated pavement, the least want of perfect regularity in the size or position of the figures is at once detected by an appearance of gentle undulations or more abrupt changes of level. This fact is made use of in detecting counterfeit notes. If two notes from the same plate be put into a stereoscope and identical figures