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Fig. 60.

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

А of confusion of the view; but in others the binocular completely overbears all opposition and reverses the

B 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 the lawn are also reversed. In Fig. 60, 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 stereoscope 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 me. 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

* These may be made either by simultaneous photographs taken at widely different longitudes on the earth's surface, or else by taking two photographs at times of extreme libration of the moon to one side and the other,

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 (as in Fig. 48, page 134). For example, in combining with the naked eyes the figures of a regularly figured wallpaper 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 combined, the combination is absolute and the plane of the combined images is perfectly flat; but if the notes be not from the same plate, but copied, slight variations are unavoidable, and such variations will show themselves in a gently wavy surface.

Monocular Pseudoscopy. There is, indeed, a monocular pseudoscopy too; for, as will be presently shown, there are other modes of judging of relative distance (perspective) besides the binocular. Thus, for example, photographs of moon craters, or actual wood carvings and moldings, are often seen in reverse of their real relief. But in all such cases the direction of relief is uncertain and often reversible at will by the imagination, like the faces of geometric diagrams of solids. But binocular pseudoscopy is not thus reversible. It has all the “sober certainty” of reality.

Different. Forms of Perspective.—In order to bring out in stronger relief the distinctive character of binocular perspective, it is necessary to mention briefly the several different forms of perspective. There are many ways in which we judge of the relative distance of objects in the field of view, all of which may be called modes of perspective.

1. Aërial Perspective. The atmosphere is neither perfectly transparent nor perfectly colorless. More and more distant objects, being seen through greater and greater depths of this medium, become therefore dimmer and dimmer and bluer and bluer. We judge of distance in this way; and if the air be more than usually clear or more than usually obscure, we may misjudge.

2. Mathematical Perspective. Objects become smaller and smaller in appearance, and nearer and nearer together, the farther away they are. Thus streets appear narrower and narrower, and the houses lower and lower, with distance. Parallel lines of all kinds, such as railway stringers, bridge timbers, etc., converge more and more to a vanishing point.

3. Monocular or Focal Perspective. Objects at the distance of the point of sight are distinct, the lenses being focally adjusted for that distance; but all objects beyond or within this distance are dim. Now, we are aware of a greater or less effort of adjustment to make a distinct image, according to the nearness or the distance of the object looked at. This is also a means of judging of the distance especially of near objects.

These three forms may all be called monocular ; for they would equally exist, and we could judge of distance, so far as these modes are concerned, equally well, if we had but one eye. But there is still another, viz. :

4. Binocular Perspective.In order to combine the images of objects near at hand, we converge the optic axes strongly; for more distant objects, less and less according to their distance. By this constant change of axial adjustment necessary for single vision, the point of optic convergence is run rapidly back and forth ; and thus, by a kind of rapid and almost unconscious triangulation, we estimate the relative distance of objects in the field of view. The man with only one eye can not judge by this method, and thus often misjudges the distance of near objects. In rapidly dipping a pen into an inkstand, or putting a stopper into a decanter, the one-eyed man can not judge so accurately as the twoeyed man. If we shut one eye and attempt to plunge the finger rapidly into the open mouth of a bottle, we are very apt to overreach or fall short.

As clearness of vision is confined to a small area about the point of sight, and rapidly fades away with increasing distance in any direction on the same plane, B0 Clearness and singleness of vision are confined to the distance of the point of sight, anl images become dim and double in passing beyond or to this side of that point. Again, as we sweep the point of sight about laterally over a wide field of view, and gather up all the distinct impressions into one mental image, so we run the point of optic convergence back and forth, gauging space, and gather up a mental picture of the relative distance of objects, in a deep field.

These different forms of perspective operate for very different distances. The focal adjustment becomes imperceptible for distances greater than about 20 feet. Judgments based on this, therefore, are limited within that distance. Binocular perspective operates perceptibly for much greater distance, perhaps a quarter of a mile; but beyond this it becomes imperceptible. The other two forms, the mathematical and aërial, operate without limit. Thus at near distance all forms of perspective coöperate. But as we go farther away first focal perspective drops out at about 20 feet; then binocular perspective at about a quarter of a mile; the other two remaining indefinitely.

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