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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.

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, so clearness and singleness of vision are confined to the distance of the point of sight, and 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, 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 im

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perceptible 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 several hundred yards; but beyond this it becomes imperceptible. The other two forms, the mathematical and aërial, operate without limit.

Now the painter can imitate the aërial perspective. He skillfully diminishes the brightness, dulls the sharpness of outline, and blues the tinge of all objects, in proportion to their supposed distance, so as to produce the effect of depth of air. He can also and still more perfectly imitate the mathematical perspective, by diminishing the size of objects and the distance between them as he passes from his foreground to his background. But he can not imitate the focal perspective, and still less can he imitate the binocular perspective. This is artificially given only in the stereoscope, and is the glory of this little instrument. Focal perspective is unimportant to the painter, because imperceptible at the distance at which pictures are usually viewed; but the want of binocular perspective in paintings interferes seriously with the completeness of the illusion. Therefore the illusion is more complete and the perspective comes out more distinctly when we look with only one eye. In a natural scene it is exactly the opposite : the perspective is far more perfect with both eyes open, because then all the forms coöperate.

CHAPTER IV.

THEORIES OF BINOCULAR PERSPECTIVE.

Wheatstone's Theory.—To Wheatstone is due the credit of having discovered the fact that two slightly dissimilar pictures—dissimilar in the same way as the two retinal images of a solid object or of a scene—when united, produce a visual effect similar to that produced by an actual solid object or an actual scene. He also invented the stereoscope to facilitate the combination of such pictures. His theory of these effects was as follows: In viewing a solid object or a scene, two slightly dissimilar images are formed in the two eyes, as already explained; but the mind completely unites or fuses them into one. Whenever there occurs such complete mental fusion of images really dissimilar in this particular way, and therefore incapable of mathematical coincidence, the result is a perception of depth of space, or solidity, or relief. In the stereoscope, therefore, he supposes that the two slightly dissimilar pictures are mentally fused into one, and hence the appearance of depth of space follows as the necessary result of this mental fusion.

This theory is still widely held by even the most recent and best physiologists; but it is evidently the result of imperfect analysis of visual impressions. In stereoscopic diagrams it is always possible to detect the doubling on which the perception of depth of space is based. It is a little more difficult in ordinary stereoscopic pictures, and in natural scenes; but practice and close observation will always detect it in these also. It is most difficult of all to detect it in the case of single solid objects ; but this is mainly because the doubling of the edges of such objects is usually out of the line of sight. Even where we can not detect the doubling, and yet binocularly perceive depth of space, such perception must be regarded as an example of unconscious cerebration. We actually ground our judgments upon impressions which do not emerge into clear consciousness.

Observe the degrees of this unconsciousness. Even the doubling of the forefinger, when held up before the eyes while we gaze at the wall, is undetected by some persons. To such the binocular perspective here seems to be a simple primary sense-perception. But the slightest scientific observation is sufficient to separate this apparently simple impression into its component elements, and thus to show that it is a judgment based on simpler elements. Next, the doubling of objects in the foreground of a scene or stereoscopic picture, when the background is regarded, fails to appear in consciousness. But analysis again shows that the perception of depth here also is not simple, but decomposable into simpler elements. Close observation again detects the elements on which judgment is based. Therefore, where we can not detect the simpler elements, we must believe that they still exist and that judgments are based upon them. Nothing can be more certain than that complete fusion never takes place; and if it seems so to us, it is only because we do not observe and analyze with sufficient care.

Wheatstone's theory therefore seems true only to

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