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taken from different points. They will differ from each other exactly as the two retinal images of the same object or scene differ, only certainly in a greater degree. Therefore, if these two photographs be binocularly combined as in the experiments previously given, they ought to and must produce a visual effect exactly like an actual object or scene; for in looking at an object or scene, we are only combining retinal images (or their external representatives) exactly like these pictures, because taken in the same way.

This is substantially the manner in which stereoscopic pictures are taken. It is not always necessary, indeed, to have two cameras; for the pictures, being permanent and not evanescent like retinal images, may be retained and combined at any time. The object or scene is often photographed from one position, and then the camera is moved a little, and the same object or scene is again photographed from the new position. The two slightly dissimilar pictures thus taken are then mounted in such wise that the right-hand picture shall be that taken by the right camera, and the left-hand picture that taken by the left camera. In other words, they are mounted so that the right picture shall be similar (except inverted) to the retinal image of the object or scene in the right eye, and the left picture to the retinal image in the left eye. The marvelous distinctness of the perception of depth of space, and therefore the marvelous resemblance to an actual object or scene, produced by binocular combination of such pictures properly taken and properly mounted, is well known.

It is easy to test whether stereoscopic pictures are properly mounted or not. Select some point or object in the foreground; measure accurately with a pair of

dividers the distance between it and the same point or object in the other picture; compare this with the distance between identical points in the extreme background of the two pictures. The distance in the latter case ought to be greater than in the former. This is the proper mounting for viewing pictures in a stereoscope. If they are to be combined with the naked eye, then the reverse mounting is better.

Combination of Stereoscopic Pictures.-Stereoscopic pictures may be easily combined by the use of the stereoscope or with the naked eyes. For inexperienced persons, however, the latter is more difficult and the illusion less complete, unless with special precautions. Nevertheless, it will be best to begin with this method, because the principles involved are thus most easily explained.

Combination with the Naked Eyes.—In combining stereoscopic pictures with the naked eyes, there are two difficulties in the way of obtaining the best results. First, it is evident that such pictures, as usually mounted, were intended to be combined beyond the plane of the card; for it is only thus that the object or scene can be seen in natural perspective, and of natural size, and at natural distance. But in thus combining, the eyes are of course looking at a distant object, and consequently parallel or nearly so. The eyes are therefore focally adjusted for a distant object, but the light comes from a very near object, viz., the card-pictures. Hence, although the pictures unite perfectly, the combined image or scene is indistinct. Myopic eyes will not experience this difficulty, and in normal eyes it may be remedied by the use of slightly convex glasses. Such glasses supplement the lenses of the eye, and make clear vision of a near object when the eyes are really

looking far away; or, in other words, make a clear image of a near object on the retina of the unadjusted eye.

Another difficulty is, that the pictures are usually so mounted that identical points are farther apart than the interocular distance, and therefore, even with the optic axes parallel-i. e., looking at an infinite distance the pictures do not combine.

This difficulty is easily removed by cutting down the inner edges of the two pic tures, in order to bring them a little nearer together, so that identical points in the background shall be equal to or a little less than the interocular distance.*

With this explanation we now proceed to give examples of naked-eye combination.

Fig. 45 represents a projection of a skeleton truncated cone made of wire, as seen from two positions a little separated from each other; in other words, as they

FIG. 45.





would be taken by two cameras for a stereoscopic card; or, again, as they would be taken on the retinæ of two eyes looking at such a skeleton truncated cone with the smaller end toward the observer.

Experiment.—If we now place a median screen 10 inches or a foot long midway between these two figures,

* In a subsequent chapter we give the method of determining with accuracy the interocular distance.

A and B, and place the nose and middle of forehead against the other edge of the screen, so that the right eye can only see A and the left eye B-assisting the eye with slightly convex glasses if necessary—and then gaze as it were at a distant object beyond the plane of the picture, the two figures will be seen to approach and finally to unite in one, and appear as a real skeleton truncated cone of a considerable height. If we are able to analyze our visual impressions, we shall find further that, when we look steadily at the larger circle or base, the smaller cone or summit is slightly double, and when we look steadily at the smaller circle or summit this becomes single, but now the larger circle or base is double; further, that it requires a greater convergence, as in looking at a nearer object, to unite the smaller circles, and a less convergence, as in looking at a more distant object, to unite the larger circles; and still further, that the lines a a' and 6 b' behave exactly like the lines described on page 122, forming a V, an inverted V, or an X, according to the distance of the point of sight; or, in other words, behave exactly like the two images of a rod held in the median plane with one end nearer than the other. In a single word, the phenomena are exactly those produced by looking at an actual skeleton cone made of wires. Thus, as in the case of an actual object, the eyes by greater and less convergence run their point of sight back and forth, uniting different parts, and thus acquire a distinct perception of depth of space between the smaller and larger circles.

The same is true of all pictures constructed on this principle, and all objects or scenes on stereoscopic cards. In these, it will be remembered, identical points in the foreground are always nearer together than identical points in the background; therefore, when the back


FIG. 46.

ground is united the foreground is double, and vice

We may represent these facts diagrammatically by Fig. 46, in which p p is the plane of the pictures ; ms, the median screen resting on the root of the nose, n; R and L, the right and left eyes. On the plane of the paper P P, a and a' represent identical points in

B the foreground, viz., the centers of the small circles in the diagram Fig. 45; and 6 and b' identical points in the background (centers of the larger circles in Fig. 45). Now when the eyes are directed toward b and W', the two visual lines will pass through these points, and the images of these two points will fall on corresponding points of the retinæ, viz., on the central spots, and will be united and seen single. But where? Manifestly at the point of optic convergence or point of sight B. Now when 6 and b' fall on corresponding points and are seen single, evidently a and a' must fall on non-corresponding points, viz., the two temporal portions of the retinæ, and are therefore seen double. When, on the other hand, by greater convergence the optic axes are turned on a and a', then the images of these fall on the central spots, and are seen single at the nearer point of sight A ; but now 6 and b' are seen double, because they fall on non-corresponding points, viz., the two nasal halves of the retinæ. Intermediate points between the background and foreground will be seen at intermediate points between B and A. Thus the point of sight runs back and forth from

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