THE PRINCIPLES OF STEREOSCOPY.

We have shown (pages 133-135) that we may have a phantom-plane where no plane exists. So also we may have a phantom-space where no space exists. Stereoscopy is the art of making such phantom-space.

We have already seen (page 112) that in binocular vision we see objects single by a combination of two similar or nearly similar images, and that therefore (page 137) it makes no difference whether the images are those of the same object or of different objects, if the images in the two cases are identical, and if we take care to cut off the monocular images which are formed in the latter case. Hence, if we draw two pictures of a rod in the two positions shown in Fig. 51, and then

FIG. 51.

combine them by converging the eyes, taking care to cut off the monocular images as directed on page 131, Fig. 46, the visual result will be exactly the same as that of an actual rod in the median line; and therefore it will look like such a rod. As in the case of the actual rod, by greater or less convergence of the optic axes we may combine successively different parts; and the eyes therefore seem to run back and forth, and we have a distinct perception of depth of space. To produce the proper effect, the two pictures of Fig. 51 ought to be combined at a distance of about one foot.

So also in the case of the book, page 141. If we exactly reverse the case described there-i. e., if we make two pictures of a book as seen by one eye and the other, and then combine them, cutting off the monocular images-we have the exact appearance of an actual solid book. The only reason why the illusion is not complete is, that there are other kinds of perspective besides the binocular; and in this case especially because there is not the same change of focal adjustment necessary for distinct image as in the case of a real object.

Now this is the principle of the stereoscope. The stereoscope is an instrument for facilitating the combination of two such pictures, and at the same time cutting off the uncombined monocular images which would tend to destroy the illusion.

Stereoscopic Pictures. When we look at an object having considerable depth in space, or at a scene, there is an image of the object or scene formed on each retina. These two images are not exactly alike, because they are taken from different points of view. Now suppose we draw two pictures exactly like these two retinal images, except inverted. Obviously these two pictures will make images on the corresponding retinæ exactly like those made by the original object on the one retina and the other, and therefore will be exactly like this object seen by one eye and then by the other. Now, we have seen the wonderful similarity of the eye to a photographic camera. Suppose, then, instead of drawing the pictures like the two retinal images, we photograph them. Two cameras are placed before an object or a scene with a distance between of two or three feet. They are like two great eyes with large interocular space. The sensitive plate represents the retina, and

the pictures the retinal images. The photographic pictures thus taken can not be exactly alike, because 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 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 by convergence, then the reverse mounting is necessary.

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.—(a) Beyond the plane of the picture. 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 pictures, 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. 52 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 would be taken by two cameras for a stereoscopic card; or, again, as they would be taken on the retina of the two eyes looking at such a skeleton truncated cone with the smaller end toward the observer.

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