eight inches from the eyes. If now, shutting the left eye, we observe the projection of the rod against the

b

wall, it will be like this—a -a being the nearer and the farther end. If we shut the right eye and open the left, the projection will be like this

These lines are exactly like the retinal images formed by the rod in the right and left eyes respectively, except that these images are inverted. Or, to express it differently, these lines would make images on the right and left retinæ respectively exactly like those made by the rod; they are the facsimiles of the external images of the rod. If we now open both eyes and fix attention on the farther end, then the nearer end will be seen double heteronymously, and the projection will be

B

thus If, on the contrary, we look at the

a'

nearer end, then this of course will be single, but the farther end will now be double homonymously, and

the projection will be thus

b

V. If, finally, we

look at the middle point, this point will of course be seen single, but both ends double, the one homonymously, the other heteronymously, and the projection will be thus-X X Or, to put it differently, the external images of the two eyes are like these lines— ° and : if these two be brought together so

a

as to unite the farther ends bb', then by greater convergence the middle points, and then by still greater convergence the nearer ends a a', the three projections above given are obtained; but it is obviously impossible to unite all parts and see single the whole rod at

once. Now, if we observe attentively, we find that in looking at the rod the eyes range back and forth by greater or less convergence, uniting successively the different parts, and thus acquire a distinct perception of the difference of distance or depth of space between the nearer and the farther end.

Experiment 3.-We take next a small thin book, and hold it as before six to eight inches distant in the median plane, a little below the horizontal plane of sight, so that the back and the upper edge are visible. If we shut the left eye, we see the back, the upper edge,

1. The retinal image

and the whole right side, thus.

formed in the right eye is exactly like this figure, except that it is inverted; this figure makes exactly the same retinal image as the book does in the right eye; it is the facsimile of the external image of the book for the right eye. If we shut the right eye and open the left, we see the back, the upper edge, and the whole left side, thusNow, if we open both eyes, we must

and do see both these images. If we look beyond the book, the two images are wholly separated, thusIf we look at the farther part, we bring these

two images together so as to unite the farther part and see it single, but the nearer part or back is double, thusIf we look at the nearer part or back, then this is seen single, but the farther edge is now double, thus. But by no effort is it possible to see it single in all parts at the same time, because these

dissimilar external images can not be wholly united. The eyes therefore range rapidly back and forth, successively uniting different parts by greater and less convergence, and thus acquire a distinct perception of distance between the back and front, and hence of depth of space.

After these simple illustrations we are now prepared to generalize. It is evident that solid objects as seen by two eyes form different mathematical projections, and therefore form different retinal images in the two eyes, and therefore also different external images. Hence the images of the same object, whether retinal or external, formed by the two eyes, are necessarily dissimilar if the object occupies considerable depth of space. But dissimilar images can not be united wholly: for when by stronger convergence we unite the nearer parts, the farther will be double; and when by less convergence we unite the farther parts, the nearer will be double. Therefore the eyes run rapidly and unconsciously back and forth, uniting successively different parts, and thus acquire the perception of depth of space occupied by the object. But what is true of a single object is true of different objects placed one beyond the other, as the two fingers in experiment 1, page 120. We can not at the same time unite nearer and more distant objects, but the point of sight runs rapidly and unconsciously back and forth, uniting them successively, and thus we acquire a perception of depth of space lying between them. Therefore, the perception of the third dimension, viz., depth or relative distance, whether in a single object or in a scene, is the result of the successive combination of the different parts of the two dissimilar images of the object or the scene: dissimilar, because taken from different points, viz., the two eyes

with the interocular distance between. This fundamental proposition will be slightly modified in our chapter on the theory of binocular perspective. In the mean time it must be clearly conceived and held fast; otherwise all that follows on stereoscopy will be unintelligible.

STEREOSCOPY.

We have already seen (page 96) that in binocular vision we see objects single by a combination of two similar or nearly similar images, and that therefore (page 118) 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. 44, and then combine them by converging the eyes, taking care to cut off the monocular images as directed on page 114, Fig. 39, the visual result will be exactly the same as that of an actual

FIG. 44.

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. 44 ought to be combined at a distance of not more than six or eight inches.

So also in the case of the book, page 123. 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