Experiment. If we now place a median screen 10 inches or a foot long midway between these two figures, 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 b b' behave exactly like the lines described on page 140, 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 or 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

FIG. 53.

foreground are always nearer together than identical points in the background; therefore, when the background is united the foreground is double and vice versa. We may represent these facts diagrammatically by Fig. 53, in which p p is the plane of the pictures; ms, the median screen resting on the root of the nose, n; RL, the right and left eyes. On the plane of the picture p p, a and a' represent identical points in the foreground, viz., the centers of the small circles in the diagram Fig. 52; and b and b' identical points in the background (centers of the larger circles in Fig. 52). Now when the eyes are directed toward b and b', 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 b 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 heteronymously. 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 b and b' are seen double homonymously, because they fall on non-corresponding points, viz., the two nasal halves of the retina. Intermediate points be

tween the background and foreground will be seen at intermediate points between B and A. Thus the point of sight runs back and forth from background B to foreground A, and we acquire a distinct perception of depth of space between these two points.

(b) Combination on this side the picture. But, for those at all practiced in binocular experiments, by far the most perfect naked-eye combination is obtained by crossing the eyes, i. e., by combining on the nearer instead of the farther side of the pictures. For this purpose, however, it is necessary that the mounting be reversed; i. e., the right-hand picture must be put on the left side, and the left-hand picture on the right side of the card. By this reversal it is evident that identical points in the background of the two pictures are nearer together than identical points in the foreground.

If, now, holding such a card before us at any convenient distance, say 18 inches or 2 feet, we converge the optic axes so that the right eye shall look across directly toward the left picture, and the left eye toward the right picture, then the two pictures will unite at the point of crossing of the optic axes (point of sight), and will be seen there in exquisite miniature, but with perfect perspective. The effect is really marvelously beautiful. For persons of slightly presbyopic eyes there will be no difficulty in getting the combined image perfectly clear. In normal eyes, as already explained (page 135), there must be dissociation between the axial and focal adjustments before the combined image is perfectly clear. For those who can not make this dissociation it may be necessary to use very slightly concave glasses. Again, if the observer is annoyed by the existence of the monocular uncombined images to the right and

left, it will be best to use two side screens, as already explained (page 131), instead of the median screen used in combining beyond the plane of the picture.

Experiment. I draw (Fig. 54) two projections of a skeleton truncated cone precisely like those represented on page 148, but reversed. It is seen, for example, that the centers of the small circles are in this case farther apart than the centers of the large circles. If, now, holding these about 18 inches distant, I combine them by crossing the optic axes, the impression of a skeleton truncated cone with the smaller end toward me is as complete as possible. The singleness of the impression at first seems perfect, but by observing attentively the lines a and a' it will be seen that they unite only in points and not throughout—that they come together as a v, thus-V, or an inverted v-, or an x-x, according to the distance of the point of sight. In other words, when by greater convergence the small circle is single, the larger circle is double; and when by less conver

gence the larger circle is single, then the smaller circle is double. And thus the eyes run the point of sight back and forth, uniting first the one and then the other, and in this way acquire a clear conception of depth of space between the smaller and larger circles. If, while the figures are combined, the page be brought nearer or

carried farther away, the cone shortens or lengthens proportionately.

FIG. 55.

These facts are illustrated by the diagram Fig. 55, in which, as before, R and L are the two eyes; n, the root of nose; PP, the plane of the pictures; a and a', identical points of the foreground, and b and b' of the background; and sc and sc', the two side-screens to cut off monocular images. When the eyes are directed toward a and a', these unite and are seen at the point of sight as a single object A, but bb' are double. When the eyes by less convergence are directed to b and b', then these are seen single at the point of sight B, but a a' are double. The point of sight runs back and forth

from A to B, and we thus acquire distinct perception of depth of space between.

Of course, any stereoscopic pictures may be combined in this way if we reverse the mounting; and I am quite sure that any one who will try it will be delighted with the beautiful miniature effect and the perfection of the perspective.

Combination by the Use of the Stereoscope.-The stereoscope is an instrument for facilitating binocular combinations beyond the plane of the pictures. By means of lenses also it supplements the lenses of the eyes, and thus makes on the retinæ perfect images of a near ob