CHAPTER II.

SUPERPOSITION OF EXTERNAL IMAGES.

In the movements of one eye, or of the two eyes if they move together equally in the same direction, as in looking to one side or the other, or up or down, objects seem to stand still, and the eyes or the point of sight to sweep over them. But if we move the eyes in opposite directions, as in converging the optic axes strongly and then allowing them to become again parallel, objects, or rather their external images, seem to sweep like trooping shadows across the field of view; or rather, the fields of view themselves seem to rotate, carrying all their images with them, in a direction contrary to the motion of the eye, and therefore (since the two eyes move in contrary directions) in directions contrary to each other. This phenomenon is not very easily observed, because it is best seen by simple convergence of the eyes on a very near point in space, without any object to direct the convergence, or in trying to look at the root of the nose. Divergence of the eyes may be produced by pressing the fingers in their external corners. In this case also the motion of the images is evident.

Evidently, then, by voluntary motion of the eyeballs in opposite directions, and the consequent motion of the

shadowy images in opposite directions, we may (if we observe the images and control the motion of the eyes) cause them, whether they belong to the same object or to different objects, to approach each other and combine successively. Many curious phenomena thus result, which it is necessary to understand before we approach the more complex phenomena, and especially before we can explain the judgments based upon these phe

nomena.

Combination of the Images of Different Objects.—We have seen that the combination of the two external images of the same object produces single vision. But the external images of different objects may also be combined. Under this head there are several cases.

1. Dissimilar Objects.-We have seen that when the two images of an object fall on corresponding points of the two retinæ, they are thrown outward as external images to the same point in space, superposed, and united, and therefore the object is seen single. If, instead of the two images of the same object, the images of two different objects fall upon corresponding points, evidently they also will be thrown to the same place in space and superposed. In this case, however, there being two objects, there will be four retinal images, only two of which will fall on corresponding points, and also four external images, only two of which will be superposed. But we may confine our attention to the superposed images, or else we may cut off the others from view, or prevent them from forming.

Experiment 1.-If the left hand and the right forefinger, or any two dissimilar objects, be held up before the eyes, say 8 to 10 inches apart, and then the eyes be converged until the right eye looks exactly toward the left hand and the left eye toward the right forefinger,

then evidently the retinal images of these two objects will fall on corresponding points, viz., on the central spots; and their corresponding external images ought to be thrown to the same place and superposed. Such is actually the fact. The phenomena as they actually appear are as follows: As the eyes begin to converge, the images of both objects double homonymously, and we see now four images. As the convergence increases, the double images separate more and more, until the left image (belonging to the left eye) of the forefinger and the right image of the hand (this belongs to the right eye) are brought together and superposed, and the forefinger is seen lying in the palm of the hand. Of course, as already explained, there will be two other images-one of the forefinger to the right, and belonging to the right eye, and one of the hand to the left, and belonging to the left eye. By shutting alternately one eye and then the other, these belongings of the several images may be tested.

Experiment 2.-Or, again, the same combination may take place without convergence of the eyes, thus: Hold up the two forefingers before the eyes a foot or so distant, and a little more than two inches apart (it should be equal to the interocular distance), and against a bright background like a white wall or the sky. Now look at the wall or the sky: the two fingers will both double, making four images; but the two middle images will unite to form what seems to be one finger. There will be therefore apparently three images: the middle one (the combined images) is opaque like an object; the other two, uncombined, are transparent like ordinary double images. In this case, as we are gazing beyond the finger, the double images are heteronymous. It is therefore the right-eye image of the

right finger (the left of its double images) and the lefteye image of the left finger (the right of its double images) which combine in the middle.

These facts and the conditions under which the combination takes place are illustrated by the accompanying diagrams. In Fig. 35 the right eye, R, is directed toward the object B, and the left eye, L, to

In both figures the letters are the same. R and L, the two eyes; A and B, two objects; a'b, Fig. 35, and ab', Fig. 36, combined images; primed letters, left-eye images; c c, central spots of retina; n, the nose; PP, plane of objects; and p p, plane of sight.

ward the object A. The retinal images of these, falling on the central spots c c, are superposed at the point of sight (where the lines of sight intersect) and seen as a'b, while two shadowy images, a and b', are seen to the right and left. Their position in the plane of sight, and as

determined by the law of direction, is given by connecting the points R A and L B. In Fig. 36 the right eye, R, is directed toward the object A, and the left eye, L, toward the object B. The point of sight is therefore beyond, at the meeting of the optic axes or lines of sight. There the combined images, ab', will be seen, while two other uncombined images will be seen at points determined by the law of direction, represented by continuing the lines RB and L A to the plane of sight. It is evident that in this case the two objects A and B must not be farther apart than the optic centers (interocular space); otherwise the lines of sight will not meet in a point of sight, and therefore the two images will not combine. Simple inspection of the diagrams will explain the phenomena, if the reader will bear in mind that capitals represent objects and small letters external images; and further, that the primed small letters represent left-eye images, the strong lines P P the actual plane of the objects, and the dotted lines pp the plane of sight or of the images.

Many persons will not at first succeed in making these experiments, on account of the difficulty which most persons experience in watching double images and controlling the movements of the eyes. To such we would recommend the following method: Let the two objects set up before the eyes in the first experiment be other than parts of the body of the observer-for example, a card and a rod, or two rods. Then, while looking at the table on which the objects lie, hold up the forefinger-or better, a pencil-between the eyes and the objects. The pencil will of course be double. Now, by bringing the pencil nearer or carrying it farther, its double images will separate or close up. Bring