upper half of either retina makes us see an object as below, on the lower half as above, the horizon; and on the right half of either retina, an impression makes us see an object to the left, on the left half one to the right, of the median line. Thus each quadrant of one retina corresponds as a whole to the geometrically similar quadrant of the other;

al

D

FIG. 9.

ar

D

and within two similar quadrants, al and ar for example, there should, if the correspondence were carried out in detail, be geometrically similar points which, if impressed at the same time by light emitted from the same object, should cause that object to appear in the same direction to either eye. Experiment verifies this surmise. If we look at the starry vault with parallel eyes, the stars all seem single; and the laws of perspective show that under the circumstances the parallel light-rays coming from each star must impinge on points within either retina which are geometrically similar to each other. Similarly, a pair of spectacles held an inch or so from the eyes seem like one large median glass. Or we may make an experiment like that with the spots. If we take two exactly similar pictures, no larger than those on an ordinary stereoscopic slide, and if we look at one with each eye (a median partition confining the view) we shall see but one flat picture, all of whose parts appear single. Identical retinal points' being impressed, both eyes see their object in the same direction, and the two objects consequently coalesce into one.

6

Here again retinal rivalry occurs if the pictures differ. And it must be noted that when the experiment is per

formed for the first time the combined picture is always far from sharp. This is due to the difficulty mentioned on p. 33, of accommodating for anything as near as the surface of the paper, whilst at the same time the convergence is relaxed so that each eye sees the picture in front of itself.

Double Images.-Ncw it is an immediate consequence of the law of identical location of images falling on geometrically similar points that images which fall upon geometrically DISPARATE points of the two retina should be seen in DISPARATE directions, and that their objects should

consequently appear in Two places, or LOOK DOUBLE. Take the parallel rays from a star falling upon two eyes which converge upon a near object, O, instead of being parallel as in the previously instanced case. The two foveæ will receive the images of 0, which therefore will look single. If then SL and SR in Fig. 10 be the parallel rays, each of them will fall upon the nasal half of the retina

which it strikes. But the two nasal halves are disparate, geometrically symmetrical, not geometrically similar. The star's image on the left eye will therefore appear as if lying to the left of 0; its image on the right eye will appear to the right of this point. The star will, in short, be seen double-homonymously' double.

Conversely, if the star be looked at directly with parallel axes, any near object like O will be seen double, because its images will affect the outer or cheek halves of the two retinæ, instead of one outer and one nasal half. The posi

tion of the images will here be reversed from that of the previous case. The right eye's image will now appear to the left, the left eye's to the right; the double images will be 'heteronymous.'

The same reasoning and the same result ought to apply where the object's place with respect to the direction of the two optic axes is such as to make its images fall not on non-similar retinal halves, but on non-similar parts of similar halves. Here, of course, the positions seen will be less widely disparate than in the other case, and the double images will appear to lie less widely apart.

Careful experiments made by many observers according to the so-called haploscopic method confirm this law, and show that corresponding points, of single visual direction, exist upon the two retina. For the detail of these one must consult the special treatises.

Vision of Solidity. This description of binocular vision follows what is called the theory of identical points. On the whole it formulates the facts correctly. The only odd thing is that we should be so little troubled by the innumerable double images which objects nearer and farther than the point looked at must be constantly producing. The answer to this is that we have trained ourselves to habits of inattention in regard to double images. So far as things interest us we turn our foveæ upon them, and they are necessarily seen single; so that if an object impresses disparate points, that may be taken as proof that it is so

unimportant for us that we needn't notice whetner it appears in one place or in two. By long practice one may acquire great expertness in detecting double images, though, as some one says, it is an art which is not to be learned completely either in one year or in two.

Where the disparity of the images is but slight it is almost impossible to see them as if double. They give rather the perception of a solid object being there. To fix our ideas, take Fig. 11. Suppose we look at the dots in the

FIG. 11.

middle of the lines a and b just as we looked at the spots in Fig. 8. We shall get the same result-i.e., they will coalesce in the median line. But the entire lines will not coalesce, for, owing to their inclination, their tops fall on the temporal, and their bottoms on the nasal, retinal halves. What we see will be two lines crossed in the middle, thus (Fig. 12):

The moment we attend to the tops of these lines, however, our foveæ tend to abandon the dots and to move upwards, and in doing so, to converge FIG. 12. somewhat, following the lines, which then appear coalescing at the top as in Fig. 13.

AV

FIG. 13.

FIG. 14.

If we think of the bottom, the eyes descend and diverge, and what we see is Fig. 14.

Running our eyes up and down the lines makes them

converge and diverge just as they would were they running

up and down some single line whose top was nearer to us than its bottom. Now, if the inclination of the lines be moderate, we may not see them double at all, but single throughout their length, when we look at the dots. Under these conditions their top does look nearer than their bottom-in other words, we see them stereoscopically; and we see them so even when our eyes are rigorously motionless. In other words, the slight disparity in the bottom-ends which would draw the foveæ divergently apart makes us see those ends farther, the slight disparity in the top ends which would draw them convergently together makes us see these ends nearer, than the point at which we look. The disparities, in short, affect our perception as the actual movements would.*

The Perception of Distance.-When we look about us at things, our eyes are incessantly moving, converging, diverging, accommodating, relaxing, and sweeping over the field. The field appears extended in three dimensions, with some of its parts more distant and some more near.

"With one eye our perception of distance is very imperfect, as illustrated by the common trick of holding a ring suspended by a string in front of a person's face, and telling him to shut one eye and pass a rod from one side through the ring. If a penholder be held erect before one eye, while the other is closed, and an attempt be made to touch it with a finger moved across towards it, an error will nearly always be made. In such cases we get the only clue from the amount of effort needed to accommodate' the eye to see the object distinctly. When we use both eyes our perception of distance is much better; when we look at an object with two eyes the visual axes are converged on it, and the nearer the object the greater the convergence. We have a pretty accurate knowledge of the degree of muscular effort required to converge the eyes on all tolerably near points. When objects are

* The simplest form of stereoscope is two tin tubes about one and one-half inches calibre, dead black inside and (for normal eyes) ten inches long. Close each end with paper not too opaque, on which an inch-long thick black line is drawn. The tubes can be looked through, one by each eye, and held either parallel or with their farther ends converging. When properly rotated, their images will show every variety of fusion and non-fusion, and stereoscopic effect.