the more active change, since it involves contraction of the ciliary muscle. When we look far off, we simply let our eyes go passive. We feel this difference in the effort when we compare the two sensations of change.

Convergence accompanies accommodation. The two eyes act as one organ; that is, when an object catches the attention, both eyeballs turn so that its images may fall on the foveæ. When the object is near, this naturally requires them to turn inwards, or converge; and as accommodation then also occurs, the two movements of convergence and accommodation form a naturally associated couple, of which it is difficult to execute either singly. Contraction of the pupil also accompanies the accommodative act. When we come to stereoscopic vision, it will appear that by much. practice one can learn to converge with relaxed accommodation, and to accommodate with parallel axes of vision. These are accomplishments which the student of psychological optics will find most useful.

Single Vision by the two Retina.-We hear single with two ears, and smell single with two nostrils, and we also see single with two eyes. The difference is that we also can see double under certain conditions, whereas under no conditions can we hear or smell double. The main conditions of single vision can be simply expressed.

In the first place, impressions on the two foveæ always appear in the same place. By no artifice can they be made to appear alongside of each other. The result is that one object, casting its images on the foveæ of the two converging eyeballs will necessarily always appear as what it is, namely, one object. Furthermore, if the eyeballs, instead of converging, are kept parallel, and two similar objects, one in front of each, cast their respective images on the foveæ, the two will also appear as one, or (in common parlance) their images will fuse."' To verify this, let the reader stare fixedly before him as if through the paper at infinite distance, with the black spots in Fig. 8 in front of his respective eyes. He

will then see the two black spots swim together, as it were, and combine into one, which appears situated between their original two positions and as if opposite the root of his nose. This combined spot is the result of the spots opposite both eyes being seen in the same place. But in addition to the combined spot, each eye sees also the spot opposite the other eye. To the right eye this appears to the left of the combined spot, to the left eye it appears to the right of it; so that what is seen is three spots, of which the middle one is seen by both eyes, and is flanked by two

FIG. 8.

others, each seen by one. That such are the facts can be tested by interposing some small opaque object so as to cut off the vision of either of the spots in the figure from the other eye. A vertical partition in the median plane, going from the paper to the nose, will effectually confine each eye's vision to the spot in front of it, and then the single combined spot will be all that appears.*

If, instead of two identical spots, we use two different figures, or two differently colored spots, as objects for the two fovea to look at, they still are seen in the same place; but since they cannot appear as a single object, they appear there alternately displacing each other from the view. This is the phenomenon called retinal rivalry.

As regards the parts of the retinæ round about the foveæ, a similar correspondence obtains. Any impression on the

*This vertical partition is introduced into stereoscopes, which otherwise would give us three pictures instead of one.

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;

eye.

FIG. 9.

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 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.

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 fovea will receive the images of O, 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 position 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