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all other contiguous figures, 1 and 2, 2 and 3, etc., all over the plane, will be similarly united, and the whole plane with all its figures will advance and be distinctly seen at the distance p' p'. When by stronger convergence alternate figures, 5 and 7, are combined at a nearer point of sight 5 on the plane py" —or (which is the

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same) when we use the plane p' p' first obtained with all its figures as a real object, and again combine contiguous figures—the whole plane advances to p" p", and is seen as a distinct object with a still smaller pattern of figures. Using the plane thus obtained again as an object, and uniting its contiguous figures, the whole


plane again advances still nearer, and the figures become still smaller at p'"p'". In this manner I have often distinctly seen a regularly figured wall or pavement on six or seven different planes coming nearer and nearer, and becoming smaller and smaller, until the nearest was within 3 inches of the eyes, and the figures in exquisite miniature, and yet the whole so apparently real that it seemed to me I could rap my knuckles against the wall or pavement. When thus looking at the nearest image, by a slight relaxation of convergence, we may drop the image and catch it on the next plane, and again drop it to each successive plane, until it falls to its natural place. In cases of extreme convergence, as in plane"", the phantom plane is not flat, but

This will be explained hereafter—Chapter III, Part III.

If the figures of the pattern are not larger than the distance between the optic centers (24 inches), then it is possible also to unite the figures beyond the real plane -i.e., on the plane P' P'. In this case the figures will be proportionately enlarged, as shown by the diagram. But it is difficult by this method to make the image clear, the reason for which we shall soon see.

In all cases of illusive images or phantoms the head ought to be held steady. If it be moved from side to side while gazing at such an image, the image will also move from side to side-in the same direction as the head if the point of sight be nearer than the object, and in the opposite direction if the point of sight be beyond the object-i. e., in both cases there is a parallactic turning about a point at the distance of the real object. It is necessary too, in all experiments on combination of images, that the interocular line should be exactly parallel with the line joining the objects to be combined ; otherwise one image will le higher than the other.

Dissociation of Consensual Adjustments.—We have said above that when the combination in case 3 (and so also in the other cases) is first obtained, the image of the figures is not distinct, but afterward becomes clear and sharp. The reason is this : The voluntary adjustment of the optic axes (axial adjustment) to a nearer distance than the object carries with it, by consensus, the focal adjustment and pupillary contraction for the same distance. But since the lenses are adjusted for a nearer distance than the object, the retinal image will be indistinct. The subsequent clearing of the image, therefore, is the result of a dissociation of the axial and focal adjustments. The optic axes are adjusted for the point of sight or distance of the illusive image or phantom, and the lenses are adjusted for the distance of the object. Some persons do not find it easy to make this dissociation, and therefore to make the illusive image perfectly clear. To presbyopic persons it is not difficult, but normal eyes will find some, though not insuperable, difficulty. All difficulty, however, may be removed by the use of glasses concave in the case of combination by squinting, and convex in the case of combination beyond the plane of the object. But of course each pair of glasses can remedy the difficulty for one distance only.

Now it becomes an interesting question : When the axial and focal adjustments are thus dissociated, with which one does the pupillary contraction ally itself? I answer, it allies itself with the focal adjustment. This may be proved as follows:

E.cperiment.-While the combination and the formation of the illusive image are taking place, let an assistant standing behind observe the pupil in a small mirror suitably placed in front and a little to one side of one eye. He will see that at first the pupil contracts strongly, associating itself with the axial and focal adjustments to the point of sight; but as soon as the illusive image clears and becomes distinct, he will observe that the pupil has enlarged again.*

General Conclusions.--It is evident, therefore, that the combination of the similar images of two different objects may produce the same visual effect as the combination of the two images of the same object. In other words, single vision, or ordinary perception of objects, is by combination of two similar images; and it makes no difference whether the two images belong to the same object or to two different but similar objects. This idea must be clearly apprehended and held fast; otherwise all that follows will be unintelligible.

Again, it is evident that two objects may be seen as one, and, contrariwise, one object may be seen as two images. We see then the absolute necessity, in binocular vision, that we should speak of seeing only external images, the signs of objects. They are usually-i. e., under ordinary conditions—the true signs, but often untrue, deceptive, illusory signs. Images the signs of objects! Does this seem strange ? Do we not continually see images in mirrors; and do we not often mistake them for objects although they are only the signs of objects ?

* I have reason to believe that this is not always the case. Prof. Le Conte Stevens, who is a very careful and competent experimenter in binocular phenomena, tells me that in his case the pupil allies itself with “the ocular convergence, and therefore does not dilate when the phantom cicars.



We now

Thus far we have investigated the case of flat objects, or of figures or colored spaces on a plane. We have shown how the images of these may be combined at pleasure, so as to give the illusory appearance of objects or figures at places and of sizes different from their real places and sizes. We come now to the more complex case of solid objects of three dimensions, and of objects situated at different distances. We have shown that we perceive relative position in two dimensions by the law of direction. But how is it with relative position in the third dimension ? proceed to show that this is due to the law of corresponding points. This brings us to the important subject of the perception of depth of space so far as this is connected with binocularity ; or, in other words, to the subject of binocular perspective. We will introduce the subject with some simple experiments.

Experiment 1.—Place one forefinger before the other in the median plane, as in experiment 3 cn page 109. As already seen, when we look at the farther finger and see it single, the nearer one is doubled heteronymously; when we look at the nearer finger and see it single, the farther one is doubled homonymously. We can not see them both single at the same time. The reason is obvious. If we shut one eye, say the left, we

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