that a straight line can be drawn through the point C perpendicular to the circumference, upon which all points are seen single also.

For other positions of the eye complicated Horoptery figures have been constructed, which we will not enter into further. The only other interesting case is when we look into the distance, standing in an erect position. As Helmholtz has shown, the ground then forms our Horopter. When we think how safely we step forwards without fixing our eyes on the ground before us, this property of the eye will not appear unimportant, for we should stumble much more frequently if we fixed our eyes, when walking, upon an object at an equal height with our eyes.

137

CHAPTER VIII.

The perception of Solidity-The Stereoscope-The Telestereoscope—The Pseudoscope-The perception of Luminosity-The struggle between the Fields of Vision.

ALTHOUGH we can prove from experience that, in binocular vision, double images really exist, and can show that only limited portions of space can be seen single, yet we are quite unconscious of the existence of such double images in our general vision. A hasty glance round the room, or through the window upon the street, convinces us that we have seen no object double, but everything single. We have learnt, further, that we are looking into space, where objects are situated at different distances, and not upon an even surface of any kind. In binocular vision we gain an idea of space, and an impression of solidity.

The conditions under which we obtain an idea of space with binocular vision are easily discovered by a simple consideration. If, for instance, we fix the eyes upon an object in the room so that we see the wall behind it, it will then conceal from view a certain portion of the wall. The portion concealed is not, however, the same for both eyes, but it lies more to the left for the

right eye, and to the right for the left eye, and if we close quickly first one eye and then the other, the object in front of the wall will appear to move from side to side. Hence, it is evident that the images on the retinæ of both eyes cannot possibly be the same; the objects seen must appear rather to merge into each other.

The difference between the two retinal pictures of course is not determined by the will but by a definite law. Suppose that we have looked at an object from two different points of view; then we shall have received two images, which bear a strong resemblance to each other. This is the case, in a less degree, with binocular vision, for the right eye has a different point of view in the head to the left.

In a special case mentioned above, we have already made use of the law under which the displacement of objects seen takes place. As a general rule it will be found that with two objects, placed one behind the other, the nearer one is displaced by the right eye to the left, and by the left eye to the right.

With a large field of vision, filled with a number of objects, it becomes very difficult to find by construction the direction and amount of displacement for both retinal images. With a single body, however, the result is much more easily attained. Let us take, as an example, a truncated pyramid of four sides, which is viewed from above. The appearance will be similar to that represented in fig. 39 (P). If, however, we look only with the right eye, then the summit of the cone will seem to be displaced towards the left, as in r, and towards the right, as in 7, if we look only with the left eye. Of course it is here supposed that the head is held perpen

dicularly over the pyramid, so that the centre of the head is perpendicular to the centre P.

Now if we look at the pyramid with both eyes, it is clear that the image r is depicted upon the right eye, and

P

d

团团

Fig. 39.

the image upon the left. These images are different, 1 yet experience shows us that both are combined so as to produce the impression of solidity.

The celebrated philosopher, Wheatstone, was the first to state that the perception of solidity depended upon the dissimilarity of the images depicted upon the retinæ of the eyes. He constructed a stereoscope of a very simple kind, in which two drawings were viewed in the fol

lowing manner: The two eyes, R and L (fig. 40), look at two mirrors, s and s, which are placed obliquely to the

eyes, and at right angles to each other. Atr is placed a drawing, one of the pyramids for example, as it appeared to the right eye; and at the corresponding picture as seen by the left eye. According to the laws of reflection, each eye now sees the image intended for it in the prolongation of the optical axes, where both images are combined so as to produce an image in relief. We think we see a single object simply because each eye sees the same object which it would see if the rays proceeded from a real object.

Wheatstone's stereoscope has been superseded by Brewster's, which is known to all. There is no need to

a

ор

Fig. 41.

R

describe its outward form. The most important part of this stereoscope consists in two lenses (fig. 41) s and s, through which the two eyes R and L look. The pictures r and respectively correspond to the right and left eye. The ray a b from the right-hand picture is refracted by the lens, so that it appears to come from c, and the same is the case with the corresponding ray for the left eye. Thus both pictures are united in the point p, where each eye seems to see its corresponding picture, and the

two pictures therefore unite to form one picture in relief.

Photography, as is well known, has been of great