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the left halves would correspond point for point; i. e., the internal or nasal half of one retina corresponds with the external or temporal half of the other, and vice versa. Or, more accurately, if the concave retinæ be covered with a system of rectangular spherical coördinates, like the lines of latitude and longitude of a globe, ab and x y being the meridian and equator, then points of similar longitude and latitude in the two retinæ, as d d', e é', are corresponding. Or, still better, suppose the two eyes or the two retinæ to be placed one upon the other, so that they coincide throughout like geometric solids; then the coincident points are also corresponding points. Of course, the central spots will be corresponding points; also points on the vertical meridians, a b, a' b', at equal distances from the central spots, will be corresponding; also points similarly situated in similar quadrants, as d d', e e', etc. It is probable that the definition just given is not mathematically exact for some eyes. It is probable that in some eyes the apparent vertical, meridian which divides the retinæ into corresponding halves is not perfectly vertical, but slightly inclined outward at the top. This would affect all the meridians slightly; but the effect is very small, and I do not find it so 'in my eyes. We shall discuss this point again (page 146).

Law of Corresponding Points.-After this explanation we reënunciate the law of corresponding points : Objects are seen single when their retinal images fall on corresponding points. If they do not fall on corresponding points, their external images are thrown to different places in space, and therefore are seen double.

Thus we see that the term "corresponding points” is used in two senses, which must be kept distinct in the mind of the reader. Every rod and cone in each

retina has its correspondent in external space, and these exchange with each other by impression and projection. Also every rod or cone of each retina has its correspondent in a rod or cone in the other retina. Now the law of corresponding points, with which we are now dealing, states that the two external or spatial correspondents of two retinal corresponding points always coin

Fig. 32.

A

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R

R and L, two eyes; 0, center of rotation of ball, or optic center; X, point of crossing

of ray-lines-nodal point; A, point of sight; D, some other point in the horoptoric circle A 00'; cc', central spots; a a, da', actual images of A and D.

cide with each other. In order to distinguish these two kinds of corresponding points from each other, the latter—i. e., corresponding points on the two retinæ-are often, and perhaps best, called “identical points,” because their external spatial representatives are really identical.

We will now apply the law. If we look directly at

GENERAL LIBRARY University ok KUCHIGAN

[graphic]

SINGLE AND DOUBLE IMAGES.

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any small object, it will be seen single, because the two retinal images fall on corresponding or identical points, viz., on the two central spots. In Fig. 32 the two eyes, R and L, are turned directly on A. The image of this object will therefore fall on the central spots c c', and the object will be seen single. Objects at nearly the same distance, as for example D, a little to the right or left or a little above or below the point of sight, are also seen single; because the retinal images d and d' are on correspondent halves—i. e., the internal or nasal half of R and the external or temporal half of 1—and at the same distance from the central spots c c', and therefore on identical points. Objects lying in a horizontal circle passing through the point of sight and the centers of the eyes, 0 O', are usually supposed to be seen single. This is nearly true, except when the point of sight is very near.

This circle has been called the horopteric circle of Müller.

Objects, as already said, beyond or nearer than the point of sight, are always seen double. The reason is, that their retinal images always fall on non-corresponding points. This is shown in the diagram Fig. 33. While the two eyes, R and L, are fixed upon A, this object will be seen single, for its images, a and a', fall upon the central spots. But if, while still looking at A, we observe B and C, we shall see that both are double. The reason is, that the images of B, viz., 60, fall upon the two nasal or internal halves of the retinæ, which are non-corresponding; while the images of C, viz., C c', fall upon the two external or temporal halves of the retinæ, which are also non-corresponding. If the external double images be all referred to the plane of sight, P p (which, however, is not the fact), as is usually represented in diagrams, then the position of the dou

ble images will be correctly represented by cc, b b'. It is seen at a glance that the images c c' of C are heteronymous, while the images b b of B are homonymous. Generally, all the field of view within the lines

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of sight, A d, A a', belongs to the temporal halves of the retinæ, while all outside of these lines belongs to the nasal halves. Or, again, double images formed by impressions on the two nasal halves of the retinæ are homonymous, while those formed by impressions on the two temporal halves are heteronymous.

Definition of Horopter.—We have seen that the object at the point of sight is seen single; and all objects at the same or nearly the same distance, but a little to the right or left, or above or below, are also either seen single, or else the doubling, if any, is usually imperceptible. On the contrary, all objects farther or nearer than the point of sight are seen double. Now the surface of single vision-i. e., the surface passing through the point of sight, all the objects lying in which are seen single—is called the horopter. Whether there is such a surface at all, and if there is, what is its form, are questions upon which the acutest observers differ. Some have made it a plane, some a spherical surface. Some, by purely geometrical methods, have given it the most curious forms and properties; while others, by purely experimental methods, have come to the conclusion that it is not a surface at all, but a line. We are not now prepared to discuss this question, but shall return and devote to it a special chapter.

Supposed Relation of the Optic Chiasm to the Law of Corresponding Points. In the optic chiasm, Fig. 20, page 54, there is certainly a partial (but only a partial) crossing of the fibers of the two optic nerves. Many physiologists connect this fact with this remarkable law. There is probably such a connection. But many go farther. They think that some of the fibers of each optic nerve cross over to the other eye, and some do not; and that those which cross over supply the internal or nasal halves, and those which do not cross over supply the temporal halves. Thus, in the diagram Fig. 34, the fibers of the right optic nerve-root 0, as it comes from the brain, go to supply the temporal half t of the right retina, and, by crossing, the nasal half n' of the left retina, and these are corresponding halves. So also the

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