will be parallel, from a short eye they will be divergent, from a long eye they will be convergent. Such rays will not come to a focus in the

FIG. 233.-DIAGRAM TO SHOW HOW OBJECTS ON THE FUNDUS OCULI ARE ILLUMINATED
AND SEEN BY THE DIRECT METHOD.

Both the eyes are supposed to be emmetropic and non-accommodated; under these conditions the vessels visible in the observed eye are slightly anterior to the rod-and-cone layer, which is supposed to be in focus, and rays from the vessels would be slightly divergent. The size of the mirror-aperture is greatly exagge

rated.

case of the normal eye (so long as its accommodation is entirely relaxed); they will have a virtual focus in the case of the short eye, a real focus in the case of the long eye; in the first case (E) no image of the retinal surface is formed, in the second (H) a virtual erect image is formed behind the eye, in the third (M) a real reversed image is formed in front of the eye (fig. 234).

H

E

M

FIG. 234.-PATH OF RAY EMERGING FROM A HYPERMETROPIC, FROM AN EMMETROPIC,
AND FROM A MYOPIC EYE.

From the emmetropic eye, E, with relaxed accommodation, the rays will be parallel and give no image.

From the hypermetropic eye, H, the rays will be divergent, and, being prolonged backwards, give a virtual erect image.,

From the myopic eye, M (or from an accommodated emmetropic eye), the rays will be convergent and give a real reversed image at f'.

The chief practical difficulty in the use of the direct method is for

the observer to maintain his eye non-accommodated. Thus, to estimate hypermetropia he has to find the strength of the convex lens which, added to his non-accommodated eye, gives distinct vision of the fundus, and it is therefore essential that he should not unconsciously exert any effort of accommodation. For the minute examination of a normal eye by the direct method the observer's eye must be non-accommodated, for a myopic eye it must be less than non-accommodated, i.e. the assistance of a concave lens is required; on the other hand, for a hypermetropic eye the observer has to accommodate or to use a convex lens behind the mirror.

The observed eye also must be non-accommodated in order that its refraction may be estimated, as well as for the minute examination of the fundus. Whereas rays emerging from a normal non-accommodated eye are parallel, rays emerging from a normal accommodated eye will be converging, i.e. such an eye will be equivalent to the myopic eye, and its vessels will not be seen by close examination unless a concave lens is used behind the mirror. Hence it will be understood that in the direct examination of the fundus: (1) a concave lens must be added behind the mirror if the observed eye is myopic; (2) a weak concave lens may be added if the observed eye is normal, in which case the observer accommodates the fundus; (3) a convex lens may be used if the observed eye is extremely hypermetropic.

Relation of retina to field of vision. In performing Scheiner's experiment the observer will have noticed that by blotting out the image which is superior, inferior,

8

FIG. 235.

с

right or left as regards its retinal position, he loses sight of the apparent image in his field of vision which is inferior, superior, left or right. In other words, impressions made on the upper, lower, right or left part of the retina excite in consciousness the sensations that objects are situated below or above, to the left or to the right, of the line of vision. We may easily recognise this to be a necessary relation when we have realised that the retinal image is reversed, objects at our feet being focussed on the upper portion of the retina, objects above our heads on its lower portion, objects to our left on its right half, objects to our right on its left half. If, as sometimes occurs, the lateral halves of the two retinæ are paralysed, say on the right side (right hemiopia), the left half of the field of vision is blotted out (left hemianopia); vice versâ, left hemiopia of

The quadrants ABCD of the field of vision are projected upon the quadrants a b c d of the retina.

the two retina will cause right hemianopia as regards the field of vision.1

VISIBLE SIDE

OF FIELD

INVISIBLE SIDE

OF FIELD

Moreover, we normally see objects single with both eyes open, although two retinal images are formed, one in each eye. This is due to the fact that when an object is looked at, its image (and those of its immediate surroundings) are focussed upon corresponding parts of the two retina. The doctrine of corresponding points will, however, be best understood by taking into account the circumstances under which, correspondence not being effected, double vision occurs. Before so doing it should be remarked that in

FIG. 236.-LEFT HEMIOPIA AND RIGHT HEMIANOPIA,

Scheiner's experiment we have experienced double vision with only one eye open; this obviously being due to the fact that we have, by means of the two pinholes, made two images of the same object fall upon different parts of the same retina.

Corresponding points.-Single vision with the two eyes and double vision with the two eyes differ in this respect, that in the former the object gives on each side of the two retinæ an image, every point of which comes to a focus upon each of two corresponding points in the two retina, while in the latter the two retinal images are not outlined upon corresponding points. In the first case the excitations caused by the two corresponding images fuse in consciousness and cause perception of a single

The unguarded use of these terms in various senses leads to much unnecessary confusion, and their meaning is sometimes only to be gathered from the context. Hemiopia is literally half-vision, while hemianopia (or hemianopsia) is halfblindness. The expression left hemiopia,' as used by different writers, may mean paralysis of the right or left halves of the retina, or blindness to the left or to the right of the subject. All ambiguity is removed by stating the sides to which vision is preserved or lost.

SUP.

SUP

object; in the second, the excitations of the two non-corresponding images do not so fuse, and the perception of an apparently double object is their consequence. Corresponding points are thus physiological pairs of points, one in the right eye, one in the left eye, from the simultaneous stimulation of which a single optical sensation results; anatomically, they are almost exactly the symmetrical points in the two retinæ that would cover each other in pairs if the two retina were superposed one upon the other, with the yellow spots as

centre.

T

аг

dr

N

d,

dr

Ст

INF.

FIG. 237.

INF.

ar,b,cr, dr, and a, b, c, d, are corresponding quadrants in the two retina, and would exactly cover each other if superposed. Each quadrant may similarly be imagined to be symmetrically divided into symmetrical corresponding parts, and each such part further subdivided into single rods and cones symmetrically situated in the two retinæ, i.e. corresponding.

The yellow spots correspond in the two eyes, and when an object is looked at, its image is formed upon each of the two yellow spots. The blind spots in the two eyes do not correspond; being situated in the nasal segment in each eye, they would not cover each other if the retina were superposed as above described. The nasal side of the left eye corresponds with the temporal side of the right eye, and the temporal side of the left eye with the nasal side of the right eye.

The horopter. The horopter is that surface or series of points in space the images of which fall upon corresponding points of the two retina. A complete exposition of the form assumed by the horopter with various positions of the eyeball would necessitate a mathematical analysis far beyond the scope of a simple text-book of physiology; we shall here restrict ourselves to the verbal definition of the 'horopter,' and to the geometrical definition of Müller's horopteric circle, which occurs when the visual axes converge upon a near object.

In this position the horopter is formed by a horizontal circle passing through the object, and through the nodal points of the two eyeballs, and by a straight line drawn through the point of fixation in the Müller's horopteric median plane tilted away from the observer.

circle is a practical illustration of prop. 21 of Book III. of Euclid, in which it is demonstrated that any given chord of a circle subtends equal angles at all points of the circumference, or, otherwise expressed, that the locus of the vertices of all triangles on the same side of the same base, with a constant angle at the vertex, is the arc of a circle.

F F

In the primary position, with the visual lines parallel and the visual plane horizontal, the horopter is formed by the distant vertical view if the retinal meridians are at absolute right angles to each other, or by a horizontal surface below the feet if—as is usually the case-the vertical retinal meridian is not at right angles to the horizontal meridian; but the construction of the horopter in these cases would transgress our limits.1

a

FIG. 238.-TO ILLUSTRATE MÜLLER'S HOROPTERIC CIRCLE.

A is the point of regard; its retinal images are formed on the yellow spots at a, a'. b, b' are corresponding points of the two retina, therefore the distance a b= the distance a' b'. n,n' are the nodal points of the two eyes. The angles a n b, a' n' b', are equal to each other and to the opposite angles, A n B, An' B; and in the triangles BC n, A C n', the opposite angles at C are equal; therefore, in these triangles the remaining angles at A and B are equal. Therefore the point B by which the corresponding images b, b' are formed must lie in the arc of a circle passing through the points B, n, and n'. Similarly, it may be shown that any other point forming corresponding images on the two retine will lie in the circular are n An'.

Double vision.-Double vision of an object with both eyes open is most apparent when the gaze is directed to a point nearer or farther than the object, in or nearly in the same line of vision. If a finger is held up in front of the face at arm's length while the eyes are adjusted to a more distant point, the finger will be

1 Students desirous of further information on the subject may refer to Helmholtz, Physiological Optics, p. 745; Hering, Beiträge z. Physiol. 1864; and in Hermann's Handbuch d. Physiol. vol. iv.