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CHAPTER II.

THE HOROPTER.

If we look at any point, the two visual lines converge and meet at that point. Its two images therefore fall on corresponding points of the two retinæ, viz., on their central spots. A small object at this point of convergence is seen absolutely single. We have called this point “ the point of sight." All objects beyond or on this side the point of sight are seen double-in the one case homonymously, in the other heteronymously -because their images do not fall on corresponding points of the two retinæ. But objects below or above, or to one side or the other side of the point of sight, may possibly be seen single also. The sum of all the points which are seen single while the point of sight remains unchanged is called the horopter. Or it may be otherwise expressed thus: Each

eye projects its own retinal images outward into space, and therefore has its own field of view crowded with its own images. When we look at any object, we bring the two external images of that object together, and superpose them at the point of sight. Now the point of sight, together with the images of all other objects or points which coalesce at that moment, lie in the horopter. The images of all objects lying in the horopter

fall on corresponding points, and are seen single; and conversely, the horopter is the surface (if it be a surface) of single vision.

Is the horopter a surface, or is it only a line? In either case, what are its form and position? These questions have tasked the ingenuity of physicists, mathematicians, and physiologists. If the position of corresponding points were certainly known, and invariable in reference to a given spatial meridian, then the question of the horopter would be a purely mathematical one. But the position of corresponding points may change in ocular motions. It is evident, then, that it is only on an experimental basis that a true theory of the horopter can be constructed. And yet the experimental determination, as usually attempted, is very unsatisfactory on account of the indistinctness of perception of objects except very near the point of sight. Therefore experiments determining the laws of ocular motion, and mathematical reasoning based upon these laws, seem to be the only sure method.

The most diverse views have therefore been held as to the nature and form of the horopter. Aguilonius, the inventor of the name, believed it to be a plane passing through the point of sight and perpendicular to the median line of sight. Others have believed it to be the surface of a sphere passing through the optic centers and the point of sight; others, a torus generated by the revolution of a circle passing through the optic centers and the point of sight, about a line joining the optic centers. The subject has been investigated with great acuteness by Prévost, Müller Meissner, Claparède, and finally by Helmholtz. Prévost and Müller determine in it, as they think, the circumference of a circle passing through the optic centers and the point of sight.

(the horopteric circle), and a line passing through the point of sight and perpendicular to the plane of the circle (horopteric vertical). The horopteric circle of Müller is shown in Fig. 66, in which 0 0' is the line between the optic centers, n n' the nodal points or points of ray-crossing, A the point of sight, and B an

FIG. 66.

n

object to the left and situated in the circumference of the circle. Of course, the images of A fall on the central spots c c'. It is seen also that the images of B fall at 6 b', at equal distances from the central spots c d', one on the nasal half and one on the temporal half, and therefore on corresponding points. The horopteric vertical of Müller passes through A and perpendicular to the plane of the circle (i. e., of the diagram).

Claparède makes the horopter a surface, of such a form that it contains a straight line passing through the point of sight and perpendicular to the visual plane, and

FIG. 67.

also such that every plane passing through the optic centers makes by intersection with this surface the circumference of a circle. In other words, he thinks that the horopter is a surface which contains the horopteric vertical, BA

B B', Fig. 67, and the horopteric circle, O A O', and in addition is further characterized by the fact that the intersection with it of every R. plane passing through the optic centers 0 0 upward as O BO' or downward as O B O' is also a circle. It is evident that, as these circles increase in size upward and downward, the horopter according to Claparède is a surface of singular and complex form.

Helmholtz arrives at results entirely different. According to him, the horopter varies according to the position of the point of sight, and is therefore very complex. He sums up his conclusions thus : *

“1. Generally the horopter is a line of double curvature produced by the intersection of two hyperboloids, which in some exceptional cases may be changed into a combination of two plane curves.

“2. For example, where the point of convergence

* Croonian Lecture, in “Proceedings of the Royal Society,” xiii (1864), p. 197; also “Optique Physiologique,” p. 901 et seq.

(point of sight) is situated in the median plane of the head, the horopter is composed of a straight line drawn through the point of convergence, and a conic section going through the optic centers and intersecting the straight line.

“3. When the point of convergence is situated in the plane which contains the primary directions of both visual lines (primary visual plane), the horopter is composed of a circle going through that point and through the optic centers (horopteric circle), and a straight line intersecting the circle.

“4. When the point of convergence is situated both in the middle plane of the head and in the primary visual plane, the horopter is composed of the horopteric circle and of a straight line going through that point.

“5. There is only one case in which the horopter is a plane, namely: when the point of convergence is situated in the middle plane of the head and at an infinite distance. Then the horopter is a plane parallel to the visual lines, and situated beneath them at a distance which is nearly as great as the distance of the feet of the observer from his eyes when he is standing. Therefore, when we look straight forward at a point on the horizon, the horopter is a horizontal plane going through our feet; it is the ground on which we stand.

“6. When we look not at an infinite distance, but at any point on the ground on which we stand which is equally distant from the two eyes, the horopter is not a plane, but the straight line which is one of its parts coincides with the ground.”

Some attempts have been made to establish the existence of the horopteric circle of Müller by means of experiments. A plane is prepared and pierced with a multitude of holes into which pegs may be set. The

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