FIG. 75.

true; for, with an interocular distance of 2 inches, two lines drawn through the optic centers, each inclined 14° with the vertical and therefore 21° with each other,

DIAGRAM SHOWING VERTICALS INCLINED 4°. (Taken from Helmholtz.)

would in fact meet about 5 feet below-i. e., about the feet. If, therefore, we place two actual rods together on the ground between the feet, and the upper ends before the pupils, the eyes being parallel, it is evident that the image of the right rod on the right retina and that of the left rod on the left retina would fall exactly on Helmholtz's apparent vertical meridian, and, if Helmholtz's views be correct, on the vertical lines of demarkation and on corresponding points of the retina, and thus would be binocularly combined and seen as a single line lying along the ground to infinite distance. And conversely, with the eyes parallel and the lines of demarkation inclined 11° with the vertical, a rod lying on the ground to infinite distance would cast its images on these lines, and therefore be seen single throughout.

FIG. 76.

There are several curious questions which force themselves on our attention here if Helmholtz's view be true. 1. If we suppose the two eyes to be placed one on the other, so that the real vertical meridians coincide, we have already seen that Helmholtz's apparent verticals or lines of demarkation will cross each other like an X, as in Fig. 76, making with each other an angle of 21°. Now the two rods 24 inches apart at the height of the eyes, and meeting below at the feet, or the rod lying along the ground to infinite distance, would

THE RETINE SUPERPOSED. -rr, line of demarkation of right eye; 11,

left eye.

occupy

with

line of demarkation of their images only the upper half of the X. But suppose the two rods, instead of stopping opposite the eyes, to continue upward to the limits of the field of view. Obviously this upper half would cast images on the lower half of the X, and therefore would be seen single also. Where shall we

refer them? Or, to express it differently, the horopter with the eyes looking at a distant horizon, according to Helmholtz, is the ground we stand on; but this is evidently pictured on the upper halves only of the two retinæ. Where is the other half of the horopter corresponding to the lower halves of the retinæ?

2. Again: According to Helmholtz, in looking at a distance the horopter is the ground we stand on, and he gives this as the reason why distance along the ground is more clearly perceived than in other positions.* On the contrary, it seems to me that it would have just the reverse effect. If the horopter were the ground we stand on, then relative distances on the ground could not be perceived by binocular perspective at all; for this is wholly dependent on the existence of double images, which could not occur in this case by the definition of the horopter. It would be therefore only by other forms of perspective that we could distinguish relative distance along the ground. But that we do perceive perspective of the ground binocularly—i. e., by double images-is proved by the fact that the perspective of the receding ground is very perfect in stereoscopic pictures, where the images of nearer points are necessarily double; for the camera has no such distinction between real and apparent verticality as Helmholtz attributes to the eye.

But it is useless to argue the point any further, for I am quite sure that the property which Helmholtz finds in his eye is not general, and therefore not normal. We have seen that in convergence the eyes rotate outward, so as to bring about the very condition of things temporarily which Helmholtz finds permanent in his eyes. I have therefore thought it possible, or

* Op. cit., p. 923.

even probable, that the same habits in early life which, by constant adapting of the eyes to vision of near objects, finally produce myopy, may also, by constant slight rotation of the eyes outward and distortion * in convergence on near objects, finally bring about a permanent condition of slight distortion and outward rotation of 11°. Helmholtz is slightly myopic.t

However this may be, I am sure there is no such relation between real and apparent vertical meridian in my eyes as that spoken of by Helmholtz. All the experiments supposed to prove such relation fail completely with me. A vertical rectangular cross appears rectangular to either eye. The lines of Helmholtz's diagram, Fig. 75, when combined beyond the plane of the diagram, either by the naked eyes or by a stereoscope, do not come together parallel, but with a decided angle, viz., 21. But when I turn the diagram upside down, and combine by squinting, then the vertical lines, being inclined the other way, as in my diagram, Fig. 68, combine perfectly by outward rotation of the eyes. I have constructed other diagrams with less and less inclination of the verticals, until the inclination was only 10', and still I detected the want of parallelism when combined beyond the plane of the diagram. Beyond this limit I could not detect it, but I believe only because the limit of perception was passed; for when the lines are made perfectly vertical, they come together perfectly parallel and unite absolutely. It is certain, therefore, that in my eyes the vertical line of demarkation coincides completely with the true vertical meridian.

Meissner alone, of all writers with whom I am ac* Simple rotation is not sufficient, because this would affect also the horizontal meridian. Op. cit, p. 914.

Meissner, "Physiologie des Sehorgans"; also "Archives des Sciences," vol. iii (1858), p. 160.

quainted, attempts to determine the horopter directly by experiment. According to him, if a stretched thread be held in the median plane at right angles to the primary visual plane, about 6 to 8 inches distant, and the point of sight be directed on the middle, the thread will not appear single, but the two images will cross each other

at the point of sight thus

ν

12

X

rr' being the right

eye image, and the left-eye image. Now, as the images are heteronymous at the upper end and homonymous at the lower end, it is evident that they will unite at some farther point above and some nearer point below. By inclining the thread in the manner indicated-i. e., by carrying the upper end farther and bringing the lower end nearer the two images come together more and more, until at a certain angle of inclination, varying with the distance of the point of sight, they unite perfectly. The thread is now in the horopter.

Experiment.-I find that the best way to succeed with Meissner's experiment is as follows: Hold a stretched black thread parallel with the surface of the glass of an open window, and within half an inch of it. Now, with the eyes in the primary position, look, not at the thread, but at some spot on the glass. It will be seen that the double images of the thread are not parallel, but make a small angle with each other, thusNow bring the lower end nearer the observer very gradually. It will be seen that the double images become more and more nearly parallel, until at a certain angle of inclination the parallelism is perfect. I have made several experiments with a view to measuring the angle of inclination for different dis