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CHAPTER IV.

VISUAL PHENOMENA IN OCULAR DIVERGENCE.

THE only normal condition of the optic axes is either parallelism or convergence. We can not voluntarily make the optic axes divergent, because there is no useful purpose subserved by such a position; there would be no meeting of the optic axes, and therefore no point of sight. All the advantages of binocular vision are conditioned on convergence only. Divergence would only confuse by giving false information. But, although the power of divergence could be of no use and has therefore never been acquired, yet under certain circumstances divergence does occur, and the curious phenomena which then follow are an admirable illustration of the principles of binocular vision already set forth. We will give a few of these phenomena.

1. In Drowsiness.-It is well known that in extreme drowsiness, when we lose control over the ocular muscles, we see double images. It is universally believed and taught by physiologists that this is the result of convergence of the optic axes in sleep. I know of no observations purporting to prove this. It is probably an inference from the contracted state of the pupils in sleep, and the fact that contraction of the pupils is

usually consensual with optic convergence.* This view is certainly false. Double images in sleepiness are certainly due to divergence, not convergence, of the optic

axes.

In extreme drowsiness I have often observed the object which I was regarding (it might be the head of a dull speaker) divide into two images, which then separated more and more, until at a distance of 30 feet they were 10 to 15 feet apart. Even under these conditions I have found it possible to make a scientific experiment. Often, control over the ocular muscles is lost even while consciousness and control over mental acts is still perfect. Often, although by effort I could retain control over the eyes, I have chosen to abandon it in order to make the following experiments.

Experiment 1.-As soon as the images are well separated, I wink the right eye: immediately the left image disappears. The images are therefore heteronymous. But convergence produces homonymous images, while parallelism and, a fortiori, divergence produce heteronymous images. In this case the heteronymous images can not be produced by mere parallelism, because this state separates the images only an interocular space, or about 2 inches, whereas the images may be separated many feet: therefore they are produced by divergence. The amount of divergence is easily calculated. At a distance of 30 feet a separation of the double images of 10 feet would require an angular divergence of the optic axes of nearly 19°; a separation of 15 feet would indicate an angular divergence of 28°.

* "In sleep and in sleepiness both eyes are turned inward and upward." "The contracted state of the irides in sleep is a consensual motion dependent on the position of the eyes, which are turned inward and upward."-Müller, "Physiology," Am. ed., pp. 810 and 535.

In every such experiment the consciousness is quickly and completely aroused, and the double images are speedily reunited, though not so speedily but that the result is unmistakable. But, lest some may regard the speedy union of the images as an objection to this experiment, we will take another.

Experiment 2.-While lying abed in the morning, if one gazes on vacancy, objects near at hand (say the bedpost) are doubled heteronymously, the images being 2 inches apart. If, while thus gazing and observing the heteronymous images, one should be overtaken by drowsiness and consequent loss of control over the ocular muscles, he will see that the already heteronymous images separate more and more. Now, if this were due to convergence, the heteronymous images would approach, unite, cross over, and become homony

mous.

It is certain, then, that in myself, in extreme drowsiness, when control over the ocular muscles is lost, and therefore presumably in sleep, the eyes diverge. I have also satisfied myself that my case is not exceptional in this respect, for my results have been verified by several other persons. I think, therefore, I may assume it as a general law.

Double vision is also a well-known phenomenon of extreme intoxication. The unnatural appearance of the eyes in such cases is due to want of parallelism of the optic axes. I have on several occasions examined the eyes of those in this sad condition, and have always found the axes divergent. This seems to arise from partial paralysis of the ocular muscles.

If we examine the eye-sockets of a human skull, we find that their axes diverge about 25°-30°. This is about the extreme divergence of the optic axes in

drowsiness. It is probable, therefore, that in a state of perfect relaxation or paralysis of the ocular muscles the optic axes coincide with the axes of the conical eyesockets, and that it requires some degree of muscular contraction to bring the optic axes to a state of parallelism, and still more to one of convergence, as in every voluntary act of sight. In the human eye, therefore, and also in that of the highest animals, there are three conditions of the optic axes: first, convergence, as when we look at a near object; second, parallelism, as when we look at a distant object or gaze on vacancy; third, divergence, when we lose control over the ocular muscles, as in drowsiness, in drunkenness, in sleep, and in death. The first requires a distinct voluntary contraction of the ocular muscles; in the second there is no voluntary action, but only that involuntary tonic contraction characteristic of the healthy waking state; in the third the relaxation is complete. The first is the active state of the eye, the second the waking passive state, the third the absolutely passive state.

2. Other Modes of producing Divergence.-But the divergence of the optic axes may be effected in other ways. In most normal eyes the passive state is one of parallelism. It is easy therefore to double homonymously the images of an object at any distance by convergence, but most persons would find it impossible voluntarily to double the images of a very distant object, as for example a star, heteronymously—i. e., by divergence. Yet under certain conditions a slight divergence is possible. For example, I find I can (and I believe most persons can) combine with the naked eyes and with natural perspective (i. e., beyond the plane of the card) stereoscopic pictures in which identical points are farther apart than the interocular distance. I can

R

not always succeed, being able to do so only when my mind is in an exceptionally passive state.

Experiment 3.-I take now a skeleton stereoscopic diagram, identical points in the background of which are separated by a space greater by an eighth of an inch than my interocular space. By holding it at arm's length so as to make the divergence as small as possible, I succeed in combining. After the combination is stable, I can bring the card nearer and nearer until it is within 5 inches of my eyes, and yet the combinaation is retained. But this corresponds to a divergence of only 110.

Experiment 4.-But by mechanical force we may make the eyes diverge 40° or 50°. This is done by pressure in the external corner of the eye. By thrusting a finger of each hand into the external corners of the eyes I can make the two images of an object directly in front separate 50°, or the images of two objects situated 25° to the right and left of the median line, and therefore 50° apart from each other, come to the front and unite.

The following diagrams represent and explain the visual phenomena in divergence of the optic axes.

In Fig. 127, which represents the actual relation of parts, m is the median line; v v, the visual lines or optic axes produced; A, an object on the median line; b b, two similar objects in the direction of the diverging visual lines; and rr, ray-lines from the object A. Fig. 128 shows the visual result if the lines in Fig. 127 were visible lines drawn on the plane described on page 231. It will be seen that by heteronymous shifting and then heteronymous rotation the whole diagram represented by Fig. 127 has been carried and rotated by the right eye to the position of the lines connected by the unprimed vinculum, and by the left eye to the position

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