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candle-flame from the right eye. Nevertheless, while gazing steadily at the flame, a really correct outline of it may be drawn on the opaque transverse screen, precisely as if it were transparent. This is illustratel and explained by the accompanying diagrams. Fig. 138 is the actual condition of things. F is the flame; ms, the median screen, resting on the nose n; ts, the transverse portion of the screen. Now, just where the

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visual line of the right eye pierces the transverse screen, viz., at f, we may draw the picture of the flame F, precisely as if it were transparent. The explanation is found by examining the visual result, Fig. 139. By the heteronymous doubling of the median and transverse screens, the left-eye image of the flame and the right-eye image of the transverse screen ts are brought together, and the flame may be seen as it were through

screen.

FIG. 140.

the opaque screen as a transparency, and drawn at f'. In order to show that the flame is seen only by one eye, I have stopped one of the combined visual lines at the

The apparent transparency of an opaque screen in this case is precisely the same as the transparent borders of an opaque screen mentioned and explained on page 275.

Experiment 4.To see through a book, a deal board, or the back of the hand, or even if necessary through a millstone. Roll up a thin pamphlet into a hard tube a half or three quarters of an inch in diameter, and hold it with the left hand between the thumb and hand, as shown in Fig. 140. Place the right eye to the end of the tube and look through the tube at the opposite wall, or still better at a map or picture hanging on the wall, while the back of the hand conceals the map or picture from the left eye. A circular spot on the wall or map will be seen through the center of the hand (Fig. 140), precisely as if there were a circular hole in the hand. Of course a book or an opaque plate of any kind may be substituted for the hand in this experiment.

The explanation is as follows: The visual line of the right eye passes through the axis of the tube and pierces the center of the circular visible area of the object regarded, while the visual line of the left eye pierces the back of the hand or the book at a point distant from the axis of the tube just an interocular space, or about 24 inches. By the right and left shifting of the fields of view already explained, the two visual lines are brought together in the middle; and therefore the center of the area regarded by the right eye and the spot on the hand or book pierced by the left visual lino are also brought together and superposed.

One thing more to complete the explanation: The impression on the right eye prevails over that on the left — the impression of the circular area obliterates that of the corresponding area on the hand or book for two reasons: first, because the circular area is strongly differentiated from the rest of the right-eye field of view (i. e., the dark interior of the tube), while the corresponding or coincident area of the left-eye field (the hand or book) is not thus differentiated; and second, because both eyes are focally adjusted for the distance of the object seen by the right eye only. Thus it happens that the right eye sees only the circular area, the rest of its field being very dark; while the left eye sees all its field except the spot corresponding to and covering the circular area. Thus the binocular observer sees the general field of the left eye (the hand or book), in the middle of which he also sees the circular area of the right-eye field. But if an ink-spot be made on the back of the hand or book just where the left visual line pierces it, the impression of this will be strong enough to resist obliteration; the strongly differentiated inkspot will be seen in the center of the circular area, as shown in Fig. 140.

CHAPTER V.

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 usually 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.

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