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fixed, and that the eye, which wants only to glance for an instant at a peripheral point of the drawing, and then goes back again to the centre, is not fatigued.

This method of finding the primary position of the eye proves at the same time that vertical and horizontal lines keep their vertical or horizontal position in the field of vision when the eye is moved from its primary direction vertically or horizontally; and you see, therefore, that these movements agree with the law which I have enunciated. That is to say, during vertical movements of the eye the vertical meridian plane keeps its vertical position, and during horizontal movements the horizontal meridian.

Now you need only bring either your own head into an inclined position, or the diagram with the lines, and repeat the experiment, putting your head at first into such a position that the centre of the diagram corresponds with the primary direction of the visual line, and moving afterwards the eye along the lines a b or c </, in either a parallel or perpendicular direction to the coloured line of the diagram, and you will find the ocular spectrum of the coloured line coinciding with those black lines which are parallel with a b. In this way, therefore, you can easily prove the law of Listing for every possible direction of the visual line.

I found the results of these experiments in complete agreement with the law of Listing for my own eyes, and for those of several other persons with normal power of vision. The eyes of very short-sighted persons, on the contrary, often show irregularities, which may be caused by the elongation of the posterior part of those eyes.

These motions of our eyes are a peculiar instance of motions which, being quite voluntary, and produced by the action of our will, are nevertheless limited as regards their extent and their combinations. We find similar limitations of motion of the eyes in other cases also. We cannot turn one eye up, the other down; we cannot move both eyes at the same time to the outer angle; we are obliged to combine always a certain degree of accommodation of the eyes to distance, with a certain angle of convergence of their axes. In these latter cases it can be proved that the faculty of producing these motions is given to our will, although our will is commonly not capable of using this faculty. We have come by experience to move our eyes with great dexterity and readiness, so that we see any visible object at the same time single and as accurately as possible; this is the only end which we have learnt to reach by muscular exertion; but we have not learnt to bring our eyes into any given position. In order to move them to the right, we must look to an object situated on our right side, or imagine such an object and search for it with our eyes. We can move them both inwards, but only when we strive to look at the back of our nose, or at an imaginary object situated near that place. But commonly there is no object which could be seen single bv turning one eye upwards, the other downwards, or both of them outwards, and we are therefore unable to bring our eyes into such positions. But it is a well known fact, that when we look at stereoscopic pictures, and increase the distance of the pictures by degrees, our eyes follow the motion of the pictures, and that we are able to combine them into an apparently single object, although our eyes are obliged to turn into diverging directions. Professor Donders, as well as myself, has found that when we look to a distant object, and put before one of our eyes a prism of glass the refracting angle of which is between 3 and 6 degrees, and turn the prism at first into such a position before the eye that its angle looks to the nose and the visual lines converge, we are able to turn the prism slowly, so that its angle looks upwards or downwards, keeping all this time the object apparently single at which we look. But when we take away the prism, so that the eyes must return to their normal position before they can see the object single, we see the object double for a short time—one image higher than the other. The images approach after some seconds of time and unite at last into one.

By these experiments it is proved that we can move both eyes outward, or one up and the other down, when we use them under such conditions that such a position is required in order that we may see the objects single at which we are looking.

I have sometimes remarked that I saw double images of single objects, when I was sleepy and tried to keep myself awake. Of these images one was sometimes higher than the other, and sometimes they were crossed, one of them being rotated round the visual line. In this state of the brain, therefore, where our will begins to lose its power, and our muscles are left to more involuntary and mechanical impulses, an abnormal rotation of the eye round the visual line is possible. I infer also from this observation, that the rotation of the eye round the visual axis cannot be effected by our will, because we have not learnt by which exertion of our will we are to effect it, and that the inability does not depend on any anatomical structure either of our nerves or of our muscles which limits the combination of motion. We should expect, on the contrary, that, if such an anatomical mechanism existed, it should come out more distinctly when the will has lost its power.

We may ask, therefore, if this peculiar manner of moving the eyes, which is determined by the law of Listing, is produced by practical •exercise on account of its affording any advantages to visual perceptions. And I believe that certain advantages are indeed connected with it.

We cannot rotate our eyes in the head, but we can rotate the head with the eyes. When we perform such a motion, looking steadily to the same point, we remark that the visible objects turn apparently a little round the fixed point, and we lose by such a motion of our eye the perception of the steadiness of the objects at which we look. Every position of the visual line is connected with a determined and constant degree of rotation, accord

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ing to the law of Donders; and in altering this rotation we should judge the position of external objects wrongly.

The same will take place when we change the direction of the visual line. Suppose the amplitude of such motions to be infinitely small; then we may consider this part of the field of vision, and the corresponding part of the retina on which it is projected, as plane surfaces. If during any motion of the eye the optic image is displaced so that in its new position it remains parallel to its former position on the retina, we shall have no apparent motions of the objects. When, on the contrary, the optic image of the visible objects is dislocated so that it is not parallel to its former position on the retina, we must expect to perceive an apparent rotation of the objects.

As long as the motions of the eye describe infinitely small angles, the eye can be moved in such a way that the optic image remains always parallel to its first position. For this end the eye must be turned round axes of rotation which are perpendicular to the visual line; and we see indeed that this is done, according to the law of Listing, when the eye is moving near its primary position. But it is not possible to fulfil this condition completely when the eye is moved through a wider area which comprises a larger part of the spherical field of view. For if we were to turn the eye always round an axis perpendicular to the visual line, it would come into very different positions after having been turned through different ways to the same final direction.

The fault, therefore, which we should strive to avoid in the motions of our eye, cannot be completely avoided, but it can be made as small as possible for the whole field of vision.

The problem, to find such a law for the motions of the eye that the sum of all the rotations round the visual line for all possible infinitely small motions of the eye throughout the whole field of vision becomes a minimum, is a problem to be solved by the calculus of variations. I have found that the solution for a circular field of vision, which corresponds nearly to the forms of the actual field of vision, gives indeed the law oi Listing.

I conclude from these researches, that the actual mode of moving the eye is that mode by which the perception of the steadiness of the objects through the whole field of vision can be kept up the best; and I suppose, therefore, that this mode of motion is produced by experience and exercise, because it is the best suited for accurate perception of the position of external objects.

But in this mode of moving, rotations round the visual line are not completely avoided when the eye is moved in a circular direction round the primary position of the visual line ; and it is easy to recognize that in such a case we are subject to optical illusions.

Turn your eyes to a horizontal line situated in the highest part of the field of vision, and let them follow this line from one end to the other. The line will appear like a curved line, the convexity of which looks downward. When you look to its right extremity, it seems to rise from the left to the right; when you look to the left extremity of the line, the left end seems to rise. In the same way, all straight lines which go through the peripheral parts of the field of vision appear to be curved, and to change their position a little, if you look to their upper or their lower ends.

This explanation relates only to Monocular vision; we have to inquire also how it influences Binocular vision.

Each eye has its field of vision, on which the visible objects appear distributed like the objects of a picture, and the two fields with their images seem to be superimposed. Those points of both fields of view which appear to be superimposed are called corresponding (or identical) points. If we look at real objects, the accurate perception of the Buperimposition of two different optical images is hindered by the perception of stereoscopic form and depth; and we unite indeed, as Mr. Wheatstone has shown, two retinal images completely into the perception of one single body, without being able to perceive the duplicity of the images, even if there are very sensible differences of their form and dimensions. To avoid this, and to find those points of both fields of view which correspond with each other, it is necessary to use figures which cannot easily be united into one stereoscopic projection.

In fig. 2 you see such figures, the right of which is drawn with white lines on a black ground, the left with black lines on a white ground. The horizontal lines of both figures are parts of the same straight lines; the vertical lines are not perfectly vertical. The upper end of those of the right figure is inclined to the right, that of the left figure to the left, by about 1^ degree.

Now I beg you to look alternately with the right and with the left eye at these figures. You will find that the angles of the right figure appear to the right eye equal to right angles, and those of the left figure so appear to the left eye; but the angles of the left figure appear to the right eye to deviate much from a right angle, as also do those of the right figure to the left eye.

"When you draw on paper a horizontal line, and another line crossing it exactly at right angles, the right superior angle will appear to your right eye too great, to your left eye too small; the other angles show corresponding deviations. To have an apparently right angle, you must make the vertical line incline by an angle of about 1^ degree for it to appear really vertical; and we must distinguish, therefore, the really vertical lines and the apparently vertical lines in our field of view.

There are several other illusions of the same kind, which I omit because they alter the images of both eyes in the same manner and have no influence upon binocular vision; for example, vertical lines appear always of greater length than horizontal lines having reallv the same length.

Now combine the two sides of fig. 2 into a stereoscopic combination, either by squinting, or with the help of a stereoscope, and you will see that the white lines of the one coincide exactly with the black lines of the other, as soon as the centres of both the figures coincide, although the vertical lines of the two figures are not parallel to each other.

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Therefore not the really vertical meridians of both fields of view correspond, as has been supposed hitherto, but the apparently vertical meridians. On the contrary, the horizontal meridians really correspond, at least for normal eyes which are not fatigued. After having kept the eyes a long

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