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hat the superior oblique muscle lowers the visual line, and the inferior raises t; but these last two muscles not only raise and lower the visual line ; hey produce also a rotation of the eye round the visual line itself, of which we shall have to speak more afterwards.

A solid body, the centre of which is fixed, and which can be turned round three different axes of rotation, can be brought into every possible position consistent with the immobility of its centre. Look, for instance, at the motions of our arm, which are provided for at the shoulder-joint by the gliding of the very accurately spherical upper extremity of the humerus in the corresponding excavation of the scapula. When we stretch out the arm horizontally, we can turn it, first, round a perpendicular axis, moving it forwards and backwards ; we can turn it, secondly, round a horizontal axis, raising it and lowering it; and lastly, after having brought it by such motions into any direction we like, we can turn it round its own longitudinal axis, which goes from the shoulder to the hand; so that even when the place of the hand in space is fixed, there are still certain different positions in which the arm can be turned.

Now let us see how far the motions of the eye can be compared to those of our arm. We can raise and lower the visual line, we can turn it to the left and to the right, we can bring it into every possible direction, throughout a certain range-as far, at least, as the connexions of the eyeball permit. So far the motions of the eye are as free as those of the arm. But when we have chosen any determinate direction of the eye, can we turn the eye round the visual line as an axis, as we can turn the arm round its longitudinal axis ?

This is a question the answer to which is connected with a curious peculiarity of our voluntary motions. In a purely mechanical sense, we must answer this question in the affirmative. Yes, there exist muscles by the action of which those rotations round the visual line can be per. formed. But when we ask, “Can we do it by an act of our will?” we must answer, “ No.” We can voluntarily turn the visual line into every possible direction, but we cannot voluntarily use the muscles of our eye in such a way as to turn it round the visual line. Whenever the direction of the visual line is fixed, the position of our eye, as far as it depends upon our will, is completely fixed and cannot be altered.

This law was first satisfactorily proved by Professor Donders, of Utrecht, who, in a very ingenious way, controlled the position of the eye by those ocular spectra which remain in the field of vision after the eye had been fixed steadily during some time upon any brightly coloured object. I have used for this purpose a diagram like fig. 1: the ground is grey paper, and in the middle, along the line ab, is placed a narrow strip of red paper on a broader strip of green paper*. The centre of the red strip is marked by two black points. When you look for about a minute steadily and without moving your eye at the centre of the diagram, the image of the

* Green is represented in the figure by white ; red by the central dark stripe.

coloured strips is projected on the nervous membrane of your eye; those parts of this membrane on which the light falls are irritated, and in consequence of this irritation, their irritability is exhausted, they are fatigued

Fig. 1.

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and they become less sensitive to that kind of light by which they were excited before. When you cease, therefore, to look at the coloured strips, and turn your eye either to the grey ground of the diagram, or to any other part of the field of vision which is of a uniform feeble degree of illumination, you will see a spectrum of the coloured strips, exhibiting the same apparent magnitude but with colours reversed, a narrow green strip being in the middle of a broader red one. The cause of this appearance is, that those parts of your retina which were excited formerly by green light are less affected by the green rays contained in white or whitish light than by rays of the complementary colour, and white light, therefore, appears to them reddish; to those parts of the nervous membrane, on the other hand, which had been fatigued by red light, white light afterwards appears to be greenish. The nervous membrane of the eye in these cases behaves nearly like the sensitive stratum in a photographic apparatus, which is altered by light during the exposure in such a way that it is impressed differently afterwards by various agents; and the impression of light on the retina may be, perhaps, of the same essential nature as the impression made upon a photographic plate. But the impression made on the living eye does not last so long as that on sensitive compounds of silver ; it vanishes very soon if the light be not too strong. Light of great intensity, like that of the sun when directly looked at, can develope very dark ocular spectra, which last a quarter of an hour, or even longer, and disturb the

perception of external objects very much, as is well known. One must be very careful to avoid the use of too strong a light in these experiments, because the nervous apparatus of the eye is easily injured by it; and the brightness of these coloured strips when illuminated by common daylight is quite sufficient for our present purpose.

Now you will perceive easily that these ocular spectra are extremely well adapted to ascertain the position of the eye-ball, because they have a fixed connexion with certain parts of the retina itself. If the eyeball could turn about its visual line as an axis, the ocular spectrum would apparently undergo the same degree of rotation ; and hence, when we move about the eye, and at last return to the same direction of the visual line, we can recognize easily and accurately whether the eye has returned into the same position as before, or whether the degree of its rotation round the visual line has been altered. Professor Donders has proved, by using this very delicate test, that the human eye, in its normal state, returns always into the same position when the visual line is brought into the same direction. The position and direction of the eye are to be determined in this case in reference to the head of the observer; and I beg you to understand always, when I say that the eye or its visual line is moved upwards or downwards, that it is moved either in the direction of the forehead or in that of the cheek; and when I say it is moved to the left or to the right, you are to understand the left or right side of the head. Therefore, when the head itself is not in its common vertical position, the vertical line here understood is not accordant with the line of the plummet.

Before the researches of Donders, some observers believed they had found a difference in the relative positions of the eye, when the head was brought into different situations. They had used either small brown spots

position of the eyeball; but their apparent results have been shown to be erroneous by the much more trustworthy method of Donders.

In the first place, therefore, we may state that the position of the eye. ball depends exclusively upon the direction of the visual line in reference to the position of the head of the observer. But now we must ask, what is the law regulating the position of the eye for every direction of its visual line? In order to define this law, we must first notice that there exists a certain direction of the visual line, which, in relation to the motions of the eye, is distinguished from all other directions of the eye; and we may call it the central or primary direction of the visual line. This direction is parallel to the median vertical plane of the head; and it is horizontal when the head of the observer, who is standing, is kept in a convenient erect position to look at distant points of the horizon. How this primary direction of the visual line may be determined practically with greater accuracy we shall see afterwards. All other directions of the visual line we may call secondary directions.

A plane which passes through the visual line of the eye, I call a meri

dian plane of the eye. Such a plane cuts through the retina in a certain line; and when the eye has been moved, we consider as the same meridian plane that plane which passes through the new direction of the visual line and the same points of the retina as before.

After having given these definitions, we may express the law of the motions of the eye in the following way :

Whenever the eye is brought into a secondary position, that meridian plane of the eye which goes through the primary direction of the visual line has the same position as it has in the primary direction of the eye.

It follows from this law that the secondary position of the eye may be found also by turning the eye from its primary position round a fixed axis which is normal as well to the primary as to the secondary of the visual line.

[The geometrical relations of these different positions were explained by the lecturer by means of a moveable globe placed on an axis like the common terrestrial globes.]

It would take too long to explain the different ways in which different observers have tried to determine the law of the motions of the eyeball. They have employed complicated apparatus for determining the angles by which the direction and the rotation of the eye were to be measured. But usually two difficulties arise from the use of such instruments containing graduated circles, in the centre of which the eye must be kept steady. In the first place, it is very difficult to fix the head of the observer so firmly that he cannot alter its position during a continuous series of observations, and that he reassumes exactly the same position of the head when he returns to his measurements after a pause,-conditions which must necessarily be fulfilled if the observations are to agree with each other. Secondly, I have found that the eye must not be kept too long a time in a direction which is near to the limits of the field of vision ; else its muscles are fatigued, and the positions of the eyeball corresponding to different directions of the visual line are somewhat altered. But if we have to measure angles on graduated circles, it is difficult to avoid keeping the eye too long in directions deviating far from the primary direction.

I think that it depended upon these causes, that the observations carried out by Meissner, Fick, and Wundt agreed very ill with each other and with the law which I have explained above, and which was first stated by Professor Listing of Göttingen, but without any experimental proof. Happily it is possible, as I found out, to prove the validity of this law by a very simple method, which is not subject to those sources of error I have named, and which I may be allowed to explain briefly.

In order to steady the attitude of the head in reference to the direction of the visual line, I have taken a little wooden board, one end of which is hollowed into a curve fitting the arch of the human teeth ; the margin of this hollow is covered with sealing-wax, into which, after it had been softened by heat and had been cooled again sufficiently, I inserted both

series of my teeth, so that I kept it firmly between my jaws. The impressions of the teeth remain indented in the sealing-wax; and when I put my teeth afterwards into these impressions, I am sure that the little board is brought exactly into the same position, relatively to my head and my eyes, as it was before. On the other end of that little board, which is kept horizontally between the teeth, a vertical piece of wood is fastened, on which I fix horizontally a little strip of card pointed at each end, so that these two points are situated about five inches before my eyes, one before the right eye, the other before the left. The length of the strip of card must be equal to the distance between the centres of the eyes, which is 68 millimetres for my own eyes. Looking now with the right eye in the direction of the right point of that strip, and with the left eye in the direction of the left point, I am sure to bring the eyes always into the same position relatively to my head, so long as the position of the strip of card on the wooden piece remains unaltered.

As a field of vision I use either a wall covered with a grey paper, in the pattern of which horizontal and vertical lines can be easily perceived, or a drawing-board covered with grey drawing-paper, on which a system of horizontal and vertical lines is drawn, as in fig. 1, and coloured stripes are fastened along the line ab.

Now the observer at first must endeavour to find out that position of his eyes which we call the primary position. In order to do this, the observer takes the wooden piece between his teeth, and brings his head into such a position that his right eye looks to the centre of the coloured stripes, in a direction perpendicular to the plane of the drawing. Then he brings his head into such an attitude that the right end of the card-strip appears in the same direction as the centre of the coloured stripe. After having steadily looked for some time to the middle of the coloured stripe, he turns away his gaze to the end of either the vertical or horizontal lines, ab, cd, which are drawn through the centre of the coloured stripe. There he will see an ocular spectrum of the coloured stripe, and will observe if it coincides with the horizontal lines of the drawing. If not, he must alter the position of the strip of card on the wooden bar to which it is fastened, till he finds that the ocular spectrum of the coloured stripe remains horizontal when any point either of the line ab or cd is looked at. When he has thus found the primary direction of his visual line for the right eye, he does the same for the left.

The ocular spectra soon vanish, but they are easily renewed by looking again to the centre of the stripes. Care must be taken that the observer looks always in a direction perpendicular to the plane of the drawing whenever he looks to the centre of the coloured stripe, and that he does not move his head. If he should have moved it, he would find it out immediately when he looks back to the strip, because the point of the cardstrip would no longer cover the centre of the coloured stripe.

So you see that the primary direction of the visual line is completely

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