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 of the iris, or red vessels in the white of the eye, to ascertain the real 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 eyeball 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

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 ab or cd, 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 ab. 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 by turning one eye upwards, the other downwards, or both of them out

wards, 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

VOL. XIII.