tains the primary visual lines [primary visual plane], the Horopter is a circle going through that point and the optic centers [Prévost's horopteric circle] and a straight line intersecting the circle [where and in what direction not stated]."

"When the point of convergence is situated as well in the middle plane of the head as in the primary visual plane, the Horopter is the circle just described [Prévost's horopteric circle] and a straight line going through that point [direction not stated]."

"There is but one case in which the Horopter is really a plane, viz: when the point of convergence is in the middle plane of the head and at an infinite distance. Then the Horopter is a plane parallel to the visual plane and beneath it, at a certain distance which depends upon the angle between the really and apparently vertical meridians, but which is nearly as great as the distance of the feet of the observer from his eyes when he is standing. Therefore, when we look at a point on the horizon, the Horopter is the ground on which we stand. a When we look at the ground on which we stand at any point equally distant from both eyes, the Horopter is not a plane, but the straight line which is one of its parts coincides completely with the horizontal plane on which we stand."

These conclusions of Helmholtz are the result of refined mathematical calculations based entirely upon the supposed constant difference between the real and apparent vertical. If this principle be true for all normal eyes, then it is probable that Helmholtz's conclusions in regard to the form and position of the Horopter are also true for those cases in which the point of sight is at considerable distance and in which, therefore, the rotation of the eye is very small. I am not able to test all of Prof. Helmholtz's conclusions by calculations based upon this principle, but I easily see that the position of the Horopter lying along the ground is the necessary consequence of a difference of 1 degrees between the real and apparent vertical when the eyes are in their primary direction. For if a line be drawn from each pupil downward, making an angle of 21° with each other or of 11° with the vertical, they would intersect each other at the distance of about five feet below the eyes or about the feet of the observer standing erect. Now if these two lines be placed thus before the observer whose eyes are in the primary direction, it is plain that their stereoscopic combination would be a line lying along the ground to infinite distance. If the difference between the real and apparent vertical be less than 1°, then the distance below the eyes of the horopteric plane would be greater. We have already shown

that if there be any such difference in our own eyes, it cannot be more than 10'; in this case the horopteric plane would be at least 35-40 feet below the eyes. But Prof. Helmholtz takes no account of rotation of the eyes on the optic axes, which greatly affects the form and position of the Horopter when the point of sight is near; and we believe that it is only when the point of sight is near, that the form and position of the Horopter is of any practical importance in vision, for it is only then that the doubling of images lying out of the Horopter is perceptible.

It has been with much hesitation that I have ventured to criticise the conclusions of so distinguished a physicist. My ability to do so, if well founded, I attribute entirely to a facility in the use of the eyes such as I have never seen equalled in the case of any other person.

Although, I believe, Meissner has arrived at truer results than any one who has yet written on this subject; yet I think his method very unsatisfactory. I have wondered at the skill and patienee which could attain such true results by such imperfect methods. I have tried Meissner's experiments without any satisfactory results, and I confess I commenced these experiments with the conviction that his theory was untenable; but contrary to my expectation his views have been in a great measure confirmed. The difficulty with Meissner's method and in fact with all previous experimental methods, as already stated, is the indistinctness of objects at any considerable distance from the point of sight in any direction. In Meissner's experiment with the three points, B', A and B (fig. 11), in lowering B' or elevating B, the indistinctness was so great that I could not tell with certainty whether the images approached each other or not; and in his second experiment with the thread, the obstinate disposition on the part of the eye to see single by stereoscopic combination even when the images cross, interferes seriously with the certainty of the result. But in my experiments, by virtue of the complete dissociation of the axial and focal adjustments, the lines are seen perfectly clearly; and by making them pass each other slowly, their relation to each other may be observed with great exactness.

I will now state my own results in regard to the Horopter. It is evident that if, in convergence, the eyes rotate on the optic axes as my experiments prove, then in this state of the eyes the Horopter cannot be a surface, but a line; and this line cannot be vertical but inclined to the visual plane. Perhaps this requires farther explanation. If the eyes in a state of convergence be fixed on a vertical line, then if the eyes rotate the line must be doubled except at the point of sight. This doubling

is the result of horizontal displacement of the two images in opposite directions, and therefore the two images may be brought together by bringing the doubled portion of the vertical line nearer or carrying it farther away. This is done in inclining the line as in fig. 11. But all points to the right and left of the horopteric line are also doubled by rotation, but this doubling is the result of vertical displacement of the images; now vertical displacement cannot be remedied by increasing or decreasing the distance, because the eyes are separated horizon-. tally. Therefore no form of surface can satisfy the conditions of single vision right and left of the horopteric line. The restriction of the Horopter to a straight line and the inclination of that line to the visual plane are therefore necessary results of rotation on the optic axes. But I have also proved this by direct experiment.

14.

If two lines, one white on black and the other black on white (fig. 14) be drawn at an angle of 14 degrees with the vertical and therefore 2 degrees with each other, then by bringing my eyes so near to them at any point aa (taking care that the median line of sight shall be perpendicular to the plane of the lines) that the visual lines without crossing shall meet beyond the diagram at the distance of seven inches from the eyes, the two lines are brought in perfect coincidence. If on the contrary the same figure be turned upside down and the eyes be placed a little farther than seven inches, so that the two points aa are brought together by crossing the optic axes at the distance of seven inches, then also the lines are brought in perfect coincidence. The accompanying figure (fig. 15) in which 00 are the eyes, A the point of sight, aH, aH and a'H', a'H' are the lines in the two positions, will explain how the stereoscopic combination takes place in each case. The line HAH is the Horopter. This experiment is difficult to perform satisfactorily. When the lines come together it is difficult to determine whether there is real coincidence or not. I have observed, however, that when the coincidence is not perfect the white and black lines seem to run spirally round each other. The best plan is to observe them at the moment of coming together or of separating. I feel quite confident of the reliability of the conclusions reached.

I made many calculations based upon these experiments and on the previous experiments on rotation of the eye, to determine the inclination of the horopteric line for different degrees

of convergence, i. e., for different distances of the point of sight. The results of these calculations

were

15.

R

a

culations of any increase or decrease with distance. For all distances the inclination seemed to come out about seven degreesin some a little less, in some a little more. Beyond three inches there seems to be a slight progressive increase rather than decrease; within three inches the action of the eyes was irregular.

I then adopted another method. I used the diagram of parallel lines (fig. 6,) and inclined it at an angle of exactly 7° from the perpendicular in the supposed direction of the 'Horopter, and at the distance of 3 feet. In this position the verticals of course all converge by perspective. I then brought together successively the lines 3 inches apart, then those 6 inches apart, then those 9 inches, 12 inches, 15 inches, 18 inches and so on even to the last, which were 30 inches apart in each case the lines seemed to come together parallel or at least the divergence, if any, was so small that I could not be sure about it. Now in this experiment the point of sight varied from 16 inches to only 2.8 inches in distance, and yet the inclination of the horopteric line seemed to be nearly the same for all, viz: 7°. If there was any difference at all it seemed to be in favor of greater inclination at greater distance. This result which I arrived at, though doubtfully by experiment alone, would be the necessary result of any residual difference between the real and apparent vertical, or in other words, any residual inclination of the vertical upon the horizontal line of demarkation of the eye in its primary position, such as Helmholtz maintains and as I have supposed possible. Still it by no means proves the existence of this residual difference.

It must not be supposed, however, because the lines 3 inches, 6 inches, 9 inches, 12 inches, &c., apart, are all brought into coincidence at the same or nearly the same inclination, that therefore the amount of rotation of the eye is the same for all. The perspective convergence of the lines, of course increases with their distance apart, and therefore the rotation of the eye necessary to bring them successively into coincidence

increases also. It is quite possible that the rotation should increase with the optic convergence, and yet the inclination of the horopteric line remain constant or even decrease with the convergence. Whether the inclination of the horopteric line increases or decreases with distance would depend upon the law of increase of rotation with increasing convergence. If it increases with distance then it is possible that when we look at the ground before us the Horopter may be a line lying along the ground, as maintained by Helmholtz.

I next tried the same experiments with the eyes inclined downward 45°. The lines do not change at all their natural perspective convergence. In all the experiments made with eyes in this position the inclination of the lines in the image was the same as in the object. I conclude therefore that in this position of the eyes the Horopter is at right-angles to the plane of vision, and since there is no rotation of the eye the Horopter in this position expands into a surface. Below this inclination the Horopter again becomes a line but inclined now the other way, i. e., the upper end toward the observer. In turning the eyes upward toward the eyebrows, I have found the rotation, except in cases of strong convergence, less than looking straight forward. I conclude therefore that in this position the horopteric line inclines less to the visual plane than it does when the visual plane is in its primary direction.*

The points in which my experiments do not confirm Meissner are 1, the increasing inclination of the horopteric line with increasing convergence. 2, the increasing rotation of the eye as well as inclination of the horopteric line under all circumstances in turning the eye upward. Again, I believe that Meissner is also wrong in supposing that the Horopter is a plane when the eyes are depressed 45°. In this position it is a surface but not a plane. It is clear that the images of points situated to the right and left of the point of sight and in the same plane with it cannot fall on corresponding points of the two retina. As to the form of this surface, I feel myself unequal to the task of its mathematical investigation, and its experimentai investigation presents, I believe, insuperable difficulties.

We have seen that the eye in convergence rotates on the optic axis. The question naturally occurs, is this rotation to be regarded in the light of an imperfection of the instrument (of which there are several examples in the structure and mechanism of the eye,) and should the law of Listing be regarded as

* As stated in note on p. 165, eyes certainly differ in this respect. In my own, if convergence be small, the outward rotation decreases with the elevation of the visual plane, becomes zero, and even is converted into an inward rotation; the inclination of the Horopter, therefore, decreases, becomes perpendicular and even inclines the other way. In some other eyes the outward rotation increases whatever be the convergence; in this case, of course, the inclination of the Horopter increases as stated by Meissner.