Visual axis

“ Whether or not, in the case of the retina, our appreciation of the coin’s roundness comes from some unconscious counting process is a problem for the specialist to decide; but at all events, when we consider that the retina and the eye are Euclidean bodies just like our rulers, the concordance between our computations of shape and size, as determined by rods, and our direct visual appreciation of shape does not appear to present much of a mystery. ”

“ If, therefore, the cut has dimensions, the cut will have and the whole of visual space .
If all the red sensations affecting the same point of the retina were regarded as identical, the cut reducing to a single element would have 0 dimension, and visual space would have 2.
And yet most often it is said that the eye gives us the sense of a third dimension, and enables us in a certain measure to recognize the distance of objects. ”

“ When it is intended that the pictures taken are to be viewed by an instrument that requires their distance from the eyes to be less than the focal length of the lens used in their formation, what is the result? Why, that they subtend an angle larger than in nature, and are consequently apparently increased in bulk; and the obvious remedy is to increase the angle between the points of generation in the exact ratio as that by which the visual distance is to be lessened. ”

“ Work built up on outline drawing to which has been added light and shade, colour, aerial perspective, &c., may eventually approximate to the perfect visual appearance. And inversely, representations approached from the point of view of pure vision, the mosaic of colour on the retina, if pushed far enough, may satisfy the mental perception of form with its touch associations. And of course the two points of view are intimately connected. You cannot put an accurate outline round an object without observing the shape it occupies in the field of vision. ”

“ A network of associations is thus formed, whereby the sensation of each retinal point is connected with all the others in a manner which is that of points in a plane. Every visible point becomes thus a point in a field, and has a felt radiation of lines of possible motion about it. Our notion of visual space has this origin, since the manifold of retinal impressions is distributed in a manner which serves as the type and exemplar of what we mean by a surface. ”

“ When the object, by moving, changes its relations to the eye, the sensation excited by its image even on the same retinal region becomes so fluctuating that we end by ascribing no absolute import whatever to the retinal space-feeling which at any moment we may receive. So complete does this overlooking of retinal magnitude become that it is next to impossible to compare the visual magnitudes of objects at different distances without making the experiment of superposition. ”

“ The size of these circles will be either larger or smaller when the principal focus of the eye is either in front of or behind the retina.8
The refractive surfaces of a perfectly formed eye are very like an ellipsoid of revolution with two axes, one of which, the major axis of the ellipse, is at the same time the optic axis and that of rotation; the other is perpendicular to it, and is equal in all meridians. Eyes, however, perfectly constructed are rarely met with. The curvature of the cornea is nearly always greater in one meridian than in another. ”

“ The movement of the eyes is rather complex. When they move together to one side or the other or up and down in a vertical plane there is no rotation of the optical axes; that is, no torsion. When the visual plane is elevated and the eyes move to the [Pg 32] right they rotate to the right; when they move to the left they rotate to the left. ”

“ If the eyes are in the position of the head 30° to the left, the left eye thus much further from the edges than the right eye, the visual angle of the left image thus much smaller than that of the right image, we find the same equality-point with the same threshold. We saw that in this position the two visual angles would be equal if the left edge were moved to +17 mm.; instead of at +17, the equality-point—when the left edge is judged—lies at -1.49, that is, at a point at which the visual angle of the left eye is more than 46" smaller than the angle of the right eye. ”

“ The apparent magnitude of an object is the same wherever the eye be placed, but the visible area, or field of view, is the greatest when the eye is nearly at the focal distance of the eye-glass. 5. The visual angle depends on the breadth of the eye-glass; for it is equal to the angle which the eye-glass subtends at the object-glass; but the breadth of the eye-glass cannot be increased beyond a certain limit, without producing colouring and distortion. ”

“ IV Perspective of a Point, Visual Rays, &c.
We perceive objects by means of the visual rays, which are imaginary straight lines drawn from the eye to the various points of the thing we are looking at. As those rays proceed from the pupil of the eye, which is a circular opening, they form themselves into a cone called the Optic Cone, the base of which increases in proportion to its distance from the eye, so that the larger the view which we wish to take in, the farther must we be removed from it. ”

“ By means of an instrument called the perimeter, the field of vision for each eye can be measured. With its aid any small object can be made to fall on any part of the retina by directing the axis of the eye to a fixed point and moving the object along one of the diameters. Suppose we wish to ascertain the field for a white object, a small white disc is moved, say, along the horizontal line, and the angles at which the retina just no longer sees it are noted. ”

“ From the figure, which represents vision with a motionless eye, it is seen that the apparent size increases as the object under observation is approached. The greater the visual angle, the more distinctly are the details of the object perceived. On the other hand, as the observer recedes from the object, the apparent size, and also the image on the retina diminishes ”

“ Such glasses produce an optical effect only in one direction. If instead of white lines I make the experiment with colored lines, it will show the mixing of colors produced by astigmatism; and if I now turn the axis of the lens, you will observe the effect of different forms of astigmatism. I show you a square (Fig. 3) : if I add a cylindrical concave glass, with its axis placed horizontally, the square becomes an oblong. ”

“ As an object becomes perceptible to us, by means of the image thereof which is formed on the retina, it will, therefore, be seen in that direction, in which the rays enter the eye to form the image, and will always be found in the line, in which the axis of a pencil of rays flowing from it enters the eye. ”

“ A small visual angle is in most eyes a condition of sharpness of definition. With a large angle, objects appear less sharply marked. Acuteness is determined by a few retinal elements, or even only one, being affected. A very minute image, if thrown on a single retinal element, is apparently sufficient to excite it. Thus it is possible to see a brilliant point in an angle even so small as 1⁄4 of a second, and a sharp eye can see a body the 1/50th of a line in diameter—that is, about the 1/600th part of an inch. ”

“ The great sweep of vision, a sweep covering a hundred subjects perhaps, is obtained by turning the eyes up or down or sideways. But to be true—that is, to see one picture at a time—the eye should be fixed like the lens of a camera, the limit of the picture being the range of the eye and no more. A departure from this rule not only confuses your perspective but crowds a number of points of interest into the square of your canvas, when there is really only one centre point before you in nature ”

“ Perhaps the most important of the images which come in to give depth, volume, solidity to the partly imagined and partly perceived ‘picture-space’ are those which are relicts of eye movements, kinæsthetic images of the convergence of the eyes and accommodation of the lenses according to the distance of the object contemplated. When, as it seems, we look past an object in a picture to some more distant object, seeming in so doing to change the focus of our eyes, we do not as a rule actually make any change. ”

“ In cases, however, where the attractions vary in their tones, measures, and shapes, and where there are qualities as well as quantities to be considered, calculations and reasoning become difficult if not impossible, and we have to depend upon visual sensitiveness. All balances of positions, as indicated by dots corresponding in tone, measure, and shape, are balances of equal attractions, and the calculation to find the center is a very simple one. ”

“ In like manner, when the eye descends to e′′, e′, e, the united image d′′′c will rise and diminish, taking the positions d′′c, d′c, dc, till it disappears on the line cm, when the eyes reach m. If the eye deviates from the vertical plane gmn, the united image will also deviate from it, and is always in a plane passing through the common axis of the two eyes and the line gm. ”

“ The normal position of the axes of human eyes is convergent or parallel but it is possible to diverge the axes. In fact, with practice it is possible to diverge the axes sufficiently to look at a point near the back of the head, although, of course, we do not see the point. ”

“ Thus we see that an image is formed on both eyes, and we consequently see the object, whatever it may be, repeated twice. By degrees, however, the eyes gain the power of converging their axes on objects at different distances, so that they fall on similar portions of each retina, and so convey a single impression to the brain. ”

“ By looking above a light, or a letter, and then trying to see it as well as when directly regarded, one can produce an illusion of several lights, or letters, arranged vertically. If the strain is great enough, there may be as many as a dozen of them. By looking to the side of the light or letter, or looking away obliquely at any angle, the images can be made to arrange themselves horizontally, or obliquely at any angle. ”

“ The normal focus is for distant objects. When we read a book the eye adapts itself to the work. The ligaments relax and the lens decreases in diameter while thickening at the centre, until its curvature is such as to focus all rays from the book sharply on the retina. If we suddenly look through the window at something outside, the ligaments pull on the lens envelope and flatten the curves.
This wonderful lens is achromatic, and free from spherical aberration and distortion of image. ”

“ The only reminder of the top view is the eye or point of vision, the picture plane that falls together for the sake of convenience with the horizon of the end view and the ray that determines the measurement point M, which is, in this suppressed reproduction, absolutely necessary, in order to find the apparent position of the real corners behind the picture plane. ”

“ If we limit visual phenomena as data to mere variations of kind and distinctness in color, we cannot account for such cases as the appearance and inversion of mathematical perspective, binocular localisation and translocation, and the distinct effect of the monocular parallax of motion, qualities which are dimensional in their nature. ”

“ The smallest defect in the similarity or equality of the figures or lines which compose a pattern, and any difference in the distance of single figures is instantly detected, and what is very remarkable a small inequality of distance in a line perpendicular to the axis of vision, or in one dimension of space, is exhibited in a magnified form at a distance coincident with the axis of vision, and in an opposite dimension of space.
A little practice will enable the observer to realize and to maintain the singular binocular vision which replaces the real picture. ”

“ The human eye is so constituted, that it can only have distinct vision, when the rays which fall on it are parallel, or nearly so; because the retina, on which the image is painted, is placed in the focus of the crystalline humor, which performs the office of a lens in collecting rays, and forming the image in the bottom of the eye. ”

“ But the chief point remains that we see the whole picture with both eyes and not with only one, and that we are constantly reminded of the flatness of the picture because the two eyes receive identical impressions. And we may add an argument nearly related to it, namely, that the screen as such is an object of our perception and demands an adaptation of the eye and an independent localization. We are drawn into this conflict of perception even when we look into a mirror. ”

“ When the camera is out of focus the picture which it produces of any object is always slightly larger than the image produced when the focus is correct; but when the eye is out of focus the picture which the mind sees may be either larger or smaller than it normally would be. To one patient the big C at ten feet appeared smaller than at either twenty feet or four inches. ”

“ This finally results in a highly organized central spot or fovea which is possessed only by man and the higher monkeys. Proceeding up the scale we also find an increasing ability to converge the optic axes on a near point so that the images of the point may coincide with the central spots of both retinas. ”