be not on the retina, but in front of or behind it. In both cases the retina cuts the pencil of refracted rays not in a single point, but in a circle of diffused light. Hence it follows that an immoveable eye can only see distinctly objects lying in one surface, and if we consider only rays of light making small angles with the axis of the eye, this surface may be considered plane. All objects or portions of objects not lying in this plane give indistinct images, in which circles of diffusion correspond to luminous points of the object.

Experience teaches us, however, that an eye is capable of seeing distinctly at almost any distance; there must therefore exist an arrangement for altering the eye, and adapting it for seeing at different distances at will. The changes which occur as the result of this arrangement are included under the term accommodation. It is not known with absolute certainty for what distance an eye is adjusted when it is not actively accommodated, but it is almost universally supposed that a normal eye when passive is adjusted for objects at an infinite distance, so that the second focal point of the eye at rest is on the retina. It follows from this that accommodation only occurs in one direction, the eye being actively accommodated for near objects.

108. It has been found by experiment that accommodation is effected by change of form in the refracting surfaces of the eye. When the eye is accommodated for near objects, the anterior surface of the crystalline lens becomes more strongly curved, and approaches nearer to the cornea; this is especially the case with the part not covered by the iris, which arches forwards through the pupil.

109. It has been seen that when the eye is at rest in any position and accommodated for an object, there is one point, the fovea centralis, where the vision is distinct, but that the vision is distinct only for a very small area about this spot. But the eye is usually in very rapid motion, and in an incredibly short space of time brings the various

points of an object into distinct view. We are thus enabled to form a clear conception of a considerably extended object or surface. This is aided also by the duration of the impression produced by a light. It has been found by experiment that this duration depends on the character of the light. For strong lights Helmholtz gives 4th of a second, and for weak lights th of a second, as the duration of the impression. Lissajou and others assign about th of a second as the lowest limit of the duration. If a spot on the retina be stimulated by a regular periodic light, whose period is sufficiently short, there will arise a continuous impression, which in intensity is equal to what would be produced were the whole incident light of any period uniformly distributed over the whole period.

110. The retina of both our eyes receive impressions when we look at any external object and in certain positions of our eyes we see two images, arising from the two retina, while in other positions we see only one image. To each point of one retina there is a corresponding point on the other; and when the images of an external point formed by the two eyes fall on corresponding points of the two retina, the point is seen single, but in other cases it is seen double. The points on the retina of an eye may be referred to two meridians formed on the retina by two planes through the axis of the eye. When the eye is directed forwards in a horizontal position, the points on the horizon have images lying on a meridian, which we may call the retinal horizon. Similarly certain lines appear vertical to an eye; the retinal image of these vertical lines is a meridian, which we may call the apparently vertical meridian. By experiment, Helmholtz concludes that the retinal horizon is actually horizontal for both eyes, but that the apparently vertical meridians are not quite perpendicular to the retinal horizon; they diverge outwards at their upper extremity. The inclination of each of these meridians to the real vertical is the same, and they include between them an angle varying from 2° 22′

to 2° 33'. Helmholtz also finds that in normal eyes, the points of distinct vision, as well as the retinal horizons and apparent verticals in the two eyes correspond; and further that corresponding points are equally distant from each retinal horizon and from each apparently vertical meridian.

111. Our most accurate estimate of the distances of visible objects depends upon our having two eyes. As we fix our gaze successively upon points at different distances we have to change the convergence of the axes of the two eyes, and from the degree of convergence of these axes when we look at any point we form an estimate of the distance of the point. Distances can however be estimated by a single eye, by observing the relative changes of position of objects, when the observer's position is changed.

Our idea of solidity also depends upon vision with two eyes. The views presented to the two eyes are slightly different, because the eyes have slightly different positions; and it is by the blending of the two impressions received upon the two retina that we receive the idea of solidity. This can be well shewn by aid of the stereoscope. This instrument was invented by Wheatstone for the purpose of combining two different photographic pictures, one of which is presented to each eye. These pictures are not exactly alike, but are taken by a camera with two lenses placed a small distance apart, so that they represent two different views such as might be presented to two eyes observing the scene. By means of mirrors or prisms the pictures are seen superimposed, and the impression produced on the mind by these superimposed views is exactly the same as if we were looking at the real scene, each object appearing in relief as it would in nature. For a perfect stereoscopic representation, the points at an infinite distance must fall on corresponding points of the two retina when the axes of the eyes are parallel. If the pictures are brought nearer to each other in the same plane than in the positions thus determined, the impression produced is exactly that of a relief picture.

112.

Vision through a lens.

To find the visual angle under which an object is seen through a lens, by an eye situated on the axis of the lens.

Let B, B' denote the linear magnitudes of the image and object, x, x' their distances from the first and second principal points, respectively, then

Let & denote the distance of the eye from the second principal point, so that the distance of the image from the eye is; then if be the angle under which the part of the image lying on one side of the axis is seen by the

E

The angle may therefore be increased so as to be brought as nearly equal to a right angle as we please, by making nearly equal to x'. The nature of vision, however, imposes a limit, because the eye is not capable of distinct vision when the point lies within a certain distance. If λ denote the least distance for distinct vision, then the greatest value of is found by putting - x' = X; we therefore get

The negative sign indicates that the image will be inverted.

113. When the image falls on the other side of the lens, a will be negative; and then tan will be made as large as possible by bringing the eye close to the lens. In this case is so small that it may usually be neglected, and we get tan 0 = ẞ/x, nearly.

From this it appears that tan may be made as large as we please by diminishing ; but there is a limit to the possible diminution of x, for x must not be sensibly less than λ. Now

The greatest visual angle under which an object may be seen distinctly, will therefore be given by the formula

The tangent of the angle subtended at the eye by the object when placed in the position of the image is B/; the ratio of these tangents is the magnifying power; and therefore, denoting the magnifying power by m,

In convex lenses f is positive, and therefore the object will appear magnified; in concave lenses f is negative, and therefore the object appears to be diminished by the lens.

114. If in the formula for tan we substitute for x' its value in terms of x, it becomes