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have a higher refractive power and a comparatively low dispersive power, and vice versa. This is the case with different kinds of glass.

Now, suppose we select a glass with excess of refractive over dispersive power for our convex lens, and one with excess of dispersive over refractive power for our plano-concave lens (Fig. 11, B), and cement these together as a compound lens: it is evident that these may be so related that the plano-concave lens shall entirely correct the dispersion of the convex lens without neutralizing its refraction, and therefore the combination will be a refractive, but not a dispersive, lens, and therefore will make an image without colored edges. Such a compound lens is called achromatic.

This is the way in which art makes achromatic lenses, and all good optical instruments have lenses thus corrected. Now, the lenses of the eye are apparently corrected in a similar manner. The eye consists of three lenses-the aqueous, the crystalline, and the vitreous. These have curvatures of different kinds and degrees the aqueous lens is convex in front and concave behind; the crystalline is bi-convex; the vitreous is concave in front. As its convex outer surface can not be regarded as a refracting surface, since this is in direct contact with the screen to be impressed, it may be considered as a plano-concave lens. The refractive powers of the material of these are also different: that of the crystalline being greatest, and the aqueous least. The dispersive powers of these have not been determined, but they probably differ in this respect also. Thus, then, we have here also a combination of different lenses, of different curvatures, and different refractive, and probably dispersive, power, and for the same purpose, viz., correction of chromatism. It is an interest

ing historic fact that the hint for correction of chromatism by combination of lenses was taken from the structure of the eye by Euler, and afterward carried out successfully by Dollond. That the chromatism of the eye is substantially corrected is shown by the complete absence of colored edges of strongly illuminated objects, and the sharp definition of objects seen by good eyes. By close observation and refined methods, it has been recently shown that the chromatism of the eye is not perfectly corrected. It can be observed if we use only the extreme colors, red and violet.* But the degree of chromatism is so small as not to interfere at all with the accuracy of vision.

4. Aberration.-Another defect, much more difficult to correct, is aberration. The form of lens most easily made has a spherical curvature. But in such a lens there is an excess of refractive power in the marginal portions as compared with the central portions; an excess increasing with the distance from the center; therefore the focal point for marginal rays is not the

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same as for the central rays, but nearer. In Fig. 12 the marginal rays, a r', a r', are brought to a focus at a", while the central rays, a r, a r, are brought to a focus at a'. The best place for the receiving screen would be at S S, between these; but even there the image would not be sharp. In such a lens there is no

* Helmholtz, "Popular Lectures," p. 216.

common focal point for all the rays, and therefore the conditions of perfect image are not fulfilled-the image This defect must be corrected. It is cor

is blurred.

rected in the best lenses.

The aberration may be greatly decreased by the use of diaphragms, which cut off all but the central rays; but in this case we get distinctness at the expense of brightness. This may be done when the light is very intense. Again, the aberration may be reduced by using several very flat lenses, instead of one thick lens. This plan is used in many instruments. But complete correction can only be made by increasing the refraction of the central portions of the lens, and this may conceivably be accomplished in two ways, viz., either by increasing the curvature of this part or by increasing its density, and therefore its refractive index. It is by the former method that art makes the correction. By mathematical calculation, it is found that the curve must be that of an ellipse. A lens, to make a perfect image, must not be a segment of a sphere, but of the end of an ellipsoid of revolution about its major axis. It is justly considered one of the greatest triumphs of science to have calculated the curve, and of art to have carried out with success the suggestion of science.

Art has not been able to achieve success by the second method. It is impossible so to graduate the increasing density of glass from the surface to the center of a lens as to correct aberration. Now, it is apparently this second method, or perhaps both, which has been adopted by nature. The crystalline lens increases in density and refractive power from surface to center, so that it may be regarded as consisting of ideal concentric layers, increasing in density and curvature until the central nucleus is a very dense and highly refractive

FIG. 13.

spherule (Fig. 13). The surface of the cornea has the form of an ellipsoid of revolution about its major axis, and therefore doubtless contributes to the same effect. In looking at very near objects, the contraction of the pupil, also, by cutting off marginal rays, tends in the same direction. However the result may be accomplished, whether by one or by both methods, it is certain that in good eyes it is completely achieved, for the clearness of vision is wholly conditioned on the sharpness of the retinal image.

SECTION SHOWING THE
STRUCTURE OF THE
LENS.

It is probable that the peculiar structure of the crystalline lens described above has also another important use in the lower animals, if not in man. Dr. Ludimar Hermann has shown that, in a homogeneous lens, while the rays from radiants near the middle of the field of view, i. e., nearly directly in front, are brought to a perfect focus, the rays from radiants situated near the margins of the field of view, i. e., of very oblique pencils, are not brought to a focus. Therefore the picture formed by such a lens is distinct in the central parts, but very indistinct on the margins. Now, this defect of a homogeneous lens, Dr. Hermann shows, is entirely corrected by the peculiar structure of the crystalline; therefore this structure confers on the eye the capacity of seeing distinctly over a wide field, without changing the position of the point of sight. This capacity he calls periscopism. We will hereafter, however, give reasons showing that this property of the crystalline can be of little value to man.

5. Adjustment for Light.—The delicate work done by the camera and by the eye requires a proper regulation

* "Archives des Sciences," vol. lxiii, p. 66. 1875.

In

of the amount of light. In both, therefore, we want some contrivance by which, when the light is very intense, a large portion may be shut out, and when the light is feeble, a larger portion may be admitted. optical instruments this is done by means of diaphragms. In the camera we have brass caps with holes of various sizes, which may be changed and adapted to the intensity of the light. In the microscope we have a circular metallic plate, with holes of various sizes. By revolving this plate we bring a larger or a smaller hole in front of the lens.

In the eye the same end is reached, in a far more perfect manner, by means of the iris. The iris (Fig.

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14, d) is an opaque circular disk, with a round hole, the pupil, in the middle. The circumference of the disk is immovably fixed to the sclerotic at its junction with the cornea; but the margin of the circular hole, or pupil, is free to move. The disk itself is composed of two sets of contractile fibers, viz., the radiating and the

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