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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

Fig. 12.





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 SS, 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 is blurred. This defect must be corrected.

It is corrected 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 only 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. 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 con-
traction 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 nearly if not
completely achieved, for the clearness of Section SHOWING
vision is wholly conditioned on the sharp-
ness of the retinal image.

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 (page 79), 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.


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. In 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. n 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

circular (Fig. 15). The radiating fibers converge from the outer margin of the iris as a fixed point, and take hold on the movable margin of the pupil, and, when they contract, pull open the pupil on every side, and thus enlarge it (Fig. 15, B). The circular fibers are concentric with the pupil, and are especially numerous and strong near the margin, forming there a band about one-twentieth of an inch wide. When they contract, they draw up the pupil, like a string about the mouth of a bag, and make it small (Fig. 15, A). We may regard the radiating fibers as elastic, and as contracting passively by elasticity when stretched; and the circular fibers as contracting actively under stimulus, like a muscle. Further, the circular fibers are in such sympathetic relation with the retina, that a stimulus of any kind, but especially its appropriate stimulus, light, applied to the latter, causes the former to contract, the extent of the contraction being of course in proportion to the intensity of the light. If, therefore, strong sunlight impresses the retina, the circular fibers immediately contract, the pupil becomes small, and a large portion of the light is shut out. When the light diminishes, as in twilight, the circular fibers relax, the previously stretched radiating fibers contract by elasticity, and enlarge the pupil. At night the pupil enlarges still more, in order to let in as much light as possible. Finally, if a solution of belladonna (which completely paralyzes the circular fibers) be dropped into the eye, the pupil enlarges so that the iris is reduced to a narrow dark ring.

Art, taking the hint from Nature, and striving to be not outdone, has recently constructed for the microscope a diaphragm somewhat on this plan, and therefore called iris diaphragm. It is composed of many very thin metallic plates, partly covering each other, so

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