if the object lie near the margin of the field of the lens. This is explained as follows:

Ordinary sunlight, as every one knows, consists of many colors mixed together, the mixture producing the impression of white. If a beam of sunlight be made to pass through a glass prism, the beam is bent: but more, the different colors are unequally bent, so that they are separated and spread out over a considerable space. This colored space is called the spectrum. In Fig. 9 the

r-v, spectrum: r, red; o, orange; y, yellow; g, green; ¿, blue; ¿, indigo; v, violet.

straight beam, a b, is bent by the prism so as to become a cd; this is called refraction. But also the different colors are unequally bent; red is bent least and violet most, the other colors lying between these extremes; thus they are spread out over a considerable colored space. This unequal refraction is called dispersion. If we look through a prism at objects, we will find that the outlines of the objects will be edged with exactly similar colors. Now all refraction is accompanied by dispersion; therefore a simple, uncorrected lens always disperses, especially on the edges where the refraction is greatest; and, therefore, also, the images made by such a lens will be edged with color. Thus the light from the radiant a (Fig. 10), being white light, is dispersed; the violet rays, being more bent, reach a focus at a',

but the red only at a", the other colors at intermediate points. There is, therefore, no place where all the rays from the radiant come to a focus-there is no commcn focal point for the radiant a. The best place

for the receiving screen would be SS, but even here there is no perfect focus. Evidently, therefore, the conditions of a perfect image are not fulfilled. This defect must be corrected. It is corrected in every good lens.

FIG. 11.

In order to understand how this is done, it must be remembered, first, that concave and convex lenses antagonize, and, if of equal refractive power, neutralize each other. Therefore, a combination of a double convex and a double concave lens, if of same material and of equal curvature, like Fig. 11, A, will produce no refraction, because the refraction produced in one direction by the convex lens is completely destroyed by refraction in the opposite direction by the concave lens. Such a combination will therefore make no image. In order that such a combination should make an image at all, it is necessary that the convexity should predominate over the concavity, as in Fig. 11, B. Again, it must be remembered that dispersion is not always in proportion to refraction. Some substances

A

B

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.

reous.

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 vitThese 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

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.

is blurred.

rected in the best lenses.

It is cor

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