But although the spherical aberration for a pencil of parallel rays cannot be made to vanish in a single lens bounded by spherical surfaces, the compound lens employed in an achromatic object glass, designed in the first instance to correct the chromatic aberration, has the further advantage of enabling us to render insensible the spherical aberration. Such a lens presents us with four spherical surfaces, the three independent ratios between the radii of which enable us to satisfy three conditions, while the scale of the system is determined by the focal length of the combination. The most important condition to satisfy is, that the chromatic aberration shall be corrected ; and if we further assume that the spherical aberration (or rather its loading term) shall vanish, we shall still have one relation between the four radii remaining disposable, whereby some further advantage may be secured, provided it be not incompatible with those already assumed, which will be known by its leading, when the condition of it is expressed analytically, to an equation having only impossible roots. Clairaut introduced the condition that the adjacent surfaces should have the same radii, one surface being convex and the other concave, so that the lenses would be everywhere in contact, and might be cemented together. Instead of this, Sir J. Herschel proposes to introduce the condition that the lens shall be aplanatic for pencils, not only of parallel, but also of slightly divergent rays. In the treatise on light above quoted (arts. 468-473 ), he has pointed out certain advantages of this method, and has computed with different dispersive ratios a table of the radii of the lenses for the compound object-glass of a telescope constructed according to this system as nearly aplanatic as possible, the compound focal length being 10.000; and, by the proportions indicated, the radii for object-glasses of any other compound focal length may be found. (On the subject of splanatic lenses for microscopes, see Mrenoseoez.) It may be well here to make a few remarks about the eye, regarded merely as an optical instrument, its general structure and functions being very fully:described under the article EYE, in the NAT. HIST. DIY. In this point of view its general office resembles that of a telescope in having to form images of distant, or moderately distant objects at its focus, which in order that the vision may be distinct must coincide with the retina. It differs, however, from a telescope, in having the whole space between the place of the first refraction and that of the focus filled with dense matter, in not having the refraction at the several surfaces centrical, and in having a much larger aperture, in comparison with the focal length, than could be tolerated in the best telescope.
On account of the magnitude of this aperture, the effect of spherical aberration might be seriously inconvenient if the media of which the eye is composed were severally homogeneous and bounded by spherical surfaces. The defecta of spherical aberration, it should.be remembered,
increase very rapidly with the aperture of a telescope, more rapidly than those of chromatic aberration. It is at the surface of the cornea that the main refraction takes place, and the protuberant form of this part of the eye seems calculated to diminish the aberration ; for we have seen that a prolate spheroid of suitable excentricity refracts accurately to a point a pencil of rays incident parallel to its axis. The increasing density of the crystalline lens in passing from its exterior to its centre has a similar tendency, since an ordinary glass lens fails to refract a pencil of parallel rays accurately to a point in consequence of the over refraction of the marginal rays compared with those incident towards the middle.
No compensation for the chromatic aberration of direct pencils seems to exist, or to be required. If a pure spectrum be thrown on a page of small print, and the page be viewed by a person of ordinary sight at the ordinary distance of reading, the print will be seen very distinctly about the bright part of the spectrum, but somewhat indistinctly from long-sighteduess in the red, and very indistinctly from shortsighted ness in the violet. Again, if the sun or a candle be viewed through several pieces of cobalt blue glass superposed, a combination which transmits only the extreme red, and the blue and violet of the spectrum, the red image and the blue image, though superposed, will not be seen in focus together. But in ordinary vision, where all the colours of the spectrum are viewed together, the confusion arising from the imperfect focusing of the fainter extremities of the spectrum is insensible.
If the eye were perfectly invariable in form, the images of objects at different distances could not all be formed on the retina, and therefore, such objects could not all be seen distinctly. The eye, however, possesses a power of adaptation, answering to the focusing of a telescope, which accompanies involuntarily the voluntary act of making the axes of the two eyes converge towards a nearer or more distant object by looking at the object.
If the cornea be too protuberant, the rays will be brought to a focus before reaching the retina (unless they come from an object close at Land), and the vision will be indistinct. A person thus affected is said to be short-sighted. If the cornea be too fiat, the rays will reach the retina before they come to a focus (unless they come from a very distant object, and perhaps not even then), and the vision will again be indistinct, such a person being said to be long-sighted. These defects, as is well known, may be corrected by the use of spectacles, re spectively concave and convex, and of suitable power. But there is another defect, consisting in the length of sight being different in different planes, which is far from uncommon, which cannot be corrected by ordinary lenses, though.it may by a properly chosen lens having one or both surfaces cylindrical. [Lzsrs.]