ACHILLES TATIUS Greeks. He institutes games in honor of his friend, and slays 12 captive Trojan youths on the funeral pyre, to satisfy the manes of Patro- clus. Priam, led by Mercury, penetrates to his tent, and prevails upon him to allow the body of Hector to be ransomed. We hear no more of Achilles in the Iliad. The accounts of his death are various. One represents him as falling by the arrow of Paris, directed by Apollo at the vulnerable heel, when he was in the temple of that god, about to espouse at the altar Polyxena, the daughter of Priam. His remains were collected in a golden urn, and a cenotaph was erected to him on the promontory of Sigeum. This monument was always an object of veneration to the Greeks ; Alexander the Great performed a pilgrimage to it, and ran naked three times around it. ACHILLES TATIUS. I. A Greek astronomer, supposed to have flourished in the 4th century of our era, and to be the author of a treatise on the sphere, a fragment of which is extant. II. A native of Alexandria, who wrote a Greek romance entitled " The Story of Leucippe and Clitophon," which has come down to us. He probably wrote near the close of the 5th cen- tury. By some biographers these two writers are considered identical. ACHMET. See AHMED. ACHMIM. See EKHMIN. ACHROMATIC LENS (Gr. a, without, and xp&pa, color). When light is refracted by any transparent medium, dispersion always takes place ; that is, the rays of different color con- tamed in white light are not equally refracted or deviated from their path. It would seem that the amount of this dispersion must always be proportional to the amount of refraction, but experiments have shown that diverse refracting substances differ considerably in this respect. Their dispersing and refracting properties are determined by passing a ray of light through solid prisms of different material, or liquid prisms enclosed between glass plates. The refracting power is then measured by the amount of deviation of the ray, and the dispersive power by the length of the colored spectrum produced. So it has been found that if the relative amounts of refraction of water, crown glass, flint glass, and oil of cassia are ex- pressed by the numbers 133, 152, 162, and 159, the amounts of dispersion or the lengths of their spectra are in ratio of 145, 203, 433, and 1,080. If the angle of a prism is increased, the refract- ing and dispersing power both increase in the same ratio ; and it is evident that two prisms of different material may be made at such an- gles that they produce the same length of spec- trum, or possess the same dispersion, but that then their refracting powers will not be the same. In figs. 1 and 2 two such prisms are represented, the first refracting more than the second, but giving equal lengths of spectra. If now two such prisms are joined in opposite directions, as represented in fig. 3, they will cause a neutralization of the equal spectra, but 6 VOL. i. 6 ACHROMATIC LENS 65 not of the unequal refraction, and therefore they will produce a deviation or refraction of FIG. 1. Refraction and Dispersion by Prisms. the rays without dispersion of the light; no colored spectrum will be produced, but only a pure white spot will be the result of such a combination, which is called an achromatic prism. This is the principle on which the lenses in all our modern telescopes, micro- scopes, photographic and other optical appara- tus are constructed. A convex lens of crown glass brings the rays together to a number of differently colored foci, of which the red rays will be the furthest from the lens, fig. 4. (See ABEEEATION, CHROMATIC.) A concave lens will throw the red rays nearer to the axis, fig. 5 ; but if this concave lens is made of flint glass (a material having a slightly greater refracting CROWN CLASS p IQ ACHROMATIC COMBINATION. Refraction and Dispersion by Lenses. but a much greater dispersive power), and ground to such a curve as completely to neu- tralize the dispersion or coloring of the first lens, while it affects its refraction only so far as to lengthen its focal distance, the combina-
