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40 out into a butterfly flame. Soon afterwards, Billwiller introduced the idea of sucking air into the flame at or just below the burner tip, and at this juncture the Naphey or Dolan burner was introduced in America, the principle (employed being to use two small and widely separated jets instead of the two openings of the union jet burner, and to make each a minute Bunsen, the acetylene dragging in from the base of the nipple enough air to surround and protect it while burning from contact with the steatite. This class of burner has been very successful, and its introduction, together with the realization of the importance of purifying the gas before combustion, has removed perhaps the most important obstacle to the use of this beautiful illuminant.

Authorities.—Dommer, L'Acetylene et ses applications. Paris, 1896.—Lewes, Acetylene. London, 1900.—Liebetanz, Calcium£arbid und Acetylen. Leipzig, 1899.—Pellxssier, L'eclairage a, 1'acetylene. Paris, 1897.—Perrodil, Le carbure de calcium et I'acitylene. Paris, 1897.—For a complete list of the various papers and memoirs on Acetylene, see Ludwig’s Fiihrer durch die gesammte Calciumcarbid- und Acchjlen-Literatur. Berlin, 1899. (v. B. L.)

Achill Island, off the west coast of Ireland, part of the county of Mayo. How under the control of the Congested Districts Board, who have made efforts to improve the condition of the people. There is now a station at Achill Sound, which is crossed by a swivel bridge, opened in 1888. Population, 4677.

Achin (Dutch Atjeh) and its dependencies form a government of Northern Sumatra, extending from 2° 53' N. on the W. coast to 4° 32' N. on the E. coast. The area of Achin is estimated at 20,520 square miles. Since 1874 the valley of the Achin river has been subjugated by the Dutch. The restriction of export and import to Achin (1888) and further regulation of the ports (1892), the death of the traitor Tuku Umar, and the successful expeditions of General van Heutsz (1898-99) on both coasts and in the valley, have broken resistance and firmly established Dutch government. A scheme to unite the coasts by a railway is under consideration. The administrative divisions are as follows—1. Great Achin (the nine districts within and beyond the military posts) with Poeloe Wai (isle) ; 2. dependencies (west coast, with the island of Simalu [Babi or Hog], north coast, east coast, and the southern settlements of Great Achin). Under the military and civil chief is a resident (for the regulation of shipping ,and Achin affairs), and under him again assistant-residents for the dependencies. Geographical knowledge of the Achin valley, river, and coast has been considerably advanced since 1874. In its upper part, near Selimun, the valley is 3 miles broad, the river having a breadth of 99 feet and a depth of l]? feet; but in its lower course, north ,of its junction with the Krung Daru, the valley broadens to 121 miles. The marshy soil is covered by rice-fields, and on higher ground by kampongs full of trees. The river at its mouth is 327 feet broad and 20-33 feet deep, but before it lies a sandbank covered at low water by a depth of only 4 feet. The coasts are low and the rivers insignificant, rising in the coast ranges and flowing through the coast states (the chief of which are Pedir, Gighen, and Samalanga on the N., Edi, Perlak, and Langsar on the E., Kluwah, Rigas, and Melabuh on the W.). The chief ports are Olehleh, the port of Kotaraja or Achin (formerly Kraton, now the seat of the Dutch Government), Segli on the N., Edi on the E., and Analabu or Melabuh on the W., all visited by steamers of the Royal Packet Company.

The relief of the soil of Achin is imperfectly understood. With regard to the west coast, Resident van Langen has spoken of the Barisan and other parallel ranges which are characteristic of the island of Sumatra, and a geological description of a small portion of the same coast has been given by the mining engineer Renaud, but the interior, possibly a continuation of the Batta plateau, is unexplored. The population of Achin in 1898 was estimated at 535,432, of whom 328 were Europeans, 3933 Chinese, 30 Arabs, and 372 other foreign Asiatics. The natives of this commercial state are of very mixed origin (Hindu, Klings, Malay, Arab). They live in kampongs, collections of houses and gardens, which combine to form mukims or districts, which again combine to form sagis, of which there are three. The chief of a mukim is called an imeum, of a sagi a panglima sagi. The people of the highlands {prang tunong) differ in many respects from those of the lowlands (prang baroh). The means of subsistence are furnished by the culture of rice, betel (penang), tobacco, and pepper, but agriculture and stock-raising both declined during the war. The following 'industries are of some importance—^gold-working, weapon-making, silk-weaving, the making of pottery, fishing and coasting trade. The value of the exports (chiefly pepper) has of late years been about £58,000, of the imports from £165,000 to £250,000.

Kruijt. Atjeh en de Atjehers. Leiden, 1877.—Van Langen. Atjeh’s Wesskud, Tijdschrift Aardrijko. Genotktsch. Amsterdam, 1888, p. 226.—Renaud. Jaarboek van het Mynwczen. 1882.— Jacobs Het famille-en Kampongleven op Groot Atjeh. Leiden, 1894. —Snouck Hurgronje. He Atjehers. Batavia, 1894. (C. M. K.)

Achinsk, a district town of Russia, East Siberia, government of Yeniseisk, 110 miles by rail W. of Krasnoyarsk, and on the Chulym river. It was founded in 1642, and remained quite insignificant till lately, when steamers began to ply on the Chulym to the gold mines. There are tanneries and soap and candle works. Population (1860), 2501; (1897), 6714.

Achromatic Objectives.—The general equation for two lenses in contact and of negligible thicknesses is,

P = A(™-1) + B(w'-1),

where P is the power of the combined system, or the reciprocal of its focal length, A and B are the sums of the reciprocals of the radii of curvatures of the first and second lenses respectively, and n and n are the indices of refraction of the materials of which these two lenses are made. It is obvious that in general the value of P varies with the refrangibility of light, i.e., with its wave-length. The mathematical condition which must obtain in order that the power shall be invariable is that the derivative of this equation shall vanish, or

dP -r-da' - - = 0n = A. + B t-. dn dn

Lenses, whether binary or multiple, subject to this condition and employed for the formation of real images are called achromatic objectives. These two equations would serve to determine the values of A and B, when P is assumed, and thus completely solve the problem in its elementary form, were it not unfortunately true that the value of the coefficient (called the dispersive ratio), for all practicable materials is far from constant throughout the range of wave-lengths which are involved in optical images. For example, for the kinds of glass most generally employed for large telescopes, this quantity varies from D80 in the extreme red to 2'20 in the extreme violet. The method of fixing upon the most advantageous value to substitute in the second equation was not obvious to the earlier opticians, even to those who produced some of the finest telescopes now in use; but it is easily demonstrated that the value should be that which obtains for light of