snow line, altitude above which or latitude beyond which snow does not melt in summer (usually called the permanent snow line), or, in winter, the line to which snow extends at a given point in time. Factors affecting the location of the snow line are the quantity of snowfall, the steepness of the slope on which snow rests, the exposure of an area to the sun and prevailing winds, the type and velocity of the winds, and the presence or absence of large bodies of water. The level of the snow line is much lower in winter than in summer. It is also affected by distance from the equator, along which it is found at an altitude of c.3 mi (5 km); in polar regions it is at sea level.

ship of the line, large, square-rigged warship, carrying from 70 to 140 guns on two or more completely armed gun decks. In the great naval wars of the 17th, 18th, and early 19th cent., ships of the line were the largest naval units employed. They passed from use with the advent of the ironclad and the battleship. One of the few remaining examples of a ship of the line is Lord Nelson's flagship, the H.M.S. Victory, which has been preserved at Portsmouth, England.

line spectrum: see spectrum.

international date line, imaginary line on the earth's surface, generally following the 180° meridian of longitude, where, by international agreement, travelers change dates. Traveling eastward across the line, one subtracts one calendar day; traveling westward, one adds a day. The date line is necessary to avoid a confusion that would otherwise result. For example, if an airplane were to travel westward with the sun, 24 hr would elapse as it circled the globe, but it would still be the same day for those in the airplane while it would be one day later for those on the ground below them. The same problem would arise if two travelers journeyed in opposite directions to a point on the opposite side of the earth, 180° of longitude distant. The eastward traveler would set his clock ahead 1 hr for each 15° of longitude (see standard time), so that his clock would gain a total of 12 hr; the westward traveler would set his clock back 1 hr for each 15°, resulting in a total loss of 12 hr. The two clocks would therefore differ by 24 hr, or one calendar day. The apparent paradox is resolved by requiring that the traveler crossing the date line change his date, thus bringing the travelers into agreement when they meet. The international date line does not follow the 180° meridian along its entire course but bends eastward around the eastern tip of Siberia, westward around the Aleutian Islands, and eastward again around various island groups in the South Pacific in order to avoid a time change in populated areas.

fall line, boundary between an upland region and a coastal plain across which rivers from the upland region drop to the plain as falls or rapids. A fall line is formed in an area where the rivers have eroded away the soft rocks of a coastal plain more quickly than the older harder rocks of an upland region. Such erosion follows a crooked line along a coast. River vessels usually cannot travel beyond a fall line and their cargoes must be unloaded there. The falls (see waterfall) also supply water power for the development of industry such as textile and grist mills. For these reasons a fall line often marks a string of developed areas, such as the break between the Appalachian rise and the coastal plain of the eastern United States, where a band of commercial and industrial cities quickly developed in the 19th cent., paralleling the line of port cities along the coasts. Typical fall-line cities on the Atlantic coast of the United States are Lowell, Mass.; Pawtucket, R.I.; Troy, N.Y.; Trenton, N.J.; Georgetown, now part of Washington, D.C.; Richmond, Va.; Raleigh, N.C.; Columbia, S.C.; and Augusta, Ga. Among the fall-line cities of the Mississippi valley are Louisville, Ky., and Minneapolis, Minn.

date line, international: see international date line.

dark-line spectrum: see spectrum.

bright-line spectrum: see spectrum.

base line: see geodesy.

assembly line, manufacturing technique in which a product is carried by some form of mechanized conveyor among stations at which the various operations necessary to its assembly are performed. It is used to assemble quickly large numbers of a uniform product. Henry Ford is often credited with establishing the first assembly line for his Model T. So long as an assembly line's output is high, the cost per unit is relatively low. It is somewhat inflexible, however, as it must be designed and installed for a particular product. Also, the operations on the product usually must be performed in a sequence that is strictly ordered. A malfunction or shortage of parts that shuts down a single assembly station necessitates shutdown of the entire line. Traditional assembly lines had come under criticism from those concerned with their effects on workers, but industrial robots now perform many of the repetitive tasks. Recent variations on the assembly-line process, such as teams of workers responsible for multiple steps, have increased productivity and employee interest.

Wallace's line, imaginary line postulated by A. R. Wallace as the dividing line between Asian and Australian fauna in the Malay Archipelago. It passes between Bali and Lombok islands and between Borneo and Sulawesi, then continues S of the Philippines and N of the Hawaiian Islands.

Oder-Neisse line, frontier established in 1945 between Germany and Poland; it followed the Oder and W Neisse rivers from the Baltic Sea to the Czechoslovak border. The boundary, desired by most Poles at the expense of Germany, came about as a result of agreements between the Soviet Union, Great Britain, and the United States at the Yalta and Potsdam conferences in 1945. The Soviet leader Joseph Stalin endorsed the Oder-Neisse line partly as a compensation for the Polish eastern territories that the USSR had annexed and partly under pressure from the USSR-sponsored Polish government. Although the boundary was originally opposed by the United States and Great Britain because it would make Poland excessively dependent upon the Soviet Union, they sanctioned it informally at Yalta in Feb., 1945. After disputed territories, including the former free city of Danzig (now Gdansk), had been in effect incorporated into Poland and their German population largely expelled, the Potsdam Conference of Aug., 1945, recognized the line as Poland's western frontier pending a peace treaty with Germany. In the absence of such a treaty, an agreement between the German Democratic Republic (East Germany) and Poland recognized the line as the permanent frontier in 1950. The West German government recognized it in 1971. In 1990, during negotiations for German reunification, the East and West German legislatures agreed to recognize the inviolability of the Polish-German border, much to the relief of neighboring states.

Mason-Dixon Line, boundary between Pennsylvania and Maryland (running between lat. 39°43'26.3″N and lat. 39°43'17.6″N), surveyed by the English team of Charles Mason, a mathematician and astronomer, and Jeremiah Dixon, a mathematician and land surveyor, between 1763 and 1767. The ambiguous description of the boundaries in the Maryland and Pennsylvania charters led to a protracted disagreement between the proprietors of the two colonies, the Penns of Pennsylvania and the Calverts of Maryland. The dispute was submitted to the English court of chancery in 1735. A compromise between two families in 1760 resulted in the appointment of Mason and Dixon. By 1767 the surveyors had run their line 244 mi (393 km) west from the Delaware border, every fifth milestone bearing the Penn and Calvert arms. The survey was completed to the western limit of Maryland in 1773; in 1779 the line was extended to mark the southern boundary of Pennsylvania with Virginia (present-day West Virginia). Before the Civil War the term "Mason-Dixon Line" popularly designated the boundary dividing the slave states from the free states, and it is still used to distinguish the South from the North.

Maginot Line, system of fortifications along the eastern frontier of France, extending from the Swiss border to the Belgian. It was named for André Maginot, who was French minister of war (1929-32) and who directed its construction. Although considered impregnable, the line was still not complete at the outbreak (1939) of World War II. Its actual strength was never tested, for the line was flanked by the Germans in their French campaign of 1940. Like fortified lines since the Great Wall of China, the chief effect it had was to create a false sense of security; it could not eliminate the necessity for mobile warfare, and that particular lesson was thoroughly learned after the French collapse of 1940.

Line Islands or Equatorial Islands, coral group, 43 sq mi (111 sq km), central and S Pacific. Once valuable for their guano deposits, the islands now have coconut groves, airfields, and meteorological stations. Of the 11 islands in the group, 8 comprise part of the Republic of Kiribati: Teraina, Tabuaeran, Kiritimati (formerly Washington, Fanning, and Christmas Islands), Malden, Starbuck, Caroline, Vostok, and Flint. Kingman Reef, Palmyra, and Jarvis Island are dependencies of the United States. The islands were uninhabited when discovered by American sailors in 1798, although a few show evidence of ancient Polynesian culture. The British government once conducted hydrogen bomb tests on Malden.

Céline, Louis Ferdinand, 1894-1961, French author, whose real name was Louis Ferdinand Destouches. Céline wrote grim, scatological, and blackly funny novels. His first and best-known work, Journey to the End of Night (1932, tr. 1934) is based on his service at the front in World War I, his travels through Africa, and his service as a League of Nations doctor. Looking back on his Paris childhood, Death on the Installment Plan (1936, tr. 1938) introduced Céline's stylistic innovation—the regular use of ellipses and apostrophes to capture the rhythm of everyday speech. Expressing a misanthropic loathing for all classes of humanity, Céline was an especially virulent anti-Semite, publishing the first of several antisemitic pamphlets (Bagatelles for a Massacre) in 1937.

Although he actually detested all ideologies, Céline was accused of collaboration with the Nazis during World War II, and after the Allied invasion of France, he fled first to Germany (1944) and then to Denmark (1945), where he was imprisoned for more than a year. In 1950 a French court convicted him of collaboration in absentia, named him a national disgrace, and sentenced him to a year in prison. The following year, however, he received judicial amnesty and returned to France. His later works include the autobiographical novels Fable for Another Time (1952, tr. 2003), the first of a two-part narrative that moves back and forth between the last days of the German occupation of France and Céline's postwar imprisonment in Denmark, and Castle to Castle (1957, tr. 1968), North (1960, tr. 1972), and Rigadoon (1961, tr. 1974), a trilogy recounting his nightmarish journey through Germany to Denmark while fleeing Allied armies during the last days of the Third Reich. Céline is now generally regarded as one of the most important and influential—as well as controversial—20th-century French novelists.

In geometry, a line that intersects a circle exactly once; in calculus, a line that touches a curve at one point and whose slope is equal to that of the curve at that point. Particularly useful as approximations of curves in the immediate vicinity of the point of tangency, tangent lines are the basis of many estimation techniques, including linear approximation. The numerical value of the slope of the tangent line to the graph of a function at any point equals that of the function's derivative at that point. This is one of the keystones of differential calculus. Seealso differential geometry.

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Type of sailing warship, the principal vessel of the West's great navies from the mid-17th to the mid-19th century. It evolved from a tactic in naval warfare known as the line of battle, in which two opposing columns of ships maneuvered to fire their guns broadside against each other. Since the largest ships carrying the biggest guns usually won these battles, this led to the construction of more big line-of-battle ships, or ships of the line. These three-masted ships were often 200 ft (60 m) long, displaced 1,200–2,000 tons (1,100–1,800 metric tons), and had crews of 600–800 men; they usually had 60–110 cannons and other guns arranged along three decks. They eventually gave way to the steam-powered battleship.

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Industrial arrangement of machines, equipment, and workers for continuous flow of workpieces in mass-production operations. An assembly line is designed by determining the sequences of operations for manufacture of each component as well as the final product. Each movement of material is made as simple and short as possible, with no cross flow or backtracking. Work assignments, numbers of machines, and production rates are programmed so that all operations performed along the line are compatible. Automated assembly lines (see automation) consist entirely of machines run by other machines and are used in such continuous-process industries as petroleum refining and chemical manufacture and in many modern automobile-engine plants. Seealso Henry Ford, interchangeable parts, Taylorism.

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In mathematics, the integral of a function of several variables defined on a line or curve that has been expressed in terms of arc length (see length of a curve). An ordinary definite integral is defined over a line segment, whereas a line integral may use a more general path, such as a parabola or a circle. Line integrals are used extensively in the theory of functions of a complex variable.

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Originally, the boundary between Maryland and Pennsylvania. The 233-mi (375-km) line was surveyed by Charles Mason and Jeremiah Dixon in 1765–68 to define the disputed boundaries between the land grants of the Penns, proprietors of Pennsylvania, and the Baltimores, proprietors of Maryland. The term was first used in congressional debates leading to the Missouri Compromise (1820) to describe the dividing line between the slave states to its south and the free-soil states to its north. It is still used as the figurative dividing line between the North and South.

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Elaborate defensive barrier in northeastern France built in the 1930s. Named after its principal creator, Andre Maginot, it was an ultramodern defensive fortification along the French-German frontier. Made of thick concrete and supplied with heavy guns, it had living quarters, supply storehouses, and underground rail lines. However, it ended at the French-Belgian frontier, which German forces crossed in May 1940. They invaded Belgium (May 10), crossed the Somme River, struck at the northern end of the line (May 12), and continued around to its rear, making it useless.

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Chain of islands, central Pacific Ocean, south of the Hawaiian Islands. The Line Islands extend 1,600 mi (2,600 km) and have a land area of 193 sq mi (500 sq km). Of the northern group, Teraina (Washington) Island and the Tabuaeran (Fanning) and Kiritimati (Christmas) atolls belong to the Republic of Kiribati, while Kingman Reef, Palmyra Atoll, and Jarvis Island are U.S. territories. Kiribati also holds the central group (Malden and Starbuck islands) and the southern group (Vostok and Flint islands and Caroline Atoll).

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