Definitions
Nearby Words

Great

[greyt]
Schism, Great, or Schism of the West, division in the Roman Catholic Church from 1378 to 1417. There was no question of faith or practice involved; the schism was a matter of persons and politics. Shortly after Gregory XI had returned the papacy from Avignon to Rome, he died (Mar. 27, 1378). The Romans feared that the papal court might be returned to Avignon, and there was rioting, with the mob demanding a Roman, or at least an Italian, pope. On Apr. 8 the 16 cardinals present elected Urban VI. The new pope was soon acting very offensively to all in the church. The cardinals met at Agnani and on Aug. 2 declared Urban's election null. At Fondi on Sept. 20 they elected Robert of Geneva pope as Clement VII. Urban VI remained in Rome, refusing to step down, and Clement VII fled to Avignon, where he reigned surrounded by the former Roman court. There were thus two lines of popes. The popes at Rome were Urban VI (1378-89), Boniface IX (1389-1404), Innocent VII (1404-6), and Gregory XII (1406-15). Those of the rival line at Avignon were Clement VII (1378-94) and Benedict XIII (1394-1417; see Luna, Pedro de). Schism within schism ensued. France withdrew from obedience to Benedict XIII and recognized no pope (1398-1403, 1408-9). Theologians of the Univ. of Paris, led by Pierre d'Ailly and John Gerson, were anxious to end the schism, and they developed the theory that popes are subject to general councils. The Council of Pisa (1409; see Pisa, Council of) was the result. This meeting declared that Gregory XII of the Roman (or Urbanist) line and Benedict XIII of the Avignon (or Clementine) line were not popes and elected another, Alexander V. He died soon after, but his energetic successor, Baldassare Cossa (John XXIII, 1410-15), detached most of Europe from his rivals. In 1414 John reluctantly convened the Council of Constance (see Constance, Council of). Gregory XII resigned. John XXIII and Benedict XIII, who refused to resign, were declared deposed by the council. Martin V was elected, and the schism was at an end. The main effects of the schism were to delay needed reforms in the church and to give rise to the conciliar theory, which was revived at the Council of Basel (see Basel, Council of). It is generally agreed by Roman Catholic scholars that the line of popes from Urban to Gregory was the canonical one.

See W. Ullmann, Origins of the Great Schism (1948, repr. 1972); B. Tierney, Foundations of the Conciliar Theory (1955, repr. 1969); E. F. Jacob, Essays in the Conciliar Epoch (3d ed. 1963); M. Gail, The Three Popes (1969); J. H. Smith, The Great Schism (1970).

Schütt, Great, Slovak Velký Žitný Ostrov, island, c.725 sq mi (1,880 sq km), SW Slovakia, in the Danubian lowlands between the Danube River and its northern arm. It extends c.55 mi (90 km) from Bratislava to Komárno. The island's fertile soil produces a variety of crops. Opposite the Great Schütt lies Szigetköz, or the Little Schütt, an island c.30 mi (50 km) long and up to c.10 mi (16 km) wide, in NW Hungary between the Danube River and its southern arm. Wheat, rye, and dairy products are produced there. In 1954 a disastrous flood submerged much of the island.
Belt, Great, and Little Belt, straits: see Store Bælt and Lille Bælt, straits, Denmark.
Seal of the United States, Great: see United States, Great Seal of the.
Trek, Great, the journey by Afrikaner farmers (Boers) who left the Cape Colony to escape British domination and eventually founded Natal, Transvaal, and the Orange Free State. Trek is an Afrikaans term, originally meaning a journey by ox wagon. In this most famous trek, 12,000 Boers left the Cape between 1835 and 1843. The Voortrekkers (as these Boers are known) migrated beyond the Orange River. After defeating resident Africans, most remained in the highveld of the interior, forming isolated communities and small states.

See E. Walker, The Great Trek (5th ed. 1965).

Khingan, Great, mountain range, China: see Hinggan Ling, Da.
or white shark

Large, aggressive shark (Carcharodon carcharias, family Lamnidae), considered the species most dangerous to humans. It is found in tropical and temperate regions of all oceans and is noted for its voracious appetite. Its diet includes fishes, sea turtles, birds, sea lions, small whales, carcasses, and ships' garbage. The great white is heavy-bodied and has a crescent-shaped tail and large, saw-edged, triangular teeth. It can reach a length of more than 20 ft (6 m) and is generally gray, bluish, or brownish, with the colour shading suddenly into a whitish belly. Though it is widely feared, only a few hundred humans are known to have ever been killed by the great white shark.

Learn more about great white shark with a free trial on Britannica.com.

Main space in a medieval manor house, monastery, or college, in which meals were eaten. In large manor houses it also served other purposes: Justice was administered there, entertainment enjoyed, and often at night its stone floor was strewn with rushes so that servants could sleep there.

Learn more about great hall with a free trial on Britannica.com.

Mounted specimen of great auk (Pinguinus impennis)

Flightless seabird (Pinguinus impennis) extinct since 1844. Great auks bred in colonies on rocky islands off North Atlantic coasts; fossil remains have been found as far south as Florida, Spain, and Italy. Their bodies were about 30 in. (75 cm) long; the wings, used for swimming underwater, were less than 6 in. (15 cm) long. They stood erect on land and had a black back and head, a white front, and a large white spot between the eye and the black bill. Great auks were hunted to extinction for food and bait. About 80 specimens are preserved in museums. Seealso auk.

Learn more about great auk with a free trial on Britannica.com.

or United Kingdom or Great Britain

Island country, western Europe, North Atlantic Ocean. It comprises Great Britain (England, Scotland, and Wales) and Northern Ireland. Area: 93,788 sq mi (242,910 sq km). Population (2005 est.): 60,020,000. Capital: London. The population is composed of English (major ethnic group), Scots, Irish, and Welsh and immigrants and their descendants from India, the West Indies, Pakistan, Bangladesh, and Africa. Languages: English (official); also Welsh, Scottish Gaelic. Religions: Christianity (Protestant [Church of England—established; Church of Scotland—national], Roman Catholic, other Christians); also Islam, Hinduism, Sikhism, Judaism. Currency: pound sterling. The country has hill, lowland, upland, highland, and mountain regions. Tin and iron ore deposits, once central to the economy, have become exhausted or uneconomical, and the coal industry, long a staple of the economy, began a steady decline in the 1950s that worsened with pit closures in the 1980s. Offshore petroleum and natural gas reserves are significant. Chief crops are barley, wheat, sugar beets, and potatoes. Major manufactures include motor vehicles, aerospace equipment, electronic data-processing and telecommunication equipment, and petrochemicals. Fishing and publishing also are important economic activities. The U.K. is a constitutional monarchy with two legislative houses; its chief of state is the sovereign, and the head of government is the prime minister.

The early pre-Roman inhabitants of Britain (see Stonehenge) were Celtic-speaking peoples, including the Brythonic people of Wales, the Picts of Scotland, and the Britons of Britain. Celts also settled in Ireland circa 500 BC. Julius Caesar invaded and took control of the area in 55–54 BC. The Roman province of Britannia endured until the 5th century AD and included present-day England and Wales. Germanic tribes, including Angles, Saxons, and Jutes, invaded Britain in the 5th century. The invasions had little effect on the Celtic peoples of Wales and Scotland. Christianity began to flourish in the 6th century. During the 8th and 9th centuries, Vikings, particularly Danes, raided the coasts of Britain. In the late 9th century Alfred the Great repelled a Danish invasion, which helped bring about the unification of England under Athelstan. The Scots attained dominance in Scotland, which was finally unified under Malcolm II (1005–34). William of Normandy (see William I) took England in 1066. The Norman kings established a strong central government and feudal state. The French language of the Norman rulers eventually merged with the Anglo-Saxon of the common people to form the English language. From the 11th century, Scotland came under the influence of the English throne. Henry II conquered Ireland in the late 12th century. His sons Richard I and John had conflicts with the clergy and nobles, and eventually John was forced to grant the nobles concessions in the Magna Carta (1215). The concept of community of the realm developed during the 13th century, providing the foundation for parliamentary government. During the reign of Edward I (1272–1307), statute law developed to supplement English common law, and the first Parliament was convened. In 1314 Robert the Bruce (see Robert I) won independence for Scotland. The house of Tudor became the ruling family of England following the Wars of the Roses (1455–85). Henry VIII (1509–47) established the Church of England and incorporated Wales as part of England.

The reign of Elizabeth I (1558–1603) began a period of colonial expansion; in 1588 British forces defeated the “invincible” Spanish Armada. In 1603 James VI of Scotland ascended the English throne, becoming James I, and established a personal union of the two kingdoms. The English Civil Wars erupted in 1642 between Royalists and Parliamentarians, ending in the execution of Charles I (1649). After 11 years of Puritan rule under Oliver Cromwell and his son (1649–60), the monarchy was restored with Charles II. In 1689, following the Glorious Revolution, Parliament proclaimed the joint sovereigns William III and Mary II, who accepted the British Bill of Rights. In 1707 England and Scotland assented to the Act of Union, forming the kingdom of Great Britain. The Hanoverians ascended the English throne in 1714, when George Louis, elector of Hanover, became George I of Great Britain. During the reign of George III, Great Britain's North American colonies won independence (1783). This was followed by a period of war (1789–1815) with Revolutionary France and later with the empire of Napoleon. In 1801 legislation united Great Britain with Ireland to create the United Kingdom of Great Britain and Ireland. Britain was the birthplace of the Industrial Revolution in the late 18th century, and it remained the world's foremost economic power until the late 19th century. During the reign of Queen Victoria (1837–1901), Britain's colonial expansion reached its zenith, though the older dominions, including Canada and Australia, were granted independence (1867 and 1901, respectively).

The U.K. entered World War I allied with France and Russia in 1914. Following the war, revolutionary disorder erupted in Ireland, and in 1921 the Irish Free State (see Ireland) was granted dominion status. Six counties of Ulster, however, remained in the U.K. as Northern Ireland. The U.K. entered World War II in 1939. Following the war, the Irish Free State became the Irish republic and left the Commonwealth. India also gained independence from the U.K. Throughout the postwar period and into the 1970s, the U.K. continued to grant independence to its overseas colonies and dependencies. With UN forces, it participated in the Korean War (1950–53). In 1956 it intervened militarily in Egypt during the Suez Crisis. It joined the European Economic Community, a forerunner of the European Union, in 1973. In 1982 it defeated Argentina in the Falkland Islands War. As a result of continuing social strife in Northern Ireland, it joined with Ireland in several peace initiatives, which eventually resulted in an agreement to establish an assembly in Northern Ireland. In 1997 referenda approved in Scotland and Wales devolved power to both countries, though both remained part of the U.K. In 1991 the U.K. joined an international coalition to reverse Iraq's conquest of Kuwait (see Persian Gulf War). In 2003 the U.K. and the U.S. attacked Iraq and overthrew the government of Ssubdotaddām Hsubdotussein (see Iraq War). Terrorist bombings in London in July 2005 killed more than 50 people.

Learn more about United Kingdom of Great Britain and Northern Ireland with a free trial on Britannica.com.

or Theodosius the Great in full Flavius Theodosius

(born Jan. 11, 347, Cauca, Gallaecia [Spain]—died Jan. 17, 395, Mediolanum) Roman emperor of the East (379–392) and of East and West (392–395). Born of Christian parents, he served in the military under his father, a general. He distinguished himself against the Sarmatians and was proclaimed coemperor by Gratian to rule in the eastern empire (379). To settle the contentious debate over true Christianity, he adopted the Nicene Creed as the Christian norm (380). He reached a treaty with the Visigoths (382). When the Spanish general Maximus overthrew the new coemperor in the western empire (387), Theodosius defeated the usurper (388) and claimed supreme authority over the whole empire (392). He argued with St. Ambrose over the role of the church in imperial affairs but did not grant power to the church. In 392 forces advocating paganism led by Arbogast and Eugenius took power in Rome. In 394 Theodosius defeated them and claimed the Christian God victorious over the pagan gods.

Learn more about Theodosius I with a free trial on Britannica.com.

known as Theodoric the Great

(born 454—died Aug. 30, 526) King of the Ostrogoths and founder of the Ostrogothic kingdom in Italy. Sent by the Byzantine emperor Zeno to invade Italy in 488, he made himself sole ruler by 493 and murdered Odoacer by treachery. With Ravenna as his capital he staved off the Franks and Bulgarians, and he held sway over a kingdom that included Sicily, Dalmatia, and some German lands. An Arian (see Arianism), he tolerated Catholicism and promoted peace between Goths and Romans.

Learn more about Theodoric with a free trial on Britannica.com.

(born March 17, 1874, Budapest, Hung., Austria-Hungary—died April 19, 1949, New York, N.Y., U.S.) Hungarian-born U.S. Reform rabbi, political activist, and Zionist leader. His family immigrated to the U.S. when he was an infant. He earned his Ph.D. at Columbia University in 1901 and was trained as a rabbi. In 1907, after declining a post at an influential congregation because of inadequate assurances of free speech in the pulpit, he founded the Free Synagogue. In 1898 he attended the Second Zionist Congress and helped found the Zionist Organization of America. A prominent member of the Democratic Party, he helped win U.S. government approval of the Balfour Declaration. In 1922 he founded the Jewish Institute of Religion, a seminary for liberal rabbis, which merged with Hebrew Union College in 1950.

Learn more about Wise, Stephen Samuel with a free trial on Britannica.com.

(born Nov. 28, 1832, London, Eng.—died Feb. 22, 1904, London) English critic and man of letters. After attending Eton College and Cambridge University, he gained entry to literary circles and in 1871 began an 11-year tenure as editor of The Cornhill Magazine, for which he wrote literary criticism. His greatest learned work was his History of English Thought in the Eighteenth Century (1876), but his most enduring legacy is the Dictionary of National Biography, which he edited from 1882 to 1891, personally writing many hundreds of its meticulous articles. He was the father of Virginia Woolf and the painter Vanessa Bell (1879–1961).

Learn more about Stephen, Sir Leslie with a free trial on Britannica.com.

(died circa AD 36, Jerusalem) First Christian martyr. As told in the Acts of the Apostles, he was a foreign-born Jew who lived in Jerusalem and joined the church at an early date. He was one of seven deacons appointed by the Apostles to care for elderly women, widows, and orphans. As a Hellenized Jew, he was strongly opposed to the Temple cult of Judaism. For expressing his opposition, he was brought before the Sanhedrin. His defense of Christianity so outraged his hearers that he was condemned to be stoned to death. One of those who assented to the execution was Saul of Tarsus (St. Paul).

Learn more about Stephen, Saint with a free trial on Britannica.com.

(born Aug. 30, 1794, Newark, N.J., U.S.—died Oct. 31, 1848, St. Louis, Mo.) U.S. Army officer. He served in the War of 1812 and later on the western frontier. At the outbreak of the Mexican War, he was ordered to seize New Mexico and California. Using diplomacy to persuade Mexican troops to withdraw, he marched unopposed to Santa Fe, where in 1846 he proclaimed a civil government for the province. Heading to California, he was informed that the conquest had already been completed by Robert F. Stockton and John C. Frémont. He arrived to discover that Mexican rebels had retaken most of the province. He then joined forces with Stockton to defeat the rebels in 1847. After initial opposition from Frémont, who had persuaded Stockton to appoint him governor, Kearny pacified the rest of California and established a stable civil government. He was then sent to Mexico, where he died of yellow fever.

Learn more about Kearny, Stephen Watts with a free trial on Britannica.com.

(born March 17, 1874, Budapest, Hung., Austria-Hungary—died April 19, 1949, New York, N.Y., U.S.) Hungarian-born U.S. Reform rabbi, political activist, and Zionist leader. His family immigrated to the U.S. when he was an infant. He earned his Ph.D. at Columbia University in 1901 and was trained as a rabbi. In 1907, after declining a post at an influential congregation because of inadequate assurances of free speech in the pulpit, he founded the Free Synagogue. In 1898 he attended the Second Zionist Congress and helped found the Zionist Organization of America. A prominent member of the Democratic Party, he helped win U.S. government approval of the Balfour Declaration. In 1922 he founded the Jewish Institute of Religion, a seminary for liberal rabbis, which merged with Hebrew Union College in 1950.

Learn more about Wise, Stephen Samuel with a free trial on Britannica.com.

(died July 9, 1228, Slindon, Sussex, Eng.) English cardinal and archbishop of Canterbury (1207–28). Langton was living in Rome when Innocent III nominated him as archbishop of Canterbury to settle a disputed election. When King John refused to allow him into England, the pope excommunicated John (1209). John finally submitted and received Langton in 1213. The new archbishop encouraged baronial opposition to the king but opposed violence. He was present at the signing of the Magna Carta (1215) and influenced its provisions on ecclesiastical liberties.

Learn more about Langton, Stephen with a free trial on Britannica.com.

(born March 22, 1930, New York, N.Y., U.S.) U.S. composer and lyricist. He studied piano and organ and at age 15 wrote his first musical under the tutelage of the musical comedy author Oscar Hammerstein II, a family friend. After studies with composer Milton Babbitt, he made his first mark on Broadway as lyricist for West Side Story (1957) and later Gypsy (1959). He wrote both music and lyrics for A Funny Thing Happened on the Way to the Forum (1962, Tony Award), A Little Night Music (1973, Tony Award), Sweeney Todd (1979, Tony Award), Sunday in the Park with George (1984, Pulitzer Prize), and Into the Woods (1987), among other works. His stage works are known for their intellectuality, musical complexity, and frequently dark tone.

Learn more about Sondheim, Stephen (Joshua) with a free trial on Britannica.com.

(born Nov. 4, 1816, Haddam, Conn., U.S.—died April 9, 1899, Washington, D.C.) U.S. jurist. After graduating from Williams College in 1837, he practiced law in New York with his brother, the legal reformer David Dudley Field (1805–94). In 1849 he moved to California, where he later joined the state supreme court. In 1863 he was appointed by Pres. Abraham Lincoln to the Supreme Court of the United States; he served until 1897. He became chief architect of the constitutional approach that largely exempted U.S. industry from government regulation after the American Civil War, basing his interpretation principally on the U.S. Constitution's 14th Amendment (1868), which had been passed as a civil-rights measure. Field's stance toward industry would be maintained by the Court until the 1930s.

Learn more about Field, Stephen J(ohnson) with a free trial on Britannica.com.

(born Sept. 10, 1941, New York, N.Y., U.S.—died May 20, 2002, New York, N.Y.) U.S. paleontologist and evolutionary biologist. He received a Ph.D. in paleontology from Columbia University and joined the faculty of Harvard University in 1967. With Niles Eldredge (b. 1943), he developed the controversial theory of punctuated equilibrium (1972), a revision of Darwinism that proposed that the evolutionary creation of new species occurs in rapid bursts over periods as short as thousands of years, which are followed by long periods of stability. He was widely known as a popularizing writer on biological and evolutionary topics, especially in Natural History magazine; his numerous books include The Panda's Thumb (1980), The Mismeasure of Man (1981), and The Structure of Evolutionary Theory (2002).

Learn more about Gould, Stephen Jay with a free trial on Britannica.com.

or Saint Stephen orig. Vajk

(born 970/975, Esztergom, Hung.—died Aug. 15, 1038, Esztergom; canonized 1083; feast day August 16) First king of Hungary (1000–38) and founder of the Hungarian state. The son of a Magyar chieftain, he was born a pagan but was later baptized as a Christian. After defeating his cousin to claim the throne, Stephen was crowned; his royal crown was a gift of Pope Sylvester II. His rule was peaceful except for an invasion by Conrad II (1030) and minor disputes with Poland and Bulgaria, and he organized Hungarian government and church administration on German models. He is the patron saint of Hungary.

Learn more about Stephen I with a free trial on Britannica.com.

in full Stephen Joseph Harper

Stephen Harper.

(born April 30, 1959, Toronto, Ont., Can.) Canadian prime minister from 2006. Harper received an M.A. degree in economics from the University of Calgary in 1991, after which he directed his career toward politics and public-policy analysis. He was elected to the Canadian House of Commons in 1993 as a member of the western-based Reform Party, but he did not seek reelection in 1997. In 2002 he returned to the House of Commons and became leader of the opposition Canadian Alliance (the successor to the Reform Party), and in 2004 he was elected head of the Conservative Party of Canada, formed by the merger of the Progressive Conservative and Canadian Alliance parties. In 2006 he led the Conservative Party to victory and became prime minister.

Learn more about Harper, Stephen with a free trial on Britannica.com.

(born May 20, 1750, Bordeaux, France—died Dec. 26, 1831, Philadelphia, Pa., U.S.) French-born American financier and philanthropist. He became a sailor at age 14; by 1774 he was commanding a French ship involved in American coastal trade with the West Indies. He settled in Philadelphia during the American Revolution and resumed trading in 1783. He developed an efficient, worldwide trading fleet and amassed a fortune. In 1812 he bought out the Bank of the United States, renaming it the Bank of Stephen Girard. During the War of 1812 he purchased government bonds, which by 1814 constituted 95percnt of the U.S.'s war loan. He bequeathed his fortune to social-welfare institutions, including Stephen Girard College for male orphans (founded 1833).

Learn more about Girard, Stephen with a free trial on Britannica.com.

(born Aug. 15, 1938, San Francisco, Calif., U.S.) U.S. jurist. He received his law degree from Harvard Law School in 1964. After clerking for Arthur Goldberg (1964–65), he taught at Harvard (1967–81). He served as special counsel (1974–75) and chief counsel (1979–81) of the U.S. Senate Judiciary Committee before being appointed to the First U.S. Circuit Court of Appeals (1980); he became its chief judge in 1990. From 1985 to 1989 he served on the commission that devised guidelines for federal sentencing. He was nominated to the Supreme Court of the United States in 1994 by Pres. Bill Clinton. He was known as a pragmatic moderate acceptable to both Republicans and Democrats.

Learn more about Breyer, Stephen (Gerald) with a free trial on Britannica.com.

(born Nov. 3, 1793, Austinville, Va., U.S.—died Dec. 27, 1836, Austin, Texas) U.S. founder of the first legal colony of English-speaking people in Texas when it was still part of Mexico. He was raised in the Missouri Territory and served in its legislature (1814–19). The economic panic in 1819 led his father to conceive a plan to colonize Texas on land obtained from the Mexican government. Austin continued the project after his father died (1821) and founded a colony of several hundred families on the Brazos River in 1822. He maintained good relations with the Mexican government. He tried to induce the Mexican government to make Texas a separate state in the Mexican confederation; when this attempt failed, he recommended in 1833 the organization of a state without waiting for the consent of the Mexican congress, and he was imprisoned. Released in 1835, he traveled to the U.S. to secure help when the Texas revolution broke out in October of that year. He is considered one of the state's founders. The city of Austin is named for him.

Learn more about Austin, Stephen (Fuller) with a free trial on Britannica.com.

(born Sept. 21, 1947, Portland, Maine, U.S.) U.S. writer. Educated at the University of Maine, he wrote a number of enormously popular books, which made him one of the world's best-selling writers. His books blend horror, the macabre, fantasy, and science fiction. Carrie (1974; film 1976), his first published novel and an immediate success, was followed by a long string of popular books, including The Shining (1977; film, 1980; television miniseries, 1997), The Dead Zone (1979; film, 1983), Pet Sematary (1983; film, 1989), and Misery (1987; film, 1990). Most of his novels have been adapted for television or film, and most have been translated into many languages.

Learn more about King, Stephen (Edwin) with a free trial on Britannica.com.

Stephen Decatur, detail from an engraving by Henry Meyer after a portrait by John Wesley Jarvis.

(born Jan. 5, 1779, Sinepuxent, Md., U.S.—died March 22, 1820, Bladensburg, Md.) U.S. naval officer. He entered the navy in 1798. In the Tripolitan War, he led a daring expedition into the harbour of Tripoli to burn a captured U.S. ship. In the War of 1812 he commanded the USS United States and captured the British ship Macedonian. In 1815 he commanded a squadron in the Mediterranean that forced a peace with the Barbary states on U.S. terms. At a banquet on his return he gave a toast that included the words “Our country, right or wrong.” In the same year he was made a navy commissioner, an office he held until he was killed in a duel.

Learn more about Decatur, Stephen with a free trial on Britannica.com.

Stephen Crane, detail of a painting by C.K. Linson, 1896.

(born Nov. 1, 1871, Newark, N.J., U.S.—died June 5, 1900, Badenweiler, Baden, Ger.) U.S. novelist and short-story writer. Crane briefly attended college before moving to New York City. His Maggie: A Girl of the Streets (1893), a sympathetic study of a slum girl's descent into prostitution, was a milestone of literary naturalism. He achieved international fame with his masterwork, The Red Badge of Courage (1895), depicting the psychological turmoil of a young Civil War soldier, and with his first book of poems, The Black Riders (1895). While traveling as a war correspondent, his ship sank and he almost drowned, resulting in his great story “The Open Boat” (1898). His story collections include The Little Regiment (1896), The Monster (1899), and Whilomville Stories (1900). He died at 28 of tuberculosis.

Learn more about Crane, Stephen with a free trial on Britannica.com.

(born July 4, 1826, Lawrenceville, Pa., U.S.—died Jan. 13, 1864, New York, N.Y.) U.S. songwriter. He began writing songs as a child, influenced in part by black church services he attended with the family's servant and by songs sung by black labourers. In 1842 he published “Open Thy Lattice, Love,” and in 1848 he sold “Oh! Susanna” for \$100; it quickly became an international hit. He later entered into a contract with the publisher Firth, Pond & Co. He was commissioned to write songs for Edwin P. Christy's minstrel show; his “Old Folks at Home” became one of the most popular songs of the century. In 1857, drinking heavily and in financial difficulties, he sold all rights to his future songs to his publishers for about \$1,900. In 1860 he moved to New York; he died penniless at age 37, leaving about 200 songs, including “Camptown Races,” “My Old Kentucky Home,” “Jeanie with the Light Brown Hair,” and “Beautiful Dreamer,” and he is universally regarded as the greatest American songwriter of the 19th century.

Learn more about Foster, Stephen (Collins) with a free trial on Britannica.com.

Leacock, photograph by Yousuf Karsh

(born Dec. 30, 1869, Swanmore, Hampshire, Eng.—died March 28, 1944, Toronto, Ont., Can.) British-born Canadian writer and lecturer. He immigrated to Canada with his parents at age six. Though he taught economics and political science at McGill University (1903–36) and wrote extensively on history and political economy, his true calling was humour. His fame rests on his many books of lighthearted sketches and essays, beginning with Literary Lapses (1910) and Nonsense Novels (1911). His humour is typically based on a comic perception of social foibles and the incongruity between appearance and reality in human conduct.

Learn more about Leacock, Stephen (Butler) with a free trial on Britannica.com.

(born Dec. 18, 1946, King William's Town, S.Af.—died Sept. 12, 1977, Pretoria) South African political activist. A former medical student, in 1968 he founded the Black Consciousness movement, designed to raise black awareness of apartheid oppression. He was officially “banned” by the South African government in 1973 and was arrested several times in 1976–77. His death from head injuries suffered in police custody made him an international martyr for South African black nationalism. The initial inquest absolved the police of wrongdoing, but in 1997 five former officers confessed to Biko's murder.

Learn more about Biko, Stephen with a free trial on Britannica.com.

(born April 23, 1813, Brandon, Vt., U.S.—died June 3, 1861, Chicago, Ill.) U.S. politician. He was elected to the U.S. House of Representatives (1843–47) and Senate (1847–61), where he strongly supported the Union and national expansion. To settle the bitter dispute over the extension of slavery to the territories, he developed the policy of popular sovereignty. He was influential in the passage of the Compromise of 1850 and the Kansas-Nebraska Act. Short and heavyset, he was dubbed “the Little Giant” for his oratorical skill. In 1858 he engaged in a number of widely publicized debates with Abraham Lincoln in a close contest for the Senate seat in Illinois (see Lincoln-Douglas Debates). The Democrats nominated Douglas for president in 1860, but a splinter group of Southerners nominated John C. Breckinridge, which divided the Democratic vote and gave the presidency to Lincoln. In 1861 he undertook a mission for Lincoln to gain support for the Union among the Southern border states and in the Northwest. His untimely death of typhoid was partly a result of these exertions.

Learn more about Douglas, Stephen A(rnold) with a free trial on Britannica.com.

known as Stephen the Great

(born 1435—died July 2, 1504) Prince of Moldavia (1457–1504). With the help of the Walachian prince Vlad III Tcedilepeş, Stephen secured the throne of Moldavia. He repelled a Hungarian invasion (1467) and later attacked Walachia (1471), by then under Turkish vassalage. He defeated invading Turks (1475, 1476) and contended with Polish and Hungarian designs on Moldavia. In 1503 Stephen signed a treaty preserving Moldavian independence at the cost of an annual tribute to the Turks.

Learn more about Stephen with a free trial on Britannica.com.

(born Feb. 28, 1909, London, Eng.—died July 16, 1995, London) English poet and critic. While an undergraduate at Oxford, Spender met the poets W.H. Auden and C. Day-Lewis. In the 1930s they became identified with politically conscious, leftist “new writing.” His poems, expressing a self-critical, compassionate personality, appear in volumes from Poems (1933) to Dolphins (1994). He was better known for his perceptive criticism, as in The Destructive Element (1935), The Making of a Poem (1955), and The Struggle of the Modern (1963), and for his association with the influential review Encounter (1953–67). He also wrote short stories, essays, and autobiography.

Learn more about Spender, Sir Stephen (Harold) with a free trial on Britannica.com.

(born March 22, 1930, New York, N.Y., U.S.) U.S. composer and lyricist. He studied piano and organ and at age 15 wrote his first musical under the tutelage of the musical comedy author Oscar Hammerstein II, a family friend. After studies with composer Milton Babbitt, he made his first mark on Broadway as lyricist for West Side Story (1957) and later Gypsy (1959). He wrote both music and lyrics for A Funny Thing Happened on the Way to the Forum (1962, Tony Award), A Little Night Music (1973, Tony Award), Sweeney Todd (1979, Tony Award), Sunday in the Park with George (1984, Pulitzer Prize), and Into the Woods (1987), among other works. His stage works are known for their intellectuality, musical complexity, and frequently dark tone.

Learn more about Sondheim, Stephen (Joshua) with a free trial on Britannica.com.

(born Feb. 28, 1909, London, Eng.—died July 16, 1995, London) English poet and critic. While an undergraduate at Oxford, Spender met the poets W.H. Auden and C. Day-Lewis. In the 1930s they became identified with politically conscious, leftist “new writing.” His poems, expressing a self-critical, compassionate personality, appear in volumes from Poems (1933) to Dolphins (1994). He was better known for his perceptive criticism, as in The Destructive Element (1935), The Making of a Poem (1955), and The Struggle of the Modern (1963), and for his association with the influential review Encounter (1953–67). He also wrote short stories, essays, and autobiography.

Learn more about Spender, Sir Stephen (Harold) with a free trial on Britannica.com.

(born March 21, 1925, London, Eng.) British director and producer. After directing plays in Stratford-upon-Avon, he became director of the Royal Opera House, Covent Garden (1947–50). He directed several innovative Shakespearean productions that aroused controversy. Appointed codirector of the Royal Shakespeare Co. in 1962, he directed critically acclaimed productions of King Lear (1962) and A Midsummer Night's Dream (1970). He won international fame with his avant-garde direction of Peter Weiss's play Marat/Sade (1964). His films include Lord of the Flies (1962), King Lear (1969), and the six-hour Mahabharata (1989). In 1970 he cofounded, with Jean-Louis Barrault, the International Centre for Theatre Research.

Learn more about Brook, Sir Peter (Stephen Paul) with a free trial on Britannica.com.

(born Nov. 28, 1832, London, Eng.—died Feb. 22, 1904, London) English critic and man of letters. After attending Eton College and Cambridge University, he gained entry to literary circles and in 1871 began an 11-year tenure as editor of The Cornhill Magazine, for which he wrote literary criticism. His greatest learned work was his History of English Thought in the Eighteenth Century (1876), but his most enduring legacy is the Dictionary of National Biography, which he edited from 1882 to 1891, personally writing many hundreds of its meticulous articles. He was the father of Virginia Woolf and the painter Vanessa Bell (1879–1961).

Learn more about Stephen, Sir Leslie with a free trial on Britannica.com.

(born Feb. 1, 1882, Compton, Que., Can.—died July 25, 1973, Quebec, Que.) Prime minister of Canada (1948–57). One of Canada's most prominent lawyers, he served in the Canadian House of Commons (1942–58) and in W.L. Mackenzie King's cabinet as minister of justice and attorney general (1942–46) and minister of external affairs (1945–48). As leader of the Liberal Party (1948), he succeeded King as prime minister. He promoted Canadian unity by equalizing provincial revenues and expanded social security and university education. He supported Canadian membership in NATO and helped establish the St. Lawrence Seaway.

Learn more about Saint Laurent, Louis (Stephen) with a free trial on Britannica.com.

(born Feb. 1, 1882, Compton, Que., Can.—died July 25, 1973, Quebec, Que.) Prime minister of Canada (1948–57). One of Canada's most prominent lawyers, he served in the Canadian House of Commons (1942–58) and in W.L. Mackenzie King's cabinet as minister of justice and attorney general (1942–46) and minister of external affairs (1945–48). As leader of the Liberal Party (1948), he succeeded King as prime minister. He promoted Canadian unity by equalizing provincial revenues and expanded social security and university education. He supported Canadian membership in NATO and helped establish the St. Lawrence Seaway.

Learn more about Saint Laurent, Louis (Stephen) with a free trial on Britannica.com.

Leacock, photograph by Yousuf Karsh

(born Dec. 30, 1869, Swanmore, Hampshire, Eng.—died March 28, 1944, Toronto, Ont., Can.) British-born Canadian writer and lecturer. He immigrated to Canada with his parents at age six. Though he taught economics and political science at McGill University (1903–36) and wrote extensively on history and political economy, his true calling was humour. His fame rests on his many books of lighthearted sketches and essays, beginning with Literary Lapses (1910) and Nonsense Novels (1911). His humour is typically based on a comic perception of social foibles and the incongruity between appearance and reality in human conduct.

Learn more about Leacock, Stephen (Butler) with a free trial on Britannica.com.

(died July 9, 1228, Slindon, Sussex, Eng.) English cardinal and archbishop of Canterbury (1207–28). Langton was living in Rome when Innocent III nominated him as archbishop of Canterbury to settle a disputed election. When King John refused to allow him into England, the pope excommunicated John (1209). John finally submitted and received Langton in 1213. The new archbishop encouraged baronial opposition to the king but opposed violence. He was present at the signing of the Magna Carta (1215) and influenced its provisions on ecclesiastical liberties.

Learn more about Langton, Stephen with a free trial on Britannica.com.

(born Nov. 2, 1913, New York, N.Y., U.S.—died Oct. 20, 1994, Century City, Calif.) U.S. film actor. He toured with circuses as an acrobat in the 1930s and served in North Africa and Italy during World War II. He first appeared in movie houses in The Killers (1946), which made him a star. He was noted for his portrayals of physically tough, emotionally sensitive characters. Lancaster's many films include Come Back, Little Sheba (1952), From Here to Eternity (1953), The Rose Tattoo (1955), Sweet Smell of Success (1957), Elmer Gantry (1960, Academy Award), The Birdman of Alcatraz (1962), The Leopard (1963), Atlantic City (1981), Local Hero (1983), and Field of Dreams (1989).

Learn more about Lancaster, Burt(on Stephen) with a free trial on Britannica.com.

(born Sept. 21, 1947, Portland, Maine, U.S.) U.S. writer. Educated at the University of Maine, he wrote a number of enormously popular books, which made him one of the world's best-selling writers. His books blend horror, the macabre, fantasy, and science fiction. Carrie (1974; film 1976), his first published novel and an immediate success, was followed by a long string of popular books, including The Shining (1977; film, 1980; television miniseries, 1997), The Dead Zone (1979; film, 1983), Pet Sematary (1983; film, 1989), and Misery (1987; film, 1990). Most of his novels have been adapted for television or film, and most have been translated into many languages.

Learn more about King, Stephen (Edwin) with a free trial on Britannica.com.

(born Aug. 30, 1794, Newark, N.J., U.S.—died Oct. 31, 1848, St. Louis, Mo.) U.S. Army officer. He served in the War of 1812 and later on the western frontier. At the outbreak of the Mexican War, he was ordered to seize New Mexico and California. Using diplomacy to persuade Mexican troops to withdraw, he marched unopposed to Santa Fe, where in 1846 he proclaimed a civil government for the province. Heading to California, he was informed that the conquest had already been completed by Robert F. Stockton and John C. Frémont. He arrived to discover that Mexican rebels had retaken most of the province. He then joined forces with Stockton to defeat the rebels in 1847. After initial opposition from Frémont, who had persuaded Stockton to appoint him governor, Kearny pacified the rest of California and established a stable civil government. He was then sent to Mexico, where he died of yellow fever.

Learn more about Kearny, Stephen Watts with a free trial on Britannica.com.

in full Stephen Joseph Harper

Stephen Harper.

(born April 30, 1959, Toronto, Ont., Can.) Canadian prime minister from 2006. Harper received an M.A. degree in economics from the University of Calgary in 1991, after which he directed his career toward politics and public-policy analysis. He was elected to the Canadian House of Commons in 1993 as a member of the western-based Reform Party, but he did not seek reelection in 1997. In 2002 he returned to the House of Commons and became leader of the opposition Canadian Alliance (the successor to the Reform Party), and in 2004 he was elected head of the Conservative Party of Canada, formed by the merger of the Progressive Conservative and Canadian Alliance parties. In 2006 he led the Conservative Party to victory and became prime minister.

Learn more about Harper, Stephen with a free trial on Britannica.com.

(born Sept. 10, 1941, New York, N.Y., U.S.—died May 20, 2002, New York, N.Y.) U.S. paleontologist and evolutionary biologist. He received a Ph.D. in paleontology from Columbia University and joined the faculty of Harvard University in 1967. With Niles Eldredge (b. 1943), he developed the controversial theory of punctuated equilibrium (1972), a revision of Darwinism that proposed that the evolutionary creation of new species occurs in rapid bursts over periods as short as thousands of years, which are followed by long periods of stability. He was widely known as a popularizing writer on biological and evolutionary topics, especially in Natural History magazine; his numerous books include The Panda's Thumb (1980), The Mismeasure of Man (1981), and The Structure of Evolutionary Theory (2002).

Learn more about Gould, Stephen Jay with a free trial on Britannica.com.

(born May 20, 1750, Bordeaux, France—died Dec. 26, 1831, Philadelphia, Pa., U.S.) French-born American financier and philanthropist. He became a sailor at age 14; by 1774 he was commanding a French ship involved in American coastal trade with the West Indies. He settled in Philadelphia during the American Revolution and resumed trading in 1783. He developed an efficient, worldwide trading fleet and amassed a fortune. In 1812 he bought out the Bank of the United States, renaming it the Bank of Stephen Girard. During the War of 1812 he purchased government bonds, which by 1814 constituted 95percnt of the U.S.'s war loan. He bequeathed his fortune to social-welfare institutions, including Stephen Girard College for male orphans (founded 1833).

Learn more about Girard, Stephen with a free trial on Britannica.com.

(born July 4, 1826, Lawrenceville, Pa., U.S.—died Jan. 13, 1864, New York, N.Y.) U.S. songwriter. He began writing songs as a child, influenced in part by black church services he attended with the family's servant and by songs sung by black labourers. In 1842 he published “Open Thy Lattice, Love,” and in 1848 he sold “Oh! Susanna” for \$100; it quickly became an international hit. He later entered into a contract with the publisher Firth, Pond & Co. He was commissioned to write songs for Edwin P. Christy's minstrel show; his “Old Folks at Home” became one of the most popular songs of the century. In 1857, drinking heavily and in financial difficulties, he sold all rights to his future songs to his publishers for about \$1,900. In 1860 he moved to New York; he died penniless at age 37, leaving about 200 songs, including “Camptown Races,” “My Old Kentucky Home,” “Jeanie with the Light Brown Hair,” and “Beautiful Dreamer,” and he is universally regarded as the greatest American songwriter of the 19th century.

Learn more about Foster, Stephen (Collins) with a free trial on Britannica.com.

(born Nov. 4, 1816, Haddam, Conn., U.S.—died April 9, 1899, Washington, D.C.) U.S. jurist. After graduating from Williams College in 1837, he practiced law in New York with his brother, the legal reformer David Dudley Field (1805–94). In 1849 he moved to California, where he later joined the state supreme court. In 1863 he was appointed by Pres. Abraham Lincoln to the Supreme Court of the United States; he served until 1897. He became chief architect of the constitutional approach that largely exempted U.S. industry from government regulation after the American Civil War, basing his interpretation principally on the U.S. Constitution's 14th Amendment (1868), which had been passed as a civil-rights measure. Field's stance toward industry would be maintained by the Court until the 1930s.

Learn more about Field, Stephen J(ohnson) with a free trial on Britannica.com.

(born April 23, 1813, Brandon, Vt., U.S.—died June 3, 1861, Chicago, Ill.) U.S. politician. He was elected to the U.S. House of Representatives (1843–47) and Senate (1847–61), where he strongly supported the Union and national expansion. To settle the bitter dispute over the extension of slavery to the territories, he developed the policy of popular sovereignty. He was influential in the passage of the Compromise of 1850 and the Kansas-Nebraska Act. Short and heavyset, he was dubbed “the Little Giant” for his oratorical skill. In 1858 he engaged in a number of widely publicized debates with Abraham Lincoln in a close contest for the Senate seat in Illinois (see Lincoln-Douglas Debates). The Democrats nominated Douglas for president in 1860, but a splinter group of Southerners nominated John C. Breckinridge, which divided the Democratic vote and gave the presidency to Lincoln. In 1861 he undertook a mission for Lincoln to gain support for the Union among the Southern border states and in the Northwest. His untimely death of typhoid was partly a result of these exertions.

Learn more about Douglas, Stephen A(rnold) with a free trial on Britannica.com.

Stephen Decatur, detail from an engraving by Henry Meyer after a portrait by John Wesley Jarvis.

(born Jan. 5, 1779, Sinepuxent, Md., U.S.—died March 22, 1820, Bladensburg, Md.) U.S. naval officer. He entered the navy in 1798. In the Tripolitan War, he led a daring expedition into the harbour of Tripoli to burn a captured U.S. ship. In the War of 1812 he commanded the USS United States and captured the British ship Macedonian. In 1815 he commanded a squadron in the Mediterranean that forced a peace with the Barbary states on U.S. terms. At a banquet on his return he gave a toast that included the words “Our country, right or wrong.” In the same year he was made a navy commissioner, an office he held until he was killed in a duel.

Learn more about Decatur, Stephen with a free trial on Britannica.com.

Stephen Crane, detail of a painting by C.K. Linson, 1896.

(born Nov. 1, 1871, Newark, N.J., U.S.—died June 5, 1900, Badenweiler, Baden, Ger.) U.S. novelist and short-story writer. Crane briefly attended college before moving to New York City. His Maggie: A Girl of the Streets (1893), a sympathetic study of a slum girl's descent into prostitution, was a milestone of literary naturalism. He achieved international fame with his masterwork, The Red Badge of Courage (1895), depicting the psychological turmoil of a young Civil War soldier, and with his first book of poems, The Black Riders (1895). While traveling as a war correspondent, his ship sank and he almost drowned, resulting in his great story “The Open Boat” (1898). His story collections include The Little Regiment (1896), The Monster (1899), and Whilomville Stories (1900). He died at 28 of tuberculosis.

Learn more about Crane, Stephen with a free trial on Britannica.com.

Grover Cleveland

(born March 18, 1837, Caldwell, N.J., U.S.—died June 24, 1908, Princeton) 22nd and 24th president of the U.S. (1885–89, 1893–97). From 1859 he practiced law in Buffalo, N.Y., where he entered Democratic Party politics. As mayor of Buffalo (1881–82), he was known as a foe of corruption. As governor of New York (1883–85), his independence earned him the hostility of Tammany Hall. Elected president in 1884, he supported civil-service reform and opposed high tariffs. Although he was narrowly defeated by Benjamin Harrison in 1888, he was reelected by a huge popular plurality in 1892. In 1893 he strongly urged Congress to repeal the Sherman Silver Purchase Act of 1890, which he blamed for the country's severe economic depression. Despite the repeal of the act, the depression continued, resulting in the Pullman Strike in 1894. An isolationist, Cleveland opposed territorial expansion. In 1895 he invoked the Monroe Doctrine in the border dispute between Britain and Venezuela. By 1896 supporters of the Free Silver Movement controlled the Democratic Party, which nominated William Jennings Bryan instead of Cleveland for president. He retired to New Jersey, where he lectured at Princeton University.

Learn more about Cleveland, (Stephen) Grover with a free trial on Britannica.com.

(born Nov. 2, 1913, New York, N.Y., U.S.—died Oct. 20, 1994, Century City, Calif.) U.S. film actor. He toured with circuses as an acrobat in the 1930s and served in North Africa and Italy during World War II. He first appeared in movie houses in The Killers (1946), which made him a star. He was noted for his portrayals of physically tough, emotionally sensitive characters. Lancaster's many films include Come Back, Little Sheba (1952), From Here to Eternity (1953), The Rose Tattoo (1955), Sweet Smell of Success (1957), Elmer Gantry (1960, Academy Award), The Birdman of Alcatraz (1962), The Leopard (1963), Atlantic City (1981), Local Hero (1983), and Field of Dreams (1989).

Learn more about Lancaster, Burt(on Stephen) with a free trial on Britannica.com.

(born March 21, 1925, London, Eng.) British director and producer. After directing plays in Stratford-upon-Avon, he became director of the Royal Opera House, Covent Garden (1947–50). He directed several innovative Shakespearean productions that aroused controversy. Appointed codirector of the Royal Shakespeare Co. in 1962, he directed critically acclaimed productions of King Lear (1962) and A Midsummer Night's Dream (1970). He won international fame with his avant-garde direction of Peter Weiss's play Marat/Sade (1964). His films include Lord of the Flies (1962), King Lear (1969), and the six-hour Mahabharata (1989). In 1970 he cofounded, with Jean-Louis Barrault, the International Centre for Theatre Research.

Learn more about Brook, Sir Peter (Stephen Paul) with a free trial on Britannica.com.

(born Aug. 15, 1938, San Francisco, Calif., U.S.) U.S. jurist. He received his law degree from Harvard Law School in 1964. After clerking for Arthur Goldberg (1964–65), he taught at Harvard (1967–81). He served as special counsel (1974–75) and chief counsel (1979–81) of the U.S. Senate Judiciary Committee before being appointed to the First U.S. Circuit Court of Appeals (1980); he became its chief judge in 1990. From 1985 to 1989 he served on the commission that devised guidelines for federal sentencing. He was nominated to the Supreme Court of the United States in 1994 by Pres. Bill Clinton. He was known as a pragmatic moderate acceptable to both Republicans and Democrats.

Learn more about Breyer, Stephen (Gerald) with a free trial on Britannica.com.

(born Dec. 18, 1946, King William's Town, S.Af.—died Sept. 12, 1977, Pretoria) South African political activist. A former medical student, in 1968 he founded the Black Consciousness movement, designed to raise black awareness of apartheid oppression. He was officially “banned” by the South African government in 1973 and was arrested several times in 1976–77. His death from head injuries suffered in police custody made him an international martyr for South African black nationalism. The initial inquest absolved the police of wrongdoing, but in 1997 five former officers confessed to Biko's murder.

Learn more about Biko, Stephen with a free trial on Britannica.com.

(born Nov. 3, 1793, Austinville, Va., U.S.—died Dec. 27, 1836, Austin, Texas) U.S. founder of the first legal colony of English-speaking people in Texas when it was still part of Mexico. He was raised in the Missouri Territory and served in its legislature (1814–19). The economic panic in 1819 led his father to conceive a plan to colonize Texas on land obtained from the Mexican government. Austin continued the project after his father died (1821) and founded a colony of several hundred families on the Brazos River in 1822. He maintained good relations with the Mexican government. He tried to induce the Mexican government to make Texas a separate state in the Mexican confederation; when this attempt failed, he recommended in 1833 the organization of a state without waiting for the consent of the Mexican congress, and he was imprisoned. Released in 1835, he traveled to the U.S. to secure help when the Texas revolution broke out in October of that year. He is considered one of the state's founders. The city of Austin is named for him.

Learn more about Austin, Stephen (Fuller) with a free trial on Britannica.com.

St. Basil, detail of a mosaic, 12th century; in the Palatine Chapel, Palermo, Sicily, Italy.

(born AD 329, Caesarea Mazaca, Cappadocia—died Jan. 1, 379, Caesarea; Western feast day January 2; Eastern feast day January 1) Early church father. Born into a Christian family in Cappadocia, he studied at Caesarea, Constantinople, and Athens and later established a monastic settlement on the family estate at Annesi. He opposed Arianism, which was supported by the emperor Valens and his own bishop Dianius, and organized resistance to it after 365. He succeeded Eusebius as bishop of Caesarea in 370. He died shortly after Valens, whose death in battle opened the way for the victory of Basil's cause. More than 300 of his letters survive; several of his Canonical Epistles have become part of canon law in Eastern Orthodoxy.

Learn more about Basil the Great, Saint with a free trial on Britannica.com.

Russian Pyotr Alekseyevich known as Peter the Great

(born June 9, 1672, Moscow, Russia—died Feb. 8, 1725, St. Petersburg) Tsar of Russia (1682–1725). Son of Tsar Alexis, he reigned jointly with his half brother Ivan V (1682–96) and alone from 1696. Interested in progressive influences from western Europe, he visited several countries there (1697–98). After returning to Russia, he introduced Western technology, modernized the government and military system, and transferred the capital to the new city of St. Petersburg (1703). He further increased the power of the monarchy at the expense of the nobles and the Orthodox church. Some of his reforms were implemented brutally, with considerable loss of life. Suspecting that his son Alexis was conspiring against him, he had Alexis tortured to death in 1718. He pursued foreign policies to give Russia access to the Baltic and Black seas, engaging in war with the Ottoman Empire (1695–96) and with Sweden in the Second Northern War (1700–21). His campaign against Persia (1722–23) secured for Russia the southern and western shores of the Caspian Sea. In 1721 he was proclaimed emperor; his wife succeeded him as the empress Catherine I. For raising Russia to a recognized place among the great European powers, Peter is widely considered one of the outstanding rulers and reformers in Russian history, but he has also been decried by nationalists for discarding much of what was unique in Russian culture, and his legacy has been seen as a model for Joseph Stalin's brutal transformation of Russian life.

Learn more about Peter I with a free trial on Britannica.com.

known as Otto the Great

(born Nov. 23, 912—died May 7, 973, Memleben, Thuringia) Duke of Saxony (936–61), German king (936–73), and emperor (962–73). He extended the frontiers of the German kingdom, winning territory from the Slavs in the east, forcing the Bohemians to pay tribute (950), and gaining influence in Denmark and Burgundy. In 951 Otto became king of the Lombards and married the queen of Italy. He quelled a rebellion by his son in 955 and defeated the Magyars in the Battle of Lechfeld. Crowned emperor by Pope John XII in 962, he deposed John in 963 and replaced him with Leo VIII. He returned to Italy (966–72) to subdue Rome, and he betrothed his son, Otto II, to a Byzantine princess (972). He also extended his authority over the church and promoted missionary activity in lands he had conquered. By his death, Otto had created the most powerful state in western Europe and laid the foundation for the later Holy Roman Empire.

Learn more about Otto I with a free trial on Britannica.com.

Chinese Wanli Changcheng

Defensive wall, northern China. One of the largest building-construction projects ever carried out, it runs (with all its branches) about 4,500 mi (7,300 km) east to west from the Bo Hai (Gulf of Chihli) to a point deep in Central Asia. Large parts of the fortification date from the 7th to the 4th century BC. In the 3rd century BC the emperor Shihuangdi connected existing defensive walls into a single system fortified by watchtowers. These served both to guard the rampart and to communicate with the capital, Xianyang (near modern Xi'an) by signal—smoke by day and fire by night. Originally constructed partly of masonry and earth, it was faced with brick in its eastern portion. It was rebuilt in later times, especially in the 15th and 16th centuries. The basic wall is about 23–26 ft (7–8 m) high; at intervals towers rise above it to varying heights. It was designated a UNESCO World Heritage site in 1987.

Learn more about Great Wall of China with a free trial on Britannica.com.

Emigration of some 12,000–14,000 Boers (see Afrikaners) from Cape Colony (South Africa) between 1835 and the early 1840s, in rebellion against British policies and in search of fresh pasturelands. The trek, regarded by Afrikaners as the origin of their nationhood, enabled the settlers to establish temporary military supremacy over the Xhosa, to penetrate into Natal and the Highveld, and to expand white settlement north to the Limpopo River. Seealso Andries Pretorius.

Learn more about Great Trek with a free trial on Britannica.com.

Slogan used in 1965 by Pres. Lyndon B. Johnson to identify his legislative program of national reform. In his first State of the Union address, Johnson described his vision of a “Great Society” that would include a “war on poverty” and federal support for education, medical care for the elderly, and legal protection for African Americans deprived of voting rights by state regulations. He also proposed a new department of housing and urban development to coordinate federal housing projects. Congress enacted almost all his programs, the largest number of such measures since the New Deal. Seealso Civil Rights Act of 1964; Medicare and Medicaid.

Learn more about Great Society with a free trial on Britannica.com.

West range of the Appalachian Mountains in the U.S. It extends along the North Carolina–Tennessee boundary and blends into the Blue Ridge to the east. The highest part lies within the Great Smoky Mountains National Park and includes Clingmans Dome, which at 6,643 ft (2,025 m) is the highest peak. Covered by forests, it was originally the domain of the Cherokee, and the area includes the Cherokee Indian Reservation and parts of the Pisgah and Cherokee national forests. The mountains form a popular resort area that includes part of the Appalachian National Scenic Trail and the Blue Ridge Parkway.

Learn more about Great Smoky Mountains with a free trial on Britannica.com.

Lake, south-central Northwest Territories, Canada. Named for the Slave Indians, it is fed by several rivers, including the Slave, and drained by the Mackenzie River into the Arctic Ocean. The lake, with an area of 11,031 sq mi (28,570 sq km), is the fifth largest in North America. It is 300 mi (500 km) long and 30–140 mi (50–225 km) wide, with a maximum depth of more than 2,000 ft (600 m). While supporting a fishing industry, the lake is an integral part of the Mackenzie River waterway.

Learn more about Great Slave Lake with a free trial on Britannica.com.

or Great Schism

(1378–1417) In Roman Catholic history, a period when there were two, and later three, rival popes, each with his own College of Cardinals. The schism began soon after the papal residence was returned to Rome from Avignon (see Avignon papacy). Urban VI was elected amid local demands for an Italian pope, but a group of cardinals with French sympathies elected an antipope, Clement VII, who took up residence at Avignon. Cardinals from both sides met at Pisa in 1409 and elected a third pope in an effort to end the schism. The rift was not healed until the Council of Constance vacated all three seats and elected Martin V as pope in 1417.

Learn more about Schism, Western with a free trial on Britannica.com.

Wasteland, northern Western Australia. It extends from Eighty Mile Beach on the Indian Ocean eastward into the Northern Territory and from the Kimberley Downs south to the Tropic of Capricorn and the Gibson Desert. An arid expanse of salt marshes and sand hills, it roughly coincides with the sedimentary Canning basin. Canning Stock Route (1,000 mi [1,600 km] long) spans the region from Wiluna via Lake Disappointment to Halls Creek.

Learn more about Great Sandy Desert with a free trial on Britannica.com.

Natural area, south-central Colorado, U.S. It lies at the eastern edge of the San Luis Valley along the western base of the Sangre de Cristo Mountains. Established in 1932 as a national monument, the 150,000-acre (60,700-hectare) region contains some of the highest inland sand dunes in the U.S., with changing crests that rise to 700 ft (215 m). In 2000 the Great Sand Dunes National Preserve was created, and after much land acquisition the monument officially became a national park in 2004.

Learn more about Great Sand Dunes National Park and Preserve with a free trial on Britannica.com.

Lake, northern Utah, U.S. It is the largest inland body of salt water in the Western Hemisphere and one of the most saline in the world. It fluctuates greatly in size, depending on rates of evaporation and the flow of the rivers into it. Its surface area has varied from about 2,400 sq mi (6,200 sq km) at its highest levels in 1873 and the mid 1980s to about 950 sq mi (2,460 sq km) at its low level in 1963. At times of median water level, it is generally less than 15 ft (4.5 m) deep. Surrounded by stretches of sand, salt land, and marsh, the lake remains isolated, though in recent years it has become important as a source of minerals, as a beach and water-sports attraction, and as a wildlife preserve.

Learn more about Great Salt Lake with a free trial on Britannica.com.

Continental slope of central North America. It stretches from the Rio Grande at the U.S.-Mexico border in the south to the Mackenzie River delta along the Arctic Ocean in the north and from the Interior Lowlands and the Canadian Shield in the east to the Rocky Mountains in the west. The plains embrace parts of 10 U.S. states and 4 Canadian provinces, covering an area of about 1,125,000 sq mi (2,900,000 sq km). A high plateau of semiarid grassland, these prairie regions in both the U.S. and Canada produce the major proportion of wheat grown in each country and are also important cattle- and sheep-herding areas. Parts of the plains have reserves of coal and lignite, petroleum, and natural gas.

Learn more about Great Plains with a free trial on Britannica.com.

or Great Ouse

River, central and eastern England. It rises in Northamptonshire and flows 156 mi (251 km) past Buckingham, Bedford, Huntington, and St. Ives to Earith, then to the North Sea. Locks make the river navigable upstream to Bedford.

Learn more about Ouse, River with a free trial on Britannica.com.

or Cybele

Cybele, terra-cotta statuette, from Camirus, Rhodes, early 5th century BC; in the British Museum, elipsis

Deity of the ancient Mediterranean world. Her cult originated in Phrygia in Asia Minor and spread to the Greek world, where she was identified with Rhea. It reached Rome by the 3rd century BC and became a major cult during the empire. Known by a variety of local names, Cybele was venerated as the universal mother of gods, humans, and animals. Her lover was the fertility god Attis. Her priests, the Galli, castrated themselves when they entered her service, and on her festival day they spattered their blood on her altar and her sacred pine tree.

Learn more about Great Mother of the Gods with a free trial on Britannica.com.

Failed industrialization campaign undertaken by the Chinese communists between 1958 and early 1960. Mao Zedong hoped to develop labour-intensive methods of industrialization that would emphasize manpower rather than the gradual purchase of heavy machinery, thereby putting to use China's dense population and obviating the need to accumulate capital. Rather than building large new factories, he proposed developing backyard steel furnaces in every village. Rural people were organized into communes where agricultural and political decisions emphasized ideological purity rather than expertise. The program was implemented so hastily and zealously that many errors occurred; these were exacerbated by a series of natural disasters and the withdrawal of Soviet technical personnel. China's agriculture was severely disrupted, causing widespread famine in 1958–62. By early 1960 the government had begun to repeal the Great Leap Forward; private plots were returned to peasants, and expertise began to be emphasized again.

Learn more about Great Leap Forward with a free trial on Britannica.com.

Chain of lakes, east-central North America. Comprising Lakes Superior, Michigan, Huron, Erie, and Ontario, it forms a natural boundary between the U.S. and Canada. The Great Lakes cover an area of about 94,850 sq mi (245,660 sq km) and constitute the largest freshwater surface in the world. Connected to form a single waterway that discharges down the St. Lawrence River into the Atlantic Ocean, with the St. Lawrence Seaway they form a shipping lane more than 2,000 mi (3,200 km) long that carries oceangoing traffic as far west as Duluth, Minn. Large quantities of iron ore, coal, grain, and manufactured goods are moved between lake ports and shipped overseas. While commercial fishing was once a major industry on the lakes, pollution and other factors led to its collapse; recovery has been slow and partial. The lakes are used for many recreational activities, including boating and sailing.

Learn more about Great Lakes with a free trial on Britannica.com.

or Great Indian Desert

Region of hot, dry desert, northwestern India and southeastern Pakistan. Its undulating surface is composed of sand dunes separated by sandy plains and low, barren hills. Several saline lakes are found there. Covering some 77,000 sq mi (200,000 sq km), it is bordered by the Indus River plain, the Aravalli Range, and the Punjab plain.

Learn more about Thar Desert with a free trial on Britannica.com.

or Great Divide

Main watershed of eastern Australia. It consists of a series of plateaus and mountain ranges roughly paralleling the coasts of Queensland, New South Wales, and Victoria that stretches for some 2,300 mi (3,700 km). Beginning in the north on the Cape York Peninsula, Queen., the range heads generally south to become the Australian Alps near the New South Wales–Victoria border. The range bends west in Victoria, ending in the Grampians, while a southern spur emerges from the Bass Strait to form the central uplands of Tasmania. First traversed by Europeans moving into the Australian Outback in 1813, the region is now important for agriculture, lumbering, and mining, and its national parks and other natural areas are major tourist attractions.

Learn more about Great Dividing Range with a free trial on Britannica.com.

Longest and most severe economic depression ever experienced by the Western world. It began in the U.S. soon after the New York Stock Market Crash of 1929 and lasted until about 1939. By late 1932 stock values had dropped to about 20percnt of their previous value, and by 1933 11,000 of the U.S.'s 25,000 banks had failed. These and other conditions, worsened by monetary policy mistakes and adherence to the gold standard, led to much-reduced levels of demand and hence of production, resulting in high unemployment (by 1932, 25–30percnt). Since the U.S. was the major creditor and financier of postwar Europe, the U.S. financial breakdown precipitated economic failures around the world, especially in Germany and Britain. Isolationism spread as nations sought to protect domestic production by imposing tariffs and quotas, ultimately reducing the value of international trade by more than half by 1932. The Great Depression contributed to political upheaval. It led to the election of U.S. Pres. Franklin Roosevelt, who introduced major changes in the structure of the U.S. economy through his New Deal. The Depression also advanced Adolf Hitler's rise to power in Germany in 1933 and fomented political extremism in other countries. Before the Great Depression, governments relied on impersonal market forces to achieve economic correction; afterward, government action came to assume a principal role in ensuring economic stability.

Learn more about Great Depression with a free trial on Britannica.com.

Breed of working dog developed at least 400 years ago in Germany, where it was used for boar hunting. Tallest of the working breeds, it stands 28–32 in. (71–81 cm) tall and weighs 120–150 lbs (54–68 kg). It has a massive, square-jawed head and elegant body lines. Its short coat is black, golden brown, brindle, blue-gray, or white with black patches. It is typically swift and alert and is noted for courage, friendliness, and dependability. There is no known reason to associate Denmark with the breed.

Learn more about Great Dane with a free trial on Britannica.com.

Lake, Northwest Territories, Canada. Lying astride the Arctic Circle, it was visited before 1800 by North West Company traders and later named for the bears that inhabited its shores. Containing many small islands, Great Bear Lake is roughly 200 mi (320 km) long and 25–110 mi (40–175 km) wide and has a maximum depth of 1,356 ft (413 m). It is the largest lake entirely within Canada and the fourth largest in North America. The lake's waters abound with fish, including the speckled trout.

Learn more about Great Bear Lake with a free trial on Britannica.com.

Extensive complex of coral reefs, shoals, and islets in the Pacific Ocean, off the northeastern coast of Australia. The largest deposit of coral in the world, it extends for more than 1,250 mi (2,000 km) along the coast of Queensland and has an area of some 135,000 sq mi (350,000 sq km). The reef has been formed over millions of years from the skeletons of a mass of living marine organisms. In addition to at least 300 species of hard coral, marine life includes anemones, worms, gastropods, lobsters, crayfish, prawns, crabs, and a variety of fishes. Encrusting red algae form the purplish red algal rim that is one of the reef's characteristic features. A major tourist attraction, nearly all of it is within Great Barrier Reef National Park; the reef was designated a UNESCO World Heritage site in 1981.

Learn more about Great Barrier Reef with a free trial on Britannica.com.

Religious revival in British North America from 1720 into the 1740s. It was part of a movement, known as Pietism or Quietism on the European continent and evangelicalism in England, that swept Western Europe in the late 17th and early 18th century under the leadership of preachers such as John Wesley. In North America the Great Awakening was a Protestant evangelical reaction against formalism and rationalism in religion, and it had a strong Calvinist element. Revivalist preachers emphasized the need for sinners to fear punishment and to hope for the unearned gift of grace from God. George Whitefield (1714–1770) was one of the most popular, preaching to huge crowds throughout the colonies in 1739–40. Jonathan Edwards also helped inspire the Great Awakening and was its most important theologian. Among its results were missions to the Indians and the founding of colleges (including Princeton Univ.). Another revival known as the Second Great Awakening occurred in New England and Kentucky in the 1790s.

Learn more about Great Awakening with a free trial on Britannica.com.

Bay of the Indian Ocean, southern Australian coast. Its generally accepted boundaries are from Cape Pasley, Western Australia, to Cape Carnot, South Australia—a distance of 720 mi (1,160 km). The head of the bight abuts on the arid Nullarbor Plain and is bounded by cliffs 200–400 ft (60–120 m) high. Near Eucla on the bight's shores is the Nuytsland Reserve. Lying in the track of the winter western winds, the bight has a reputation for storms and rough seas.

Learn more about Great Australian Bight with a free trial on Britannica.com.

Greek Constantinos

(born Aug. 2, 1868, Athens, Greece—died Jan. 11, 1923, Palermo, Italy) King of Greece (1913–17, 1920–22). Son of King George I of the Hellenes (1845–1913), he was educated in Germany and was commander in chief of Greek forces in the Balkan Wars. He succeeded his father in 1913, but his neutralist, yet essentially pro-German, attitude during World War I caused the Allies and his Greek opponents to depose him in 1917. He was restored to the throne in 1920, but, after a catastrophic war in Anatolia, he abdicated in favor of his son, George II, in 1922.

Learn more about Constantine I with a free trial on Britannica.com.

or Carolus Magnus (“Charles the Great”)

(born April 2, c. 742—died Jan. 28, 814, Aachen, Austrasia) King of the Franks (768–814) and emperor (800–14). The elder son of the Frankish king Pippin III (the Short), he ruled the Frankish kingdom jointly with his brother Carloman until the latter's death in 771. He then became sole king of the Franks and began a series of campaigns to conquer and Christianize neighbouring kingdoms. He defeated and became king of the Lombards in northern Italy (774). His expedition against the Muslims in Spain failed (778), but he successfully annexed Bavaria (788). Charlemagne fought against the Saxons for many years, finally defeating and Christianizing them in 804. He subdued the Avars of the Danube and gained control of many of the Slav states. With the exception of the British Isles, southern Italy, and part of Spain, he united in one vast state almost all the Christian lands of western Europe. His coronation as emperor at Rome on Christmas Day, 800, after restoring Leo III to the papacy, marks the revival of the empire in Latin Europe and was the forerunner of the Holy Roman Empire. Charlemagne established his capital at Aachen (Aix-la-Chapelle), where he built a magnificent palace. He invited many scholars and poets to assist him in the promotion of the religious and cultural revival known as the Carolingian renaissance. He also codifed the laws and increased the use of writing in government and society. He was succeeded on his death by his son Louis the Pious, whom Charlemagne had crowned coemperor in 813. Seealso Carolingian dynasty.

Learn more about Charlemagne with a free trial on Britannica.com.

St. Basil, detail of a mosaic, 12th century; in the Palatine Chapel, Palermo, Sicily, Italy.

(born AD 329, Caesarea Mazaca, Cappadocia—died Jan. 1, 379, Caesarea; Western feast day January 2; Eastern feast day January 1) Early church father. Born into a Christian family in Cappadocia, he studied at Caesarea, Constantinople, and Athens and later established a monastic settlement on the family estate at Annesi. He opposed Arianism, which was supported by the emperor Valens and his own bishop Dianius, and organized resistance to it after 365. He succeeded Eusebius as bishop of Caesarea in 370. He died shortly after Valens, whose death in battle opened the way for the victory of Basil's cause. More than 300 of his letters survive; several of his Canonical Epistles have become part of canon law in Eastern Orthodoxy.

Learn more about Basil the Great, Saint with a free trial on Britannica.com.

or Alexander III

(born 356 BC, Pella, Macedonia—died June 13, 323 BC, Babylon) King of Macedonia (336–323) and the greatest military leader of antiquity. The son of Philip II of Macedonia, he was taught by Aristotle. He soon showed military brilliance, helping win the Battle of Chaeronea at age 18. He succeeded his assassinated father in 336 and promptly took Thessaly and Thrace; he brutally razed Thebes except for its temples and the house of Pindar. Such destruction was to be his standard method, and other Greek states submitted meekly. In 334 he crossed to Persia and defeated a Persian army at the Granicus River. He is said to have cut the Gordian knot in Phrygia (333), by which act, according to legend, he was destined to rule all Asia. At the Battle of Issus in 333, he defeated another army, this one led by the Persian king Darius III, who managed to escape. He then took Syria and Phoenicia, cutting off the Persian fleet from its ports. In 332 he completed a seven-month siege of Tyre, considered his greatest military achievement, and then took Egypt. There he received the pharaohs' double crown, founded Alexandria, and visited the oracle of the god Amon, the basis of his claim to divinity. In control of the eastern Mediterranean coast, in 331 he defeated Darius in a decisive battle at Gaugamela, though Darius again escaped. He next took the province of Babylon. He burnt Xerxes' palace at Persepolis, Persia, in 330, and he envisioned an empire ruled jointly by Macedonians and Persians. He continued eastward, quashing real or imagined conspiracies among his men and taking control to the Oxus and Jaxartes rivers, founding cities (most named Alexandria) to hold the territory. Conquering what is now Tajikistan, he married the princess Roxana and embraced Persian absolutism, adopting Persian dress and enforcing Persian court customs. By 326 he reached the Hyphasis in India, where his weary men mutinied; he turned back, marching and pillaging down the Indus, and reached Susa with much loss of life. He continued to promote his unpopular policy of racial fusion, a seeming attempt to form a Persian-Macedonian master race. When his favourite, Hephaestion (324), died, Alexander gave him a hero's funeral and demanded that divine honours be given at his own funeral. He fell ill at Babylon after long feasting and drinking and died at age 33. He was buried in Alexandria, Egypt. His empire, the greatest that had existed to that time, extended from Thrace to Egypt and from Greece to the Indus valley.

Learn more about Alexander the Great with a free trial on Britannica.com.

The great-circle distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere's interior). Because spherical geometry is rather different from ordinary Euclidean geometry, the equations for distance take on a different form. The distance between two points in Euclidean space is the length of a straight line from one point to the other. On the sphere, however, there are no straight lines. In non-Euclidean geometry, straight lines are replaced with Geodesics. Geodesics on the sphere are the great circles (circles on the sphere whose centers are coincident with the center of the sphere).

Between any two points on a sphere which are not directly opposite each other, there is a unique great circle. The two points separate the great circle into two arcs. The length of the shorter arc is the great-circle distance between the points. A great circle endowed with such a distance is the Riemannian circle.

Between two points which are directly opposite each other, called antipodal points, there are infinitely many great circles, but all great circle arcs between antipodal points have the same length, i.e. half the circumference of the circle, or $pi r$, where r is the radius of the sphere.

Because the Earth is approximately spherical (see Earth radius), the equations for great-circle distance are important for finding the shortest distance between points on the surface of the Earth, and so have important applications in navigation.

The geographical formula

Let $phi_s,lambda_s; phi_f,lambda_f;!$ be the geographical latitude and longitude of two points (a base "standpoint" and the destination "forepoint"), respectively, $Deltalambda;!$ the longitude difference and $Deltawidehat\left\{sigma\right\};!$ the (spherical) angular difference/distance, or central angle, which can be constituted from the spherical law of cosines:

$\left\{color\left\{white\right\}Big|\right\}Deltawidehat\left\{sigma\right\}=arccosbig\left(cosphi_scosphi_fcosDeltalambda+sinphi_ssinphi_fbig\right).;!$

The distance d, i.e. the arc length, for a sphere of radius r and $Deltawidehat\left\{sigma\right\}!$ given in radians, is then:

$d = r Deltawidehat\left\{sigma\right\}.$

This arccosine formula above can have large rounding errors for the common case where the distance is small, however, so it is not normally used. Instead, an equation known historically as the haversine formula was preferred, which is much more accurate for small distances:

$\left\{color\left\{white\right\}frac\left\{bigg|\right\}$ =2arcsinleft(sqrt{sin^2left(frac{phi_f-phi_s}{2}right)+cos{phi_s}cos{phi_f}sin^2left(frac{Deltalambda}{2}right)}right).;!

(Historically, the use of this formula was simplified by the availability of tables for the haversine function: hav(θ) = sin2(θ/2).)

Although this formula is accurate for most distances, it too suffers from rounding errors for the special (and somewhat unusual) case of antipodal points (on opposite ends of the sphere). A more complicated formula that is accurate for all distances is the Vincenty formula:

$\left\{color\left\{white\right\}frac\left\{bigg$
>Deltawidehat{sigma}=arctanleft(frac{sqrt{left(cosphi_fsinDeltalambdaright)^2+left(cosphi_ssinphi_f-sinphi_scosphi_fcosDeltalambdaright)^2}}{sinphi_ssinphi_f+cosphi_scosphi_fcosDeltalambda}right);;!

(When programming a computer, one should use the `atan2()` function rather than the ordinary arctangent function (`atan()`), in order to simplify handling of the case where the denominator is zero.)

If r is the great-circle radius of the sphere, then the great-circle distance is $r,Deltawidehat\left\{sigma\right\};!$.

Note: above, accuracy refers to rounding errors only; all formulas themselves are exact (for a sphere).

Spherical distance on the Earth

The shape of the Earth more closely resembles a flattened spheroid with extreme values for the radius of arc, or arcradius—the radius of curvature, of 6335.437 km at the equator (vertically) and 6399.592 km at the poles, and having an average great-circle radius of 6372.795 km (3438.461 nautical miles). (Note that "arcradius" or "radius of curvature" is not the distance from the center of the earth to the surface. The distance from the center to the surface is smaller at the poles than at the equator; the arcradius is larger at the poles than at the equator.) Using a sphere with a radius of 6372.795 km thus results in an error of up to about 0.5%.

A worked example

In order to use this formula for anything practical you will need two sets of coordinates. For example, the latitude and longitude of two airports:

• Nashville International Airport (BNA) in Nashville, TN, USA: N 36°7.2', W 86°40.2'
• Los Angeles International Airport (LAX) in Los Angeles, CA, USA: N 33°56.4', W 118°24.0'

First, convert these coordinates to decimal degrees (Sign × (Deg + (Min + Sec / 60) / 60)) and radians (× π / 180) before you can use them effectively in a formula. After conversion, the coordinates become:

• BNA: $phi_s= 36.12^circapprox 0.6304mbox\left\{ rad\right\};;;lambda_s=-86.67^circapprox -1.5127mbox\left\{ rad\right\};;!$
• LAX: $phi_f= 33.94^circapprox 0.5924mbox\left\{ rad\right\};;;lambda_f=-118.40^circapprox -2.0665mbox\left\{ rad\right\};;!$

Using these values in the angular difference/distance equation:

$r,Deltawidehat\left\{sigma\right\}approx 6372.795times0.45306 approx 2887.259mbox\left\{ km\right\}.;!$

Thus the distance between LAX and BNA is about 2887 km or 1794 miles (× 0.62137) or 1558 nautical miles (× 0.539553).