(T. AS.)

CALAFAT, a town of Rumania in the department of Doljiu; on the river Danube, opposite the Bulgarian fortress of Vidin. Pop. (1900) 7113. Calafat is an important centre of the grain trade, and is connected by a branch line with the principal Walachian railways, and by a steam ferry with Vidin. It was founded in the 14th century by Genoese colonists, who employed large numbers of workmen (Calfats) in repairing ships—which industry gave its name to the place. In 1854 a Russian force was defeated at Calafat by the Turks under Ahmed Pasha, who surprised the enemy's camp.

CALAH (so in the Bible; Kalah in the Assyrian inscriptions), an ancient city situated in the angle formed by the Tigris and [v.04 p.0965] the upper Zab, 19 m. S. of Nineveh, and one of the capitals of Assyria. According to the inscriptions, it was built by Shalmaneser I. about 1300 B.C., as a residence city in place of the older Assur. After that it seems to have fallen into decay or been destroyed, but was restored by Assur-nasir-pal, about 880 B.C., and from that time to the overthrow of the Assyrian power it remained a residence city of the Assyrian kings. It shared the fate of Nineveh, was captured and destroyed by the Medes and Babylonians toward the close of the 7th century, and from that time has remained a ruin. The site was discovered by Sir A.H. Layard, in 1845, in the tel of Nimrud. Hebrew tradition (in the J narrative, Genesis x. 11, 12) mentions Calah as built by Nimrod. Modern Arabic tradition likewise ascribes the ruins, like those of Birs Nimrud, near Babylon, to Nimrod, because they are the most prominent ruins of that region. Similarly the ancient dike in the river Tigris at this point is ascribed to Nimrod. The ruin mounds of Nimrud consist of an oblong enclosure, formed by the walls of the ancient city, of which fifty-eight towers have been traced on the N. and about fifty on the E. In the S.W. corner of this oblong is an elevated platform in the form of a rectangular parallelogram, some 600 yds. from N. to S. and 400 yds. from E. to W., raised on an average about 40 ft. above the plain, with a lofty cone 140 ft. high in the N.W. corner. This is the remains of the raised platform of unbaked brick, faced with baked bricks and stone, on which stood the principal palaces and temples of the city, the cone at the N.W. representing the ziggurat, or stage-tower, of the principal temple. Originally on the banks of the Tigris, this platform now stands some distance E. of the river. Here Layard conducted excavations from 1845 to 1847, and again from 1849 to 1851. The means at his disposal were inadequate, his excavations were incomplete and also unscientific in that his prime object was the discovery of inscriptions and museum objects; but he was wonderfully successful in achieving the results at which he aimed, and the numerous statues, monuments, inscribed stones, bronze objects and the like found by him in the ruins of Calah are among the most precious possessions of the British Museum. Excavations were also conducted by Hormuzd Rassan in 1852-1854, and again in 1878, and by George Smith in 1873. But while supplementing in some important respects Layard's excavations, this later work added relatively little to his discoveries whether of objects or of facts. The principal buildings discovered at Calah are:—(a) the North-West palace, south of the ziggurat, one of the most complete and perfect Assyrian buildings known, about 350 ft. square, consisting of a central court, 129 ft. by 90 ft., surrounded by a number of halls and chambers. This palace was originally constructed by Assur-nasir-pal I. (885-860 B.C.), and restored and reoccupied by Sargon (722-705 B.C.). In it were found the winged lions, now in the British Museum, the fine series of sculptured bas-reliefs glorifying the deeds of Assur-nasir-pal in war and peace, and the large collection of bronze vessels and implements, numbering over 200 pieces; (b) the Central palace, in the interior of the mound, toward its southern end, erected by Shalmaneser II. (860-825 B.C.) and rebuilt by Tiglath-pileser III. (745-727 B.C.). Here were found the famous black obelisk of Shalmaneser, now in the British Museum, in the inscription on which the tribute of Jehu, son of Omri, is mentioned, the great winged bulls, and also a fine series of slabs representing the battles and sieges of Tiglath-pileser; (c) the South-West palace, in the S.W. corner of the platform, an uncompleted building of Esarhaddon (681-668 B.C.), who robbed the North-West and Central palaces, effacing the inscriptions of Tiglath-pileser, to obtain material for his construction; (d) the smaller West palace, between the South-West and the North-West palaces, a construction of Hadad-nirari or Adadnirari III. (812-783 B.C.); (e) the South-East palace, built by Assur-etil-ilani, after 626 B.C., for his harem, in the S.E. corner of the platform, above the remains of an older similar palace of Shalmaneser; (f) two small temples of Assur-nasir-pal, in connexion with the ziggurat in the N.W. corner; and (g) a temple called E-Zida, and dedicated to Nebo, near the South-East palace. From the number of colossal figures of Nebo discovered here it would appear that the cult of Nebo was a favourite one, at least during the later period. The other buildings on the E. side of the platform had been ruined by the post-Assyrian use of the mound for a cemetery, and for tunnels for the storage and concealment of grain. While the ruins of Calah were remarkably rich in monumental material, enamelled bricks, bronze and ivory objects and the like, they yielded few of the inscribed clay tablets found in such great numbers at Nineveh and various Babylonian sites. Not a few of the astrological and omen tablets in the Kuyunjik collection of the British Museum, however, although found at Nineveh, were executed, according to their own testimony, at Calah for the rab-dup-šarrē or principal librarian during the reigns of Sargon and Sennacherib (716-684 B.C.). From this it would appear that there was at that time at Calah a library or a collection of archives which was later removed to Nineveh. In the prestige of antiquity and religious renown, Calah was inferior to the older capital, Assur, while in population and general importance it was much inferior to the neighbouring Nineveh. There is no proper ground for regarding it, as some Biblical scholars of a former generation did, through a false interpretation of the book of Jonah, as a part or suburb of Nineveh.

See A.H. Layard, Nineveh and its Remains (London, 1849); George Smith, Assyrian Discoveries (London, 1883); Hormuzd Rassam, Ashur and the Land of Nimrod (London and New York, 1897).

(J. P. PE.)

CALAHORRA (anc. Calagurris), a city of northern Spain, in the province of Logrono; on the left bank of the river Cidacos, which enters the Ebro 3 m. E., and on the Bilbao-Saragossa railway. Pop. (1900) 9475. Calahorra is built on the slope of a hill overlooking the wide Ebro valley, which supplies its markets with an abundance of grain, wine, oil and flax. Its cathedral, which probably dates from the foundation of the see of Calahorra in the 5th century, was restored in 1485, and subsequently so much altered that little of the original Gothic structure survives. The Casa Santa, annually visited by many thousands of pilgrims on the 31st of August, is said to contain the bodies of the martyrs Emeterius and Celedonius, who were beheaded in the 3rd or 4th century, on the site now occupied by the cathedral. Their heads, according to local legend, were cast into the Ebro, and, after floating out to sea and rounding the Iberian peninsula, are now preserved at Santander.

The chief remains of the Roman Calagurris are the vestiges of an aqueduct and an amphitheatre. Calagurris became famous in 76 B.C., when it was successfully defended against Pompey by the adherents of Sertorius. Four years later it was captured by Pompey's legate, Afranius, after starvation had reduced the garrison to cannibalism. Under Augustus (31 B.C.-A.D. 14) Calagurris received the privileges of Roman citizenship, and at a later date it was given the additional name of Nassica to distinguish it from the neighbouring town of Calagurris Fibularensis, the exact site of which is uncertain. The rhetorician Quintilian was born at Calagurris Nassica about A.D. 35.

CALAIS, a seaport and manufacturing town of northern France, in the department of Pas-de-Calais, 18 m. E.S.E. of Dover, and 185 m. N. of Paris by the Northern railway. Pop. (1906) 59,623. Calais, formerly a celebrated fortress, is defended by four forts, not of modern construction, by a citadel built in 1560, which overlooks it on the west, and by batteries. The old town stands on an island hemmed in by the canal and the harbour basins, which divide it from the much more extensive manufacturing quarter of St Pierre, enveloping it on the east and south. The demolition of the ramparts of Old Calais was followed by the construction of a new circle of defences, embracing both the old and new quarters, and strengthened by a deep moat. In the centre of the old town is the Place d'Armes, in which stands the former hotel-de-ville (rebuilt in 1740, restored in 1867), with busts of Eustache de St Pierre, Francis, duke of Guise, and Cardinal Richelieu. The belfry belongs to the 16th and early 17th century. Close by is the Tour du Guet, or watch-tower, used as a lighthouse until 1848. The church of Notre-Dame, built during the English occupancy of Calais, has a [v.04 p.0966] fine high altar of the 17th century; its lofty tower serves as a landmark for sailors. A gateway flanked by turrets (14th century) is a relic of the Hotel de Guise, built as a gild hall for the English woolstaplers, and given to the duke of Guise as a reward for the recapture of Calais. The modern town-hall and a church of the 19th century are the chief buildings of the quarter of St Pierre. Calais has a board of trade-arbitrators, a tribunal and a chamber of commerce, a commercial and industrial school, and a communal college.

The harbour is entered from the roads by way of a channel leading to the outer harbour which communicates with a floating basin 22 acres in extent, on the east, and with the older and less commodious portion of the harbour to the north and west of the old town. The harbour is connected by canals with the river Aa and the navigable waterways of the department.

Calais is the principal port for the continental passenger traffic with England carried on by the South-Eastern & Chatham and the Northern of France railways. The average number of passengers between Dover and Calais for the years 1902-1906 inclusive was 315,012. Trade is chiefly with the United Kingdom. The principal exports are wines, especially champagne, spirits, hay, straw, wool, potatoes, woven goods, fruit, glass-ware, lace and metal-ware. Imports include cotton and silk goods, coal, iron and steel, petroleum, timber, raw wool, cotton yarn and cork. During the five years 1901-1905 the average annual value of exports was L8,388,000 (L6,363,000 in the years 1896-1900), of imports L4,145,000 (L3,759,000 in 1896-1900). In 1905, exclusive of passenger and mail boats, there entered the port 848 vessels of 312,477 tons and cleared 857 of 305,284 tons, these being engaged in the general carrying trade of the port. The main industry of Calais is the manufacture of tulle and lace, for which it is the chief centre in France. Brewing, saw-milling, boat-building, and the manufacture of biscuits, soap and submarine cables are also carried on. Deep-sea and coast fishing for cod, herring and mackerel employ over 1000 of the inhabitants.

Calais was a petty fishing-village, with a natural harbour at the mouth of a stream, till the end of the 10th century. It was first improved by Baldwin IV., count of Flanders, in 997, and afterwards, in 1224, was regularly fortified by Philip Hurepel, count of Boulogne. It was besieged in 1346, after the battle of Crecy, by Edward III. and held out resolutely by the bravery of Jean de Vienne, its governor, till after nearly a year's siege famine forced it to surrender. Its inhabitants were saved from massacre by the devotion of Eustache de St Pierre and six of the chief citizens, who were themselves spared at the prayer of Queen Philippa. The city remained in the hands of the English till 1558, when it was taken by Francis, duke of Guise, at the head of 30,000 men from the ill-provided English garrison, only 800 strong, after a siege of seven days. From this time the Calaisis or territory of Calais was known as the Pays Reconquis. It was held by the Spaniards from 1595 to 1598, but was restored to France by the treaty of Vervins.

CALAIS, a city and sub-port of entry of Washington county, Maine, U.S.A., on the Saint Croix river, 12 m. from its mouth, opposite Saint Stephens, New Brunswick, with which it is connected by bridges. Pop. (1890) 7290;(1900) 7655 (1908 being foreign-born); (1910) 6116. It is served by the Washington County railway (102.5 m. to Washington Junction, where it connects with the Maine Central railway), and by steamboat lines to Boston, Portland and Saint Johns. In the city limits are the post-offices of Calais, Milltown and Red Beach. The city has a small public library. The valley here is wide and deep, the banks of the river bold and picturesque, and the tide rises and falls about 25 ft. The city has important interests in lumber, besides foundries, machine shops, granite works—there are several granite (notably red granite) quarries in the vicinity—a tannery, and manufactories of shoes and calcined plaster. Big Island, now in the city of Calais, was visited in the winter of 1604-1605 by Pierre du Guast, sieur de Monts. Calais was first settled in 1779, was incorporated as a town in 1809, and was chartered as a city in 1851.

CALAIS and ZETES (the Boreadae), in Greek mythology, the winged twin sons of Boreas and Oreithyia. On their arrival with the Argonauts at Salmydessus in Thrace, they liberated their sister Cleopatra, who had been thrown into prison with her two sons by her husband Phineus, the king of the country (Sophocles, Antigone, 966; Diod. Sic. iv. 44). According to another story, they delivered Phineus from the Harpies (q.v.), in pursuit of whom they perished (Apollodorus i. 9; iii. 15). Others say that they were slain by Heracles near the island of Tenos, in consequence of a quarrel with Tiphys, the pilot of the Argonauts, or because they refused to wait during the search for Hylas, the favourite of Heracles (Hyginus, Fab., 14. 273; schol. on Apollonius Rhodius i. 1304). They were changed by the gods into winds, and the pillars over their tombs in Tenos were said to wave whenever the wind blew from the north. Like the Harpies, Calais and Zetes are obvious personifications of winds. Legend attributed the foundation of Cales in Campania to Calais (Silius Italicus viii. 512).

CALAMINE, a mineral species consisting of zinc carbonate, ZnCO_3, and forming an important ore of zinc. It is rhombohedral in crystallization and isomorphous with calcite and chalybite. Distinct crystals are somewhat rare; they have the form of the primitive rhombohedron (rr' = 72 deg. 20'), the faces of which are generally curved and rough. Botryoidal and stalactitic masses are more common, or again the mineral may be compact and granular or loose and earthy. As in the other rhombohedral carbonates, the crystals possess perfect cleavages parallel to the faces of the rhombohedron. The hardness is 5; specific gravity, 4.4. The colour of the pure mineral is white; more often it is brownish, sometimes green or blue: a bright-yellow variety containing cadmium has been found in Arkansas, and is known locally as "turkey-fat ore." The pure material contains 52% of zinc, but this is often partly replaced isomorphously by small amounts of iron and manganese, traces of calcium and magnesium, and sometimes by copper or cadmium.

Calamine is found in beds and veins in limestone rocks, and is often associated with galena and blende. It is a product of alteration of blende, having been formed from this by the action of carbonated waters; or in many cases the zinc sulphide may have been first oxidized to sulphate, which in solution acted on the surrounding limestone, producing zinc carbonate. The latter mode of origin is suggested by the frequent occurrence of calamine pseudomorphous after calcite, that is, having the form of calcite crystals. Deposits of calamine have been extensively mined in the limestones of the Mendip Hills, in Derbyshire, and at Alston Moor in Cumberland. It also occurs in large amount in the province of Santander in Spain, in Missouri, and at several other places where zinc ores are mined. The best crystals of the mineral were found many years ago at Chessy near Lyons; these are rhombohedra of a fine apple-green colour. A translucent botryoidal calamine banded with blue and green is found at Laurion in Greece, and has sometimes been cut and polished for small ornaments such as brooches.

The name calamine (German, Galmei), from lapis calaminaris, a Latin corruption of cadmia ([Greek: kadmia]), the old name for zinc ores in general (G. Agricola in 1546 derived it from the Latin calamus, a reed), was early used indiscriminately for the carbonate and the hydrous silicate of zinc, and even now both species are included by miners under the same term. The two minerals often closely resemble each other in appearance, and can usually only be distinguished by chemical analysis; they were first so distinguished by James Smithson in 1803. F.S. Beudant in 1832 restricted the name calamine to the hydrous silicate and proposed the name "smithsonite" for the carbonate, and these meanings of the terms are now adopted by Dana and many other mineralogists. Unfortunately, however, in England (following Brooke and Miller, 1852) these designations have been reversed, calamine being used for the carbonate and smithsonite for the silicate. This unfortunate confusion is somewhat lessened by the use of the terms zinc-spar and hemimorphite (q.v.) for the carbonate and silicate respectively.

(L. J. S.)

[v.04 p.0967] CALAMIS, an Athenian sculptor of the first half of the 5th century B.C. He made statues of Apollo the averter of ill, Hermes the ram-bearer, Aphrodite and other deities, as well as part of a chariot group for Hiero, king of Syracuse. His works are praised by ancient critics for delicacy and grace, as opposed to breadth and force. Archaeologists are disposed to regard the bronze charioteer recently found at Delphi as a work of Calamis; but the evidence is not conclusive (see GREEK ART).

CALAMY, EDMUND, known as "the elder" (1600-1666), English Presbyterian divine, was born of Huguenot descent in Walbrook, London, in February 1600, and educated at Pembroke Hall, Cambridge, where his opposition to the Arminian party, then powerful in that society, excluded him from a fellowship. Nicholas Felton, bishop of Ely, however, made him his chaplain, and gave him the living of St Mary, Swaffham Prior, which he held till 1626. He then removed to Bury St Edmunds, where he acted as lecturer for ten years, retiring when his bishop (Wren) insisted on the observance of certain ceremonial articles. In 1636 he was appointed rector (or perhaps only lecturer) of Rochford in Essex, which was so unhealthy that he had soon to leave it, and in 1639 he was elected to the perpetual curacy of St Mary Aldermanbury in London, where he had a large following. Upon the opening of the Long Parliament he distinguished himself in defence of the Presbyterian cause, and had a principal share in writing the conciliatory work known as Smectymnuus, against Bishop Joseph Hall's presentation of episcopacy. The initials of the names of the several contributors formed the name under which it was published, viz., S. Marshal, E. Calamy, T. Young, M. Newcomen and W. Spurstow. Calamy was an active member in the Westminster assembly of divines, and, refusing to advance to Congregationalism, found in Presbyterianism the middle course which best suited his views of theology and church government. He opposed the execution of Charles I., lived quietly under the Commonwealth, and was assiduous in promoting the king's return; for this he was afterwards offered the bishopric of Coventry and Lichfield, but declined it, it is said, on his wife's persuasion. He was made one of Charles's chaplains, and vainly tried to secure the legal ratification of Charles's declaration of the 25th of October 1660. He was ejected for Nonconformity in 1662, and was so affected by the sight of the devastation caused by the great fire of London that he died shortly afterwards, on the 29th of October 1666. He was buried in the ruins of his church, near the place where the pulpit had stood. His publications are almost entirely sermons. His eldest son (Edmund), known as "the younger," was educated at Cambridge, and was ejected from the rectory of Moreton, Essex, in 1662. He was of a retiring disposition and moderate views, and died in 1685.

CALAMY, EDMUND (1671-1732), English Nonconformist divine, the only son of Edmund Calamy "the younger," was born in London, in the parish of St Mary Aldermanbury, on the 5th of April 1671. He was sent to various schools, including Merchant Taylors', and in 1688 proceeded to the university of Utrecht. While there, he declined an offer of a professor's chair in the university of Edinburgh made to him by the principal, William Carstares, who had gone over on purpose to find suitable men for such posts. After his return to England in 1691 he began to study divinity, and on Baxter's advice went to Oxford, where he was much influenced by Chillingworth. He declined invitations from Andover and Bristol, and accepted one as assistant to Matthew Sylvester at Blackfriars (1692). In June 1694 he was publicly ordained at Annesley's meeting-house in Little St Helen's, and soon afterwards was invited to become assistant to Daniel Williams in Hand Alley, Bishopsgate. In 1702 he was chosen one of the lecturers in Salters' Hall, and in 1703 he succeeded Vincent Alsop as pastor of a large congregation in Westminster. In 1709 Calamy made a tour through Scotland, and had the degree of doctor of divinity conferred on him by the universities of Edinburgh, Aberdeen and Glasgow. Calamy's forty-one publications are mainly sermons, but his fame rests on his nonconformist biographies. His first essay was a table of contents to Baxter's Narrative of his life and times, which was sent to the press in 1696; he made some remarks on the work itself and added to it an index, and, reflecting on the usefulness of the book, he saw the expediency of continuing it, as Baxter's history came no further than the year 1684. Accordingly, he composed an abridgment of it, with an account of many other ministers who were ejected after the restoration of Charles II.; their apology, containing the grounds of their nonconformity and practice as to stated and occasional communion with the Church of England; and a continuation of their history until the year 1691. This work was published in 1702. The most important chapter (ix.) is that which gives a detailed account of the ministers ejected in 1662; it was afterwards published as a distinct volume. He afterwards published a moderate defence of Nonconformity, in three tracts, in answer to some tracts of Benjamin, afterwards Bishop, Hoadly. In 1713 he published a second edition (2 vols.) of his Abridgment of Baxter's History, in which, among various additions, there is a continuation of the history through the reigns of William and Anne, down to the passing of the Occasional Bill. At the end is subjoined the reformed liturgy, which was drawn up and presented to the bishops in 1661. In 1718 he wrote a vindication of his grandfather and several other persons against certain reflections cast upon them by Laurence Echard in his History of England. In 1719 he published The Church and the Dissenters Compar'd as to Persecution, and in 1728 appeared his Continuation of the Account of the ejected ministers and teachers, a volume which is really a series of emendations of the previously published account. He died on the 3rd of June 1732, having been married twice and leaving six of his thirteen children to survive him. Calamy was a kindly man, frankly self-conscious, but very free from jealousy. He was an able diplomatist and generally secured his ends. His great hero was Baxter, of whom he wrote three distinct memoirs. His eldest son Edmund (the fourth) was a Presbyterian minister in London and died 1755; another son (Edmund, the fifth) was a barrister who died in 1816; and this one's son (Edmund, the sixth) died in 1850, his younger brother Michael, the last of the direct Calamy line, surviving till 1876.

CALARASHI (Călărasi), the capital of the Jalomitza department, Rumania, situated on the left bank of the Borcea branch of the Danube, amid wide fens, north of which extends the desolate Baragan Steppe. Pop. (1900) 11,024. Calarashi has a considerable transit trade in wheat, linseed, hemp, timber and fish from a broad mere on the west or from the Danube. Small vessels carry cargo to Braila and Galatz, and a branch railway from Calarashi traverses the Steppe from south to north, and meets the main line between Bucharest and Constantza.

CALAS, JEAN (1698-1762), a Protestant merchant at Toulouse, whose legal murder is a celebrated case in French history. His wife was an Englishwoman of French extraction. They had three sons and three daughters. His son Louis had embraced the Roman Catholic faith through the persuasions of a female domestic who had lived thirty years in the family. In October 1761 another son, Antoine, hanged himself in his father's warehouse. The crowd, which collected on so shocking a discovery, took up the idea that he had been strangled by the family to prevent him from changing his religion, and that this was a common practice among Protestants. The officers of justice adopted the popular tale, and were supplied by the mob with what they accepted as conclusive evidence of the fact. The fraternity of White Penitents buried the body with great ceremony, and performed a solemn service for the deceased as a martyr; the Franciscans followed their example; and these formalities led to the popular belief in the guilt of the unhappy family. Being all condemned to the rack in order to extort confession, they appealed to the parlement; but this body, being as weak as the subordinate magistrates, sentenced the father to the torture, ordinary and extraordinary, to be broken alive upon the wheel, and then to be burnt to ashes; which decree was carried into execution on the 9th of March 1762. Pierre Calas, the surviving son, was banished for life; the rest were acquitted. The distracted widow, however, found some friends, and among them Voltaire, who laid her case before the council of state at [v.04 p.0968] Versailles. For three years he worked indefatigably to procure justice, and made the Calas case famous throughout Europe (see VOLTAIRE). Finally the king and council unanimously agreed to annul the proceeding of the parlement of Toulouse; Calas was declared to have been innocent, and every imputation of guilt was removed from the family.

See Causes celebres, tome iv.; Raoul Allier, Voltaire et Calas, une erreur judiciaire au XVIII^e siecle (Paris, 1898); and biographies of Voltaire.

CALASH (from Fr. caleche, derived from Polish kolaska, a wheeled carriage), a light carriage with a folding hood; the Canadian calash is two-wheeled and has a seat for the driver on the splash-board. The word is also used for a kind of hood made of silk stretched over hoops, formerly worn by women.

CALASIAO, a town of the province of Pangasinan, Luzon, Philippine Islands, on a branch of the Agno river, about 4 m. S. by E. of Dagupan, the N. terminal of the Manila & Dagupan railway. Pop. (1903) 16,539. In 1903, after the census had been taken, the neighbouring town of Santa Barbara (pop. 10,367) was annexed to Calasiao. It is in the midst of a fertile district and has manufactures of hats and various woven fabrics.

CALASIO, MARIO DI (1550-1620), Italian Minorite friar, was born at a small town in the Abruzzi whence he took his name. Joining the Franciscans at an early age, he devoted himself to Oriental languages and became an authority on Hebrew. Coming to Rome he was appointed by Paul V., whose confessor he was, to the chair of Scripture at Ara Coeli, where he died on the 1st of February 1620. Calasio is known by his Concordantiae sacrorum Bibliorum hebraicorum, published in 4 vols. (Rome, 1622), two years after his death, a work which is based on Nathan's Hebrew Concordance (Venice, 1523). For forty years Calasio laboured on this work, and he secured the assistance of the greatest scholars of his age. The Concordance evinces great care and accuracy. All root-words are treated in alphabetical order and the whole Bible has been collated for every passage containing the word, so as to explain the original idea, which is illustrated from the cognate usages of the Chaldee, Syrian, Rabbinical Hebrew and Arabic. Calasio gives under each Hebrew word the literal Latin translation, and notes any existing differences from the Vulgate and Septuagint readings. An incomplete English translation of the work was published in London by Romaine in 1747. Calasio also wrote a Hebrew grammar, Canones generates linguae sanctatae (Rome, 1616), and the Dictionarium hebraicum (Rome, 1617).

CALATAFIMI, a town of the province of Trapani, Sicily, 30 m. W.S.W. of Palermo direct (511/2 m. by rail). Pop. (1901) 11,426. The name of the town is derived from the Saracenic castle of Kalat-al-Fimi (castle of Euphemius), which stands above it. The principal church contains a fine Renaissance reredos in marble. Samuel Butler, the author of Erewhon, did much of his work here. The battlefield where Garibaldi won his first victory over the Neapolitans on the 15th of May 1860, lies 2 m. S.W.

CALATAYUD, a town of central Spain, in the province of Saragossa, at the confluence of the rivers Jalon and Jiloca, and on the Madrid-Saragossa and Calatayud-Sagunto railways. Pop. (1900) 11,526. Calatayud consists of a lower town, built on the left bank of the Jalon, and an upper or Moorish town, which contains many dwellings hollowed out of the rock above and inhabited by the poorer classes. Among a number of ecclesiastical buildings, two collegiate churches are especially noteworthy. Santa Maria, originally a mosque, has a lofty octagonal tower and a fine Renaissance doorway, added in 1528; while Santo Sepulcro, built in 1141, and restored in 1613, was long the principal church of the Spanish Knights Templar. In commercial importance Calatayud ranks second only to Saragossa among the Aragonese towns, for it is the central market of the exceptionally fertile expanse watered by the Jalon and Jiloca. About 2 m. E. are the ruins of the ancient Bilbilis, where the poet Martial was born c. A.D. 40. It was celebrated for its breed of horses, its armourers, its gold and its iron; but Martial also mentions its unhealthy climate, due to the icy winds which sweep down from the heights of Moncayo (7705 ft.) on the north. In the middle ages the ruins were almost destroyed to provide stone for the building of Calatayud, which was founded by a Moorish amir named Ayub and named Kalat Ayub, "Castle of Ayub." Calatayud was captured by Alphonso I. of Aragon in 1119.

CALATIA, an ancient town of Campania, Italy, 6 m. S.E. of Capua, on the Via Appia, near the point where the Via Popillia branches off from it. It is represented by the church of St. Giacomo alle Galazze. The Via Appia here, as at Capua, abandons its former S.E. direction for a length of 2000 Oscan ft. (18041/2 English ft.), for which it runs due E. and then resumes its course S.E. There are no ruins, but a considerable quantity of debris; and the pre-Roman necropolis was partially excavated in 1882. Ten shafts lined with slabs of tufa which were there found may have been the approaches to tombs or may have served as wells. The history of Calatia is practically that of its more powerful neighbour Capua, but as it lay near the point where the Via Appia turns east and enters the mountains, it had some strategic importance. In 313 B.C. it was taken by the Samnites and recaptured by the dictator Q. Fabius; the Samnites captured it again in 311, but it must have been retaken at an unknown date. In the 3rd century we find it issuing coins with an Oscan legend, but in 211 B.C. it shared the fate of Capua. In 174 we hear of its walls being repaired by the censors. In 59 B.C. a colony was established here by Caesar.

See Ch. Huelsen in Pauly-Wissowa, Realencyclopaedie, iii. 1334 (Stuttgart, 1899).

CALAVERAS SKULL, a famous fossil cranium, reported by Professor J.D. Whitney as found (1886) in the undisturbed auriferous gravels of Calaveras county, California. The discovery at once raised the still discussed question of "tertiary man" in the New World. Doubt has been thrown on the genuineness of the find, as the age of the gravels is disputed and the skull is of a type corresponding exactly with that of the present Indian inhabitants of the district. Whitney assigns the fossil to late Tertiary (Pliocene) times, and concludes that "man existed in California previous to the cessation of volcanic activity in the Sierra Nevada, to the epoch of the greatest extension of the glaciers in that region and to the erosion of the present river canons and valleys, at a time when the animal and vegetable creation differed entirely from what they now are...." The specimen is preserved in the Peabody museum, Cambridge, Mass.

CALBAYOG, a town of the province of Samar, Philippine Islands, on the W. coast at the mouth of the Calbayog river, about 30 m. N.W. of Catbalogan, the capital, in lat. 12 deg. 3' N. Pop. (1903) 15,895. Calbayog has an important export trade in hemp, which is shipped to Manila. Copra is also produced in considerable quantity, and there is fine timber in the vicinity. There are hot springs near the town. The neighbouring valleys of the Gandara and Hippatan rivers are exceedingly fertile, but in 1908 were uncultivated. The climate is very warm, but healthy. The language is Visayan.

CALBE, or KALBE, a town of Germany, on the Saale, in Prussian Saxony. It is known as Calbe-an-der-Saale, to distinguish it from the smaller town of Calbe on the Milde in the same province. Pop. (1905) 12,281. It is a railway junction, and among its industries are wool-weaving and the manufacture of cloth, paper, stoves, sugar and bricks. Cucumbers and onions are cultivated, and soft coal is mined in the neighbourhood.

CALCAR (or KALCKER), JOHN DE (1499-1546), Italian painter, was born at Calcar, in the duchy of Cleves. He was a disciple of Titian at Venice, and perfected himself by studying Raphael. He imitated those masters so closely as to deceive the most skilful critics. Among his various pieces is a Nativity, representing the angels around the infant Christ, which he arranged so that the light emanated wholly from the child. He died at Naples.

CALCEOLARIA, in botany, a genus belonging to the natural order Scrophulariaceae, containing about 150 species of herbaceous or shrubby plants, chiefly natives of the South American Andes of Peru and Chile. The calceolaria of the present day has [v.04 p.0969] been developed into a highly decorative plant, in which the herbaceous habit has preponderated. The plants are now very generally raised annually from seed, which is sown about the end of June in a mixture of loam, leaf-mould and sand, and, being very small, must be only slightly covered. When the plants are large enough to handle they are pricked out an inch or two apart into 3-inch or 5-inch pots; when a little more advanced they are potted singly. They should be wintered in a greenhouse with a night temperature of about 40 deg., occupying a shelf near the light. By the end of February they should be moved into 8-inch or 10-inch pots, using a compost of three parts good turfy loam, one part leaf-mould, and one part thoroughly rotten manure, with a fair addition of sand. They need plenty of light and air, but must not be subjected to draughts. When the pots get well filled with roots, they must be liberally supplied with manure water. In all stages of growth the plants are subject to the attacks of the green-fly, for which they must be fumigated.

The so-called shrubby calceolarias used for bedding are increased from cuttings, planted in autumn in cold frames, where they can be wintered, protected from frost by the use of mats and a good layer of litter placed over the glass and round the sides.

CALCHAQUI, a tribe of South American Indians, now extinct, who formerly occupied northern Argentina. Stone and other remains prove them to have reached a high degree of civilization. They offered a vigorous resistance to the first Spanish colonists coming from Chile.

CALCHAS, of Mycenae or Megara, son of Thestor, the most famous soothsayer among the Greeks at the time of the Trojan war. He foretold the duration of the siege of Troy, and, when the fleet was detained by adverse winds at Aulis, he explained the cause and demanded the sacrifice of Iphigeneia. When the Greeks were visited with pestilence on account of Chryseis, he disclosed the reasons of Apollo's anger. It was he who suggested that Neoptolemus and Philoctetes should be fetched from Scyros and Lemnos to Troy, and he was one of those who advised the construction of the wooden horse. When the Greeks, on their journey home after the fall of Troy, were overtaken by a storm, Calchas is said to have been thrown ashore at Colophon. According to another story, he foresaw the storm and did not attempt to return by sea. It had been predicted that he should die when he met his superior in divination; and the prophecy was fulfilled in the person of Mopsus, whom Calchas met in the grove of the Clarian Apollo near Colophon. Having been beaten in a trial of soothsaying, Calchas died of chagrin or committed suicide. He had a temple and oracle in Apulia.

Ovid, Metam. xii. 18 ff.; Homer, Iliad i. 68, ii. 322; Strabo vi. p. 284, xiv. p. 642.

CALCITE, a mineral consisting of naturally occurring calcium carbonate, CaCO_3, crystallizing in the rhombohedral system. With the exception of quartz, it is the most widely distributed of minerals, whilst in the beautiful development and extraordinary variety of form of its crystals it is surpassed by none. In the massive condition it occurs as large rock-masses (marble, limestone, chalk) which are often of organic origin, being formed of the remains of molluscs, corals, crinoids, &c., the hard parts of which consist largely of calcite.

The name calcite (Lat. calx, calcis, meaning burnt lime) is of comparatively recent origin, and was first applied, in 1836, to the "barleycorn" pseudomorphs of calcium carbonate after celestite from Sangerhausen in Thuringia; it was not until about 1843 that the name was used in its present sense. The mineral had, however, long been known under the names calcareous spar and calc-spar, and the beautifully transparent variety called Iceland-spar had been much studied. The strong double refraction and perfect cleavages of Iceland-spar were described in detail by Erasmus Bartholinus in 1669 in his book Experimenta Crystalli Islandici disdiaclastici; the study of the same mineral led Christiaan Huygens to discover in 1690 the laws of double refraction, and E.L. Malus in 1808 the polarization of light.

An important property of calcite is the great ease with which it may be cleaved in three directions; the three perfect cleavages are parallel to the faces of the primitive rhombohedron, and the angle between them was determined by W.H. Wollaston in 1812, with the aid of his newly invented reflective goniometer, to be 74 deg. 55'. The cleavage is of great help in distinguishing calcite from other minerals of similar appearance. The hardness of 3 (it is readily scratched with a knife), the specific gravity of 2.72, and the fact that it effervesces briskly in contact with cold dilute acids are also characters of determinative value.



Crystals of calcite are extremely varied in form, but, as a rule, they may be referred to four distinct habits, namely: rhombohedral, prismatic, scalenohedral and tabular. The primitive rhombohedron, r {100} (fig. 1), is comparatively rare except in combination with other forms. A flatter rhombohedron, e {110}, is shown in fig. 2, and a more acute one, f {11-1}, in fig. 3. These three rhombohedra are related in such a manner that, when in combination, the faces of r truncate the polar edges of f, and the faces of e truncate the edges of r. The crystal of prismatic habit shown in fig. 4 is a combination of the prism m {2-1-1} and the rhombohedron e {110}; fig. 5 is a combination of the scalenohedron v {20-1} and the rhombohedron r {100}; and the crystal of tabular habit represented in fig. 6 is a combination of the basal pinacoid c {111}, prism m {2-1-1}, and rhombohedron e {110}. In these figures only six distinct forms (r, e, f, m, v, c) are represented, but more than 400 have been recorded for calcite, whilst the combinations of them are almost endless.

Depending on the habits of the crystals, certain trivial names have been used, such, for example, as dog-tooth-spar for the crystals of scalenohedral habit, so common in the Derbyshire lead mines and limestone caverns; nail-head-spar for crystals terminated by the obtuse rhombohedron e, which are common in the lead mines of Alston Moor in Cumberland; slate-spar (German Schieferspath) for crystals of tabular habit, and sometimes as thin as paper: cannon-spar for crystals of prismatic habit terminated by the basal pinacoid c.

Calcite is also remarkable for the variety and perfection of its twinned crystals. Twinned crystals, though not of infrequent occurrence, are, however, far less common than simple (untwinned) crystals. No less than four well-defined twin-laws are to be distinguished:—



i. Twin-plane c (111).—Here there is rotation of one portion with respect to the other through 180 deg. about the principal (trigonal) axis, which is perpendicular to the plane c (111); or the same result may be obtained by reflection across this plane. Fig. 7 shows a prismatic crystal (like fig. 4) twinned in this manner, and fig. 8 represents a twinned scalenohedron v {20-1}.

ii. Twin-plane e (110).—The principal axes of the two portions are inclined at an angle of 52 deg. 301/2'. Repeated twinning on this plane is very common, and the twin-lamellae (fig. 9) to which it gives rise are often to be observed in the grains of calcite of crystalline limestones which have been subjected to pressure. This lamellar twinning is of secondary origin; it may be readily produced artificially by pressure, for example, by pressing a knife into the edge of a cleavage rhombohedron.

[v.04 p.0970] iii. Twin-plane r (100).—Here the principal axes of the two portions are nearly at right angles (89 deg. 14'), and one of the directions of cleavage in both portions is parallel to the twin-plane. Fine crystals of prismatic habit twinned according to this law were formerly found in considerable numbers at Wheal Wrey in Cornwall, and of scalenohedral habit at Eyam in Derbyshire and Cleator Moor in Cumberland; those from the last two localities are known as "butterfly twins" or "heart-shaped twins" (fig. 10), according to their shape.

iv. Twin-plane f (11-1).—The principal axes are here inclined at 53 deg. 46'. This is the rarest twin-law of calcite.

Calcite when pure, as in the well-known Iceland-spar, is perfectly transparent and colourless. The lustre is vitreous. Owing to the presence of various impurities, the transparency and colour may vary considerably. Crystals are often nearly white or colourless, usually with a slight yellowish tinge. The yellowish colour is in most cases due to the presence of iron, but in some cases it has been proved to be due to organic matter (such as apocrenic acid) derived from the humus overlying the rocks in which the crystals were formed. An opaque calcite of a grass-green colour, occurring as large cleavage masses in central India and known as hislopite, owes its colour to enclosed "green-earth" (glauconite and celadonite). A stalagmitic calcite of a beautiful purple colour, from Reichelsdorf in Hesse, is coloured by cobalt.

Optically, calcite is uniaxial with negative bi-refringence, the index of refraction for the ordinary ray being greater than for the extraordinary ray; for sodium-light the former is 1.6585 and the latter 1.4862. The difference, 0.1723, between these two indices gives a measure of the bi-refringence or double refraction.

Although the double refraction of some other minerals is greater than that of calcite (e.g. for cinnabar it is 0.347, and for calomel 0.683), yet this phenomenon can be best demonstrated in calcite, since it is a mineral obtainable in large pieces of perfect transparency. Owing to the strong double refraction and the consequent wide separation of the two polarized rays of light traversing the crystal, an object viewed through a cleavage rhombohedron of Iceland-spar is seen double, hence the name doubly-refracting spar. Iceland-spar is extensively used in the construction of Nicol's prisms for polariscopes, polarizing microscopes and saccharimeters, and of dichroscopes for testing the pleochroism of gem-stones.

Chemically, calcite has the same composition as the orthorhombic aragonite (q.v.), these minerals being dimorphous forms of calcium carbonate. Well-crystallized material, such as Iceland-spar, usually consists of perfectly pure calcium carbonate, but at other times the calcium may be isomorphously replaced by small amounts of magnesium, barium, strontium, manganese, zinc or lead. When the elements named are present in large amount we have the varieties dolomitic calcite, baricalcite, strontianocalcite, ferrocalcite, manganocalcite, zincocalcite and plumbocalcite, respectively.

Mechanically enclosed impurities are also frequently present, and it is to these that the colour is often due. A remarkable case of enclosed impurities is presented by the so-called Fontainbleau limestone, which consists of crystals of calcite of an acute rhombohedral form (fig. 3) enclosing 50 to 60% of quartz-sand. Similar crystals, but with the form of an acute hexagonal pyramid, and enclosing 64% of sand, have recently been found in large quantity over a wide area in South Dakota, Nebraska and Wyoming. The case of hislopite, which encloses up to 20% of "green earth," has been noted above.

In addition to the varieties of calcite noted above, some others, depending on the state of aggregation of the material, are distinguished. A finely fibrous form is known as satin-spar (q.v.), a name also applied to fibrous gypsum: the most typical example of this is the snow-white material, often with a rosy tinge and a pronounced silky lustre, which occurs in veins in the Carboniferous shales of Alston Moor in Cumberland. Finely scaly varieties with a pearly lustre are known as argentine and aphrite (German Schaumspath); soft, earthy and dull white varieties as agaric mineral, rock-milk, rock-meal, &c.—these form a transition to marls, chalk, &c. Of the granular and compact forms numerous varieties are distinguished (see LIMESTONE and MARBLE). In the form of stalactites calcite is of extremely common occurrence. Each stalactite usually consists of an aggregate of radially arranged crystalline individuals, though sometimes it may consist of a single individual with crystal faces developed at the free end. Onyx-marbles or Oriental alabaster (see ALABASTER) and other stalagmitic deposits also consist of calcite, and so do the allied deposits of travertine, calc-sinter or calc-tufa.

The modes of occurrence of calcite are very varied. It is a common gangue mineral in metalliferous deposits, and in the form of crystals is often associated with ores of lead, iron, copper and silver. It is a common product of alteration in igneous rocks, and frequently occurs as well-developed crystals in association with zeolites lining the amygdaloidal cavities of basaltic and other rocks. Veins and cavities in limestones are usually lined with crystals of calcite. The wide distribution, under various conditions, of crystallized calcite is readily explained by the solubility of calcium carbonate in water containing carbon dioxide, and the ease with which the material is again deposited in the crystallized state when the carbon dioxide is liberated by evaporation. On this also depends the formation of stalactites and calc-sinter.

Localities at which beautifully crystallized specimens of calcite are found are extremely numerous. For beauty of crystals and variety of forms the haematite mines of the Cleator Moor district in west Cumberland and the Furness district in north Lancashire are unsurpassed. The lead mines of Alston in Cumberland and of Derbyshire, and the silver mines of Andreasberg in the Harz and Guanajuato in Mexico have yielded many fine specimens. From the zinc mines of Joplin in Missouri enormous crystals of golden-yellow and amethystine colours have been recently obtained. At all the localities here mentioned the crystals occur with metalliferous ores. In Iceland the mode of occurrence is quite distinct, the mineral being here found in a cavity in basalt.

The quarry, which since the 19th century has supplied the famous Iceland-spar, is in a cavity in basalt, the cavity itself measuring 12 by 5 yds. in area and about 10 ft. in height. It is situated quite close to the farm Helgustadir, about an hour's ride from the trading station of Eskifjordur on Reydar Fjordur, on the east coast of Iceland. This cavity when first found was filled with pure crystallized masses and enormous crystals. The crystals measure up to a yard across, and are rhombohedral or scalenohedral in habit; their faces are usually dull and corroded or coated with stilbite. In recent years much of the material taken out has not been of sufficient transparency for optical purposes, and this, together with the very limited supply, has caused a considerable rise in price. Only very occasionally has calcite from any locality other than Iceland been used for the construction of a Nicol's prism.

(L. J. S.)

CALCIUM [symbol Ca, atomic weight 40.0 (O=16)], a metallic chemical element, so named by Sir Humphry Davy from its [v.04 p.0971] occurrence in chalk (Latin calx). It does not occur in nature in the free state, but in combination it is widely and abundantly diffused. Thus the sulphate constitutes the minerals anhydrite, alabaster, gypsum, and selenite; the carbonate occurs dissolved in most natural waters and as the minerals chalk, marble, calcite, aragonite; also in the double carbonates such as dolomite, bromlite, barytocalcite; the fluoride as fluorspar; the fluophosphate constitutes the mineral apatite; while all the more important mineral silicates contain a proportion of this element.

Extraction.—Calcium oxide or lime has been known from a very remote period, and was for a long time considered to be an elementary or undecomposable earth. This view was questioned in the 18th century, and in 1808 Sir Humphry Davy (Phil. Trans., 1808, p. 303) was able to show that lime was a combination of a metal and oxygen. His attempts at isolating this metal were not completely successful; in fact, metallic calcium remained a laboratory curiosity until the beginning of the 20th century. Davy, inspired by his successful isolation of the metals sodium and potassium by the electrolysis of their hydrates, attempted to decompose a mixture of lime and mercuric oxide by the electric current; an amalgam of calcium was obtained, but the separation of the mercury was so difficult that even Davy himself was not sure as to whether he had obtained pure metallic calcium. Electrolysis of lime or calcium chloride in contact with mercury gave similar results. Bunsen (Ann., 1854, 92, p. 248) was more successful when he electrolysed calcium chloride moistened with hydrochloric acid; and A. Matthiessen (Jour. Chem. Soc., 1856, p. 28) obtained the metal by electrolysing a mixture of fused calcium and sodium chlorides. Henri Moissan obtained the metal of 99% purity by electrolysing calcium iodide at a low red heat, using a nickel cathode and a graphite anode; he also showed that a more convenient process consisted in heating the iodide with an excess of sodium, forming an amalgam of the product, and removing the sodium by means of absolute alcohol (which has but little action on calcium), and the mercury by distillation.

The electrolytic isolation of calcium has been carefully investigated, and this is the method followed for the commercial production of the metal. In 1902 W. Borchers and L. Stockem (Zeit. fuer Electrochemie, 1902, p. 8757) obtained the metal of 90% purity by electrolysing calcium chloride at a temperature of about 780 deg., using an iron cathode, the anode being the graphite vessel in which the electrolysis was carried out. In the same year, O. Ruff and W. Plato (Ber. 1902, 35, p. 3612) employed a mixture of calcium chloride (100 parts) and fluorspar (16.5 parts), which was fused in a porcelain crucible and electrolysed with a carbon anode and an iron cathode. Neither of these processes admitted of commercial application, but by a modification of Ruff and Plato's process, W. Ruthenau and C. Suter have made the metal commercially available. These chemists electrolyse either pure calcium chloride, or a mixture of this salt with fluorspar, in a graphite vessel which serves as the anode. The cathode consists of an iron rod which can be gradually raised. On electrolysis a layer of metallic calcium is formed at the lower end of this rod on the surface of the electrolyte; the rod is gradually raised, the thickness of the layer increases, and ultimately a rod of metallic calcium, forming, as it were, a continuation of the iron cathode, is obtained. This is the form in which calcium is put on the market.

An idea as to the advance made by this method is recorded in the variation in the price of calcium. At the beginning of 1904 it was quoted at 5s. per gram, L250 per kilogram or L110 per pound; about a year later the price was reduced to 21s. per kilogram, or 12s. per kilogram in quantities of 100 kilograms. These quotations apply to Germany; in the United Kingdom the price (1905) varied from 27s. to 30s. per kilogram (12s. to 13s. per lb.).

Properties.—A freshly prepared surface of the metal closely resembles zinc in appearance, but on exposure to the air it rapidly tarnishes, becoming yellowish and ultimately grey or white in colour owing to the information of a surface layer of calcium hydrate. A faint smell of acetylene may be perceived during the oxidation in moist air; this is probably due to traces of calcium carbide. It is rapidly acted on by water, especially if means are taken to remove the layer of calcium hydrate formed on the metal; alcohol acts very slowly. In its chemical properties it closely resembles barium and strontium, and to some degree magnesium; these four elements comprise the so-called metals of the "alkaline earths." It combines directly with most elements, including nitrogen; this can be taken advantage of in forming almost a perfect vacuum, the oxygen combining to form the oxide, CaO, and the nitrogen to form the nitride, Ca3N2. Several of its physical properties have been determined by K. Arndt (Ber., 1904, 37, p. 4733). The metal as prepared by electrolysis generally contains traces of aluminium and silica. Its specific gravity is 1.54, and after remelting 1.56; after distillation it is 1.52. It melts at about 800 deg., but sublimes at a lower temperature.

_Compounds._—Calcium hydride, obtained by heating electrolytic calcium in a current of hydrogen, appears in commerce under the name hydrolite. Water decomposes it to give hydrogen free from ammonia and acetylene, 1 gram yielding about 100 ccs. of gas (Prats Aymerich, _Abst. J.C.S._, 1907, ii p. 460). Calcium forms two oxides—the monoxide, CaO, and the dioxide, CaO_2. The monoxide and its hydrate are more familiarly known as lime (_q.v._) and slaked-lime. The dioxide was obtained as the hydrate, CaO_2.8H_2O, by P. Thenard (_Ann. Chim. Phys._, 1818, 8, p. 213), who precipitated lime-water with hydrogen peroxide. It is permanent when dry; on heating to 130 deg. C. it loses water and gives the anhydrous dioxide as an unstable, pale buff-coloured powder, very sparingly soluble in water. It is used as an antiseptic and oxidizing agent.

Whereas calcium chloride, bromide, and iodide are deliquescent solids, the fluoride is practically insoluble in water; this is a parallelism to the soluble silver fluoride, and the insoluble chloride, bromide and iodide. _Calcium fluoride_, CaF_2, constitutes the mineral fluor-spar (_q.v._), and is prepared artificially as an insoluble white powder by precipitating a solution of calcium chloride with a soluble fluoride. One part dissolves in 26,000 parts of water. _Calcium chloride_, CaCl_2, occurs in many natural waters, and as a by-product in the manufacture of carbonic acid (carbon dioxide), and potassium chlorate. Aqueous solutions deposit crystals containing 2, 4 or 6 molecules of water. Anhydrous calcium chloride, prepared by heating the hydrate to 200 deg. (preferably in a current of hydrochloric acid gas, which prevents the formation of any oxychloride), is very hygroscopic, and is used as a desiccating agent. It fuses at 723 deg.. It combines with gaseous ammonia and forms crystalline compounds with certain alcohols. The crystallized salt dissolves very readily in water with a considerable absorption of heat; hence its use in forming "freezing mixtures." A temperature of -55 deg.C. is obtained by mixing 10 parts of the hexahydrate with 7 parts of snow. A saturated solution of calcium chloride contains 325 parts of CaCl_2 to 100 of water at the boiling point (179.5 deg.). Calcium iodide and bromide are white deliquescent solids and closely resemble the chloride.

Chloride of lime or "bleaching powder" is a calcium chlor-hypochlorite or an equimolecular mixture of the chloride and hypochlorite (see ALKALI MANUFACTURE and BLEACHING).

_Calcium carbide_, CaC_2, a compound of great industrial importance as a source of acetylene, was first prepared by F. Wohler. It is now manufactured by heating lime and carbon in the electric furnace (see ACETYLENE). Heated in chlorine or with bromine, it yields carbon and calcium chloride or bromide; at a dull red heat it burns in oxygen, forming calcium carbonate, and it becomes incandescent in sulphur vapour at 500 deg., forming calcium sulphide and carbon disulphide. Heated in the electric furnace in a current of air, it yields calcium cyanamide (see CYANAMIDE).

_Calcium carbonate_, CaCO_3, is of exceptionally wide distribution in both the mineral and animal kingdoms. It constitutes the bulk of the chalk deposits and limestone rocks; it forms over one-half of the mineral dolomite and the rock magnesium limestone; it occurs also as the dimorphous minerals aragonite (_q.v._) and calcite (_q.v._). Tuff (_q.v._) and travertine are calcareous deposits found in volcanic districts. Most natural waters contain it dissolved in carbonic acid; this confers "temporary hardness" on the water. The dissipation of the dissolved carbon dioxide results in the formation of "fur" in kettles or boilers, and if the solution is falling, as from the roof of a cave, in the formation of stalactites and stalagmites. In the animal kingdom it occurs as both calcite and aragonite in the tests of the foraminifera, echinoderms, brachiopoda, and mollusca; also in the skeletons of sponges and corals. Calcium carbonate is obtained as a white precipitate, almost insoluble in water (1 part requiring 10,000 of water for solution), by mixing solutions of a carbonate and a calcium salt. Hot or dilute cold solutions deposit minute orthorhombic crystals of aragonite, cold saturated or moderately strong solutions, hexagonal (rhombohedral) crystals of calcite. Aragonite is the least stable form; crystals have been found altered to calcite.

Calcium nitride, Ca3N2, is a greyish-yellow powder formed by heating calcium in air or nitrogen; water decomposes it with evolution of ammonia (see H. Moissan, Compt. Rend., 127, p. 497).

_Calcium nitrate_, Ca(NO_3)_2.4H_2O, is a highly deliquescent salt, [v.04 p.0972] crystallizing in monoclinic prisms, and occurring in various natural waters, as an efflorescence in limestone caverns, and in the neighbourhood of decaying nitrogenous organic matter. Hence its synonyms, "wall-saltpetre" and "lime-saltpetre"; from its disintegrating action on mortar, it is sometimes referred to as "saltpetre rot." The anhydrous nitrate, obtained by heating the crystallized salt, is very phosphorescent, and constitutes "Baldwin's phosphorus." A basic nitrate, Ca(NO_3)_2.Ca(OH)_2.3H_2O, is obtained by dissolving calcium hydroxide in a solution of the normal nitrate.

Calcium phosphide, Ca3P2, is obtained as a reddish substance by passing phosphorus vapour over strongly heated lime. Water decomposes it with the evolution of spontaneously inflammable hydrogen phosphide; hence its use as a marine signal fire ("Holmes lights"), (see L. Gattermann and W. Haussknecht, Ber., 1890, 23, p. 1176, and H. Moissan, Compt. Rend., 128, p. 787).

Of the calcium orthophosphates, the normal salt, Ca_3(PO_4)_2, is the most important. It is the principal inorganic constituent of bones, and hence of the "bone-ash" of commerce (see PHOSPHORUS); it occurs with fluorides in the mineral apatite (_q.v._); and the concretions known as coprolites (_q.v._) largely consist of this salt. It also constitutes the minerals ornithite, Ca_3(PO_4)_2.2H_2O, osteolite and sombrerite. The mineral brushite, CaHPO_4.2H_2O, which is isomorphous with the acid arsenate pharmacolite, CaHAsO_4.2H_2O, is an acid phosphate, and assumes monoclinic forms. The normal salt may be obtained artificially, as a white gelatinous precipitate which shrinks greatly on drying, by mixing solutions of sodium hydrogen phosphate, ammonia, and calcium chloride. Crystals may be obtained by heating di-calcium pyrophosphate, Ca_2P_2O_7, with water under pressure. It is insoluble in water; slightly soluble in solutions of carbonic acid and common salt, and readily soluble in concentrated hydrochloric and nitric acid. Of the acid orthophosphates, the mono-calcium salt, CaH_4(PO_4)_2, may be obtained as crystalline scales, containing one molecule of water, by evaporating a solution of the normal salt in hydrochloric or nitric acid. It dissolves readily in water, the solution having an acid reaction. The artificial manure known as "superphosphate of lime" consists of this salt and calcium sulphate, and is obtained by treating ground bones, coprolites, &c., with sulphuric acid. The di-calcium salt, Ca_2H_2(PO_4)_2, occurs in a concretionary form in the ureters and cloaca of the sturgeon, and also in guano. It is obtained as rhombic plates by mixing dilute solutions of calcium chloride and sodium phosphate, and passing carbon dioxide into the liquid. Other phosphates are also known.

_Calcium monosulphide_, CaS, a white amorphous powder, sparingly soluble in water, is formed by heating the sulphate with charcoal, or by heating lime in a current of sulphuretted hydrogen. It is particularly noteworthy from the phosphorescence which it exhibits when heated, or after exposure to the sun's rays; hence its synonym "Canton's phosphorus," after John Canton (1718-1772), an English natural philosopher. The sulphydrate or hydrosulphide, Ca(SH)_2, is obtained as colourless, prismatic crystals of the composition Ca(SH)_2.6H_2O, by passing sulphuretted hydrogen into milk of lime. The strong aqueous solution deposits colourless, four-sided prisms of the hydroxy-hydrosulphide, Ca(OH)(SH). The disulphide, CaS_2 and pentasulphide, CaS_5, are formed when milk of lime is boiled with flowers of sulphur. These sulphides form the basis of Balmain's luminous paint. An oxysulphide, 2CaS.CaO, is sometimes present in "soda-waste," and orange-coloured, acicular crystals of 4CaS.CaSO_4.18H_2O occasionally settle out on the long standing of oxidized "soda- or alkali-waste" (see ALKALI MANUFACTURE).

_Calcium sulphite_, CaSO_3, a white substance, soluble in water, is prepared by passing sulphur dioxide into milk of lime. This solution with excess of sulphur dioxide yields the "bisulphite of lime" of commerce, which is used in the "chemical" manufacture of wood-pulp for paper making.

_Calcium sulphate_, CaSO_4, constitutes the minerals anhydrite (_q.v._), and, in the hydrated form, selenite, gypsum (_q.v._), alabaster (_q.v._), and also the adhesive plaster of Paris (see CEMENT). It occurs dissolved in most natural waters, which it renders "permanently hard." It is obtained as a white crystalline precipitate, sparingly soluble in water (100 parts of water dissolve 24 of the salt at 15 deg.C.), by mixing solutions of a sulphate and a calcium salt; it is more soluble in solutions of common salt and hydrochloric acid, and especially of sodium thiosulphate.

Calcium silicates are exceptionally abundant in the mineral kingdom. Calcium metasilicate, CaSiO3, occurs in nature as monoclinic crystals known as tabular spar or wollastonite; it may be prepared artificially from solutions of calcium chloride and sodium silicate. H. Le Chatelier (Annales des mines, 1887, p. 345) has obtained artificially the compounds: CaSiO3, Ca2SiO4, Ca3Si2O7, and Ca3SiO5. (See also G. Oddo, Chemisches Centralblatt, 1896, 228.) Acid calcium silicates are represented in the mineral kingdom by gyrolite, H2Ca2(SiO3)3.H2O, a lime zeolite, sometimes regarded as an altered form of apophyllite (q.v.), which is itself an acid calcium silicate containing an alkaline fluoride, by okenite, H2Ca(SiO3)2.H2O, and by xonalite 4CaSiO3.H2O. Calcium silicate is also present in the minerals: olivine, pyroxenes, amphiboles, epidote, felspars, zeolites, scapolites (qq.v.).

Detection and Estimation.—Most calcium compounds, especially when moistened with hydrochloric acid, impart an orange-red colour to a Bunsen flame, which when viewed through green glass appears to be finch-green; this distinguishes it in the presence of strontium, whose crimson coloration is apt to mask the orange-red calcium flame (when viewed through green glass the strontium flame appears to be a very faint yellow). In the spectroscope calcium exhibits two intense lines—an orange line ([alpha]), ([lambda] 6163), a green line ([beta]), ([lambda] 4229), and a fainter indigo line. Calcium is not precipitated by sulphuretted hydrogen, but falls as the carbonate when an alkaline carbonate is added to a solution. Sulphuric acid gives a white precipitate of calcium sulphate with strong solutions; ammonium oxalate gives calcium oxalate, practically insoluble in water and dilute acetic acid, but readily soluble in nitric or hydrochloric acid. Calcium is generally estimated by precipitation as oxalate which, after drying, is heated and weighed as carbonate or oxide, according to the degree and duration of the heating.

CALCULATING MACHINES. Instruments for the mechanical performance of numerical calculations, have in modern times come into ever-increasing use, not merely for dealing with large masses of figures in banks, insurance offices, &c., but also, as cash registers, for use on the counters of retail shops. They may be classified as follows:—(i.) Addition machines; the first invented by Blaise Pascal (1642). (ii.) Addition machines modified to facilitate multiplication; the first by G.W. Leibnitz (1671). (iii.) True multiplication machines; Leon Bolles (1888), Steiger (1894). (iv.) Difference machines; Johann Helfrich von Mueller (1786), Charles Babbage (1822). (v.) Analytical machines; Babbage (1834). The number of distinct machines of the first three kinds is remarkable and is being constantly added to, old machines being improved and new ones invented; Professor R. Mehmke has counted over eighty distinct machines of this type. The fullest published account of the subject is given by Mehmke in the Encyclopaedie der mathematischen Wissenschaften, article "Numerisches Rechnen," vol. i., Heft 6 (1901). It contains historical notes and full references. Walther von Dyck's Catalogue also contains descriptions of various machines. We shall confine ourselves to explaining the principles of some leading types, without giving an exact description of any particular one.



Practically all calculating machines contain a "counting work," a series of "figure disks" consisting in the original form of horizontal circular disks (fig. 1), on which the figures 0, 1, 2, to 9 are marked. Each disk can turn about its vertical axis, and is covered by a fixed plate with a hole or "window" in it through which one figure can be seen. On turning the disk through one-tenth of a revolution this figure will be changed into the next higher or lower. Such turning may be called a "step," positive [Sidenote: Addition machines.] if the next higher and negative if the next lower figure appears. Each positive step therefore adds one unit to the figure under the window, while two steps add two, and so on. If a series, say six, of such figure disks be placed side by side, their windows lying in a row, then any number of six places can be made to appear, for instance 000373. In order to add 6425 to this number, the disks, counting from right to left, have to be turned 5, 2, 4 and 6 steps respectively. If this is done the sum 006798 will appear. In case the sum of the two figures at any disk is greater than 9, if for instance the last figure to be added is 8 instead of 5, the sum for this disk is 11 and the 1 only will appear. Hence an arrangement for "carrying" has to be introduced. This may be done as follows. The axis of a figure disk contains a wheel with ten teeth. Each figure disk has, besides, one long tooth which when its 0 passes the window turns the next wheel to the left, one tooth forward, and hence the figure disk one step. The actual mechanism is not quite so simple, because the long teeth as described would gear also into the wheel to the right, and besides would interfere with each other. They must therefore be replaced by a somewhat more complicated arrangement, which has been done in various ways not necessary to describe more fully. On the way in which this is done, however, depends to a great extent the durability and trustworthiness of any arithmometer; in fact, it is often its weakest point. If to the series of figure disks arrangements are added for turning each disk through a required number of steps, [v.04 p.0973] we have an addition machine, essentially of Pascal's type. In it each disk had to be turned by hand. This operation has been simplified in various ways by mechanical means. For pure addition machines key-boards have been added, say for each disk nine keys marked 1 to 9. On pressing the key marked 6 the disk turns six steps and so on. These have been introduced by Stettner (1882), Max Mayer (1887), and in the comptometer by Dorr Z. Felt of Chicago. In the comptograph by Felt and also in "Burrough's Registering Accountant" the result is printed.

These machines can be used for multiplication, as repeated addition, but the process is laborious, depending for rapid execution [Sidenote: MODIFIED ADDITION MACHINES.] essentially on the skill of the operator.[1] To adapt an addition machine, as described, to rapid multiplication the turnings of the separate figure disks are replaced by one motion, commonly the turning of a handle. As, however, the different disks have to be turned through different steps, a contrivance has to be inserted which can be "set" in such a way that by one turn of the handle each disk is moved through a number of steps equal to the number of units which is to be added on that disk. This may be done by making each of the figure disks receive on its axis a ten-toothed wheel, called hereafter the A-wheel, which is acted on either directly or indirectly by another wheel (called the B-wheel) in which the number of teeth can be varied from 0 to 9. This variation of the teeth has been effected in different ways. Theoretically the simplest seems to be to have on the B-wheel nine teeth which can be drawn back into the body of the wheel, so that at will any number from 0 to 9 can be made to project. This idea, previously mentioned by Leibnitz, has been realized by Bohdner in the "Brunsviga." Another way, also due to Leibnitz, consists in inserting between the axis of the handle bar and the A-wheel a "stepped" cylinder. This may be considered as being made up of ten wheels large enough to contain about twenty teeth each; but most of these teeth are cut away so that these wheels retain in succession 9, 8, ... 1, 0 teeth. If these are made as one piece they form a cylinder with teeth of lengths from 9, 8 ... times the length of a tooth on a single wheel.



In the diagrammatic vertical section of such a machine (fig. 2) FF is a figure disk with a conical wheel A on its axis. In the covering plate HK is the window W. A stepped cylinder is shown at B. The axis Z, which runs along the whole machine, is turned by a handle, and itself turns the cylinder B by aid of conical wheels. Above this cylinder lies an axis EE with square section along which a wheel D can be moved. The same axis carries at E' a pair of conical wheels C and C', which can also slide on the axis so that either can be made to drive the A-wheel. The covering plate MK has a slot above the axis EE allowing a rod LL' to be moved by aid of a button L, carrying the wheel D with it. Along the slot is a scale of numbers 0 1 2 ... 9 corresponding with the number of teeth on the cylinder B, with which the wheel D will gear in any given position. A series of such slots is shown in the top middle part of Steiger's machine (fig. 3). Let now the handle driving the axis Z be turned once round, the button being set to 4. Then four teeth of the B-wheel will turn D and with it the A-wheel, and consequently the figure disk will be moved four steps. These steps will be positive or forward if the wheel C gears in A, and consequently four will be added to the figure showing at the window W. But if the wheels CC' are moved to the right, C' will gear with A moving backwards, with the result that four is subtracted at the window. This motion of all the wheels C is done simultaneously by the push of a lever which appears at the top plate of the machine, its two positions being marked "addition" and "subtraction." The B-wheels are in fixed positions below the plate MK. Level with this, but separate, is the plate KH with the window. On it the figure disks are mounted.

This plate is hinged at the back at H and can be lifted up, thereby throwing the A-wheels out of gear. When thus raised the figure disks can be set to any figures; at the same time it can slide to and fro so that an A-wheel can be put in gear with any C-wheel forming with it one "element." The number of these varies with the size of the machine. Suppose there are six B-wheels and twelve figure disks. Let these be all set to zero with the exception of the last four to the right, these showing 1 4 3 2, and let these be placed opposite the last B-wheels to the right. If now the buttons belonging to the latter be set to 3 2 5 6, then on turning the B-wheels all once round the latter figures will be added to the former, thus showing 4 6 8 8 at the windows. By aid of the axis Z, this turning of the B-wheels is performed simultaneously by the movement of one handle. We have thus an addition machine. If it be required to multiply a number, say 725, by any number up to six figures, say 357, the buttons are set to the figures 725, the windows all showing zero. The handle is then turned, 725 appears at the windows, and successive turns add this number to the first. Hence seven turns show the product seven times 725. Now the plate with the A-wheels is lifted and moved one step to the right, then lowered and the handle turned five times, thus adding fifty times 725 to the product obtained. Finally, by moving the piate again, and turning the handle three times, the required product is obtained. If the machine has six B-wheels and twelve disks the product of two six-figure numbers can be obtained. Division is performed by repeated subtraction. The lever regulating the C-wheel is set to subtraction, producing negative steps at the disks. The dividend is set up at the windows and the divisor at the buttons. Each turn of the handle subtracts the divisor once. To count the number of turns of the handle a second set of windows is arranged with number disks below. These have no carrying arrangement, but one is turned one step for each turn of the handle. The machine described is essentially that of Thomas of Colmar, which was the first that came into practical use. Of earlier machines those of Leibnitz, Mueller (1782), and Hahn (1809) deserve to be mentioned (see Dyck, Catalogue). Thomas's machine has had many imitations, both in England and on the Continent, with more or less important alterations. Joseph Edmondson of Halifax has given it a circular form, which has many advantages.

The accuracy and durability of any machine depend to a great extent on the manner in which the carrying mechanism is constructed. Besides, no wheel must be capable of moving in any other way than that required; hence every part must be locked and be released only when required to move. Further, any disk must carry to the next only after the carrying to itself has been completed. If all were to carry at the same time a considerable force would be required to turn the handle, and serious strains would be introduced. It is for this reason that the B-wheels or cylinders have the greater part of the circumference free from teeth. Again, the carrying acts generally as in the machine described, in one sense only, and this involves that the handle be turned always in the same direction. Subtraction therefore cannot be done by turning it in the opposite way, hence the two wheels C and C' are introduced. These are moved all at once by one lever acting on a bar shown at R in section (fig. 2).

In the Brunsviga, the figure disks are all mounted on a common horizontal axis, the figures being placed on the rim. On the side of each disk and rigidly connected with it lies its A-wheel with which it can turn independent of the others. The B-wheels, all fixed on another horizontal axis, gear directly on the A-wheels. By an ingenious contrivance the teeth are made to appear from out of the rim to any desired number. The carrying mechanism, too, is different, and so arranged that the handle can be turned either way, no special setting being required for subtraction or division. It is extremely handy, taking up much less room than the others. Professor Eduard Selling of Wuerzburg has invented an altogether different machine, which has been made by Max Ott, of Munich. The B-wheels are replaced by lazy-tongs. To the joints of these the ends of racks are pinned; and as they are stretched out the racks are moved forward 0 to 9 steps, according to the joints they are pinned to. The racks gear directly in the A-wheels, and the figures are placed on cylinders as in the Brunsviga. The carrying is done continuously by a train of epicycloidal wheels. The working is thus rendered very smooth, without the jerks which the ordinary carrying tooth produces; but the arrangement has the disadvantage that the resulting figures do not appear in a straight line, a figure followed by a 5, for instance, being already carried half a step forward. This is not a serious matter in the hands of a mathematician or an operator using the machine constantly, but it is serious for casual work. Anyhow, it has prevented the machine from being a commercial success, and it is not any longer made. For ease and rapidity of working it surpasses all others. Since the lazy-tongs allow of an extension equivalent to five turnings of the handle, if the multiplier is 5 or under, one push forward will do the [v.04 p.0974] same as five (or less) turns of the handle, and more than two pushes are never required.



The Steiger-Egli machine is a multiplication machine, of which fig. 3 gives a picture as it appears to the manipulator. The lower [Sidenote: Multiplication machines.] part of the figure contains, under the covering plate, a carriage with two rows of windows for the figures marked ff and gg. On pressing down the button W the carriage can be moved to right or left. Under each window is a figure disk, as in the Thomas machine. The upper part has three sections. The one to the right contains the handle K for working the machine, and a button U for setting the machine for addition, multiplication, division, or subtraction. In the middle section a number of parallel slots are seen, with indices which can each be set to one of the numbers 0 to 9. Below each slot, and parallel to it, lies a shaft of square section on which a toothed wheel, the A-wheel, slides to and fro with the index in the slot. Below these wheels again lie 9 toothed racks at right angles to the slots. By setting the index in any slot the wheel below it comes into gear with one of these racks. On moving the rack, the wheels turn their shafts and the figure disks gg opposite to them. The dimensions are such that a motion of a rack through 1 cm. turns the figure disk through one "step" or adds 1 to the figure under the window. The racks are moved by an arrangement contained in the section to the left of the slots. There is a vertical plate called the multiplication table block, or more shortly, the block. From it project rows of horizontal rods of lengths varying from 0 to 9 centimetres. If one of these rows is brought opposite the row of racks and then pushed forward to the right through 9 cm., each rack will move and add to its figure disk a number of units equal to the number of centimetres of the rod which operates on it. The block has a square face divided into a hundred squares. Looking at its face from the right—i.e. from the side where the racks lie—suppose the horizontal rows of these squares numbered from 0 to 9, beginning at the top, and the columns numbered similarly, the 0 being to the right; then the multiplication table for numbers 0 to 9 can be placed on these squares. The row 7 will therefore contain the numbers 63, 56, ... 7, 0. Instead of these numbers, each square receives two "rods" perpendicular to the plate, which may be called the units-rod and the tens-rod. Instead of the number 63 we have thus a tens-rod 6 cm. and a units-rod 3 cm. long. By aid of a lever H the block can be raised or lowered so that any row of the block comes to the level of the racks, the units-rods being opposite the ends of the racks.

The action of the machine will be understood by considering an example. Let it be required to form the product 7 times 385. The indices of three consecutive slots are set to the numbers 3, 8, 5 respectively. Let the windows gg opposite these slots be called a, b, c. Then to the figures shown at these windows we have to add 21, 56, 35 respectively. This is the same thing as adding first the number 165, formed by the units of each place, and next 2530 corresponding to the tens; or again, as adding first 165, and then moving the carriage one step to the right, and adding 253. The first is done by moving the block with the units-rods opposite the racks forward. The racks are then put out of gear, and together with the block brought back to their normal position; the block is moved sideways to bring the tens-rods opposite the racks, and again moved forward, adding the tens, the carriage having also been moved forward as required. This complicated movement, together with the necessary carrying, is actually performed by one turn of the handle. During the first quarter-turn the block moves forward, the units-rods coming into operation. During the second quarter-turn the carriage is put out of gear, and moved one step to the right while the necessary carrying is performed; at the same time the block and the racks are moved back, and the block is shifted so as to bring the tens-rods opposite the racks. During the next two quarter-turns the process is repeated, the block ultimately returning to its original position. Multiplication by a number with more places is performed as in the Thomas. The advantage of this machine over the Thomas in saving time is obvious. Multiplying by 817 requires in the Thomas 16 turns of the handle, but in the Steiger-Egli only 3 turns, with 3 settings of the lever H. If the lever H is set to 1 we have a simple addition machine like the Thomas or the Brunsviga. The inventors state that the product of two 8-figure numbers can be got in 6-7 seconds, the quotient of a 6-figure number by one of 3 figures in the same time, while the square root to 5 places of a 9-figure number requires 18 seconds.

Machines of far greater powers than the arithmometers mentioned have been invented by Babbage and by Scheutz. A description is impossible without elaborate drawings. The following account will afford some idea of the working of Babbage's difference machine. Imagine a number of striking clocks placed in a row, each with only an hour hand, and with only the striking apparatus retained. Let the hand of the first clock be turned. As it comes opposite a number on the dial the clock strikes that number of times. Let this clock be connected with the second in such a manner that by each stroke of the first the hand of the second is moved from one number to the next, but can only strike when the first comes to rest. If the second hand stands at 5 and the first strikes 3, then when this is done the second will strike 8; the second will act similarly on the third, and so on. Let there be four such clocks with hands set to the numbers 6, 6, 1, 0 respectively. Now set the third clock striking 1, this sets the hand of the fourth clock to 1; strike the second (6), this puts the third to 7 and the fourth to 8. Next strike the first (6); this moves the other hands to 12, 19, 27 respectively, and now repeat the striking of the first. The hand of the fourth clock will then give in succession the numbers 1, 8, 27, 64, &c., being the cubes of the natural numbers. The numbers thus obtained on the last dial will have the differences given by those shown in succession on the dial before it, their differences by the next, and so on till we come to the constant difference on the first dial. A function

y = a + bx + cx^2 + dx^3 + ex^4

gives, on increasing x always by unity, a set of values for which the fourth difference is constant. We can, by an arrangement like the above, with five clocks calculate y for x = 1, 2, 3, ... to any extent. This is the principle of Babbage's difference machine. The clock dials have to be replaced by a series of dials as in the arithmometers described, and an arrangement has to be made to drive the whole by turning one handle by hand or some other power. Imagine further that with the last clock is connected a kind of typewriter which prints the number, or, better, impresses the number in a soft substance from which a stereotype casting can be taken, and we have a machine which, when once set for a given formula like the above, will automatically print, or prepare stereotype plates for the printing of, tables of the function without any copying or typesetting, thus excluding all possibility of errors. Of this "Difference engine," as Babbage called it, a part was finished in 1834, the government having contributed L17,000 towards the cost. This great expense was chiefly due to the want of proper machine tools.

Meanwhile Babbage had conceived the idea of a much more powerful machine, the "analytical engine," intended to perform any series of possible arithmetical operations. Each of these was to be communicated to the machine by aid of cards with holes punched in them into which levers could drop. It was long taken for granted that Babbage left complete plans; the committee of the British Association appointed to consider this question came, however, to the conclusion (Brit. Assoc. Report, 1878, pp. 92-102) that no detailed working drawings existed at all; that the drawings left were only diagrammatic and not nearly sufficient to put into the hands of a draughtsman for making working plans; and "that in the present state of the design it is not more than a theoretical possibility." A full account of the work done by Babbage in connexion with calculating machines, and much else published by others in connexion therewith, is contained in a work published by his son, General Babbage.



Slide rules are instruments for performing logarithmic calculations mechanically, and are extensively used, especially where [Sidenote: Slide rules.] only rough approximations are required. They are almost as old as logarithms themselves. Edmund Gunter drew a "logarithmic line" on his "Scales" as follows (fig. 4):—On a line AB lengths are set off to scale to represent the common logarithms of the numbers 1 2 3 ... 10, and the points thus obtained are marked with these numbers. [v.04 p.0975] As log 1 = 0, the beginning A has the number 1 and B the number 10, hence the unit of length is AB, as log 10 = 1. The same division is repeated from B to C. The distance 1,2 thus represents log 2, 1,3 gives log 3, the distance between 4 and 5 gives log 5 - log 4 = log 5/4, and so for others. In order to multiply two numbers, say 2 and 3, we have log 2 x 3 = log 2 + log 3. Hence, setting off the distance 1,2 from 3 forward by the aid of a pair of compasses will give the distance log 2 + log 3, and will bring us to 6 as the required product. Again, if it is required to find 4/5 of 7, set off the distance between 4 and 5 from 7 backwards, and the required number will be obtained. In the actual scales the spaces between the numbers are subdivided into 10 or even more parts, so that from two to three figures may be read. The numbers 2, 3 ... in the interval BC give the logarithms of 10 times the same numbers in the interval AB; hence, if the 2 in the latter means 2 or .2, then the 2 in the former means 20 or 2.

Soon after Gunter's publication (1620) of these "logarithmic lines," Edmund Wingate (1672) constructed the slide rule by repeating the logarithmic scale on a tongue or "slide," which could be moved along the first scale, thus avoiding the use of a pair of compasses. A clear idea of this device can be formed if the scale in fig. 4 be copied on the edge of a strip of paper placed against the line A C. If this is now moved to the right till its 1 comes opposite the 2 on the first scale, then the 3 of the second will be opposite 6 on the top scale, this being the product of 2 and 3; and in this position every number on the top scale will be twice that on the lower. For every position of the lower scale the ratio of the numbers on the two scales which coincide will be the same. Therefore multiplications, divisions, and simple proportions can be solved at once.

Dr John Perry added log log scales to the ordinary slide rule in order to facilitate the calculation of a^x or e^x according to the formula log loga^x = log loga + logx. These rules are manufactured by A.G. Thornton of Manchester.

Many different forms of slide rules are now on the market. The handiest for general use is the Gravet rule made by Tavernier-Gravet in Paris, according to instructions of the mathematician V.M.A. Mannheim of the Ecole Polytechnique in Paris. It contains at the back of the slide scales for the logarithms of sines and tangents so arranged that they can be worked with the scale on the front. An improved form is now made by Davis and Son of Derby, who engrave the scales on white celluloid instead of on box-wood, thus greatly facilitating the readings. These scales have the distance from one to ten about twice that in fig. 4. Tavernier-Gravet makes them of that size and longer, even 1/2 metre long. But they then become somewhat unwieldy, though they allow of reading to more figures. To get a handy long scale Professor G. Fuller has constructed a spiral slide rule drawn on a cylinder, which admits of reading to three and four figures. The handiest of all is perhaps the "Calculating Circle" by Boucher, made in the form of a watch. For various purposes special adaptations of the slide rules are met with—for instance, in various exposure meters for photographic purposes. General Strachey introduced slide rules into the Meteorological Office for performing special calculations. At some blast furnaces a slide rule has been used for determining the amount of coke and flux required for any weight of ore. Near the balance a large logarithmic scale is fixed with a slide which has three indices only. A load of ore is put on the scales, and the first index of the slide is put to the number giving the weight, when the second and third point to the weights of coke and flux required.

By placing a number of slides side by side, drawn if need be to different scales of length, more complicated calculations may be performed. It is then convenient to make the scales circular. A number of rings or disks are mounted side by side on a cylinder, each having on its rim a log-scale.

The "Callendar Cable Calculator," invented by Harold Hastings and manufactured by Robert W. Paul, is of this kind. In it a number of disks are mounted on a common shaft, on which each turns freely unless a button is pressed down whereby the disk is clamped to the shaft. Another disk is fixed to the shaft. In front of the disks lies a fixed zero line. Let all disks be set to zero and the shaft be turned, with the first disk clamped, till a desired number appears on the zero line; let then the first disk be released and the second clamped and so on; then the fixed disk will add up all the turnings and thus give the product of the numbers shown on the several disks. If the division on the disks is drawn to different scales, more or less complicated calculations may be rapidly performed. Thus if for some purpose the value of say ab cubed [root]c is required for many different values of a, b, c, three movable disks would be needed with divisions drawn to scales of lengths in the proportion 1: 3: 1/2. The instrument now on sale contains six movable disks.

Continuous Calculating Machines or Integrators.—In order to measure the length of a curve, such as the road on a map, a [Sidenote: Curvometers.] wheel is rolled along it. For one revolution of the wheel the path described by its point of contact is equal to the circumference of the wheel. Thus, if a cyclist counts the number of revolutions of his front wheel he can calculate the distance ridden by multiplying that number by the circumference of the wheel. An ordinary cyclometer is nothing but an arrangement for counting these revolutions, but it is graduated in such a manner that it gives at once the distance in miles. On the same principle depend a number of instruments which, under various fancy names, serve to measure the length of any curve; they are in the shape of a small meter chiefly for the use of cyclists. They all have a small wheel which is rolled along the curve to be measured, and this sets a hand in motion which gives the reading on a dial. Their accuracy is not very great, because it is difficult to place the wheel so on the paper that the point of contact lies exactly over a given point; the beginning and end of the readings are therefore badly defined. Besides, it is not easy to guide the wheel along the curve to which it should always lie tangentially. To obviate this defect more complicated curvometers or kartometers have been devised. The handiest seems to be that of G. Coradi. He uses two wheels; the tracing-point, halfway between them, is guided along the curve, the line joining the wheels being kept normal to the curve. This is pretty easily done by eye; a constant deviation of 8 deg. from this direction produces an error of only 1%. The sum of the two readings gives the length. E. Fleischhauer uses three, five or more wheels arranged symmetrically round a tracer whose point is guided along the curve; the planes of the wheels all pass through the tracer, and the wheels can only turn in one direction. The sum of the readings of all the wheels gives approximately the length of the curve, the approximation increasing with the number of the wheels used. It is stated that with three wheels practically useful results can be obtained, although in this case the error, if the instrument is consistently handled so as always to produce the greatest inaccuracy, may be as much as 5%.