(1671-1732), who acquired reputation as the biographer of the ejected clergy. He was born in London, April 5, 1671, educated among the Dissenters and in Holland (1688-91); was pastor in London, 1692, and died there June 3, 1732. He was held in high regard, and his Nonconformists' Memorial (1778), as it is now called, a book which underwent important changes while in the author's hands, is the best source of knowledge respecting the 2000 ministers ejected from the Church of England by the Act of Conformity. Consult Palmer, Abridgment of Nonconformists' Memorial (London, 1802-03), and his autobiog raphy, Historical Account of My Own Life (London, 1830).

CALANCHA, kå-län'chå, ANTONIO DE LA

(1584-1654). A Peruvian chronicler. Early in life he entered the Augustinian Order at Lima, and afterwards traveled extensively through Peru for the purpose of examining the ancient ruins of that country and of recording its traditions. As a chronicler of the Augustins at Lima he wrote the important history (completed in 1633), which has been translated into French, under the title Histoire de l'église du Pérou aux antipodes et d'un grand progrès de l'église en la conversion de Gentils par la prédication des religieux ermites de l'ordre Saint-Augustin (1653). CAL'AND, or KALAND. A brotherhood of Roman Catholics devoted to charitable and devotional works, dating from the Thirteenth Century, and of considerable extent in Germany, Switzerland, and France. It degenerated so far that it was suppressed before the Reformation, its property being confiscated for public purposes. CALANDO, kå-län'dô (It., slackening, from calare, to lower, diminish, decrease). A musical term which means diminishing by degrees in power (from forte to piano) as well as in rapidity, thus combining both the decrescendo or diminuendo (q.v.) and ritardando (q.v.) effects, but in a somewhat slighter degree.

CALANDRA, kå-län'drå, GIOVANNI BATTISTA (1586-c.1648). An Italian mosaicist, born in Vercelli. During the Pontificate of Urban VIII. it was discovered that dampness had begun to affect the paintings in Saint Peter's. It was considered advisable to replace certain of the pictures by copies in mosaic, and Calandra was the first to employ this art, afterwards brought to a much greater perfection by Christofori. He copied the "Saint Michael" of Cesari d'Arpino, and the four doctors of the Church by d'Arpino, Sacchi, Romanelli, and others.

CALANDRELLI, käʼlån-drěl'lê, ALEXANDER (1834-). A German sculptor, born in Berlin. He studied at the Academy in that city in 1847, and afterwards took a course with Friedrich Drake and August Fischer. His important works are decorative designs for the city hall of Berlin; a bronze relief, typifying the Danish War ("Statue of Victory", ib.); "Monument of Victory" (fifth municipal district, ib.); a marble statue of Cornelius (entrance-hall of Berlin Museum); an equestrian statue of Frederick William IV. (entrance to National Gallery, Berlin); an equestrian statue of Emperor William I. (Bromberg); a statue of the Elector Frederick I. (Siegesallee, Berlin).

CALANDRINO, kä'lån-dre'nô. An unfortunate character in Boccaccio's Decameron, the story of whose mishaps creates great amusement.

CALANDRONE, kä'lån-drō'nå (It.). A small variety of clarinet used by the Italian peasants, on which they play simple melodies, and also sometimes accompany their national songs. It has the holes of the common flute, but the intonation is produced as in the common pipe.

CALAN THA. The heroine of Ford's Broken Heart, daughter of King Amyclos of Laconia. She dies suddenly after being told of the deaths of all whom she holds dear. The scene of the has been strongly condemned by Hazlitt as 'unannouncement is a ballroom, and the episode natural.'

CAL'ANUS (Gk. Káλavos, Kalanos, from Skt.

kalyana, the fortunate'). A Hindu philosopher, apparently a Brahman ascetic, whose real name, for some time in the camp of Alexander the according to Plutarch, was Sphines. He was Great at the invitation of the conqueror, but having become seriously ill, he was burned alive at his own request at Persepolis.

CALAPAN, kä'lå-pän'. The capital of the island of Mindoro, Philippines, situated at the northeastern extremity of the island. It has a harbor and a fort. Population, in 1898, 5585.

CALAPE, kå-lä'pâ. A town of Bohol, Philippines, situated on the western coast, 26 miles north of Tagbilaran. Population, in 1898, 10,000.

CALAS, kȧ'lås' or kå'là', JEAN (1698-1762). A Protestant merchant of Toulouse, whose judicial murder was the cause of an agitation in which Voltaire took the leading part. It resulted in the amelioration of the legal position of Protestants in France, and particularly discredited the administration of justice under the declining monarchy. Calas was accused of murdering his son because he wished to become a Roman Catholic. The son had probably committed suicide, and there was no evidence to support the accusation, which originated in a mob, and was fostered by Roman Catholic religious societies, the White Penitents, and the Franciscans, who treated the suicide with the honors due to a martyr. After a trial which lasted a whole winter, the Parliament of Toulouse, by a majority of eight to five, condemned Calas to death on the rack and confiscated the estate of the family. Calas's widow made Voltaire's acquaintance in Switzerland, and he actively took up her cause. After long labor he secured a rehearing of the case and the Parliament of Paris declared Calas innocent and restored the estate to the family. The chief magistrate was degraded and fined. Consult Coquerel, Jean Calas et sa famille (Paris, 1858); and for Voltaire's part in the matter, Kreiten, Voltaire (Freiburg, 1878).

CALASIAO, kå-lä'sê-ä'ô. A town of Luzon, Philippines, in the Province of Pangasinan, 9 miles southeast of Lingayen. Population, in 1898, 13,750.

CALATAFIMI, kå-lä'tå-fe'mê. A city of Sicily, 57 miles southwest of Palermo (Map: Italy, G 10). On a hill beside the town, and 1115 feet above the sea, is the castle, of Moorish design, now used as a prison. From it is a splendid view of the Temple of Segesta (q.v.) and of a mountainous landscape. The town had its name, Kalat al-Fimi, from the Saracens, who captured it in 828. In 1860 Garibaldi won his

first victory over the Neapolitan troops on a field 2 miles to the southwest, marked by a monument erected in 1892. The cheeses of the district have more than a local reputation. Population (commune), in 1881, 10,000; in 1901, 11,426.

CALATAYUD, kå-lä'tå-yoOD' (Ar. kalat, castle + Ayub, a Moorish king). A city of Aragon, Spain, situated on the Jalón, near its junction with the Jiloca, about 48 miles southwest of Saragossa (Map: Spain, E 2). It is built at the base of two rocky ridges, 1700 feet in height, out of the ruins of ancient Bilbilis, which lay about 2 miles to the east. The city is divided into a new and old portion, the former with several fine streets and handsome squares, while the latter is composed of mean buildings and narrow, crooked streets. Cala tayud has ruins of a noble Moorish castle, two collegiate churches, and a Dominican convent. It manufactures silk, linen, and hempen fabrics, woolens, paper, leather, etc., and carries on a trade in agricultural produce. Population, in 1897, 10,900.

CALATRAVA, kä ́lå-trä’vå. A military and religious Order in Spain, instituted in 1158, in the reign of Sancho III. of Castile. It received the town of Calatrava as a perpetual gift, on condition that it should defend it against the Moors. The Order was confirmed by Pope Alexander III., in 1164, and very soon came to render effective service in the wars against the

Mohammedans. While the Christian States in Spain were exhausting themselves by internal strife, the Order of Calatrava was the main bulwark against the Moors. In 1197 the latter captured Calatrava and the knights removed to Salvatierra. In 1212, however, they not only recovered Calatrava, but had an important share in the deadly blow which was struck at the power of the Almoravides. In 1213 Calatrava united with the Order of Avis. The power of the Knights of Calatrava was shown at the time they joined the Orders of Alcántara and Santiago in exacting from Alfonso XI. a guarantee of their liberties and customs. The later history of Calatrava is a series of civil wars between the grand masters, which became so troublesome to the Government that Ferdinand and Isabella, in 1487-88, prohibited a new election and secured the grand-mastership to the Crown by a Papal

On

bull in 1493. Later Charles V. made the Order perpetual, with the King of Castile as head. In 1808 Calatrava became an Order of merit. March 13, 1872, the Order was suppressed by the republican Government, but was reorganized by

Alfonso XII., June 13, 1874. Those who entered the Order took the vows of poverty and obedience. At first marriage was forbidden, but Paul III. in 1540 made this concession, and gradually the Order lost most of its religious character. The original garb was black, but in 1396 Benedict XIII. (antipope) allowed the knights to adopt The present dress is a mantle of white, decorated with a red cross, cut out in the form of lilies.

the red cross.

CALATRAVA, JOSÉ MARÍA (1781-1846). A Spanish statesman, born at Mérida. He became known as an eminent orator of the Liberal Party, and became a member of the Junta of Estremadura in 1808 and of the General Junta in 1810. Because of his radical views he was exiled

upon the restoration of Ferdinand VII., in 1814, but returned to Spain after the King's deposition. In 1821 he was elected to the Cortes, and in 1823 he became Minister of Justice, but when, through the intervention of the French, Ferdinand regained absolute power (1823), Calatrava was again banished. He lived in London until 1830, when he returned to Spain, became Minister of Foreign Affairs (1836), and was prominent in the parliamentary movement which resulted in the adoption of the more liberal Constitution of 1837. When Queen Isabella assumed the Government, in 1843, he was made a Senator.

CALATRAVA LA VIEJA, lä vуã'нȧ (Sр., Calatrava the Old, from Ar. kalat, castle Rabah, a man's name), or OLD CALATRAVA. A ruined city of Spain, near Valdepeñas, situated on the Guadiana. In the Middle Ages it was a strongly fortified place; but nothing 1ow remains save a single tower. Calatrava la Vieja was captured from the Moors by Alfonzo VII. of Castile, and given to the Templars; unable to defend it, they returned the gift to Sancho III. (1157). Raymond, Abbot of Fitero, and Diego Velasquez here instituted the Order of Calatrava (q.v.) in 1158. In 1197 the Moors captured Calatrava la Vieja, but it was retaken in 1212. About 1217 the Knights of Calatrava la Vieja built a convent in Nueva (New Calatrava). the neighborhood, naming the place Calatrava la

CALAUA, kå-lä'wå, or CALAWA. A MaTheir speech is lay people in northern Luzon.

mixed. See PHILIPPINES.

CALAVERAS (käl'å-vā'ras) GROVE. The nearest to San Francisco of the California groves of big trees. The grove is 70 by 1100 yards in extent, and contains about 100 of the big trees, of which the "Keystone State," the highest now standing, has an altitude of 325 feet and a circumference of 45 feet. The "Mother of the Forest" is 61 feet, and the "Father of the Forest," not standing, is 112 feet in circumference. The grove is State property under a commissioner.

CALAVERAS RIVER. A small river of central California, and a tributary of the San Joaquin, which it joins just below Stockton (Map: California, C 2). It rises in the Sierras of Calaveras County and pursues a southwesterly course.

CALAVERAS SKULL. A much-discussed

human cranium reported to have been found in auriferous gravels below lava-beds near Angel, Calaveras County, Cal. The specimen was described by J. D. Whitney, and is preserved in factory accounts of the object and its associations the Peabody Museum, Harvard University. Satishave been published by Holmes in the Smithsonian Report for 1901 and elsewhere. ARCHEOLOGY, AMERICAN.

See

third being fresh-water deposits, and the second of marine formation. The strata are highly fossiliferous; the animal remains include mammalia, reptiles, and a large variety of lower life-forms. The Calcaire Grossier is represented in the English Tertiary by the Bracklesham beds; in the United States the Claiborne beds are equivalent to a portion of it.

CALCAR, käl'kär, HANS VON. See KALKAR, JOHANN STEPHAN VON.

CALCA'REOUS ROCK (Lat. calcarius, pertaining to lime, from calx, limestone, lime). Rock containing much lime, especially that in which the lime occurs in the form of carbonate (CaCO3). Calcareous rocks may be chemically formed, as in the case of tufa, where lime carbonate in solution is precipitated through evaporation or other causes. They are generally aqueous rocks, and have been deposited in bodies of either marine or fresh water; the calcareous content has been supplied by the fossilized remains of the hard parts of animals that inhabited these waters. Thus many Paleozoic limestones are composed of shells, corals, and crinoidal fragments, while others, like chalk, consist of foraminifera and fragments of other minute organisms. A crystalline structure varying in degree from that of partially crystallized limestones to the granular statuary marble, is produced in calcareous rocks by metamorphic action. Oölite is a calcareous rock composed of small, concretionary, egg-like grains, resembling the roe of fish. The existence of the carbonate in rocks can be readily detected by the application of dilute nitric or muriatic acid, which causes effervescence through the liberation of carbonic acid. Quicklime is obtained from calcareous rocks by calcining them, i.e. by driving off the carbonic acid and other volatile matter by heat. Calcareous soils, often of great fertility, are produced from the disintegration of calcareous rocks. See ROCK; OÖLITE; SOIL; LIMESTONE; CALCAREOUS TUFA.

CALCAREOUS TU'FA (It. tufa, from Lat. tofus, tufa, tuff), CALC-SINTER, TRAVERTINE, STALACTITE, ONYX MARBLES. Forms of carbonate of lime deposited from solution in springs, in limestone caverns, or by the evaporation of water in lakes, in the form of calcite or aragonite. When free from impurity they are white or translucent, but commonly they are stained with other substances, taking on yellow, gray, brown, or other colors. They have a spongy or cellular or concretionary structure, are banded, and often show rings of growth. A great variety of forms is exhibited, massive, tubular, botryoidal, stalactitic, or the forms of vegetable and animal remains which they sometimes incrust. Calcareous tufa has often been quarried and used for building purposes; the stone is quite soft when newly quarried and acquires hardness and solidity through exposure to the atmosphere. The temples of Pæstum, Italy, built several centuries before the commencement of our era, were constructed of such massive calcareous tufa. CALCAREOUS ROCK; LIMESTONE; ROCK.

See

CALCASIEU, käl'kå-shū. A river of southwest Louisiana, its headstream, Cypress Branch, rising in the parish of Natchitoches (Map: Louisiana, B 3). It pursues a course at first southeast, then southwest, and empties into Lake Calcasieu (nearly 20 miles long and 3 to 6 miles wide), VOL. IV.-2.

which is connected with the Gulf of Mexico by the narrow Calcasieu Pass. By means of numerous branches, chiefly from the west, it drains a large area in southwest Louisiana, and is navigable for small boats for about 130 miles.

CAL'CEOLAʼRIA (Neo-Lat., from Lat. calceolus, a little shoe, referring to the part of the corolla resembling a slipper). A genus of plants of the order Scrophulariacea. There are numerous species, natives of South America, chiefly of that part of the Andes which is more than 9000 feet above the sea, a few of them reaching almost to the upper limits of vegetation. Some are found in lower and warmer situations, and some in the southern extremity of the American continent, others occurring in New Zealand and Mexico. They are so abundant in some parts of Chile and Peru as to give a peculiar aspect to the landscape. The calyx in this genus is four-partite; the corolla, twolipped, the lower lip remarkably inflated, so as to form a bag; and the shape of the whole in some species considerably resembling that of a slipper. Some of the species are shrubby, some herbaceous, almost all the herbaceous species being perennial. Many of them have corymbs of numerous showy flowers. Yellow is the color which chiefly prevails in the flowers, and next to it purple; but the art of the gardener has succeeded in producing varieties and hybrids which exhibit many other rich and delicate tints. Calceolarias have been prominent in floriculture since about 1830, the curious appearance of the flowers combining with their beauty to render them attractive, and in no genus is the production of hybrids more easily or frequently effected. They are easily propagated by cuttings. Few plants require more liberal supplies of water. They are generally treated in the United States as half hardy or as greenhouse plants, and only the herbaceous forms are well known. Some of the species are used in South America for dyeing. The roots of Calceolaria arachnoidea, which is claimed to be one of the parents of many of the hybrids, are largely employed in Chile, under the name of relbum, for dyeing For illustration, see

woolen cloths crimson. GREENHOUSE PLANTS.

CALCHAQUI, kål-chä'kê. A tribe formerly living on the western border of the Chaco, about the present Tucuman, Argentina. Great walls of cut stone found in their ancient territory, and stone-built tombs in which are found mummies and deposits of gold and copper ornaments, attest a considerable degree of civilization, which may have been due to the Incas, who conquered the Calchaqui about the year 1450. Interesting details of their customs and home life are given by the earliest missionaries. They have been long extinct, unless, as Tschudi surmises, a refugee remnant still survives on the northern coast of Chile. Even their linguistic affiliation is a matter of conjecture.

CALCHAS, kål'kās (Gk. Káλxas, Kalchas). The prophet of the Greek army before Troy, gifted by Apollo with knowledge of the past and future. Through his counsel Achilles, Neoptolemus, and Philoctetes were brought to the army. At Aulis he advised the sacrifice of Iphigenia (q.v.) to appease Artemis, and foretold the length of the war. The common tradition made him go from Troy to Colophon, where, at the

oracle of Apollo at Clarus, he met the prophet Mopsus, who defeated him in a contest of prophecy, whereupon he died of grief. His grave was shown in Italy.

CALCIFEROUS (Lat. cala, lime ferre, to bear). The term given to a subdivision of the Ordovician system. It is usually a sandy magnesian limestone, known as the calciferous sand rock. It is found in Canada and New York, extending southward through New Jersey and Pennsylvania. Its equivalent is also to be seen in the magnesian limestones of Iowa, Missouri, and Michigan. The formation is now known as the Beekmantown beds, from the locality near the village of that name in New York State. See OR

DOVICIAN.

CALCIMINE (Lat. calx, limestone). A composition of zinc-white and glue sizing mixed with water, and applied as a finish to the plastered ceilings and side-walls of rooms. By adding coloring matter, any color desired may be produced.

CALCINATION,

or CALCINING (Fr., Med. Lat. calcinatio, from Lat. calx, lime). The process of heating or roasting in furnaces, kilns, or heaps the various metallic ores, limestones, cement-mixtures, etc. It is resorted to as the first stage in the extraction of the majority of the common metals from their ores, is an essential process in lime and cement manufacture, and is a process of oxidation. See IRON AND STEEL; CEMENT.

CALCITE (Lat. cala, lime), CALCAREOUS SPAR, or CALC-SPAR. An anhydrous calcium carbonate that crystallizes in the hexagonal system, and differs from the mineral aragonite only in its form of crystallization. The massive and crystalline varieties are known as limestone, marble, and chalk (qq.v.), and are found almost universally, and in all geological formations. It is generally white or colorless, although pale shades of gray, red, green, blue, violet, and yellow are known, and, owing to the presence of impurities, even black and brown varieties are found. The crystallized varieties include the dog-tooth spar, the acute scalenohedral, crystals of which suggest its name; similarly, the name of nailhead spar has been suggested by the form of its truncated crystals; satin spar is a fine fibrous variety with a silky lustre. Iceland spar, originally found in basalt rocks in Iceland, is a fine, colorless, translucent variety, with the property of double refraction; the finest specimens of this variety are used for making polarizing prisms. Calcite is found chiefly in the following localities: Andreasberg in the Harz Mountains, Alston Moor and Egremont, Cumberland, and Matlock, Derbyshire, England, and Rossie, N. Y., the copper-mines at Lake Superior, and Warsaw, Ill., in the United States.

CALCIUM (Neo-Lat., from Lat. cala, lime). A metallic element isolated by Sir Humphry Davy in 1808. The name is derived from the Latin cala, lime, showing that calcium is the metal contained in lime. Calcium is not found

native, but occurs extensively in combination with other elements in the forms of calcite (including limestone, marble, and chalk), aragonite, dolomite, selenite, gypsum, etc. It is also found in river and spring waters and in the bodies of plants and animals. Spectrum analysis has revealed its presence in the sun. Davy obtained

metallic calcium by the electrolysis of calcium chloride in the presence of mercury, the metal remaining as a powder on heating the amalgam thus produced. Calcium (symbol, Ca; atomic weight, 40.07) is a lustrous, clear, yellowishwhite, very ductile, and malleable metal of specific gravity 1.57. It melts at a red heat. The metal itself has no commercial application, although it is capable of forming a crystalline alloy with zinc. It is readily oxidized in the air, even at ordinary temperatures, and when heated to redness it burns with a very bright yellow flame. Like sodium and potassium, it decomposes water with evolution of hydrogen. With the non-metallic elements it is capable of forming compounds which are generally colorless and have an acrid taste. The more important of these compounds are described under their special

names.

CALCIUM CARBIDE, CaC.. A compound of calcium and carbon. It was originally discovered in 1836 by Edmund Davy, who produced it simply as a laboratory curiosity. In 1862 Wöhler prepared it in Göttingen, and about the same time Berthelot, in Paris, obtained it, but only in small quantities. In 1892 Thomas L. Willson, in Spray, N. C., found that by heating a mixture of lime and carbon in an electrical furnace, calcium carbide and carbon monoxide were formed. Almost simultaneously Henri Moissan, in Paris, announced his discovery of a similar method for its production. Its property of decomposing water with the formation of acetylene gas had already long been known, and the foregoing method just described made possible the economical production of acetylene gas for illuminating purposes, and accordingly that industry has since been largely developed, especially in the United States. The calcium carbide, or carbide, as it is called commercially, is now largely manufactured at Niagara Falls, N. Y., and Sault Ste. Marie, Mich.; and also at various places in Europe. The process consists essentially in submitting a mixture of powdered lime and coke-dust to the action of carbon electrodes in a furnace at a temperature of about 3300° C. The fused material is allowed to cool and harden, after which it is removed. Calcium carbide is a hard, brownish crystalline compound with a metallic lustre and a specific gravity of 2.22, that is non-inflammable, infusible, and insoluble in most acids and all alkalies; is absolutely unaffected by jars, concussions, or time, and is an inert and stable substance, except when brought Its principal use is

into contact with water.

for the manufacture of acetylene. Since its commercial introduction into the United States, its manufacture has passed into the control of a single corporation, who report that over 7000 tons of carbide were consumed in the year ending June 1, 1899. Its history and methods of production have been largely described in the various technical journals, and the Acetylene Gas Journal, published in Buffalo, N. Y., is devoted to the exploitation of the new illuminant. Consult, also, Thompson, Acetylene Gas: Its Nature, Properties, and Uses; also Calcium Carbide: Its Composition, Properties, and Method of Manufacture (London, 1899). See ACETYLENE.

CALCIUM LIGHT. See DRUMMOND LIGHT. CAL CRAFT, JOHN WILLIAM. The nom de plume of John William Cole. See BRIDE OF LAMMERMOOR, THE.

CALCULATING MACHINES (from Lat. calculare, to reckon, compute; see CALCULUS). Mechanical contrivances designed to facilitate computations, to relieve the calculator from the mental strain of his work, and to insure greater accuracy in results. Calculating machines exist in various forms, and are now made in such perfection that large business houses and banks regard them as a necessity, while many scientific computations would have been abandoned but for their help. An instrument which is used for the purpose of illustration or instruction in number work is called a reckoning apparatus, but one which automatically produces the results of number combinations involving the union of different orders is called a calculating machine.

The earliest known instrument of calculation of any importance is the abacus. The Chinese lay claim to its invention. Its use by the Egyptians as early as B.C. 460 is definitely asserted by

A notable example of this type is the set of rods invented by Napier and known as virgulæ; or, popularly, as Napier's rods or bones. These consist of flat pieces of bone or ivory, divided into squares, which (on ten of the rods) are subdivided by diagonals into triangles, except the squares at the upper ends of the rods, which spaces are numbered from 1 to 9.

To illustrate the process of multiplication, consider the product of 5978 by 937. Arrange the proper rods, as in the figure, so that the numbers at the top indicate the multiplicand, and on the left place the rod headed 1. In this rod find the right-hand figure of the multiplier, which in this case is 7. Passing across this horizontal row, add obliquely the two rows of corresponding digits, writing the results in each case as the digits of the first partial product. For example, the first figure on the right is 6; this is written in the units place in the first partial product. Next add the 5 and 9 in the adjoining oblique row, which gives 4 in the tens place, with 1 to carry. This makes 8 in the hundreds column. Proceed in the same way with the other figures of the multiplier, and add the partial products as in ordinary multiplication.

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9

2

8

ARRANGEMENT OF NAPIER'S RODS.

Herodotus. It was probably used by the Babylonians, and certainly by the Greeks and Romans, from whom it spread to all Europe. It has existed in various forms-the knotted strings, the sand-board, the pebble-tray, the counters, and the frame of beads. The last form is still in use, known as the Chinese swanpan, the Russian Stchoty, or the Japanese SoroBan. The ordinary swan-pan consists of a frame divided into two sections, holding several parallel rods, each containing several movable beads. In the Chinese swan-pan, each bead on the bottom row in the right division represents one unit, and each on the bottom row in the left division represents five units. In the next higher row the value of each bead is ten times as great, and so on.

The first improvement over the ancient abacus consisted in the use of counters, on a plan attributed, probably erroneously, to Boethius. Later these counters bore numbers, and were attached to rods, disks, or cylinders, which could be moved so as to indicate the desired results.

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The chief point of improvement over the primitive abacus consists in supplying the instrument with moving scales, which enable the calculator to form number combinations without actually counting together the different addends. Kummer (1847) accomplished this by running parallel rods in grooves; Lagrous (1828) by concentric rings; Djakoff and Webb by bands on rollers.

Another form of the calculating machine is the slide rule, which is more generally employed than any other class of calculating instruments, particularly by engineers and statisticians. In its simplest form it consists of two rules, arranged to slide on each other, and so divided into scales that by sliding the rules backward or forward until a selected number on one scale is made to coincide with a selected number on the other, the desired result is read off directly on a third scale. By means of a duplex slide rule, where the rule may be set for four factors instead of two, more complicated problems may be solved. Revolving slide rules are employed to increase the virtual length of the scales and the number of decimal places to which results may be read. In the Thacher calculating instrument, a cylinder 4 inches in diameter and 18 inches long revolves within a framework of triangular bars, each of which contains a scale on two sides. The scales contain 33,000 divisions and 17,000 engraved figures, executed on a dividing machine made expressly for the purpose. Fuller's spiral slide rule consists of a wooden cylinder containing a spiral scale 42 feet long.

Circular slide rules, resembling watches, are also made. The slide-rule principle is also employed in instruments used to work out specific problems, such as the flow of water in pipes, or the strength of beams. Such computers may be either like the ordinary slide rule, with scales in terms of the factors involved, or, as in the various Cox computers, there may be a founda