Part 27

§ 18. _Ratio of Specific Heats._--According to the elementary kinetic theory of an ideal gas, the molecules of which are so small and so far apart that their mutual actions may be neglected, the kinetic energy of translation of the molecules is proportional to the absolute temperature, and is equal to 3/2 of pv, the product of the pressure and the volume, per unit mass. The expansion per degree at constant pressure is v/[theta] = R/p. The external work of expansion per degree is equal to R, being the product of the pressure and the expansion, and represents the difference of the specific heats S - s, at constant pressure and volume, assuming as above that the internal work of expansion is negligible. If the molecules are supposed to be like smooth, hard, elastic spheres, incapable of receiving any other kind of energy except that of translation, the specific heat at constant volume would be the increase per degree of the kinetic energy namely 3pv/2[theta] - 3R/2, that at constant pressure would be 5R/2, and the ratio of the specific heats would be 5/3 or 1.666. This appears to be actually the case for monatomic gases such as mercury vapour (Kundt and Warburg, 1876), argon and helium (Ramsay, 1896). For diatomic or compound gases Clerk Maxwell supposed that the molecule would also possess energy of rotation, and endeavoured to prove that in this case the energy would be equally divided between the six degrees of freedom, three of translation and three of rotation, if the molecule were regarded as a rigid body incapable of vibration-energy. In this case we should have s = 3R, S = 4R, S/s = 4/3 = 1.333. In 1879 Maxwell considered it one of the greatest difficulties which the kinetic theory had yet encountered, that in spite of the many other degrees of freedom of vibration revealed by the spectroscope, the experimental value of the ratio S/s was 1.40 for so many gases, instead of being less than 4/3. Somewhat later L. Boltzmann suggested that a diatomic molecule regarded as a rigid dumb-bell or figure of rotation, might have only five effective degrees of freedom, since the energy of rotation about the axis of symmetry could not be altered by collisions between the molecules. The theoretical value of the ratio S/s in this case would be the required 7/5. For a rigid molecule on this theory the smallest value possible would be 4/3. Since much smaller values are found for more complex molecules, we may suppose that, in these cases, the energy of rotation of a polyatomic molecule may be greater than its energy of translation, or else that heat is expended in splitting up molecular aggregates, and increasing energy of vibration. A hypothesis doubtfully attributed to Maxwell is that each additional atom in the molecule is equivalent to two extra degrees of freedom. From an m-atomic molecule we should then have S/s = 1 + 2/(2m + 1). This gives a series of ratios 5/3, 7/5, 9/7, 11/9, &c., for 1, 2, 3, 4, &c., atoms in the molecule, values which fall within the limits of experimental error in many cases. It is not at all clear, however, that energy of vibration should bear a constant ratio to that of translation, although this would probably be the case for rotation. For the simpler gases, which are highly diathermanous and radiate badly even at high temperature, the energy of vibration is probably very small, except under the special conditions which produce luminosity in flames and electric discharges. For such gases, assuming a constant ratio of rotation to translation, the specific heat at low pressures would be very nearly constant. For more complex molecules the radiative and absorptive powers are known to be much greater. The energy of vibration may be appreciable at ordinary temperatures, and would probably increase more rapidly than that of translation with rise of temperature, especially near a point of dissociation. This would account for an increase of S, and a diminution of the ratio S/s, with rise of temperature which apparently occurs in many vapours. The experimental evidence, however, is somewhat conflicting, and further investigations are very desirable on the variation of specific heat with temperature. Given the specific heat as a function of the temperature, its variation with pressure may be determined from the characteristic equation of the gas. The direct methods of measuring the ratio S/s, by the velocity of sound and by adiabatic expansion, are sufficiently described in many text-books.

§ 19. _Atomic and Molecular Heats._--The ideal atomic heat is the thermal capacity of a gramme-atom in the ideal state of monatomic gas at constant volume. This would be nearly three calories. For a diatomic gas, the molecular heat would be nearly five calories, or the atomic heat of a gas in the diatomic state would be 2.5. Estimated at constant pressure the atomic heat would be 3.5. Some authors adopt 2.5 and some 3.5 for the ideal atomic heat. The atomic heat of a metal in the solid state is in most cases larger than six calories at ordinary temperatures. Considering the wide variations in the physical condition and melting points, the comparatively close agreement of the atomic heats of the metals at ordinary temperatures, known as Dulong and Petit's Law, is very remarkable. The specific heats as a rule increase with rise of temperature, in some cases, e.g. iron and nickel, very rapidly. According to W.A. Tilden (_Phil. Trans.,_ 1900), the atomic heats of pure nickel and cobalt, as determined from experiments at the boiling-points of O2, and CO2, diminish so rapidly at temperatures below 0° C. as to suggest that they would reach the value 2.42 at the absolute zero. This is the value of the minimum of atomic heat calculated by Perry from diatomic hydrogen, but the observations themselves might be equally well represented by taking the imaginary limit 3, since the quantity actually observed is the mean specific heat between 0° and -182.5° C. Subsequent experiments on other metals at low temperatures did not indicate a similar diminution of specific heat, so that it may be doubted whether the atomic heats really approach the ideal value at the absolute zero. No doubt there must be approximate relations between the atomic and molecular heats of similar elements and compounds, but considering the great variations of specific heat with temperature and physical state, in alloys, mixtures or solutions, and in allotropic or other modifications, it would be idle to expect that the specific heat of a compound could be accurately deduced by any simple additive process from that of its constituents.

AUTHORITIES.--Joule's _Scientific Papers_ (London, 1890); Ames and Griffiths, _Reports to the International Congress_ (Paris, 1900), "On the Mechanical Equivalent of Heat," and "On the Specific Heat of Water"; Griffiths, _Thermal Measurement of Energy_ (Cambridge, 1901); Callendar and Barnes, _Phil. Trans._ A, 1901, "On the Variation of the Specific Heat of Water"; for combustion methods, see article THERMOCHEMISTRY, and treatises by Thomsen, Pattison-Muir and Berthelot; see also articles THERMODYNAMICS and VAPORIZATION. (H. L. C.)

CALOVIUS, ABRAHAM (1612-1686), German Lutheran divine, was born at Mohrungen in east Prussia, on the 16th of April 1612. After studying at Königsberg, in 1650 he was appointed professor of theology at Wittenberg, where he afterwards became general superintendent and primarius. He died on the 25th of February 1686. Calovius was the most noteworthy of the champions of Lutheran orthodoxy in the 17th century. He strongly opposed the Catholics, Calvinists and Socinians, attacked in

## particular the reconciliation policy or "syncretism" of Georg Calixtus

(cf. the _Consensus repetitus fidei vere lutheranae,_ 1665), and as a writer of polemics he had few equals. His chief dogmatic work, _Systema locorum theologicorum_ (12 vols. 1655-1677), represents the climax of Lutheran scholasticism. In his _Biblia Illustrata_ (4 vols.), written from the point of view of a very strict belief in inspiration, his object is to refute the statements made by Hugo Grotius in his Commentaries. His _Historia Syncretistica_ (1682) was suppressed.

CALPURNIUS, TITUS, Roman bucolic poet, surnamed SICULUS from his birthplace or from his imitation of the style of the Sicilian Theocritus, most probably flourished during the reign of Nero. Eleven eclogues have been handed down to us under his name, of which the last four, from metrical considerations and express MS. testimony, are now generally attributed to Nemesianus (q.v.), who lived in the time of the emperor Carus and his sons (latter half of the 3rd century A.D.). Hardly anything is known of the life of Calpurnius; we gather from the poems themselves (in which he is obviously represented by "Corydon") that he was in poor circumstances and was on the point of emigrating to Spain, when "Meliboeus" came to his aid. Through his influence Calpurnius apparently secured a post at Rome. The time at which Calpurnius lived has been much discussed, but all the indications seem to point to the time of Nero. The emperor is described as a handsome youth, like Mars and Apollo, whose accession marks the beginning of a new golden age, prognosticated by the appearance of a comet, doubtless the same that appeared some time before the death of Claudius; he exhibits splendid games in the amphitheatre (probably the wooden amphitheatre erected by Nero in 57); and in the words

maternis causam qui vicit Iulis[1] (i. 45),

there is a reference to the speech delivered in Greek by Nero on behalf of the Ilienses (Suetonius, _Nero_, 7; Tacitus, _Annals_, xii. 58), from whom the Julii derived their family.[2] Meliboeus, the poet's patron, has been variously identified with Columella, Seneca the philosopher, and C. Calpurnius Piso. Although the sphere of Meliboeus's literary

## activity (as indicated in iv. 53) suits none of these, what is known of

Calpurnius Piso fits in well with what is said of Meliboeus by the poet, who speaks of his generosity, his intimacy with the emperor, and his interest in tragic poetry. His claim is further supported by the poem _De Laude Pisonis_ (ed. C.F. Weber, 1859) which has come down to us without the name of the author, but which there is considerable reason for attributing to Calpurnius.[3] The poem exhibits a striking similarity with the eclogues in metre, language and subject-matter. The author of the _Laus_ is young, of respectable family and desirous of gaining the favour of Piso as his Maecenas. Further, the similarity between the two names can hardly be accidental; it is suggested that the poet may have been adopted by the courtier, or that he was the son of a freedman of Piso. The attitude of the author of the _Laus_ towards the subject of the panegyric seems to show less intimacy than the relations between Corydon and Meliboeus in the eclogues, and there is internal evidence that the _Laus_ was written during the reign of Claudius (Teuffel-Schwabe, _Hist, of Rom. Lit._ § 306, 6).

Mention may here be made of the fragments of two short hexameter poems in an Einsiedeln MS., obviously belonging to the time of Nero, which if not written by Calpurnius, were imitated from him.

Although there is nothing original in Calpurnius, he is "a skilful literary craftsman." Of his models the chief is Virgil, of whom (under the name of Tityrus) he speaks with great enthusiasm; he is also indebted to Ovid and Theocritus. Calpurnius is "a fair scholar, and an apt courtier, and not devoid of real poetical feeling. The bastard style of pastoral cultivated by him, in which the description of nature is made the writer's pretext, while ingenious flattery is his real purpose, nevertheless excludes genuine pleasure, and consequently genuine poetical achievement. He may be fairly compared to the minor poets of the reign of Anne" (Garnett).

Calpurnius was first printed in 1471, together with Silius Italicus and has been frequently republished, generally with Gratius Faliscus and Nemesianus. The separate authorship of the eclogues of Calpurnius and Nemesianus was established by M. Haupt's _De Carminibus bucolicis Calpurnii et Nemesiani_ (1854). Editions by H. Schenkl (1885), with full introduction and _index verborum_, and by C.H. Keene (1887), with introduction, commentary and appendix. English verse translation by E.J.L. Scott (1891); see H.E. Butler, _Post-Augustan Poetry_ (Oxford, 1909), pp. 150 foil., and F. Skutsch in Pauly-Wissowa's _Realencyclopädie_, iii. 1 (1897). (J. H. F.)

FOOTNOTES:

[1] _Iulis_ for _in ulnis_ according to the best MS. tradition.

[2] According to Dr R. Garnett (and Mr Greswell, as stated in Conington's _Virgil_, i. p. 123, note) the emperor referred to is the younger Gordian (A.D. 238). His arguments in favour of this will be found in the article on Calpurnius by him in the 9th edition of the _Encyclopaedia Britannica_ and in the _Journal of Philology_, xvi., 1888; see in answer J.P. Postgate, "The Comet of Calpurnius Siculus" in _Classical Review_, June 1902. Dean Merivale (_Hist. of the Romans under the Empire_, ch. 60) and Pompei, "Intorno al Tempo del Poeta Calpurnio" in _Atti del Istituto Veneto_, v. 6 (1880), identify the amphitheatre with the Colosseum (Flavian amphitheatre) and assign Calpurnius to the reign of Domitian.

[3] It has been variously ascribed to Virgil, Ovid, Lucan, Statius and Saleius Bassus.

CALTAGIRONE, a city and episcopal see of the province of Catania, Sicily, situated 1999 ft. above sea-level, 36 m. S.W. of Catania direct (55 m. by rail). Pop. (1881) 25,978; (1901) town 35,116; commune 45,956. It is well built, and is said to be the most civilized provincial town in Sicily. Extensive Sicel cemeteries have been explored to the north of the town (_Not. Scavi_, 1904, 65), and a Greek necropolis of the 6th and 5th centuries B.C. has been found to the south-east (_ibid._ 132). Remains of buildings of Roman date have also been discovered; but the name of the ancient city which stood here is unknown. The present name is a corruption of the Saracen _Kalat-al-Girche_ (the castle of Girche, the chieftain who fortified it).

CALTANISETTA, a town and episcopal see of Sicily, the capital of a province of the same name, 60 m. S.E. of Palermo direct and 83 m. by rail, situated 1930 ft. above sea-level. Pop. (1901) 43,303. The town is of Saracenic origin, as its name _Kalat-al-Nisa_, the "Ladies' Castle," indicates, and some ruins of the old castle (called _Pietrarossa_) still exist. Otherwise the town contains no buildings of artistic or historical interest, but it commands striking views. It is the centre of the Sicilian sulphur industry and the seat of a royal school of mines. Two miles east is the interesting Norman abbey of S. Spirito.

CALTROP (from the Mid. Eng. _calketrappe_, probably derived from the Lat. _calx_, a heel, and _trappa_, Late Lat. for a snare), an iron ball, used as an obstacle against cavalry, with four spikes so arranged, that however placed in or on the ground, one spike always points upwards. It is also the botanical name for several species of thistles.

CALUIRE-ET-CUIRE, a town of eastern France, in the department of Rhone, 2½ m. N. by E. of Lyons by rail. Pop. (1906) 9255. It has manufactures of coarse earthenware and hard-ware, copper and bronze foundries and nursery-gardens.

CALUMET (Norm. Fr. form of _chalumet_, from Lat. _calamus_, a reed), the name given by the French in Canada to the "peace-pipe" of the American Indians. This pipe occupied among the tribes a position of peculiar symbolic significance, and was the object of profound veneration. It was smoked on all ceremonial occasions, even on declarations of war, but its special use was at the making of treaties of peace. It was usually about 2½ ft. long, and in the west the bowl was made of red pipes tone (catlinite), a fine-grained, easily-worked stone of a rich red colour found chiefly in the Côteau des Prairies west of Big Stone Lake, Dakota. The quarries were formerly neutral ground among the warring Indian tribes, many sacred traditions being associated with the locality and its product (Longfellow, _Hiawatha_, i.). The pipe stem was of reed decorated with eagles' quills or women's hair. Native tobacco mixed with willow-bark or sumac leaves was smoked. The pipe was offered as a supreme proof of hospitality to distinguished strangers, and its refusal was regarded as a grievous affront. In the east and south-east, the bowl was of white stone, sometimes pierced with several stem holes so that many persons might smoke at once.

See Joseph D. Macguire (exhaustive report,640 pages), "Pipes and Smoking Customs of the American Aborigines" in _Smithsonian Report_ (American Bureau of Ethnology) for 1897, vol. i.; and authorities quoted in _Handbook of American Indians_ (Washington, 1907).

CALUMPIT, a town of the province of Bulacán, Luzon, Philippine Islands, at the junction of the Quiñgua river with the Rio Grande de la Pampanga, about 25 m. N.W. of Manila. Pop. (1903) 13,897. It is served by the Manila & Dagupan railway, and the bridge across the Rio Grande is one of the longest in the Philippines. The surrounding country is a fertile plain, producing large quantities of rice, as well as sugar, Indian corn and a variety of fruits. Calumpit has a large rice-mill and one of the largest markets in the Philippines. The bridge, convent and church of the town were fired and completely destroyed by insurgent troops in 1899. The language is Tagalog.

CALVADOS, a department of north-western France, formed in 1790 out of Bessin, Cinglais, Hiémois, Bocage, the Campagne de Caen, Auge and the western part of Lieuvin. Pop. (1906) 403,431. Area, 2197 sq. m. It received its name from a ledge of rocks, stretching along the coast for a distance of about 15 m. between the mouths of the rivers Orne and Vire. It is bounded N. by the English Channel, E. by the department of Eure, S. by that of Orne, W. by that of Manche. The Bocage, or south-western part of the department, is elevated, being crossed from south-east to north-west by the hills of Normandy, the highest of which is 1197 ft.; the rest of the surface is gently undulating, and consists of extensive valleys watered by numerous streams which fall into the English Channel. The coast, formed by cliffs, sandy beaches or reefs, is generally inaccessible, except at the mouths of the principal rivers, such as the Touques, the Dives, the Orne and the Vire, which are navigable at high tide for several miles inland. Trouville is the chief of the numerous coast resorts. The climate, though humid and variable, is healthy. The raising of cattle, sheep and horses is the mainstay of the agriculture of the department. Pasture is good and abundant in the east and north-west, and there is a large export trade in the butter, eggs and cheese (Camembert, Livarot, Pont l'Evêque) of these districts, carried on by Honfleur, Isigny and other ports. The plain of Caen is a great centre for horse breeding. Wheat, oats, barley, colza and potatoes are the chief crops. The orchards of Auge and Bessin produce a superior kind of cider, of which upwards of 40,000,000 gallons are made in the department; a large quantity of cider brandy (eau-de-vie de Calvados) is distilled. Poultry to a considerable amount is sent to the Paris markets, and there is a large output of honey and wax. The spinning and weaving of wool and cotton are the chief industries. Besides these, paper-mills, oil-mills, tanneries, saw-mills, shipbuilding yards, rope-works, dye-works, distilleries and bleach-fields, scattered throughout the department, give employment to a number of hands. There are productive iron-mines and building-stone, slate and lime are plentiful. Fisheries, chiefly of lobster, oyster (Courseulles), herring and mackerel, are prosecuted. Coal, timber, grain, salt-fish and cement are among the imports; exports include iron, dairy products and sand. Caen and Honfleur are the most important commercial ports. There is a canal 9 m. in length from Caen to Ouistreham on the coast. The department is served by the Ouest-Êtat railway. It is divided into the six arrondissements (38 cantons, 763 communes) of Caen, Falaise, Bayeux, Vire, Lisieux and Pont l'Evêque. Caen, the capital, is the seat of a court of appeal and the centre of an _académie_ (educational division). The department forms the diocese of Bayeux, in the ecclesiastical province of Rouen, and belongs to the region of the III. army-corps. The other principal towns are Falaise, Lisieux, Condé-sur-Noireau, Vire, Honfleur and Trouville (q.v.).

Amongst the great number of medieval churches which the department possesses, the fine Gothic church of St. Pierre-sur-Dives is second in importance only to those of Lisieux and Bayeux; that of Norrey, a good example of the Norman-Gothic style, and that of Tour-en-Bessin, in which Romanesque and Gothic architecture are mingled, are of great interest. Fontaine-Henri has a fine château of the 15th and 16th centuries.

CALVART, DENIS (1540-1619), Flemish painter, was born at Antwerp. After studying landscape-painting for some time in his native city he went to Bologna, where he perfected himself in the anatomy of the human form under Prospero Fontana, and so completely lost the mannerism of Flemish art that his paintings appear to be the work of an Italian. From Bologna he went to Rome, where he assisted Lorenzo Sabbatini (1533-1577) in his works for the papal palace, and devoted much of his time to copying and studying the works of Raphael. He ultimately returned to Bologna and founded a school, of which the greatest ornaments are Guido and Domenichino. His works are especially admired for the power of grouping and colouring which they display.

CALVARY, the conventional English rendering of the _calvaria_ of the Vulgate, the Latin version of the Greek _[Greek: kranion]_, both meaning "skull" and representing the Hebrew Golgotha, the name given to the scene of Christ's crucifixion. The term "a Calvary" is applied to a sculptured representation of the Crucifixion, either inside a church, or adjoining one in the open air. There are many examples of the latter in France, Italy and Spain. Among the most important are the Sacro Monte (1486) at Varallo in Piedmont, and those at Guimiliau (1581), Plougastel (1602), St Thegonnec (1610), and Pleyben near Quimper (1670), in Brittany, all in good preservation.

CALVÉ EMMA (1864- ), Spanish operatic soprano, was born at Madrid, and trained in Paris, making her first important appearance in opera at Brussels in 1882. She sang mainly in Paris for some years, but in 1892 was first engaged at Covent Garden, London, and at once became famous as the most vivid Carmen (in Bizet's opera) of the day.