THE ENCYCLOPÆDIA BRITANNICA

A DICTIONARY OF ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION

ELEVENTH EDITION

VOLUME IX SLICE II
Ehud to Electroscope

Articles in This Slice

EHUD, in the Bible, a “judge” who delivered Israel from the Moabites (Judg. iii. 12-30). He was sent from Ephraim to bear tribute to Eglon king of Moab, who had crossed over the Jordan and seized the district around Jericho. Being, like the Benjamites, left-handed (cf. xx. 16), he was able to conceal a dagger and strike down the king before his intentions were suspected. He locked Eglon in his chamber and escaped. The men from Mt Ephraim collected under his leadership and by seizing the fords of the Jordan were able to cut off the Moabites. He is called the son of Gera a Benjamite, but since both Ehud and Gera are tribal names (2 Sam. xvi. 5, 1 Chron. viii. 3, 5 sq.) it has been thought that this notice is not genuine. The tribe of Benjamin rarely appears in the old history of the Hebrews before the time of Saul. See further [Benjamin]; [Judges].

EIBENSTOCK, a town of Germany, in the kingdom of Saxony, near the Mulde, on the borders of Bohemia, 17 m. by rail S.S.E. of Zwickau. Pop. (1905) 7460. It is a principal seat of the tambour embroidery which was introduced in 1775 by Clara Angermann. It possesses chemical and tobacco manufactories, and tin and iron works. It has also a large cattle market. Eibenstock, together with Schwarzenberg, was acquired by purchase in 1533 by Saxony and was granted municipal rights in the following year.

EICHBERG, JULIUS (1824-1893), German musical composer, was born at Düsseldorf on the 13th of June 1824. When he was nineteen he entered the Brussels Conservatoire, where he took first prizes for violin-playing and composition. For eleven years he occupied the post of professor in the Conservatoire of Geneva. In 1857 he went to the United States, staying two years in New York and then proceeding to Boston, where he became director of the orchestra at the Boston Museum. In 1867 he founded the Boston Conservatory of Music. Eichberg published several educational works on music; and his four operettas, The Doctor of Alcantara, The Rose of Tyrol, The Two Cadis and A Night in Rome, were highly popular. He died in Boston on the 18th of January 1893.

EICHENDORFF, JOSEPH, FREIHERR VON (1788-1857), German poet and romance-writer, was born at Lubowitz, near Ratibor, in Silesia, on the 10th of March 1788. He studied law at Halle and Heidelberg from 1805 to 1808. After a visit to Paris he went to Vienna, where he resided until 1813, when he joined the Prussian army as a volunteer in the famous Lützow corps. When peace was concluded in 1815, he left the army, and in the following year he was appointed to a judicial office at Breslau. He subsequently held similar offices at Danzig, Königsberg and Berlin. Retiring from public service in 1844, he lived successively in Danzig, Vienna, Dresden and Berlin. He died at Neisse on the 26th of November 1857. Eichendorff was one of the most distinguished of the later members of the German romantic school. His genius was essentially lyrical. Thus he is most successful in his shorter romances and dramas, where constructive power is least called for. His first work, written in 1811, was a romance, Ahnung und Gegenwart (1815). This was followed at short intervals by several others, among which the foremost place is by general consent assigned to Aus dem Leben eines Taugenichts (1826), which has often been reprinted. Of his dramas may be mentioned Ezzelin von Romano (1828); and Der letzte Held von Marienburg (1830), both tragedies; and a comedy, Die Freier (1833). He also translated several of Calderon’s religious dramas (Geistliche Schauspiele, 1846). It is, however, through his lyrics (Gedichte, first collected 1837) that Eichendorff is best known; he is the greatest lyric poet of the romantic movement. No one has given more beautiful expression than he to the poetry of a wandering life; often, again, his lyrics are exquisite word pictures interpreting the mystic meaning of the moods of nature, as in Nachts, or the old-time mystery which yet haunts the twilight forests and feudal castles of Germany, as in the dramatic lyric Waldesgespräch or Auf einer Burg. Their language is simple and musical, which makes them very suitable for singing, and they have been often set, notably by Schubert and Schumann.

In the later years of his life Eichendorff published several works on subjects in literary history and criticism such as Über die ethische und religiöse Bedeutung der neuen romantischen Poesie in Deutschland (1847), Der deutsche Roman des 18. Jahrhunderts in seinem Verhältniss zum Christenthum (1851), and Geschichte der poetischen Litteratur Deutschlands (1856), but the value of these works is impaired by the author’s reactionary standpoint. An edition of his collected works in six volumes, appeared at Leipzig in 1870.

Eichendorff’s Sämtliche Werke appeared in 6 vols., 1864 (reprinted 1869-1870); his Sämtliche poetische Werke in 4 vols. (1883). The latest edition is that edited by R. von Gottschall in 4 vols. (1901). A good selection edited by M. Kaoch will be found in vol. 145 of Kürschner’s Deutsche Nationalliteratur (1893). Eichendorff’s critical writings were collected in 1866 under the title Vermischte Schriften (5 vols.). Cp. H. von Eichendorff’s biographical introduction to the Sämtliche Werke; also H. Keiter, Joseph von Eichendorff (Cologne, 1887); H.A. Krüger, Der junge Eichendorff (Oppeln, 1898).

EICHHORN, JOHANN GOTTFRIED (1752-1827), German theologian, was born at Dörrenzimmern, in the principality of Hohenlohe-Oehringen, on the 16th of October 1752. He was educated at the state school in Weikersheim, where his father was superintendent, at the gymnasium at Heilbronn and at the university of Göttingen (1770-1774), studying under J.D. Michaelis. In 1774 he received the rectorship of the gymnasium at Ohrdruf, in the duchy of Gotha, and in the following year was made professor of Oriental languages at Jena. On the death of Michaelis in 1788 he was elected professor ordinarius at Göttingen, where he lectured not only on Oriental languages and on the exegesis of the Old and New Testaments, but also on political history. His health was shattered in 1825, but he continued his lectures until attacked by fever on the 14th of June 1827. He died on the 27th of that month. Eichhorn has been called “the founder of modern Old Testament criticism.” He first properly recognized its scope and problems, and began many of its most important discussions. “My greatest trouble,” he says in the preface to the second edition of his Einleitung, “I had to bestow on a hitherto unworked field—on the investigation of the inner nature of the Old Testament with the help of the Higher Criticism (not a new name to any humanist).” His investigations led him to the conclusion that “most of the writings of the Hebrews have passed through several hands.” He took for granted that all the so-called supernatural facts relating to the Old and New Testaments were explicable on natural principles. He sought to judge them from the standpoint of the ancient world, and to account for them by the superstitious beliefs which were then generally in vogue. He did not perceive in the biblical books any religious ideas of much importance for modern times; they interested him merely historically and for the light they cast upon antiquity. He regarded many books of the Old Testament as spurious, questioned the genuineness of 2 Peter and Jude, denied the Pauline authorship of Timothy and Titus, and suggested that the canonical gospels were based upon various translations and editions of a primary Aramaic gospel. He did not appreciate as sufficiently as David Strauss and the Tübingen critics the difficulties which a natural theory has to surmount, nor did he support his conclusions by such elaborate discussions as they deemed necessary.

His principal works were—Geschichte des Ostindischen Handels vor Mohammed (Gotha, 1775); Allgemeine Bibliothek der biblischen Literatur (10 vols., Leipzig, 1787-1801); Einleitung in das Alte Testament (3 vols., Leipzig, 1780-1783); Einleitung in das Neue Testament (1804-1812); Einleitung in die apokryphischen Bücher des Alten Testaments (Gött., 1795); Commentarius in apocalypsin Joannis (2 vols., Gött., 1791); Die Hebr. Propheten (3 vols., Gött., 1816-1819); Allgemeine Geschichte der Cultur und Literatur des neuern Europa (2 vols., Gött., 1796-1799); Literärgeschichte (1st vol., Gött., 1799, 2nd ed. 1813, 2nd vol. 1814); Geschichte der Literatur von ihrem Anfange bis auf die neuesten Zeiten (5 vols., Gött., 1805-1812); Übersicht der Französischen Revolution (2 vols., Gött., 1797); Weltgeschichte (3rd ed., 5 vols., Gött., 1819-1820); Geschichte der drei letzten Jahrhunderte (3rd ed., 6 vols., Hanover, 1817-1818); Urgeschichte des erlauchten Hauses der Welfen (Hanover, 1817).

See R.W. Mackay, The Tübingen School and its Antecedents (1863), pp. 103 ff.; Otto Pfleiderer, Development of Theology (1890), p. 209; T.K. Cheyne, Founders of Old Testament Criticism (1893), pp. 13 ff.

EICHHORN, KARL FRIEDRICH (1781-1854), German jurist, son of the preceding, was born at Jena on the 20th of November 1781. He entered the university of Göttingen in 1797. In 1805 he obtained the professorship of law at Frankfort-on-Oder, holding it till 1811, when he accepted the same chair at Berlin. On the call to arms in 1813 he became a captain of horse, and received at the end of the war the decoration of the Iron Cross. In 1817 he was offered the chair of law at Göttingen, and, preferring it to the Berlin professorship, taught there with great success till ill-health compelled him to resign in 1828. His successor in the Berlin chair having died in 1832, he again entered on its duties, but resigned two years afterwards. In 1832 he also received an appointment in the ministry of foreign affairs, which, with his labours on many state committees and his legal researches and writings, occupied him till his death at Cologne on the 4th of July 1854. Eichhorn is regarded as one of the principal authorities on German constitutional law. His chief work is Deutsche Staats- und Rechtsgeschichte (Göttingen, 1808-1823, 5th ed. 1843-1844). In company with Savigny and J.F.L. Göschen he founded the Zeitschrift für geschichtliche Rechtswissenschaft. He was the author besides of Einleitung in das deutsche Privatrecht mit Einschluss des Lehnrechts (Gött., 1823) and the Grundsätze des Kirchenrechts der Katholischen und der Evangelischen Religionspartei in Deutschland, 2 Bde. (ib., 1831-1833).

See Schulte, Karl Friedrich Eichhorn, sein Leben und Wirken (1884).

EICHSTÄTT, a town and episcopal see of Germany, in the kingdom of Bavaria, in the deep and romantic valley of the Altmühl, 35 m. S. of Nuremberg, on the railway to Ingolstadt and Munich. Pop. (1905) 7701. The town, with its numerous spires and remains of medieval fortifications, is very picturesque. It has an Evangelical and seven Roman Catholic churches, among the latter the cathedral of St Wilibald (first bishop of Eichstätt),—with the tomb of the saint and numerous pictures and relics,—the church of St Walpurgis, sister of Wilibald, whose remains rest in the choir, and the Capuchin church, a copy of the Holy Sepulchre. Of its secular buildings the most noticeable are the town hall and the Leuchtenberg palace, once the residence of the prince bishops and later of the dukes of Leuchtenberg (now occupied by the court of justice of the district), with beautiful grounds. The Wilibaldsburg, built on a neighbouring hill in the 14th century by Bishop Bertold of Hohenzollern, was long the residence of the prince bishops of Eichstätt, and now contains an historical museum. There are an episcopal lyceum, a clerical seminary, a classical and a modern school, and numerous religious houses. The industries of the town include bootmaking, brewing and the production of lithographic stones.

Eichstätt (Lat. Aureatum or Rubilocus) was originally a Roman station which, after the foundation of the bishopric by Boniface in 745, developed into a considerable town, which was surrounded with walls in 908. The bishops of Eichstätt were princes of the Empire, subject to the spiritual jurisdiction of the archbishops of Mainz, and ruled over considerable territories in the Circle of Franconia. In 1802 the see was secularized and incorporated in Bavaria. In 1817 it was given, with the duchy of Leuchtenberg, as a mediatized domain under the Bavarian crown, by the king of Bavaria to his son-in-law Eugène de Beauharnais, ex-viceroy of Italy, henceforth styled duke of Leuchtenberg. In 1855 it reverted to the Bavarian crown.

EICHWALD, KARL EDUARD VON (1795-1876), Russian geologist and physician, was born at Mitau in Courland on the 4th of July 1795. He became doctor of medicine and professor of zoology in Kazañ in 1823; four years later professor of zoology and comparative anatomy at Vilna; in 1838 professor of zoology, mineralogy and medicine at St Petersburg; and finally professor of palaeontology in the institute of mines in that city. He travelled much in the Russian empire, and was a keen observer of its natural history and geology. He died at St Petersburg on the 10th of November 1876. His published works include Reise auf dem Caspischen Meere und in den Caucasus, 2 vols. (Stuttgart and Tübingen, 1834-1838); Die Urwelt Russlands (St Petersburg, 1840-1845); Lethaea Rossica, ou paléontologie de la Russie, 3 vols. (Stuttgart, 1852-1868), with Atlases.

EIDER, a river of Prussia, in the province of Schleswig-Holstein. It rises to the south of Kiel, in Lake Redder, flows first north, then west (with wide-sweeping curves), and after a course of 117 m. enters the North Sea at Tönning. It is navigable up to Rendsburg, and is embanked through the marshes across which it runs in its lower course. Since the reign of Charlemagne, the Eider (originally Ägyr Dör—Neptune’s gate) was known as Romani terminus imperii and was recognized as the boundary of the Empire in 1027 by the emperor Conrad II., the founder of the Salian dynasty. In the controversy arising out of the Schleswig-Holstein Question, which culminated in the war of Austria and Prussia against Denmark in 1864, the Eider gave its name to the “Eider Danes,” the intransigeant Danish party which maintained that Schleswig (Sonderjylland, South Jutland) was by nature and historical tradition an integral part of Denmark. The Eider Canal (Eider-Kanal), which was constructed between 1777 and 1784, leaves the Eider at the point where the river turns to the west and enters the Bay of Kiel at Holtenau. It was hampered by six sluices, but was used annually by some 4000 vessels, and until its conversion in 1887-1895 into the Kaiser Wilhelm Canal afforded the only direct connexion between the North Sea and the Baltic.

EIDER (Icelandic, Ædur), a large marine duck, the Somateria mollissima of ornithologists, famous for its down, which, from its extreme lightness and elasticity, is in great request for filling bed-coverlets. This bird generally frequents low rocky islets near the coast, and in Iceland and Norway has long been afforded every encouragement and protection, a fine being inflicted for killing it during the breeding-season, or even for firing a gun near its haunts, while artificial nesting-places are in many localities contrived for its further accommodation. From the care thus taken of it in those countries it has become exceedingly tame at its chief resorts, which are strictly regarded as property, and the taking of eggs or down from them, except by authorized persons, is severely punished by law. In appearance the eider is somewhat clumsy, though it flies fast and dives admirably. The female is of a dark reddish-brown colour barred with brownish-black. The adult male in spring is conspicuous by his pied plumage of velvet-black beneath, and white above: a patch of shining sea-green on his head is only seen on close inspection. This plumage he is considered not to acquire until his third year, being when young almost exactly like the female, and it is certain that the birds which have not attained their full dress remain in flocks by themselves without going to the breeding-stations. The nest is generally in some convenient corner among large stones, hollowed in the soil, and furnished with a few bits of dry grass, seaweed or heather. By the time that the full number of eggs (which rarely if ever exceeds five) is laid the down is added. Generally the eggs and down are taken at intervals of a few days by the owners of the “eider-fold,” and the birds are thus kept depositing both during the whole season; but some experience is needed to ensure the greatest profit from each commodity. Every duck is ultimately allowed to hatch an egg or two to keep up the stock, and the down of the last nest is gathered after the birds have left the spot. The story of the drake’s furnishing down, after the duck’s supply is exhausted is a fiction. He never goes near the nest. The eggs have a strong flavour, but are much relished by both Icelanders and Norwegians. In the Old World the eider breeds in suitable localities from Spitsbergen to the Farne Islands off the coast of Northumberland—where it is known as St Cuthbert’s duck. Its food consists of marine animals (molluscs and crustaceans), and hence the young are not easily reared in captivity. The eider of the New World differs somewhat, and has been described as a distinct species (S. dresseri). Though much diminished in numbers by persecution, it is still abundant on the coast of Newfoundland and thence northward. In Greenland also eiders are very plentiful, and it is supposed that three-fourths of the supply of down sent to Copenhagen comes from that country. The limits of the eider’s northern range are not known, but the Arctic expedition of 1875 did not meet with it after leaving the Danish settlements, and its place was taken by an allied species, the king-duck (S. spectabilis), a very beautiful bird which sometimes appears on the British coast. The female greatly resembles that of the eider, but the male has a black chevron on his chin and a bright orange prominence on his forehead, which last seems to have given the species its English name. On the west coast of North America the eider is represented by a species (S. v-nigrum) with a like chevron, but otherwise resembling the Atlantic bird. In the same waters two other fine species are also found (S. fischeri and S. stelleri), one of which (the latter) also inhabits the Arctic coast of Russia and East Finmark and has twice reached England. The Labrador duck (S. labradoria), now extinct, also belongs to this group.

(A. N.)

EIFEL, a district of Germany, in the Prussian Rhine Province, between the Rhine, the Moselle and the frontier of the grand duchy of Luxemburg. It is a hilly region, most elevated in the eastern part (Hohe Eifel), where there are several points from 2000 up to 2410 ft. above sea-level. In the west is the Schneifels or Schnee-Eifel; and the southern part, where the most picturesque scenery and chief geological interest is found, is called the Vorder Eifel.

The Eifel is an ancient massif of folded Devonian rocks upon the margins of which, near Hillesheim and towards Bitburg and Trier, rest unconformably the nearly undisturbed sandstones, marls and limestones of the Trias. On the southern border, at Wittlich, the terrestrial deposits of the Permian Rothliegende are also met with. The slates and sandstones of the Lower Devonian form by far the greater part of the region; but folded amongst these, in a series of troughs running from south-west to north-east lie the fossiliferous limestones of the Middle Devonian, and occasionally, as for example near Büdesheim, a few small patches of the Upper Devonian. Upon the ancient floor of folded Devonian strata stand numerous small volcanic cones, many of which, though long extinct, are still very perfect in form. The precise age of the eruptions is uncertain. The only sign of any remaining volcanic activity is the emission in many places of carbon dioxide and of heated waters. There is no historic or legendary record of any eruption, but nevertheless the eruptions must have continued to a very recent geological period. The lavas of Papenkaule are clearly posterior to the excavation of the valley of the Kyll, and an outflow of basalt has forced the Uess to seek a new course. The volcanic rocks occur both as tuffs and as lava-flows. They are chiefly leucite and nepheline rocks, such as leucitite, leucitophyre and nephelinite, but basalt and trachyte also occur. The leucite lavas of Niedermendig contain haüyne in abundance. The most extensive and continuous area of volcanic rocks is that surrounding the Laacher See and extending eastwards to Neuwied and Coblenz and even beyond the Rhine.

The numerous so-called crater-lakes or maare of the Eifel present several features of interest. They do not, as a rule, lie in true craters at the summit of volcanic cones, but rather in hollows which have been formed by explosions. The most remarkable group is that of Daun, where the three depressions of Gemünd, Weinfeld and Schalkenmehren have been hollowed out in the Lower Devonian strata. The first of these shows no sign of either lavas or scoriae, but volcanic rocks occur on the margins of the other two. The two largest lakes in the Eifel region, however, are the Laacher See in the hills west of Andernach on the Rhine, and the Pulvermaar S.E. of the Daun group, with its shores of peculiar volcanic sand, which also appears in its waters as a black powder (pulver).

EIFFEL TOWER. Erected for the exposition of 1889, the Eiffel Tower, in the Champ de Mars, Paris, is by far the highest artificial structure in the world, and its height of 300 metres (984 ft.) surpasses that of the obelisk at Washington by 429 ft., and that of St Paul’s cathedral by 580 ft. Its framework is composed essentially of four uprights, which rise from the corners of a square measuring 100 metres on the side; thus the area it covers at its base is nearly 2½ acres. These uprights are supported on huge piers of masonry and concrete, the foundations for which were carried down, by the aid of iron caissons and compressed air, to a depth of about 15 metres on the side next the Seine, and about 9 metres on the other side. At first they curve upwards at an angle of 54°; then they gradually become straighter, until they unite in a single shaft rather more than half-way up. The first platform, at a height of 57 metres, has an area of 5860 sq. yds., and is reached either by staircases or lifts. The next, accessible by lifts only, is 115 metres up, and has an area of 32 sq. yds; while the third, at 276, supports a pavilion capable of holding 800 persons. Nearly 25 metres higher up still is the lantern, with a gallery 5 metres in diameter. The work of building this structure, which is mainly composed of iron lattice-work, was begun on the 28th of January 1887, and the full height was reached on the 13th of March 1889. Besides being one of the sights of Paris, to which visitors resort in order to enjoy the extensive view that can be had from its higher galleries on a clear day, the tower is used to some extent for scientific and semi-scientific purposes; thus meteorological observations are carried on. The engineer under whose direction the tower was constructed was Alexandre Gustave Eiffel (born at Dijon on the 15th of December 1832), who had already had a wide experience in the construction of large metal bridges, and who designed the huge sluices for the Panama Canal, when it was under the French company.

EILDON HILLS, a group of three conical hills, of volcanic origin, in Roxburghshire, Scotland, 1 m. S. by E. of Melrose, about equidistant from Melrose and St Boswells stations on the North British railway. They were once known as Eldune—the Eldunum of Simeon of Durham (fl. 1130)—probably derived from the Gaelic aill, “rock,” and dun, “hill”; but the name is also said to be a corruption of the Cymric moeldun, “bald hill.” The northern peak is 1327 ft. high, the central 1385 ft. and the southern 1216 ft. Whether or not the Roman station of Trimontium was situated here is matter of controversy. According to General William Roy (1726-1790) Trimontium—so called, according to this theory, from the triple Eildon heights—was Old Melrose; other authorities incline to place the station on the northern shore of the Solway Firth. The Eildons have been the subject of much legendary lore. Michael Scot (1175-1234), acting as a confederate of the Evil One (so the fable runs) cleft Eildon Hill, then a single cone, into the three existing peaks. Another legend states that Arthur and his knights sleep in a vault beneath the Eildons. A third legend centres in Thomas of Erceldoune. The Eildon Tree Stone, a large moss-covered boulder, lying on the high road as it bends towards the west within 2 m. of Melrose, marks the spot where the Fairy Queen led him into her realms in the heart of the hills. Other places associated with this legend may still be identified. Huntly Banks, where “true Thomas” lay and watched the queen’s approach, is half a mile west of the Eildon Tree Stone, and on the west side of the hills is Bogle Burn, a streamlet that feeds the Tweed and probably derives its name from his ghostly visitor. Here, too, is Rhymer’s glen, although the name was invented by Sir Walter Scott, who added the dell to his Abbotsford estate. Bowden, to the south of the hills, was the birthplace of the poets Thomas Aird (1802-1876) and James Thomson, and its parish church contains the burial-place of the dukes of Roxburghe. Eildon Hall is a seat of the duke of Buccleuch.

EILENBURG, a town of Germany, in the Prussian province of Saxony, on an island formed by the Mulde, 31 m. E. from Halle, at the junction of the railways Halle-Cottbus and Leipzig-Eilenburg. Pop. (1905) 15,145. There are three churches, two Evangelical and one Roman Catholic. The industries of the town include the manufacture of chemicals, cloth, quilting, calico, cigars and agricultural implements, bleaching, dyeing, basket-making, carriage-building and trade in cattle. In the neighbourhood is the iron foundry of Erwinhof. Opposite the town, on the steep left bank of the Mulde, is the castle from which it derives its name, the original seat of the noble family of Eulenburg. This castle (Ilburg) is mentioned in records of the reigns of Henry the Fowler as an important outpost against the Sorbs and Wends. The town itself, originally called Mildenau, is of great antiquity. It is first mentioned as a town in 981, when it belonged to the house of Wettin and was the chief town of the East Mark. In 1386 it was incorporated in the margraviate of Meissen. In 1815 it passed to Prussia.

See Gundermann, Chronik der Stadt Eilenburg (Eilenburg, 1879).

EINBECK, or Eimbeck, a town of Germany, in the Prussian province of Hanover, on the Ilm, 50 m. by rail S. of Hanover. Pop. (1905) 8709. It is an old-fashioned town with many quaint wooden houses, notable among them the “Northeimhaus,” a beautiful specimen of medieval architecture. There are several churches, among them the Alexanderkirche, containing the tombs of the princes of Grubenhagen, and a synagogue. The schools include a Realgymnasium (i.e. predominantly for “modern” subjects), technical schools for the advanced study of machine-making, for weaving and for the textile industries, a preparatory training-college and a police school. The industries include brewing, weaving and the manufacture of cloth, carpets, tobacco, sugar, leather-grease, toys and roofing-felt.

Einbeck grew up originally round the monastery of St Alexander (founded 1080), famous for its relic of the True Blood. It is first recorded as a town in 1274, and in the 14th century was the seat of the princes of Grubenhagen, a branch of the ducal house of Brunswick. The town subsequently joined the Hanseatic League. In the 15th century it became famous for its beer (“Eimbecker,” whence the familiar “Bock”). In 1540 the Reformation was introduced by Duke Philip of Brunswick-Saltzderhelden (d. 1551), with the death of whose son Philip II. (1596) the Grubenhagen line became extinct. In 1626, during the Thirty Years’ War, Einbeck was taken by Pappenheim and in October 1641 by Piccolomini. In 1643 it was evacuated by the Imperialists. In 1761 its walls were razed by the French.

See H.L. Harland, Gesch. der Stadt Einbeck, 2 Bde. (Einbeck, 1854-1859; abridgment, ib. 1881).

EINDHOVEN, a town in the province of North Brabant, Holland, and a railway junction 8 m. by rail W. by S. of Helmond. Pop. (1900) 4730. Like Tilburg and Helmond it has developed in modern times into a flourishing industrial centre, having linen, woollen, cotton, tobacco and cigar, matches, &c., factories and several breweries.

EINHARD (c. 770-840), the friend and biographer of Charlemagne; he is also called Einhartus, Ainhardus or Heinhardus, in some of the early manuscripts. About the 10th century the name was altered into Agenardus, and then to Eginhardus, or Eginhartus, but, although these variations were largely used in the English and French languages, the form Einhardus, or Einhartus, is unquestionably the right one.

According to the statement of Walafrid Strabo, Einhard was born in the district which is watered by the river Main, and his birth has been fixed at about 770. His parents were of noble birth, and were probably named Einhart and Engilfrit; and their son was educated in the monastery of Fulda, where he was certainly residing in 788 and in 791. Owing to his intelligence and ability he was transferred, not later than 796, from Fulda to the palace of Charlemagne by abbot Baugulf; and he soon became very intimate with the king and his family, and undertook various important duties, one writer calling him domesticus palatii regalis. He was a member of the group of scholars who gathered around Charlemagne and was entrusted with the charge of the public buildings, receiving, according to a fashion then prevalent, the scriptural name of Bezaleel (Exodus xxxi. 2 and xxxv. 30-35) owing to his artistic skill. It has been supposed that he was responsible for the erection of the basilica at Aix-la-Chapelle, where he resided with the emperor, and the other buildings mentioned in chapter xvii. of his Vita Karoli Magni, but there is no express statement to this effect. In 806 Charlemagne sent him to Rome to obtain the signature of Pope Leo III. to a will which he had made concerning the division of his empire; and it was possibly owing to Einhard’s influence that in 813, after the death of his two elder sons, the emperor made his remaining son, Louis, a partner with himself in the imperial dignity. When Louis became sole emperor in 814 he retained his father’s minister in his former position; then in 817 made him tutor to his son, Lothair, afterwards the emperor Lothair I.; and showed him many other marks of favour. Einhard married Emma, or Imma, a sister of Bernharius, bishop of Worms, and a tradition of the 12th century represented this lady as a daughter of Charlemagne, and invented a romantic story with regard to the courtship which deserves to be noticed as it frequently appears in literature. Einhard is said to have visited the emperor’s daughter regularly and secretly, and on one occasion a fall of snow made it impossible for him to walk away without leaving footprints, which would lead to his detection. This risk, however, was obviated by the foresight of Emma, who carried her lover across the courtyard of the palace; a scene which was witnessed by Charlemagne, who next morning narrated the occurrence to his counsellors, and asked for their advice. Very severe punishments were suggested for the clandestine lover, but the emperor rewarded the devotion of the pair by consenting to their marriage. This story is, of course, improbable, and is further discredited by the fact that Einhard does not mention Emma among the number of Charlemagne’s children. Moreover, a similar story has been told of a daughter of the emperor Henry III. It is uncertain whether Einhard had any children. He addressed a letter to a person named Vussin, whom he calls fili and mi nate, but, as Vussin is not mentioned in documents in which his interests as Einhard’s son would have been concerned, it is possible that he was only a young man in whom he took a special interest. In January 815 the emperor Louis I. bestowed on Einhard and his wife the domains of Michelstadt and Mulinheim in the Odenwald, and in the charter conveying these lands he is called simply Einhardus, but, in a document dated the 2nd of June of the same year, he is referred to as abbot. After this time he is mentioned as head of several monasteries: St Peter, Mount Blandin and St Bavon at Ghent, St Servais at Maastricht, St Cloud near Paris, and Fontenelle near Rouen, and he also had charge of the church of St John the Baptist at Pavia.

During the quarrels which took place between Louis I. and his sons, in consequence of the emperor’s second marriage, Einhard’s efforts were directed to making peace, but after a time he grew tired of the troubles and intrigues of court life. In 818 he had given his estate at Michelstadt to the abbey of Lorsch, but he retained Mulinheim, where about 827 he founded an abbey and erected a church, to which he transported some relics of St Peter and St Marcellinus, which he had procured from Rome. To Mulinheim, which was afterwards called Seligenstadt, he finally retired in 830. His wife, who had been his constant helper, and whom he had not put away on becoming an abbot, died in 836, and after receiving a visit from the emperor, Einhard died on the 14th of March 840. He was buried at Seligenstadt, and his epitaph was written by Hrabanus Maurus. Einhard was a man of very short stature, a feature on which Alcuin wrote an epigram. Consequently he was called Nardulus, a diminutive form of Einhardus, and his great industry and activity caused him to be likened to an ant. He was also a man of learning and culture. Reaping the benefits of the revival of learning brought about by Charlemagne, he was on intimate terms with Alcuin, was well versed in Latin literature, and knew some Greek. His most famous work is his Vita Karoli Magni, to which a prologue was added by Walafrid Strabo. Written in imitation of the De vitis Caesarum of Suetonius, this is the best contemporary account of the life of Charlemagne, and could only have been written by one who was very intimate with the emperor and his court. It is, moreover, a work of some artistic merit, although not free from inaccuracies. It was written before 821, and having been very popular during the middle ages, was first printed at Cologne in 1521. G.H. Pertz collated more than sixty manuscripts for his edition of 1829, and others have since come to light. Other works by Einhard are: Epistolae, which are of considerable importance for the history of the times; Historia translationis beatorum Christi martyrum Marcellini et Petri, which gives a curious account of how the bones of these martyrs were stolen and conveyed to Seligenstadt, and what miracles they wrought; and De adoranda cruce, a treatise which has only recently come to light, and which has been published by E. Dümmler in the Neues Archiv der Gesellschaft für ältere deutsche Geschichtskunde, Band xi. (Hanover, 1886). It has been asserted that Einhard was the author of some of the Frankish annals, and especially of part of the annals of Lorsch (Annales Laurissenses majores), and part of the annals of Fulda (Annales Fuldenses). Much discussion has taken place on this question, and several of the most eminent of German historians, Ranke among them, have taken part therein, but no certain decision has been reached.

The literature on Einhard is very extensive, as nearly all those who deal with Charlemagne, early German and early French literature, treat of him. Editions of his works are by A. Teulet, Einhardi omnia quae extant opera (Paris, 1840-1843), with a French translation; P. Jaffé, in the Bibliotheca rerum Germanicarum, Band iv. (Berlin, 1867); G.H. Pertz in the Monumenta Germaniae historica, Bände i. and ii. (Hanover, 1826-1829), and J.P. Migne in the Patrologia Latina, tomes 97 and 104 (Paris, 1866). The Vita Karoli Magni, edited by G.H. Pertz and G. Waitz, has been published separately (Hanover, 1880). Among the various translations of the Vita may be mentioned an English one by W. Glaister (London, 1877) and a German one by O. Abel (Leipzig, 1893). For a complete bibliography of Einhard, see A. Potthast, Bibliotheca historica, pp. 394-397 (Berlin, 1896), and W. Wattenbach, Deutschlands Geschichtsquellen, Band i. (Berlin, 1904).

(A. W. H.*)

EINHORN, DAVID (1809-1879), leader of the Jewish reform movement in the United States of America, was born in Bavaria. He was a supporter of the principles of Abraham Geiger (q.v.), and while still in Germany advocated the introduction of prayers in the vernacular, the exclusion of nationalistic hopes from the synagogue service, and other ritual modifications. In 1855 he migrated to America, where he became the acknowledged leader of reform, and laid the foundation of the régime under which the mass of American Jews (excepting the newly arrived Russians) now worship. In 1858 he published his revised prayer book, which has formed the model for all subsequent revisions. In 1861 he strongly supported the anti-slavery party, and was forced to leave Baltimore where he then ministered. He continued his work first in Philadelphia and later in New York.

(I. A.)

EINSIEDELN, the most populous town in the Swiss canton of Schwyz. It is built on the right bank of the Alpbach (an affluent of the Sihl), at a height of 2908 ft. above the sea-level on a rather bare moorland, and by rail is 25 m. S.E. of Zürich, or by a round-about railway route about 38 m. north of Schwyz, with which it communicates directly over the Hacken Pass (4649 ft.) or the Holzegg Pass (4616 ft.). In 1900 the population was 8496, all (save 75) Romanists and all (save 111) German-speaking. The town is entirely dependent on the great Benedictine abbey that rises slightly above it to the east. Close to its present site Meinrad, a hermit, was murdered in 861 by two robbers, whose crime was made known by Meinrad’s two pet ravens. Early in the 10th century Benno, a hermit, rebuilt the holy man’s cell, but the abbey proper was not founded till about 934, the church having been consecrated (it is said by Christ Himself) in 948. In 1274 the dignity of a prince of the Holy Roman Empire was confirmed by the emperor to the reigning abbot. Originally under the protection of the counts of Rapperswil (to which town on the lake of Zürich the old pilgrims’ way still leads over the Etzel Pass, 3146 ft., with its chapel and inn), this position passed by marriage with their heiress in 1295 to the Laufenburg or cadet line of the Habsburgs, but from 1386 was permanently occupied by Schwyz. A black wooden image of the Virgin and the fame of St Meinrad caused the throngs of pilgrims to resort to Einsiedeln in the middle ages, and even now it is much frequented, particularly about the 14th of September. The existing buildings date from the 18th century only, while the treasury and the library still contain many precious objects, despite the sack by the French in 1798. There are now about 100 fully professed monks, who direct several educational institutions. The Black Virgin has a special chapel in the stately church. Zwingli was the parish priest of Einsiedeln 1516-1518 (before he became a Protestant), while near the town Paracelsus (1493-1541), the celebrated philosopher, was born.

See Father O. Ringholz, Geschichte d. fürstl. Benediktinerstiftes Einsiedeln, vol. i. (to 1526), (Einsiedeln, 1904).

(W. A. B. C.)

EISENACH, a town of Germany, second capital of the grand-duchy of Saxe-Weimar-Eisenach, lies at the north-west foot of the Thuringian forest, at the confluence of the Nesse and Hörsel, 32 m. by rail W. from Erfurt. Pop. (1905) 35,123. The town mainly consists of a long street, running from east to west. Off this are the market square, containing the grand-ducal palace, built in 1742, where the duchess Hélène of Orleans long resided, the town-hall, and the late Gothic St Georgenkirche; and the square on which stands the Nikolaikirche, a fine Romanesque building, built about 1150 and restored in 1887. Noteworthy are also the Klemda, a small castle dating from 1260; the Lutherhaus, in which the reformer stayed with the Cotta family in 1498; the house in which Sebastian Bach was born, and that (now a museum) in which Fritz Reuter lived (1863-1874). There are monuments to the two former in the town, while the resting-place of the latter in the cemetery is marked by a less pretentious memorial. Eisenach has a school of forestry, a school of design, a classical school (Gymnasium) and modern school (Realgymnasium), a deaf and dumb school, a teachers’ seminary, a theatre and a Wagner museum. The most important industries of the town are worsted-spinning, carriage and wagon building, and the making of colours and pottery. Among others are the manufacture of cigars, cement pipes, iron-ware and machines, alabaster ware, shoes, leather, &c., cabinet-making, brewing, granite quarrying and working, tile-making, and saw- and corn-milling.

The natural beauty of its surroundings and the extensive forests of the district have of late years attracted many summer residents. Magnificently situated on a precipitous hill, 600 ft. above the town to the south, is the historic Wartburg (q.v.), the ancient castle of the landgraves of Thuringia, famous as the scene of the contest of Minnesingers immortalized in Wagner’s Tannhäuser, and as the place where Luther, on his return from the diet of Worms in 1521, was kept in hiding and made his translation of the Bible. On a high rock adjacent to the Wartburg are the ruins of the castle of Mädelstein.

Eisenach (Isenacum) was founded in 1070 by Louis II. the Springer, landgrave of Thuringia, and its history during the middle ages was closely bound up with that of the Wartburg, the seat of the landgraves. The Klemda, mentioned above, was built by Sophia (d. 1284), daughter of the landgrave Louis IV., and wife of Duke Henry II. of Brabant, to defend the town against Henry III., margrave of Meissen, during the succession contest that followed the extinction of the male line of the Thuringian landgraves in 1247. The principality of Eisenach fell to the Saxon house of Wettin in 1440, and in the partition of 1485 formed part of the territories given to the Ernestine line. It was a separate Saxon duchy from 1596 to 1638, from 1640 to 1644, and again from 1662 to 1741, when it finally fell to Saxe-Weimar. The town of Eisenach, by reason of its associations, has been a favourite centre for the religious propaganda of Evangelical Germany, and since 1852 it has been the scene of the annual conference of the German Evangelical Church, known as the Eisenach conference.

See Trinius, Eisenach und Umgebung (Minden, 1900); and H.A. Daniel, Deutschland (Leipzig, 1895), and further references in U. Chevalier, “Répertoire des sources,” &c., Topo-bibliogr. (Montbéliard, 1894-1899), s.v.

EISENBERG (Isenberg), a town of Germany, in the duchy of Saxe-Altenburg, on a plateau between the rivers Saale and Elster, 20 m. S.W. from Zeitz, and connected with the railway Leipzig-Gera by a branch to Crossen. Pop. (1905) 8824. It possesses an old castle, several churches and monuments to Duke Christian of Saxe-Eisenberg (d. 1707), Bismarck, and the philosopher Karl Christian Friedrich Krause (q.v.). Its principal industries are weaving, and the manufacture of machines, ovens, furniture, pianos, porcelain and sausages.

See Back, Chronik der Sladt und des Amtes Eisenberg (Eisenb., 1843).

EISENERZ (“Iron ore”), a market-place and old mining town in Styria, Austria, 68 m. N.W. of Graz by rail. Pop. (1900) 6494. It is situated in a deep valley, dominated on the east by the Pfaffenstein (6140 ft.), on the west by the Kaiserschild (6830 ft.), and on the south by the Erzberg (5030 ft.). It has an interesting example of a medieval fortified church, a Gothic edifice founded by Rudolph of Habsburg in the 13th century and rebuilt in the 16th. The Erzberg or Ore Mountain furnishes such rich ore that it is quarried in the open air like stone, in the summer months. There is documentary evidence of the mines having been worked as far back as the 12th century. They afford employment to two or three thousand hands in summer and about half as many in winter, and yield some 800,000 tons of iron per annum. Eisenerz is connected with the mines by the Erzberg railway, a bold piece of engineering work, 14 m. long, constructed on the Abt’s rack-and-pinion system. It passes through some beautiful scenery, and descends to Vordernberg (pop. 3111), an important centre of the iron trade situated on the south side of the Erzberg. Eisenerz possesses, in addition, twenty-five furnaces, which produce iron, and particularly steel, of exceptional excellence. A few miles to the N.W. of Eisenerz lies the castle of Leopoldstein, and near it the beautiful Leopoldsteiner Lake. This lake, with its dark-green water, situated at an altitude of 2028 ft., and surrounded on all sides by high peaks, is not big, but is very deep, having a depth of 520 ft.

EISLEBEN (Lat. Islebia), a town of Germany, in the Prussian province of Saxony, 24 m. W. by N. from Halle, on the railway to Nordhausen and Cassel. Pop. (1905) 23,898. It is divided into an old and a new town (Altstadt and Neustadt). Among its principal buildings are the church of St Andrew (Andreaskirche), which contains numerous monuments of the counts of Mansfeld; the church of St Peter and St Paul (Peter-Paulkirche), containing the font in which Luther was baptized; the royal gymnasium (classical school), founded by Luther shortly before his death in 1546; and the hospital. Eisleben is celebrated as the place where Luther was born and died. The house in which he was born was burned in 1689, but was rebuilt in 1693 as a free school for orphans. This school fell into decay under the régime of the kingdom of Westphalia, but was restored in 1817 by King Frederick William III. of Prussia, who, in 1819, transferred it to a new building behind the old house. The house in which Luther died was restored towards the end of the 19th century, and his death chamber is still preserved. A bronze statue of Luther by Rudolf Siemering (1835-1905) was unveiled in 1883. Eisleben has long been the centre of an important mining district (Luther was a miner’s son), the principal products being silver and copper. It possesses smelting works and a school of mining.

The earliest record of Eisleben is dated 974. In 1045, at which time it belonged to the counts of Mansfeld, it received the right to hold markets, coin money, and levy tolls. From 1531 to 1710 it was the seat of the cadet line of the counts of Mansfeld-Eisleben. After the extinction of the main line of the counts of Mansfeld, Eisleben fell to Saxony, and, in the partition of Saxony by the congress of Vienna in 1815, was assigned to Prussia.

See G. Grössler, Urkundliche Gesch. Eislebens bis zum Ende des 12. Jahrhunderts (Halle, 1875); Chronicon Islebiense; Eisleben Stadtchronik aus den Jahren 1520-1738, edited from the original, with notes by Grössler and Sommer (Eisleben, 1882).

EISTEDDFOD (plural Eisteddfodau), the national bardic congress of Wales, the objects of which are to encourage bardism and music and the general literature of the Welsh, to maintain the Welsh language and customs of the country, and to foster and cultivate a patriotic spirit amongst the people. This institution, so peculiar to Wales, is of very ancient origin.[1] The term Eisteddfod, however, which means “a session” or “sitting,” was probably not applied to bardic congresses before the 12th century.

The Eisteddfod in its present character appears to have originated in the time of Owain ap Maxen Wledig, who at the close of the 4th century was elected to the chief sovereignty of the Britons on the departure of the Romans. It was at this time, or soon afterwards, that the laws and usages of the Gorsedd were codified and remodelled, and its motto of “Y gwir yn erbyn y byd” (The truth against the world) given to it. “Chairs” (with which the Eisteddfod as a national institution is now inseparably connected) were also established, or rather perhaps resuscitated, about the same time. The chair was a kind of convention where disciples were trained, and bardic matters discussed preparatory to the great Gorsedd, each chair having a distinctive motto. There are now existing four chairs in Wales,—namely, the “royal” chair of Powys, whose motto is “A laddo a leddir” (He that slayeth shall be slain); that of Gwent and Glamorgan, whose motto is “Duw a phob daioni” (God and all goodness); that of Dyfed, whose motto is “Calon wrth galon” (Heart with heart); and that of Gwynedd, or North Wales, whose motto is “Iesu,” or “O Iesu! na’d gamwaith” (Jesus, or Oh Jesus! suffer not iniquity).

The first Eisteddfod of which any account seems to have descended to us was one held on the banks of the Conway in the 6th century, under the auspices of Maelgwn Gwynedd, prince of North Wales. Maelgwn on this occasion, in order to prove the superiority of vocal song over instrumental music, is recorded to have offered a reward to such bards and minstrels as should swim over the Conway. There were several competitors, but on their arrival on the opposite shore the harpers found themselves unable to play owing to the injury their harps had sustained from the water, while the bards were in as good tune as ever. King Cadwaladr also presided at an Eisteddfod about the middle of the 7th century.

Griffith ap Cynan, prince of North Wales, who had been born in Ireland, brought with him from that country many Irish musicians, who greatly improved the music of Wales. During his long reign of 56 years he offered great encouragement to bards, harpers and minstrels, and framed a code of laws for their better regulation. He held an Eisteddfod about the beginning of the 12th century at Caerwys in Flintshire, “to which there repaired all the musicians of Wales, and some also from England and Scotland.” For many years afterwards the Eisteddfod appears to have been held triennially, and to have enforced the rigid observance of the enactments of Griffith ap Cynan. The places at which it was generally held were Aberffraw, formerly the royal seat of the princes of North Wales; Dynevor, the royal castle of the princes of South Wales; and Mathrafal, the royal palace of the princes of Powys: and in later times Caerwys in Flintshire received that honourable distinction, it having been the princely residence of Llewelyn the Last. Some of these Eisteddfodau were conducted in a style of great magnificence, under the patronage of the native princes. At Christmas 1107 Cadwgan, the son of Bleddyn ap Cynfyn, prince of Powys, held an Eisteddfod in Cardigan Castle, to which he invited the bards, harpers and minstrels, “the best to be found in all Wales”; and “he gave them chairs and subjects of emulation according to the custom of the feasts of King Arthur.” In 1176 Rhys ab Gruffydd, prince of South Wales, held an Eisteddfod in the same castle on a scale of still greater magnificence, it having been proclaimed, we are told, a year before it took place, “over Wales, England, Scotland, Ireland and many other countries.”

On the annexation of Wales to England, Edward I. deemed it politic to sanction the bardic Eisteddfod by his famous statute of Rhuddlan. In the reign of Edward III. Ifor Hael, a South Wales chieftain, held one at his mansion. Another was held in 1451, with the permission of the king, by Griffith ab Nicholas at Carmarthen, in princely style, where Dafydd ab Edmund, an eminent poet, signalized himself by his wonderful powers of versification in the Welsh metres, and whence “he carried home on his shoulders the silver chair” which he had fairly won. Several Eisteddfodau, were held, one at least by royal mandate, in the reign of Henry VII. In 1523 one was held at Caerwys before the chamberlain of North Wales and others, by virtue of a commission issued by Henry VIII. In the course of time, through relaxation of bardic discipline, the profession was assumed by unqualified persons, to the great detriment of the regular bards. Accordingly in 1567 Queen Elizabeth issued a commission for holding an Eisteddfod at Caerwys in the following year, which was duly held, when degrees were conferred on 55 candidates, including 20 harpers. From the terms of the royal proclamation we find that it was then customary to bestow “a silver harp” on the chief of the faculty of musicians, as it had been usual to reward the chief bard with “a silver chair.” This was the last Eisteddfod appointed by royal commission, but several others of some importance were held during the 16th and 17th centuries, under the patronage of the earl of Pembroke, Sir Richard Neville, and other influential persons. Amongst these the last of any particular note was one held in Bewper Castle, Glamorgan, by Sir Richard Basset in 1681.

During the succeeding 130 years Welsh nationality was at its lowest ebb, and no general Eisteddfod on a large scale appears to have been held until 1819, though several small ones were held under the auspices of the Gwyneddigion Society, established in 1771,—the most important being those at Corwen (1789), St Asaph (1790) and Caerwys (1798).

At the close of the Napoleonic wars, however, there was a general revival of Welsh nationality, and numerous Welsh literary societies were established throughout Wales, and in the principal English towns. A large Eisteddfod was held under distinguished patronage at Carmarthen in 1819, and from that time to the present they have been held (together with numerous local Eisteddfodau), almost without intermission, annually. The Eisteddfod at Llangollen in 1858 is memorable for its archaic character, and the attempts then made to revive the ancient ceremonies, and restore the ancient vestments of druids, bards and ovates.

To constitute a provincial Eisteddfod it is necessary that it should be proclaimed by a graduated bard of a Gorsedd a year and a day before it takes place. A local one may be held without such a proclamation. A provincial Eisteddfod generally lasts three, sometimes four days. A president and a conductor are appointed for each day. The proceedings commence with a Gorsedd meeting, opened with sound of trumpet and other ceremonies, at which candidates come forward and receive bardic degrees after satisfying the presiding bard as to their fitness. At the subsequent meetings the president gives a brief address; the bards follow with poetical addresses; adjudications are made, and prizes and medals with suitable devices are given to the successful competitors for poetical, musical and prose compositions, for the best choral and solo singing, and singing with the harp or “Pennillion singing”[2] as it is called, for the best playing on the harp or stringed or wind instruments, as well as occasionally for the best specimens of handicraft and art. In the evening of each day a concert is given, generally attended by very large numbers. The great day of the Eisteddfod is the “chair” day—usually the third or last day—the grand event of the Eisteddfod being the adjudication on the chair subject, and the chairing and investiture of the fortunate winner. This is the highest object of a Welsh bard’s ambition. The ceremony is an imposing one, and is performed with sound of trumpet. (See also the articles [Bard], [Celt]: Celtic Literature, and [Wales].)

(R. W.*)

[1] According to the Welsh Triads and other historical records, the Gorsedd or assembly (an essential part of the modern Eisteddfod, from which indeed the latter sprung) is as old at least as the time of Prydain the son of Ædd the Great, who lived many centuries before the Christian era. Upon the destruction of the political ascendancy of the Druids, the Gorsedd lost its political importance, though it seems to have long afterwards retained its institutional character as the medium for preserving the laws, doctrines and traditions of bardism.

[2] According to Jones’s Bardic Remains, “To sing ‘Pennillion’ with a Welsh harp is not so easily accomplished as may be imagined. The singer is obliged to follow the harper, who may change the tune, or perform variations ad libitum, whilst the vocalist must keep time, and end precisely with the strain. The singer does not commence with the harper, but takes the strain up at the second, third or fourth bar, as best suits the ‘pennill’ he intends to sing.... Those are considered the best singers who can adapt stanzas of various metres to one melody, and who are acquainted with the twenty-four measures according to the bardic laws and rules of composition.”

EJECTMENT (Lat. e, out, and jacere, to throw), in English law, an action for the recovery of the possession of land, together with damages for the wrongful withholding thereof. In the old classifications of actions, as real or personal, this was known as a mixed action, because its object was twofold, viz. to recover both the realty and personal damages. It should be noted that the term “ejectment” applies in law to distinct classes of proceedings—ejectments as between rival claimants to land, and ejectments as between those who hold, or have held, the relation of landlord and tenant. Under the Rules of the Supreme Court, actions in England for the recovery of land are commenced and proceed in the same manner as ordinary actions. But the historical interest attaching to the action of ejectment is so great as to render some account of it necessary.

The form of the action as it prevailed in the English courts down to the Common Law Procedure Act 1852 was a series of fictions, among the most remarkable to be found in the entire body of English law. A, the person claiming title to land, delivered to B, the person in possession, a declaration in ejectment in which C and D, fictitious persons, were plaintiff and defendant. C stated that A had devised the land to him for a term of years, and that he had been ousted by D. A notice signed by D informed B of the proceedings, and advised him to apply to be made defendant in D’s place, as he, D, having no title, did not intend to defend the suit. If B did not so apply, judgment was given against D, and possession of the lands was given to A. But if B did apply, the Court allowed him to defend the action only on condition that he admitted the three fictitious averments—the lease, the entry and the ouster—which, together with title, were the four things necessary to maintain an action of ejectment. This having been arranged the action proceeded, B being made defendant instead of D. The names used for the fictitious parties were John Doe, plaintiff, and Richard Roe, defendant, who was called “the casual ejector.” The explanation of these mysterious fictions is this. The writ de ejectione firmae was invented about the beginning of the reign of Edward III. as a remedy to a lessee for years who had been ousted of his term. It was a writ of trespass, and carried damages, but in the time of Henry VII., if not before that date, the courts of common law added thereto a species of remedy neither warranted by the original writ nor demanded by the declaration, viz. a judgment to recover so much of the term as was still to run, and a writ of possession thereupon. The next step was to extend the remedy—limited originally to leaseholds—to cases of disputed title to freeholds. This was done indirectly by the claimant entering on the land and there making a lease for a term of years to another person; for it was only a term that could be recovered by the action, and to create a term required actual possession in the granter. The lessee remained on the land, and the next person who entered even by chance was accounted an ejector of the lessee, who then served upon him a writ of trespass and ejectment. The case then went to trial as on a common action of trespass; and the claimant’s title, being the real foundation of the lessee’s right, was thus indirectly determined. These proceedings might take place without the knowledge of the person really in possession; and to prevent the abuse of the action a rule was laid down that the plaintiff in ejectment must give notice to the party in possession, who might then come in and defend the action. When the action came into general use as a mode of trying the title to freeholds, the actual entry, lease and ouster which were necessary to found the action were attended with much inconvenience, and accordingly Lord Chief Justice Rolle during the Protectorate (c. 1657) substituted for them the fictitious averments already described. The action of ejectment is now only a curiosity of legal history. Its fictitious suitors were swept away by the Common Law Procedure Act of 1852. A form of writ was prescribed, in which the person in possession of the disputed premises by name and all persons entitled to defend the possession were informed that the plaintiff claimed to be entitled to possession, and required to appear in court to defend the possession of the property or such part of it as they should think fit. In the form of the writ and in some other respects ejectment still differed from other actions. But, as already mentioned, it has now been assimilated (under the name of action for the recovery of lands) to ordinary actions by the Rules of the Supreme Court. It is commenced by writ of summons, and—subject to the rules as to summary judgments (v. inf.)—proceeds along the usual course of pleadings and trial to judgment; but is subject to one special rule, viz: that except by leave of the Court or a judge the only claims which may be joined with one for recovery of land are claims in respect of arrears of rent or double value for holding over, or mesne profits (i.e. the value of the land during the period of illegal possession), or damages for breach of a contract under which the premises are held or for any wrong or injury to the premises claimed (R.S.C., O. xviii. r. 2). These claims were formerly recoverable by an independent action.

With regard to actions for the recovery of land—apart from the relationship of landlord and tenant—the only point that need be noted is the presumption of law in favour of the actual possessor of the land in dispute. Where the action is brought by a landlord against his tenant, there is of course no presumption against the landlord’s title arising from the tenant’s possession. By the Common Law Procedure Act 1852 (ss. 210-212) special provision was made for the prompt recovery of demised premises where half a year’s rent was in arrear and the landlord was entitled to re-enter for non-payment. These provisions are still in force, but advantage is now more generally taken of the summary judgment procedure introduced by the Rules of the Supreme Court (Order 3, r. 6.). This procedure may be adopted when (a) the tenant’s term has expired, (b) or has been duly determined by notice to quit, or (c) has become liable to forfeiture for non-payment of rent, and applies not only to the tenant but to persons claiming under him. The writ is specially endorsed with the plaintiff’s claim to recover the land with or without rent or mesne profits, and summary judgment obtained if no substantial defence is disclosed. Where an action to recover land is brought against the tenant by a person claiming adversely to the landlord, the tenant is bound, under penalty of forfeiting the value of three years’ improved or rack rent of the premises, to give notice to the landlord in order that he may appear and defend his title. Actions for the recovery of land, other than land belonging to spiritual corporations and to the crown, are barred in 12 years (Real Property Limitation Acts 1833 (s. 29) and 1874 (s. 1). A landlord can recover possession in the county court (i.) by an action for the recovery of possession, where neither the value of the premises nor the rent exceeds £100 a year, and the tenant is holding over (County Courts Acts of 1888, s. 138, and 1903, s. 3); (ii.) by “an action of ejectment,” where (a) the value or rent of the premises does not exceed £100, (b) half a year’s rent is in arrear, and (c) no sufficient distress (see [Rent]) is to be found on the premises (Act of 1888, s. 139; Act of 1903, s. 3; County Court Rules 1903, Ord. v. rule 3). Where a tenant at a rent not exceeding £20 a year of premises at will, or for a term not exceeding 7 years, refuses nor neglects, on the determination or expiration of his interest, to deliver up possession, such possession may be recovered by proceedings before justices under the Small Tenements Recovery Act 1838, an enactment which has been extended to the recovery of allotments. Under the Distress for Rent Act 1737, and the Deserted Tenements Act 1817, a landlord can have himself put by the order of two justices into premises deserted by the tenant where half a year’s rent is owing and no sufficient distress can be found.

In Ireland, the practice with regard to the recovery of land is regulated by the Rules of the Supreme Court 1891, made under the Judicature (Ireland) Act 1877; and resembles that of England. Possession may be recovered summarily by a special indorsement of the writ, as in England; and there are analogous provisions with regard to the recovery of small tenements (see Land Act, 1860 ss. 84 and 89). The law with regard to the ejectment or eviction of tenants is consolidated by the Land Act 1860. (See ss. 52-66, 68-71, and further under [Landlord and Tenant].)

In Scotland, the recovery of land is effected by an action of “removing” or summary ejection. In the case of a tenant “warning” is necessary unless he is bound by his lease to remove without warning. In the case of possessors without title, or a title merely precarious, no warning is needed. A summary process of removing from small holdings is provided for by Sheriff Courts (Scotland) Acts of 1838 and 1851.

In the United States, the old English action of ejectment was adopted to a very limited extent, and where it was so adopted has often been superseded, as in Connecticut, by a single action for all cases of ouster, disseisin or ejectment. In this action, known as an action of disseisin or ejectment, both possession of the land and damages may be recovered. In some of the states a tenant against whom an action of ejectment is brought by a stranger is bound under a penalty, as in England, to give notice of the claim to the landlord in order that he may appear and defend his title.

In French law the landlord’s claim for rent is fairly secured by the hypothec, and by summary powers which exist for the seizure of the effects of defaulting tenants. Eviction or annulment of a lease can only be obtained through the judicial tribunals. The Civil Code deals with the position of a tenant in case of the sale of the property leased. If the lease is by authentic act (acte authentique) or has an ascertained date, the purchaser cannot evict the tenant unless a right to do so was reserved on the lease (art. 1743), and then only on payment of an indemnity (arts. 1744-1747). If the lease is not by authentic act, or has not an ascertained date, the purchaser is not liable for indemnity (art. 1750). The tenant of rural lands is bound to give the landlord notice of acts of usurpation (art. 1768). There are analogous provisions in the Civil Codes of Belgium (arts. 1743 et seq.), Holland (arts. 1613, 1614), Portugal (art. 1572); and see the German Civil Code (arts. 535 et seq.). In many of the colonies there are statutory provisions for the recovery of land or premises on the lines of English law (cf. Ontario, Rev. Stats. 1897, c. 170. ss. 19 et seq.; Manitoba, Rev. Stats. 1902, c. 1903). In others (e.g. New Zealand, Act. No. 55 of 1893, ss. 175-187; British Columbia, Revised Statutes, 1897, c. 182: Cyprus, Ord. 15 of 1895) there has been legislation similar to the Small Tenements Recovery Act 1838.

Authorities.—English Law: Cole on Ejectment; Digby, History of Real Property (3rd ed., London, 1884); Pollock and Maitland, History of English Law (Cambridge, 1895); Foa, Landlord and Tenant (4th ed., London, 1907); Fawcett, Landlord and Tenant (London, 1905). Irish Law: Nolan and Kane’s Statutes relating to the Law of Landlord and Tenant (5th ed., Dublin, 1898); Wylie’s Judicature Acts (Dublin, 1900). Scots Law: Hunter on Landlord and Tenant (4th ed., Edin., 1878); Erskine’s Principles (20th ed., Edin., 1903). American Law: Two Centuries’ Growth of American Law (New York and London, 1901); Bouvier’s Law Dictionary (Boston and London, 1897); Stimson, American Statute Law (Boston, 1886).

(A. W. R.)

EKATERINBURG, a town of Russia, in the government of Perm, 311 m. by rail S.E. of the town of Perm, on the Iset river, near the E. foot of the Ural Mountains, in 56° 49′ N. and 60° 35′ E., at an altitude of 870 ft. above sea-level. It is the most important town of the Urals. Pop. (1860) 19,830; (1897) 55,488. The streets are broad and regular, and several of the houses of palatial proportions. In 1834 Ekaterinburg was made the see of a suffragan bishop of the Orthodox Greek Church. There are two cathedrals—St Catherine’s, founded in 1758, and that of the Epiphany, in 1774—and a museum of natural history, opened in 1853. Ekaterinburg is the seat of the central mining administration of the Ural region, and has a chemical laboratory for the assay of gold, a mining school, the Ural Society of Naturalists, and a magnetic and meteorological observatory. Besides the government mint for copper coinage, which dates from 1735, the government engineering works, and the imperial factory for the cutting and polishing of malachite, jasper, marble, porphyry and other ornamental stones, the industrial establishments comprise candle, paper, soap and machinery works, flour and woollen mills, and tanneries. There is a lively trade in cattle, cereals, iron, woollen and silk goods, and colonial products; and two important fairs are held annually. Nearly forty gold and platinum mines, over thirty iron-works, and numerous other factories are scattered over the district, while wheels, travelling boxes, hardware, boots and so forth are extensively made in the villages. Ekaterinburg took its origin from the mining establishments founded by Peter the Great in 1721, and received its name in honour of his wife, Catherine I. Its development was greatly promoted in 1763 by the diversion of the Siberian highway from Verkhoturye to this place.

EKATERINODAR, a town of South Russia, chief town of the province of Kubañ, on the right bank of the river Kubañ, 85 m. E.N.E. of Novo-rossiysk on the railway to Rostov-on-Don, and in 45° 3′ N. and 38° 50′ E. It is badly built, on a swampy site exposed to the inundations of the river; and its houses, with few exceptions, are slight structures of wood and plaster. Founded by Catherine II. in 1794 on the site of an old town called Tmutarakan, as a small fort and Cossack settlement, its population grew from 9620 in 1860 to 65,697 in 1897. It has various technical schools, an experimental fruit-farm, a military hospital, and a natural history museum. A considerable trade is carried on, especially in cereals.

EKATERINOSLAV, a government of south Russia, having the governments of Poltava and Kharkov on the N., the territory of the Don Cossacks on the E., the Sea of Azov and Taurida on the S., and Kherson on the W. Area, 24,478 sq. m. Its surface is undulating steppe, sloping gently south and north, with a few hills reaching 1200 ft. in the N.E., where a slight swelling (the Don Hills) compels the Don to make a great curve eastwards. Another chain of hills, to which the eastward bend of the Dnieper is due, rises in the west. These hills have a crystalline core (granites, syenites and diorites), while the surface strata belong to the Carboniferous, Permian, Cretaceous and Tertiary formations. The government is rich in minerals, especially in coal—the mines lie in the middle of the Donets coalfield—iron ores, fireclay and rock-salt, and every year the mining output increases in quantity, especially of coal and iron. Granite, limestone, grindstone, slate, with graphite, manganese and mercury are found. The government is drained by the Dnieper, the Don and their tributaries (e.g. the Donets and Volchya) and by several affluents (e.g. the Kalmius) of the Sea of Azov. The soil is the fertile black earth, but the crops occasionally suffer from drought, the average annual rainfall being only 15 in. Forests are scarce. Pop. (1860) 1,138,750; (1897) 2,118,946, chiefly Little Russians, with Great Russians, Greeks (48,740), Germans (80,979), Rumanians and a few gypsies. Jews constitute 4.7% of the population. The estimated population in 1906 was 2,708,700.

Wheat and other cereals are extensively grown; other noteworthy crops are potatoes, tobacco and grapes. Nearly 40,000 persons find occupation in factories, the most important being iron-works and agricultural machinery works, though there are also tobacco, glass, soap and candle factories, potteries, tanneries and breweries. In the districts of Mariupol the making of agricultural implements and machinery is carried on extensively as a domestic industry in the villages. Bees are kept in very considerable numbers. Fishing employs many persons in the Don and the Dnieper. Cereals are exported in large quantities via the Dnieper, the Sevastopol railway, and the port of Mariupol. The chief towns of the eight districts, with their populations in 1897, are Ekaterinoslav (135,552 inhabitants in 1900), Alexandrovsk (28,434), Bakhmut (30,585), Mariupol (31,772), Novomoskovsk (12,862), Pavlograd (17,188), Slavyanoserbsk (3120), and Verkhne-dnyeprovsk (11,607).

EKATERINOSLAV, a town of Russia, capital of the government of the same name, on the right bank of the Dnieper above the rapids, 673 m. by rail S.S.W. of Moscow, in 48° 21′ N. and 35° 4′ E., at an altitude of 210 ft. Pop. (1861) 18,881, without suburbs; (1900) 135,552. If the suburb of Novyikoindak be included, the town extends for upwards of 4 m. along the river. The oldest part lies very low and is much exposed to floods. Contiguous to the towns on the N.W. is the royal village of Novyimaidani or the New Factories. The bishop’s palace, mining academy, archaeological museum and library are the principal public buildings. The house now occupied by the Nobles Club was formerly inhabited by the author and statesman Potemkin. Ekaterinoslav is a rapidly growing city, with a number of technical schools, and is an important depot for timber floated down the Dnieper, and also for cereals. Its iron-works, flour-mills and agricultural machinery works give occupation to over 5000 persons. In fact since 1895 the city has become the centre of numerous Franco-Belgian industrial undertakings. In addition to the branches just mentioned, there are tobacco factories and breweries. Considerable trade is carried on in cattle, cereals, horses and wool, there being three annual fairs. On the site of the city there formerly stood the Polish castle of Koindak, built in 1635, and destroyed by the Cossacks. The existing city was founded by Potemkin in 1786, and in the following year Catherine II. laid the foundation-stone of the cathedral, though it was not actually built until 1830-1835. On the south side of it is a bronze statue of the empress, put up in 1846. Paul I. changed the name of the city to Novo-rossiysk, but the original name was restored in 1802.

EKHOF, KONRAD (1720-1778), German actor, was born in Hamburg on the 12th of August 1720. In 1739 he became a member of Johann Friedrich Schönemann’s (1704-1782) company in Lüneburg, and made his first appearance there on the 15th of January 1740 as Xiphares in Racine’s Mithridate. From 1751 the Schönemann company performed mainly in Hamburg and at Schwerin, where Duke Christian Louis II. of Mecklenburg-Schwerin made them comedians to the court. During this period Ekhof founded a theatrical academy, which, though short-lived, was of great importance in helping to raise the standard of German acting and the status of German actors. In 1757 Ekhof left Schönemann to join Franz Schuch’s company at Danzig; but he soon returned to Hamburg, where, in conjunction with two other actors, he succeeded Schönemann in the direction of the company. He resigned this position, however, in favour of H.G. Koch, with whom he acted until 1764, when he joined K.E. Ackermann’s company. In 1767 was founded the National Theatre at Hamburg, made famous by Lessing’s Hamburgische Dramaturgie, and Ekhof was the leading member of the company. After the failure of the enterprise Ekhof was for a time in Weimar, and ultimately became co-director of the new court theatre at Gotha. This, the first permanently established theatre in Germany, was opened on the 2nd of October 1775. Ekhof’s reputation was now at its height; Goethe called him the only German tragic actor; and in 1777 he acted with Goethe and Duke Charles Augustus at a private performance at Weimar, dining afterwards with the poet at the ducal table. He died on the 16th of June 1778. His versatility may be judged from the fact that in the comedies of Goldoni and Molière he was no less successful than in the tragedies of Lessing and Shakespeare. He was regarded by his contemporaries as an unsurpassed exponent of naturalness on the stage; and in this respect he has been not unfairly compared with Garrick. His fame, however, was rapidly eclipsed by that of Friedrich U.L. Schröder. His literary efforts were chiefly confined to translations from French authors.

See H. Uhde, biography of Ekhof in vol. iv. of Der neue Plutarch (1876), and J. Rüschner, K. Ekhofs Leben und Wirken (1872). Also H. Devrient, J.F. Schönemann und seine Schauspielergesellschaft (1895).

EKRON (better, as in the Septuagint and Josephus, Accaron, Ἀκκαρών), a royal city of the Philistines commonly identified with the modern Syrian village of ‘Aḳir, 5 m. from Ramleh, on the southern slope of a low ridge separating the plain of Philistia from Sharon. It lay inland and off the main line of traffic. Though included by the Israelites within the limits of the tribe of Judah, and mentioned in Judges xix. as one of the cities of Dan, it was in Philistine possession in the days of Samuel, and apparently maintained its independence. According to the narrative of the Hebrew text, here differing from the Greek text and Josephus (which read Askelon), it was the last town to which the ark was transferred before its restoration to the Israelites. Its maintenance of a sanctuary of Baal Zebub is mentioned in 2 Kings i. From Assyrian inscriptions it has been gathered that Padi, king of Ekron, was for a time the vassal of Hezekiah of Judah, but regained his independence when the latter was hard pressed by Sennacherib. A notice of its history in 147 B.C. is found in 1 Macc. x. 89; after the fall of Jerusalem A.D. 70 it was settled by Jews. At the time of the crusades it was still a large village. Recently a Jewish agricultural colony has been settled there. The houses are built of mud, and in the absence of visible remains of antiquity, the identification of the site is questionable. The neighbourhood is fertile.

(R. A. S. M.)

ELABUGA, a town of Russia, in the government of Vyatka, on the Kama river, 201 m. by steamboat down the Volga from Kazan and then up the Kama. It has flour-mills, and carries on a brisk trade in exporting corn. Pop. (1897) 9776.

The famous Ananiynskiy Mogilnik (burial-place) is on the right bank of the Kama, 3 m. above the town. It was discovered in 1858, was excavated by Alabin, Lerch and Nevostruyev, and has since supplied extremely valuable collections belonging to the Stone, Bronze and Iron Ages. It consisted of a mound, about 500 ft. in circumference, adorned with decorated stones (which have disappeared), and contained an inner wall, 65 ft. in circumference, made of uncemented stone flags. Nearly fifty skeletons were discovered, mostly lying upon charred logs, surrounded with cinerary urns filled with partially burned bones. A great variety of bronze decorations and glazed clay pearls were strewn round the skeletons. The knives, daggers and arrowpoints are of slate, bronze and iron, the last two being very rough imitations of stone implements. One of the flags bore the image of a man, without moustaches or beard, dressed in a costume and helmet recalling those of the Circassians.

ELAM, the name given in the Bible to the province of Persia called Susiana by the classical geographers, from Susa or Shushan its capital. In one passage, however (Ezra iv. 9), it is confined to Elymais, the north-western part of the province, and its inhabitants distinguished from those of Shushan, which elsewhere (Dan. viii. 2) is placed in Elam. Strabo (xv. 3. 12, &c.) makes Susiana a part of Persia proper, but a comparison of his account with those of Ptolemy (vi. 3. 1, &c.) and other writers would limit it to the mountainous district to the east of Babylonia, lying between the Oroatis and the Tigris, and stretching from India to the Persian Gulf. Along with this mountainous district went a fertile low tract of country on the western side, which also included the marshes at the mouths of the Euphrates and Tigris and the north-eastern coast land of the Gulf. This low tract, though producing large quantities of grain, was intensely hot in summer; the high regions, however, were cool and well watered.

The whole country was occupied by a variety of tribes, speaking agglutinative dialects for the most part, though the western districts were occupied by Semites. Strabo (xi. 13. 3, 6), quoting from Nearchus, seems to include the Susians under the Elymaeans, whom he associates with the Uxii, and places on the frontiers of Persia and Susa; but Pliny more correctly makes the Eulaeus the boundary between Susiana and Elymais (N.H. vi. 29-31). The Uxii are described as a robber tribe in the mountains adjacent to Media, and their name is apparently to be identified with the title given to the whole of Susiana in the Persian cuneiform inscriptions, Uwaja, i.e. “Aborigines.” Uwaja is probably the origin of the modern Khuzistan, though Mordtmann would derive the latter from

“a sugar-reed.” Immediately bordering on the Persians were the Amardians or Mardians, as well as the people of Khapirti (Khatamti, according to Scheil), the name given to Susiana in the Neo-Susian texts. Khapirti appears as Apir in the inscriptions of Mal-Amir, which fix the locality of the district. Passing over the Messabatae, who inhabited a valley which may perhaps be the modern Māh-Sabadan, as well as the level district of Yamutbal or Yatbur which separated Elam from Babylonia, and the smaller districts of Characene, Cabandene, Corbiana and Gabiene mentioned by classical authors, we come to the fourth principal tribe of Susiana, the Cissii (Aesch. Pers. 16; Strabo xv. 3. 2) or Cossaei (Strabo xi. 5. 6, xvi. 11. 17; Arr. Ind. 40; Polyb. v. 54, &c.), the Kassi of the cuneiform inscriptions. So important were they, that the whole of Susiana was sometimes called Cissia after them, as by Herodotus (iii. 91, v. 49, &c.). In fact Susiana was only a late name for the country, dating from the time when Susa had been made a capital of the Persian empire. In the Sumerian texts of Babylonia it was called Numma, “the Highlands,” of which Elamtu or Elamu, “Elam,” was the Semitic translation. Apart from Susa, the most important part of the country was Anzan (Anshan, contracted Assan), where the native population maintained itself unaffected by Semitic intrusion. The exact position of Anzan is still disputed, but it probably included originally the site of Susa and was distinguished from it only when Susa became the seat of a Semitic government. In the lexical tablets Anzan is given as the equivalent of Elamtu, and the native kings entitle themselves kings of “Anzan and Susa,” as well as “princes of the Khapirti.”

The principal mountains of Elam were on the north, called Charbanus and Cambalidus by Pliny (vi. 27, 31), and belonging to the Parachoathras chain. There were numerous rivers flowing into either the Tigris or the Persian Gulf. The most important were the Ulai or Eulaeus (Kūran) with its tributary the Pasitigris, the Choaspes (Kerkhah), the Coprates (river of Diz called Ititē in the inscriptions), the Hedyphon or Hedypnus (Jerrāhi), and the Croatis (Hindyan), besides the monumental Surappi and Ukni, perhaps to be identified with the Hedyphon and Oroatis, which fell into the sea in the marshy region at the mouth of the Tigris. Shushan or Susa, the capital now marked by the mounds of Shush, stood near the junction of the Choaspes and Eulaeus (see [Susa]); and Badaca, Madaktu in the inscriptions, lay between the Shapur and the river of Diz. Among the other chief cities mentioned in the inscriptions may be named Naditu, Khaltemas, Din-sar, Bubilu, Bit-imbi, Khidalu and Nagitu on the sea-coast. Here, in fact, lay some of the oldest and wealthiest towns, the sites of which have, however, been removed inland by the silting up of the shore. J. de Morgan’s excavations at Susa have thrown a flood of light on the early history of Elam and its relations to Babylon. The earliest settlement there goes back to neolithic times, but it was already a fortified city when Elam was conquered by Sargon of Akkad (3800 B.C.) and Susa became the seat of a Babylonian viceroy. From this time onward for many centuries it continued under Semitic suzerainty, its high-priests, also called “Chief Envoys of Elam, Sippara and Susa,” bearing sometimes Semitic, sometimes native “Anzanite” names. One of the kings of the dynasty of Ur built at Susa. Before the rise of the First Dynasty of Babylon, however, Elam had recovered its independence, and in 2280 B.C. the Elamite king Kutur-Nakhkhunte made a raid in Babylonia and carried away from Erech the image of the goddess Nanā. The monuments of many of his successors have been discovered by de Morgan and their inscriptions deciphered by v. Scheil. One of them was defeated by Ammi-zadoq of Babylonia (c. 2100 B.C.); another would have been the Chedor-laomer (Kutur-Lagamar) of Genesis xiv. One of the greatest builders among them was Untas-Gal (the pronunciation of the second element in the name is uncertain). About 1330 B.C. Khurba-tila was captured by Kuri-galzu III., the Kassite king of Babylonia, but a later prince Kidin-Khutrutas avenged his defeat, and Sutruk-Nakhkhunte (1220 B.C.) carried fire and sword through Babylonia, slew its king Zamama-sum-iddin and carried away a stela of Naram-Sin and the famous code of laws of Khammurabi from Sippara, as well as a stela of Manistusu from Akkuttum or Akkad. He also conquered the land of Asnunnak and carried off from Padan a stela belonging to a refugee from Malatia. He was succeeded by his son who was followed on the throne by his brother, one of the great builders of Elam. In 750 B.C. Umbadara was king of Elam; Khumban-igas was his successor in 742 B.C. In 720 B.C. the latter prince met the Assyrians under Sargon at Dur-ili in Yamutbal, and though Sargon claims a victory the result was that Babylonia recovered its independence under Merodach-baladan and the Assyrian forces were driven north. From this time forward it was against Assyria instead of Babylonia that Elam found itself compelled to exert its strength, and Elamite policy was directed towards fomenting revolt in Babylonia and assisting the Babylonians in their struggle with Assyria. In 716 B.C. Khumban-igas died and was followed by his nephew, Sutruk-Nakhkhunte. He failed to make head against the Assyrians; the frontier cities were taken by Sargon and Merodach-baladan was left to his fate. A few years later (704 B.C.) the combined forces of Elam and Babylonia were overthrown at Kis, and in the following year the Kassites were reduced to subjection. The Elamite king was dethroned and imprisoned in 700 B.C. by his brother Khallusu, who six years later marched into Babylonia, captured the son of Sennacherib, whom his father had placed there as king, and raised a nominee of his own, Nergal-yusezib, to the throne. Khallusu was murdered in 694 B.C., after seeing the maritime part of his dominions invaded by the Assyrians. His successor Kudur-Nakhkhunte invaded Babylonia; he was repulsed, however, by Sennacherib, 34 of his cities were destroyed, and he himself fled from Madaktu to Khidalu. The result was a revolt in which he was killed after a reign of ten months. His brother Umman-menan at once collected allies and prepared for resistance to the Assyrians. But the terrible defeat at Khalulē broke his power; he was attacked by paralysis shortly afterwards, and Khumba-Khaldas II. followed him on the throne (689 B.C.). The new king endeavoured to gain Assyrian favour by putting to death the son of Merodach-baladan, but was himself murdered by his brothers Urtaki and Teumman (681 B.C.), the first of whom seized the crown. On his death Teumman succeeded and almost immediately provoked a quarrel with Assur-bani-pal by demanding the surrender of his nephews who had taken refuge at the Assyrian court. The Assyrians pursued the Elamite army to Susa, where a battle was fought on the banks of the Eulaeus, in which the Elamites were defeated, Teumman captured and slain, and Umman-igas, the son of Urtaki, made king, his younger brother Tammaritu being given the district of Khidalu. Umman-igas afterwards assisted in the revolt of Babylonia under Samas-sum-yukin, but his nephew, a second Tammaritu, raised a rebellion against him, defeated him in battle, cut off his head and seized the crown. Tammaritu marched to Babylonia; while there, his officer Inda-bigas made himself master of Susa and drove Tammaritu to the coast whence he fled to Assur-bani-pal. Inda-bigas was himself overthrown and slain by a new pretender, Khumba-Khaldas III., who was opposed, however, by three other rivals, two of whom maintained themselves in the mountains until the Assyrian conquest of the country, when Tammaritu was first restored and then imprisoned, Elam being utterly devastated. The return of Khumba-Khaldas led to a fresh Assyrian invasion; the Elamite king fled from Madaktu to Dur-undasi; Susa and other cities were taken, and the Elamite army almost exterminated on the banks of the Ititē. The whole country was reduced to a desert, Susa was plundered and razed to the ground, the royal sepulchres were desecrated, and the images of the gods and of 32 kings “in silver, gold, bronze and alabaster,” were carried away. All this must have happened about 640 B.C. After the fall of the Assyrian empire Elam was occupied by the Persian Teispes, the forefather of Cyrus, who, accordingly, like his immediate successors, is called in the inscriptions “king of Anzan.” Susa once more became a capital, and on the establishment of the Persian empire remained one of the three seats of government, its language, the Neo-Susian, ranking with the Persian of Persepolis and the Semitic of Babylon as an official tongue. In the reign of Darius, however, the Susianians attempted to revolt, first under Assina or Atrina, the son of Umbadara, and later under Martiya, the son of Issainsakria, who called himself Immanes; but they gradually became completely Aryanized, and their agglutinative dialects were supplanted by the Aryan Persian from the south-east.

Elam, “the land of the cedar-forest,” with its enchanted trees, figured largely in Babylonian mythology, and one of the adventures of the hero Gilgamesh was the destruction of the tyrant Khumbaba who dwelt in the midst of it. A list of the Elamite deities is given by Assur-bani-pal; at the head of them was In-Susinak, “the lord of the Susians,”—a title which went back to the age of Babylonian suzerainty,—whose image and oracle were hidden from the eyes of the profane. Nakhkhunte, according to Scheil, was the Sun-goddess, and Lagamar, whose name enters into that of Chedor-laomer, was borrowed from Semitic Babylonia.

See W.K. Loftus, Chaldaea and Susiana (1857); A. Billerbeck, Susa (1893); J. de Morgan, Mémoires de la Délégation en Perse (9 vols., 1899-1906).

(A. H. S.)

ELAND (= elk), the Dutch name for the largest of the South African antelopes (Taurotragus oryx), a species near akin to the kudu, but with horns present in both sexes, and their spiral much closer, being in fact screw-like instead of corkscrew-like. There is also a large dewlap, while old bulls have a thick forelock. In the typical southern form the body-colour is wholly pale fawn, but north of the Orange river the body is marked by narrow vertical white lines, this race being known as T. oryx livingstonei. In Senegambia the genus is represented by T. derbianus, a much larger animal, with a dark neck; while in the Bahr-el-Ghazal district there is a gigantic local race of this species (T. derbianus giganteus).

(R. L.*)

ELASTICITY. 1. Elasticity is the property of recovery of an original size or shape. A body of which the size, or shape, or both size and shape, have been altered by the application of forces may, and generally does, tend to return to its previous size and shape when the forces cease to act. Bodies which exhibit this tendency are said to be elastic (from Greek, ἐλαύνειν, to drive). All bodies are more or less elastic as regards size; and all solid bodies are more or less elastic as regards shape. For example: gas contained in a vessel, which is closed by a piston, can be compressed by additional pressure applied to the piston; but, when the additional pressure is removed, the gas expands and drives the piston outwards. For a second example: a steel bar hanging vertically, and loaded with one ton for each square inch of its sectional area, will have its length increased by about seven one-hundred-thousandths of itself, and its sectional area diminished by about half as much; and it will spring back to its original length and sectional area when the load is gradually removed. Such changes of size and shape in bodies subjected to forces, and the recovery of the original size and shape when the forces cease to act, become conspicuous when the bodies have the forms of thin wires or planks; and these properties of bodies in such forms are utilized in the construction of spring balances, carriage springs, buffers and so on.

It is a familiar fact that the hair-spring of a watch can be coiled and uncoiled millions of times a year for several years without losing its elasticity; yet the same spring can have its shape permanently altered by forces which are much greater than those to which it is subjected in the motion of the watch. The incompleteness of the recovery from the effects of great forces is as important a fact as the practical completeness of the recovery from the effects of comparatively small forces. The fact is referred to in the distinction between “perfect” and “imperfect” elasticity; and the limitation which must be imposed upon the forces in order that the elasticity may be perfect leads to the investigation of “limits of elasticity” (see §§ 31, 32 below). Steel pianoforte wire is perfectly elastic within rather wide limits, glass within rather narrow limits; building stone, cement and cast iron appear not to be perfectly elastic within any limits, however narrow. When the limits of elasticity are not exceeded no injury is done to a material or structure by the action of the forces. The strength or weakness of a material, and the safety or insecurity of a structure, are thus closely related to the elasticity of the material and to the change of size or shape of the structure when subjected to forces. The “science of elasticity” is occupied with the more abstract side of this relation, viz. with the effects that are produced in a body of definite size, shape and constitution by definite forces; the “science of the strength of materials” is occupied with the more concrete side, viz. with the application of the results obtained in the science of elasticity to practical questions of strength and safety (see [Strength of Materials]).

2. Stress.—Every body that we know anything about is always under the action of forces. Every body upon which we can experiment is subject to the force of gravity, and must, for the purpose of experiment, be supported by other forces. Such forces are usually applied by way of pressure upon a portion of the surface of the body; and such pressure is exerted by another body in contact with the first. The supported body exerts an equal and opposite pressure upon the supporting body across the portion of surface which is common to the two. The same thing is true of two portions of the same body. If, for example, we consider the two portions into which a body is divided by a (geometrical) horizontal plane, we conclude that the lower portion supports the upper portion by pressure across the plane, and the upper portion presses downwards upon the lower portion with an equal pressure. The pressure is still exerted when the plane is not horizontal, and its direction may be obliquely inclined to, or tangential to, the plane. A more precise meaning is given to “pressure” below. It is important to distinguish between the two classes of forces: forces such as the force of gravity, which act all through a body, and forces such as pressure applied over a surface. The former are named “body forces” or “volume forces,” and the latter “surface tractions.” The action between two portions of a body separated by a geometrical surface is of the nature of surface traction. Body forces are ultimately, when the volumes upon which they act are small enough, proportional to the volumes; surface tractions, on the other hand, are ultimately, when the surfaces across which they act are small enough, proportional to these surfaces. Surface tractions are always exerted by one body upon another, or by one part of a body upon another part, across a surface of contact; and a surface traction is always to be regarded as one aspect of a “stress,” that is to say of a pair of equal and opposite forces; for an equal traction is always exerted by the second body, or part, upon the first across the surface.

3. The proper method of estimating and specifying stress is a matter of importance, and its character is necessarily mathematical. The magnitudes of the surface tractions which compose a stress are estimated as so much force (in dynes or tons) per unit of area (per sq. cm. or per sq. in.). The traction across an assigned plane at an assigned point is measured by the mathematical limit of the fraction F/S, where F denotes the numerical measure of the force exerted across a small portion of the plane containing the point, and S denotes the numerical measure of the area of this portion, and the limit is taken by diminishing S indefinitely. The traction may act as “tension,” as it does in the case of a horizontal section of a bar supported at its upper end and hanging vertically, or as “pressure,” as it does in the case of a horizontal section of a block resting on a horizontal plane, or again it may act obliquely or even tangentially to the separating plane. Normal tractions are reckoned as positive when they are tensions, negative when they are pressures. Tangential tractions are often called “shears” (see § 7 below). Oblique tractions can always be resolved, by the vector law, into normal and tangential tractions. In a fluid at rest the traction across any plane at any point is normal to the plane, and acts as pressure. For the complete specification of the “state of stress” at any point of a body, we should require to know the normal and tangential components of the traction across every plane drawn through the point. Fortunately this requirement can be very much simplified (see §§ 6, 7 below).

4. In general let ν denote the direction of the normal drawn in a specified sense to a plane drawn through a point O of a body; and let Tν denote the traction exerted across the plane, at the point O, by the portion of the body towards which ν is drawn upon the remaining portion. Then Tν is a vector quantity, which has a definite magnitude (estimated as above by the limit of a fraction of the form F/S) and a definite direction. It can be specified completely by its components Xν, Yν, Zν, referred to fixed rectangular axes of x, y, z. When the direction of ν is that of the axis of x, in the positive sense, the components are denoted by Xx, Yx, Zx; and a similar notation is used when the direction of ν is that of y or z, the suffix x being replaced by y or z.

5. Every body about which we know anything is always in a state of stress, that is to say there are always internal forces acting between the parts of the body, and these forces are exerted as surface tractions across geometrical surfaces drawn in the body. The body, and each part of the body, moves under the action of all the forces (body forces and surface tractions) which are exerted upon it; or remains at rest if these forces are in equilibrium. This result is expressed analytically by means of certain equations—the “equations of motion” or “equations of equilibrium” of the body.

Let ρ denote the density of the body at any point, X, Y, Z, the components parallel to the axes of x, y, z of the body forces, estimated as so much force per unit of mass; further let ƒx, ƒy, ƒz denote the components, parallel to the same axes, of the acceleration of the particle which is momentarily at the point (x, y, z). The equations of motion express the result that the rates of change of the momentum, and of the moment of momentum, of any portion of the body are those due to the action of all the forces exerted upon the portion by other bodies, or by other portions of the same body. For the changes of momentum, we have three equations of the type

∫ ∫ ∫ ρ Xdx dy dz + ∫ ∫ XνdS = ∫ ∫ ∫ ρ ƒxdx dy dz,

(1)

in which the volume integrations are taken through the volume of the portion of the body, the surface integration is taken over its surface, and the notation Xν is that of § 4, the direction of ν being that of the normal to this surface drawn outwards. For the changes of moment of momentum, we have three equations of the type

∫ ∫ ∫ ρ (yZ − zY) dx dy dz + ∫ ∫ (yZν − zYν) dS = ∫ ∫ ∫ ρ (yƒz − zƒy) dx dy dz.

(2)

The equations (1) and (2) are the equations of motion of any kind of body. The equations of equilibrium are obtained by replacing the right-hand members of these equations by zero.

6. These equations can be used to obtain relations between the values of Xν, Yν, ... for different directions ν. When the equations are applied to a very small volume, it appears that the terms expressed by surface integrals would, unless they tend to zero limits in a higher order than the areas of the surfaces, be very great compared with the terms expressed by volume integrals. We conclude that the surface tractions on the portion of the body which is bounded by any very small closed surface, are ultimately in equilibrium. When this result is interpreted for a small portion in the shape of a tetrahedron, having three of its faces at right angles to the co-ordinate axes, it leads to three equations of the type

Xν = Xx cos(x, ν) + Xy cos(y, ν) + Xz cos(z, ν),

(1)

where ν is the direction of the normal (drawn outwards) to the remaining face of the tetrahedron, and (x, ν) ... denote the angles which this normal makes with the axes. Hence Xν, ... for any direction ν are expressed in terms of Xx,.... When the above result is interpreted for a very small portion in the shape of a cube, having its edges parallel to the co-ordinate axes, it leads to the equations

Yz = Zy,    Zx = Xz,    Xy = Yx.

(2)

When we substitute in the general equations the particular results which are thus obtained, we find that the equations of motion take such forms as

(3)

and the equations of moments are satisfied identically. The equations of equilibrium are obtained by replacing the right-hand members by zero.

7. A state of stress in which the traction across any plane of a set of parallel planes is normal to the plane, and that across any perpendicular plane vanishes, is described as a state of “simple tension” (“simple pressure” if the traction is negative). A state of stress in which the traction across any plane is normal to the plane, and the traction is the same for all planes passing through any point, is described as a state of “uniform tension” (“uniform pressure” if the traction is negative). Sometimes the phrases “isotropic tension” and “hydrostatic pressure” are used instead of “uniform” tension or pressure. The distinction between the two states, simple tension and uniform tension, is illustrated in fig. 1.

A state of stress in which there is purely tangential traction on a plane, and no normal traction on any perpendicular plane, is described as a state of “shearing stress.” The result (2) of § 6 shows that tangential tractions occur in pairs. If, at any point, there is tangential traction, in any direction, on a plane parallel to this direction, and if we draw through the point a plane at right angles to the direction of this traction, and therefore containing the normal to the first plane, then there is equal tangential traction on this second plane in the direction of the normal to the first plane. The result is illustrated in fig. 2, where a rectangular block is subjected on two opposite faces to opposing tangential tractions, and is held in equilibrium by equal tangential tractions applied to two other faces.

Through any point there always pass three planes, at right angles to each other, across which there is no tangential traction. These planes are called the “principal planes of stress,” and the (normal) tractions across them the “principal stresses.” Lines, usually curved, which have at every point the direction of a principal stress at the point, are called “lines of stress.”

8. It appears that the stress at any point of a body is completely specified by six quantities, which can be taken to be the Xx, Yy, Zz and Yz, Zx, Xy of § 6. The first three are tensions (pressures if they are negative) across three planes parallel to fixed rectangular directions, and the remaining three are tangential tractions across the same three planes. These six quantities are called the “components of stress.” It appears also that the components of stress are connected with each other, and with the body forces and accelerations, by the three partial differential equations of the type (3) of § 6. These equations are available for the purpose of determining the state of stress which exists in a body of definite form subjected to definite forces, but they are not sufficient for the purpose (see § 38 below). In order to effect the determination it is necessary to have information concerning the constitution of the body, and to introduce subsidiary relations founded upon this information.

9. The definite mathematical relations which have been found to connect the components of stress with each other, and with other quantities, result necessarily from the formation of a clear conception of the nature of stress. They do not admit of experimental verification, because the stress within a body does not admit of direct measurement. Results which are deduced by the aid of these relations can be compared with experimental results. If any discrepancy were observed it would not be interpreted as requiring a modification of the concept of stress, but as affecting some one or other of the subsidiary relations which must be introduced for the purpose of obtaining the theoretical result.

10. Strain.—For the specification of the changes of size and shape which are produced in a body by any forces, we begin by defining the “average extension” of any linear element or “filament” of the body. Let l0 be the length of the filament before the forces are applied, l its length when the body is subjected to the forces. The average extension of the filament is measured by the fraction (l − l0)/l0. If this fraction is negative there is “contraction.” The “extension at a point” of a body in any assigned direction is the mathematical limit of this fraction when one end of the filament is at the point, the filament has the assigned direction, and its length is diminished indefinitely. It is clear that all the changes of size and shape of the body are known when the extension at every point in every direction is known.

The relations between the extensions in different directions around the same point are most simply expressed by introducing the extensions in the directions of the co-ordinate axes and the angles between filaments of the body which are initially parallel to these axes. Let exx, eyy, ezz denote the extensions parallel to the axes of x, y, z, and let eyz, ezx, exy denote the cosines of the angles between the pairs of filaments which are initially parallel to the axes of y and z, z and x, x and y. Also let e denote the extension in the direction of a line the direction cosines of which are l, m, n. Then, if the changes of size and shape are slight, we have the relation

e = exxl² + eyym² + ezzn² + eyzmn + ezxnl + exylm.

The body which undergoes the change of size or shape is said to be “strained,” and the “strain” is determined when the quantities exx, eyy, ezz and eyz, ezx, exy defined above are known at every point of it. These quantities are called “components of strain.” The three of the type exx are extensions, and the three of the type eyz are called “shearing strains” (see § 12 below).

11. All the changes of relative position of particles of the body are known when the strain is known, and conversely the strain can be determined when the changes of relative position are given. These changes can be expressed most simply by the introduction of a vector quantity to represent the displacement of any particle.

When the body is deformed by the action of any forces its particles pass from the positions which they occupied before the action of the forces into new positions. If x, y, z are the co-ordinates of the position of a particle in the first state, its co-ordinates in the second state may be denoted by x + u, y + v, z + w. The quantities, u, v, w are the “components of displacement.” When these quantities are small, the strain is connected with them by the equations

exx = ∂u / ∂x,    eyy = ∂v / ∂y,    ezz = ∂w / ∂z,

(1)

12. These equations enable us to determine more exactly the nature of the “shearing strains” such as exy. Let u, for example, be of the form sy, where s is constant, and let v and w vanish. Then exy = s, and the remaining components of strain vanish. The nature of the strain (called “simple shear”) is simply appreciated by imagining the body to consist of a series of thin sheets, like the leaves of a book, which lie one over another and are all parallel to a plane (that of x, z); and the displacement is seen to consist in the shifting of each sheet relative to the sheet below in a direction (that of x) which is the same for all the sheets. The displacement of any sheet is proportional to its distance y from a particular sheet, which remains undisplaced. The shearing strain has the effect of distorting the shape of any portion of the body without altering its volume. This is shown in fig. 3, where a square ABCD is distorted by simple shear (each point moving parallel to the line marked xx) into a rhombus A′B′C′D′, as if by an extension of the diagonal BD and a contraction of the diagonal AC, which extension and contraction are adjusted so as to leave the area unaltered. In the general case, where u is not of the form sy and v and w do not vanish, the shearing strains such as exy result from the composition of pairs of simple shears of the type which has just been explained.

13. Besides enabling us to express the extension in any direction and the changes of relative direction of any filaments of the body, the components of strain also express the changes of size of volumes and areas. In particular, the “cubical dilatation,” that is to say, the increase of volume per unit of volume, is expressed by the quantity exx + eyy + ezz or ∂u / ∂x + ∂v / ∂y + ∂w / ∂z. When this quantity is negative there is “compression.”

14. It is important to distinguish between two types of strain: the “rotational” type and the “irrotational” type. The distinction is illustrated in fig. 3, where the figure A″B″C″D″ is obtained from the figure ABCD by contraction parallel to AC and extension parallel to BD, and the figure A′B′C′D′ can be obtained from ABCD by the same contraction and extension followed by a rotation through the angle A″OA′. In strains of the irrotational type there are at any point three filaments at right angles to each other, which are such that the particles which lie in them before strain continue to lie in them after strain. A small spherical element of the body with its centre at the point becomes a small ellipsoid with its axes in the directions of these three filaments. In the case illustrated in the figure, the lines of the filaments in question, when the figure ABCD is strained into the figure A″B″C″D″, are OA, OB and a line through O at right angles to their plane. In strains of the rotational type, on the other hand, the single existing set of three filaments (issuing from a point) which cut each other at right angles both before and after strain do not retain their directions after strain, though one of them may do so in certain cases. In the figure, the lines of the filaments in question, when the figure ABCD is strained into A′B′C′D′, are OA, OB and a line at right angles to their plane before strain, and after strain they are OA′, OB′, and the same third line. A rotational strain can always be analysed into an irrotational strain (or “pure” strain) followed by a rotation.

Analytically, a strain is irrotational if the three quantities

vanish, rotational if any one of them is different from zero. The halves of these three quantities are the components of a vector quantity called the “rotation.”

15. Whether the strain is rotational or not, there is always one set of three linear elements issuing from any point which cut each other at right angles both before and after strain. If these directions are chosen as axes of x, y, z, the shearing strains eyz, ezx, exy vanish at this point. These directions are called the “principal axes of strain,” and the extensions in the directions of these axes the “principal extensions.”

16. It is very important to observe that the relations between components of strain and components of displacement imply relations between the components of strain themselves. If by any process of reasoning we arrive at the conclusion that the state of strain in a body is such and such a state, we have a test of the possibility or impossibility of our conclusion. The test is that, if the state of strain is a possible one, then there must be a displacement which can be associated with it in accordance with the equations (1) of § 11.

We may eliminate u, v, w from these equations. When this is done we find that the quantities exx, ... eyz are connected by the two sets of equations

(1)

and

(2)

These equations are known as the conditions of compatibility of strain-components. The components of strain which specify any possible strain satisfy them. Quantities arrived at in any way, and intended to be components of strain, if they fail to satisfy these equations, are not the components of any possible strain; and the theory or speculation by which they are reached must be modified or abandoned.

When the components of strain have been found in accordance with these and other necessary equations, the displacement is to be found by solving the equations (1) of § 11, considered as differential equations to determine u, v, w. The most general possible solution will differ from any other solution by terms which contain arbitrary constants, and these terms represent a possible displacement. This “complementary displacement” involves no strain, and would be a possible displacement of an ideal perfectly rigid body.

17. The relations which connect the strains with each other and with the displacement are geometrical relations resulting from the definitions of the quantities and not requiring any experimental verification. They do not admit of such verification, because the strain within a body cannot be measured. The quantities (belonging to the same category) which can be measured are displacements of points on the surface of a body. For example, on the surface of a bar subjected to tension we may make two fine transverse scratches, and measure the distance between them before and after the bar is stretched. For such measurements very refined instruments are required. Instruments for this purpose are called barbarously “extensometers,” and many different kinds have been devised. From measurements of displacement by an extensometer we may deduce the average extension of a filament of the bar terminated by the two scratches. In general, when we attempt to measure a strain, we really measure some displacements, and deduce the values, not of the strain at a point, but of the average extensions of some particular linear filaments of a body containing the point; and these filaments are, from the nature of the case, nearly always superficial filaments.

18. In the case of transparent materials such as glass there is available a method of studying experimentally the state of strain within a body. This method is founded upon the result that a piece of glass when strained becomes doubly refracting, with its optical principal axes at any point in the directions of the principal axes of strain (§ 15) at the point. When the piece has two parallel plane faces, and two of the principal axes of strain at any point are parallel to these faces, polarized light transmitted through the piece in a direction normal to the faces can be used to determine the directions of the principal axes of the strain at any point. If the directions of these axes are known theoretically the comparison of the experimental and theoretical results yields a test of the theory.

19. Relations between Stresses and Strains.—The problem of the extension of a bar subjected to tension is the one which has been most studied experimentally, and as a result of this study it is found that for most materials, including all metals except cast metals, the measurable extension is proportional to the applied tension, provided that this tension is not too great. In interpreting this result it is assumed that the tension is uniform over the cross-section of the bar, and that the extension of longitudinal filaments is uniform throughout the bar; and then the result takes the form of a law of proportionality connecting stress and strain: The tension is proportional to the extension. Similar results are found for the same materials when other methods of experimenting are adopted, for example, when a bar is supported at the ends and bent by an attached load and the deflexion is measured, or when a bar is twisted by an axial couple and the relative angular displacement of two sections is measured. We have thus very numerous experimental verifications of the famous law first enunciated by Robert Hooke in 1678 in the words “Ut Tensio sic vis”; that is, “the Power of any spring is in the same proportion as the Tension (—stretching) thereof.” The most general statement of Hooke’s Law in modern language would be:—Each of the six components of stress at any point of a body is a linear function of the six components of strain at the point. It is evident from what has been said above as to the nature of the measurement of stresses and strains that this law in all its generality does not admit of complete experimental verification, and that the evidence for it consists largely in the agreement of the results which are deduced from it in a theoretical fashion with the results of experiments. Of such results one of a general character may be noted here. If the law is assumed to be true, and the equations of motion of the body (§ 5) are transformed by means of it into differential equations for determining the components of displacement, these differential equations admit of solutions which represent periodic vibratory displacements (see § 85 below). The fact that solid bodies can be thrown into states of isochronous vibration has been emphasized by G.G. Stokes as a peremptory proof of the truth of Hooke’s Law.

20. According to the statement of the generalized Hooke’s Law the stress-components vanish when the strain-components vanish. The strain-components contemplated in experiments upon which the law is founded are measured from a zero of reckoning which corresponds to the state of the body subjected to experiment before the experiment is made, and the stress-components referred to in the statement of the law are those which are called into action by the forces applied to the body in the course of the experiment. No account is taken of the stress which must already exist in the body owing to the force of gravity and the forces by which the body is supported. When it is desired to take account of this stress it is usual to suppose that the strains which would be produced in the body if it could be freed from the action of gravity and from the pressures of supports are so small that the strains produced by the forces which are applied in the course of the experiment can be compounded with them by simple superposition. This supposition comes to the same thing as measuring the strain in the body, not from the state in which it was before the experiment, but from an ideal state (the “unstressed” state) in which it would be entirely free from internal stress, and allowing for the strain which would be produced by gravity and the supporting forces if these forces were applied to the body when free from stress. In most practical cases the initial strain to be allowed for is unimportant (see §§ 91-93 below).

21. Hooke’s law of proportionality of stress and strain leads to the introduction of important physical constants: the moduluses of elasticity of a body. Let a bar of uniform section (of area ω) be stretched with tension T, which is distributed uniformly over the section, so that the stretching force is Twω, and let the bar be unsupported at the sides. The bar will undergo a longitudinal extension of magnitude T/E, where E is a constant quantity depending upon the material. This constant is called Young’s modulus after Thomas Young, who introduced it into the science in 1807. The quantity E is of the same nature as a traction, that is to say, it is measured as a force estimated per unit of area. For steel it is about 2.04 × 1012 dynes per square centimetre, or about 13,000 tons per sq. in.

22. The longitudinal extension of the bar under tension is not the only strain in the bar. It is accompanied by a lateral contraction by which all the transverse filaments of the bar are shortened. The amount of this contraction is σT/E, where σ is a certain number called Poisson’s ratio, because its importance was at first noted by S.D. Poisson in 1828. Poisson arrived at the existence of this contraction, and the corresponding number σ, from theoretical considerations, and his theory led him to assign to σ the value ¼. Many experiments have been made with the view of determining σ, with the result that it has been found to be different for different materials, although for very many it does not differ much from ¼. For steel the best value (Amagat’s) is 0.268. Poisson’s theory admits of being modified so as to agree with the results of experiment.

23. The behaviour of an elastic solid body, strained within the limits of its elasticity, is entirely determined by the constants E and σ if the body is isotropic, that is to say, if it has the same quality in all directions around any point. Nevertheless it is convenient to introduce other constants which are related to the action of particular sorts of forces. The most important of these are the “modulus of compression” (or “bulk modulus”) and the “rigidity” (or “modulus of shear”). To define the modulus of compression, we suppose that a solid body of any form is subjected to uniform hydrostatic pressure of amount p. The state of stress within it will be one of uniform pressure, the same at all points, and the same in all directions round any point. There will be compression, the same at all points, and proportional to the pressure; and the amount of the compression can be expressed as p/k. The quantity k is the modulus of compression. In this case the linear contraction in any direction is p/3k; but in general the linear extension (or contraction) is not one-third of the cubical dilatation (or compression).

24. To define the rigidity, we suppose that a solid body is subjected to forces in such a way that there is shearing stress within it. For example, a cubical block may be subjected to opposing tractions on opposite faces acting in directions which are parallel to an edge of the cube and to both the faces. Let S be the amount of the traction, and let it be uniformly distributed over the faces. As we have seen (§ 7), equal tractions must act upon two other faces in suitable directions in order to maintain equilibrium (see fig. 2 of § 7). The two directions involved may be chosen as axes of x, y as in that figure. Then the state of stress will be one in which the stress-component denoted by Xy is equal to S, and the remaining stress-components vanish; and the strain produced in the body is shearing strain of the type denoted by exy. The amount of the shearing strain is S/μ, and the quantity μ is the “rigidity.”

25. The modulus of compression and the rigidity are quantities of the same kind as Young’s modulus. The modulus of compression of steel is about 1.43 × 1012 dynes per square centimetre, the rigidity is about 8.19 × 1011 dynes per square centimetre. It must be understood that the values for different specimens of nominally the same material may differ considerably.

The modulus of compression k and the rigidity μ of an isotropic material are connected with the Young’s modulus E and Poisson’s ratio σ of the material by the equations

k = E / 3(1 − 2σ),   μ = E / 2(1 + σ).

26. Whatever the forces acting upon an isotropic solid body may be, provided that the body is strained within its limits of elasticity, the strain-components are expressed in terms of the stress-components by the equations

exx = (Xx − σYy − σZz) / E,   eyz = Yz / μ,

eyy = (Yy − σZz − σXx) / E,   ezx = Zx / μ,

ezz = (Zz − σXx − σYy) / E,   exy = Xy / μ.

(1)

If we introduce a quantity λ, of the same nature as E or μ, by the equation

λ = Eσ / (1 + σ)(1 − 2σ),

(2)

we may express the stress-components in terms of the strain-components by the equations

Xx = λ(exx + eyy + ezz) + 2μexx,   Yz = μeyz,

Yy = λ(exx + eyy + ezz) + 2μeyy,   Zx = μezx,

Zz = λ(exx + eyy + ezz) + 2μezz,   Xy = μexy;

(3)

and then the behaviour of the body under the action of any forces depends upon the two constants λ and μ. These two constants were introduced by G. Lamé in his treatise of 1852. The importance of the quantity μ had been previously emphasized by L.J. Vicat and G.G. Stokes.

27. The potential energy per unit of volume (often called the “resilience”) stored up in the body by the strain is equal to

½ (λ + 2μ) (exx + eyy + ezz)² + ½μ (e²yz + e²zx + e²xy − 4eyyezz − 4ezzexx − 4exxeyy),

or the equivalent expression

½ [(X²x + Y²y + Z²z) − 2σ (YyZz + ZzXx + XxYy) + 2 (1 + σ) (Y²z + Z²x + X²y)] / E.

The former of these expressions is called the “strain-energy-function.”

28. The Young’s modulus E of a material is often determined experimentally by the direct method of the extensometer (§ 17), but more frequently it is determined indirectly by means of a result obtained in the theory of the flexure of a bar (see §§ 47, 53 below). The rigidity μ is usually determined indirectly by means of results obtained in the theory of the torsion of a bar (see §§ 41, 42 below). The modulus of compression k may be determined directly by means of the piezometer, as was done by E.H. Amagat, or it may be determined indirectly by means of a result obtained in the theory of a tube under pressure, as was done by A. Mallock (see § 78 below). The value of Poisson’s ratio σ is generally inferred from the relation connecting it with E and μ or with E and k, but it may also be determined indirectly by means of a result obtained in the theory of the flexure of a bar (§ 47 below), as was done by M.A. Cornu and A. Mallock, or directly by a modification of the extensometer method, as has been done recently by J. Morrow.

29. The elasticity of a fluid is always expressed by means of a single quantity of the same kind as the modulus of compression of a solid body. To any increment of pressure, which is not too great, there corresponds a proportional cubical compression, and the amount of this compression for an increment δp of pressure can be expressed as δp/k. The quantity that is usually tabulated is the reciprocal of k, and it is called the coefficient of compressibility. It is the amount of compression per unit increase of pressure. As a physical quantity it is of the same dimensions as the reciprocal of a pressure (or of a force per unit of area). The pressures concerned are usually measured in atmospheres (1 atmosphere = 1.014 × 106 dynes per sq. cm.). For water the coefficient of compressibility, or the compression per atmosphere, is about 4.5 × 10-5. This gives for k the value 2.22 × 1010 dynes per sq. cm. The Young’s modulus and the rigidity of a fluid are always zero.

30. The relations between stress and strain in a material which is not isotropic are much more complicated. In such a material the Young’s modulus depends upon the direction of the tension, and its variations about a point are expressed by means of a surface of the fourth degree. The Poisson’s ratio depends upon the direction of the contracted lateral filaments as well as upon that of the longitudinal extended ones. The rigidity depends upon both the directions involved in the specification of the shearing stress. In general there is no simple relation between the Young’s moduluses and Poisson’s ratios and rigidities for assigned directions and the modulus of compression. Many materials in common use, all fibrous woods for example, are actually aeolotropic (that is to say, are not isotropic), but the materials which are aeolotropic in the most regular fashion are natural crystals. The elastic behaviour of crystals has been studied exhaustively by many physicists, and in particular by W. Voigt. The strain-energy-function is a homogeneous quadratic function of the six strain-components, and this function may have as many as 21 independent coefficients, taking the place in the general case of the 2 coefficients λ, μ which occur when the material is isotropic—a result first obtained by George Green in 1837. The best experimental determinations of the coefficients have been made indirectly by Voigt by means of results obtained in the theories of the torsion and flexure of aeolotropic bars.

31. Limits of Elasticity.—A solid body which has been strained by considerable forces does not in general recover its original size and shape completely after the forces cease to act. The strain that is left is called set. If set occurs the elasticity is said to be “imperfect,” and the greatest strain (or the greatest load) of any specified type, for which no set occurs, defines the “limit of perfect elasticity” corresponding to the specified type of strain, or of stress. All fluids and many solid bodies, such as glasses and crystals, as well as some metals (copper, lead, silver) appear to be perfectly elastic as regards change of volume within wide limits; but malleable metals and alloys can have their densities permanently increased by considerable pressures. The limits of perfect elasticity as regards change of shape, on the other hand, are very low, if they exist at all, for glasses and other hard, brittle solids; but a class of metals including copper, brass, steel, and platinum are very perfectly elastic as regards distortion, provided that the distortion is not too great. The question can be tested by observation of the torsional elasticity of thin fibres or wires. The limits of perfect elasticity are somewhat ill-defined, because an experiment cannot warrant us in asserting that there is no set, but only that, if there is any set, it is too small to be observed.

32. A different meaning may be, and often is, attached to the phrase “limits of elasticity” in consequence of the following experimental result:—Let a bar be held stretched under a moderate tension, and let the extension be measured; let the tension be slightly increased and the extension again measured; let this process be continued, the tension being increased by equal increments. It is found that when the tension is not too great the extension increases by equal increments (as nearly as experiment can decide), but that, as the tension increases, a stage is reached in which the extension increases faster than it would do if it continued to be proportional to the tension. The beginning of this stage is tolerably well marked. Some time before this stage is reached the limit of perfect elasticity is passed; that is to say, if the load is removed it is found that there is some permanent set. The limiting tension beyond which the above law of proportionality fails is often called the “limit of linear elasticity.” It is higher than the limit of perfect elasticity. For steel bars of various qualities J. Bauschinger found for this limit values varying from 10 to 17 tons per square inch. The result indicates that, when forces which produce any kind of strain are applied to a solid body and are gradually increased, the strain at any instant increases proportionally to the forces up to a stage beyond that at which, if the forces were removed, the body would completely recover its original size and shape, but that the increase of strain ceases to be proportional to the increase of load when the load surpasses a certain limit. There would thus be, for any type of strain, a limit of linear elasticity, which exceeds the limit of perfect elasticity.

33. A body which has been strained beyond the limit of linear elasticity is often said to have suffered an “over-strain.” When the load is removed, the set which can be observed is not entirely permanent; but it gradually diminishes with lapse of time. This phenomenon is named “elastic after-working.” If, on the other hand, the load is maintained constant, the strain is gradually increased. This effect indicates a gradual flowing of solid bodies under great stress; and a similar effect was observed in the experiments of H. Tresca on the punching and crushing of metals. It appears that all solid bodies under sufficiently great loads become “plastic,” that is to say, they take a set which gradually increases with the lapse of time. No plasticity is observed when the limit of linear elasticity is not exceeded.

34. The values of the elastic limits are affected by overstrain. If the load is maintained for some time, and then removed, the limit of linear elasticity is found to be higher than before. If the load is not maintained, but is removed and then reapplied, the limit is found to be lower than before. During a period of rest a test piece recovers its elasticity after overstrain.

35. The effects of repeated loading have been studied by A. Wöhler, J. Bauschinger, O. Reynolds and others. It has been found that, after many repetitions of rather rapidly alternating stress, pieces are fractured by loads which they have many times withstood. It is not certain whether the fracture is in every case caused by the gradual growth of minute flaws from the beginning of the series of tests, or whether the elastic quality of the material suffers deterioration apart from such flaws. It appears, however, to be an ascertained result that, so long as the limit of linear elasticity is not exceeded, repeated loads and rapidly alternating loads do not produce failure of the material.

36. The question of the conditions of safety, or of the conditions in which rupture is produced, is one upon which there has been much speculation, but no completely satisfactory result has been obtained. It has been variously held that rupture occurs when the numerically greatest principal stress exceeds a certain limit, or when this stress is tension and exceeds a certain limit, or when the greatest difference of two principal stresses (called the “stress-difference”) exceeds a certain limit, or when the greatest extension or the greatest shearing strain or the greatest strain of any type exceeds a certain limit. Some of these hypotheses appear to have been disproved. It was held by G.F. Fitzgerald (Nature, Nov. 5, 1896) that rupture is not produced by pressure symmetrically applied all round a body, and this opinion has been confirmed by the recent experiments of A. Föppl. This result disposes of the greatest stress hypothesis and also of the greatest strain hypothesis. The fact that short pillars can be crushed by longitudinal pressure disposes of the greatest tension hypothesis, for there is no tension in the pillar. The greatest extension hypothesis failed to satisfy some tests imposed by H. Wehage, who experimented with blocks of wrought iron subjected to equal pressures in two directions at right angles to each other. The greatest stress-difference hypothesis and the greatest shearing strain hypothesis would lead to practically identical results, and these results have been held by J.J. Guest to accord well with his experiments on metal tubes subjected to various systems of combined stress; but these experiments and Guest’s conclusion have been criticized adversely by O. Mohr, and the question cannot be regarded as settled. The fact seems to be that the conditions of rupture depend largely upon the nature of the test (tensional, torsional, flexural, or whatever it may be) that is applied to a specimen, and that no general formula holds for all kinds of tests. The best modern technical writings emphasize the importance of the limits of linear elasticity and of tests of dynamical resistance (§ 87 below) as well as of statical resistance.

37. The question of the conditions of rupture belongs rather to the science of the strength of materials than to the science of elasticity (§ 1); but it has been necessary to refer to it briefly here, because there is no method except the methods of the theory of elasticity for determining the state of stress or strain in a body subjected to forces. Whatever view may ultimately be adopted as to the relation between the conditions of safety of a structure and the state of stress or strain in it, the calculation of this state by means of the theory or by experimental means (as in § 18) cannot be dispensed with.

38. Methods of determining the Stress in a Body subjected to given Forces.—To determine the state of stress, or the state of strain, in an isotropic solid body strained within its limits of elasticity by given forces, we have to use (i.) the equations of equilibrium, (ii.) the conditions which hold at the bounding surface, (iii.) the relations between stress-components and strain-components, (iv.) the relations between strain-components and displacement. The equations of equilibrium are (with notation already used) three partial differential equations of the type

(1)

The conditions which hold at the bounding surface are three equations of the type

Xx cos (x, ν) + Xy cos (y, ν) + Zx cos (z, ν) = Xν,

(2)

where ν denotes the direction of the outward-drawn normal to the bounding surface, and Xν denotes the x-component of the applied surface traction. The relations between stress-components and strain-components are expressed by either of the sets of equations (1) or (3) of § 26. The relations between strain-components and displacement are the equations (1) of § 11, or the equivalent conditions of compatibility expressed in equations (1) and (2) of § 16.

39. We may proceed by either of two methods. In one method we eliminate the stress-components and the strain-components and retain only the components of displacement. This method leads (with notation already used) to three partial differential equations of the type

(3)

and three boundary conditions of the type

(4)

In the alternative method we eliminate the strain-components and the displacements. This method leads to a system of partial differential equations to be satisfied by the stress-components. In this system there are three equations of the type

(1 bis)

three of the type

(5)

and three of the type

(6)

the equations of the two latter types being necessitated by the conditions of compatibility of strain-components. The solutions of these equations have to be adjusted so that the boundary conditions of the type (2) may be satisfied.

40. It is evident that whichever method is adopted the mathematical problem is in general very complicated. It is also evident that, if we attempt to proceed by help of some intuition as to the nature of the stress or strain, our intuition ought to satisfy the tests provided by the above systems of equations. Neglect of this precaution has led to many errors. Another source of frequent error lies in the neglect of the conditions in which the above systems of equations are correct. They are obtained by help of the supposition that the relative displacements of the parts of the strained body are small. The solutions of them must therefore satisfy the test of smallness of the relative displacements.

41. Torsion.—As a first example of the application of the theory we take the problem of the torsion of prisms. This problem, considered first by C.A. Coulomb in 1784, was finally solved by B. de Saint-Venant in 1855. The problem is this:—A cylindrical or prismatic bar is held twisted by terminal couples; it is required to determine the state of stress and strain in the interior. When the bar is a circular cylinder the problem is easy. Any section is displaced by rotation about the central-line through a small angle, which is proportional to the distance z of the section from a fixed plane at right angles to this line. This plane is a terminal section if one of the two terminal sections is not displaced. The angle through which the section z rotates is τz, where τ is a constant, called the amount of the twist; and this constant τ is equal to G/μI, where G is the twisting couple, and I is the moment of inertia of the cross-section about the central-line. This result is often called “Coulomb’s law.” The stress within the bar is shearing stress, consisting, as it must, of two sets of equal tangential tractions on two sets of planes which are at right angles to each other. These planes are the cross-sections and the axial planes of the bar. The tangential traction at any point of the cross-section is directed at right angles to the axial plane through the point, and the tangential traction on the axial plane is directed parallel to the length of the bar. The amount of either at a distance r from the axis is μτr or Gr/I. The result that G = μτI can be used to determine μ experimentally, for τ may be measured and G and I are known.

42. When the cross-section of the bar is not circular it is clear that this solution fails; for the existence of tangential traction, near the prismatic bounding surface, on any plane which does not cut this surface at right angles, implies the existence of traction applied to this surface. We may attempt to modify the theory by retaining the supposition that the stress consists of shearing stress, involving tangential traction distributed in some way over the cross-sections. Such traction is obviously a necessary constituent of any stress-system which could be produced by terminal couples around the axis. We should then know that there must be equal tangential traction directed along the length of the bar, and exerted across some planes or other which are parallel to this direction. We should also know that, at the bounding surface, these planes must cut this surface at right angles. The corresponding strain would be shearing strain which could involve (i.) a sliding of elements of one cross-section relative to another, (ii.) a relative sliding of elements of the above mentioned planes in the direction of the length of the bar. We could conclude that there may be a longitudinal displacement of the elements of the cross-sections. We should then attempt to satisfy the conditions of the problem by supposing that this is the character of the strain, and that the corresponding displacement consists of (i.) a rotation of the cross-sections in their planes such as we found in the case of the circle, (ii.) a distortion of the cross-sections into curved surfaces by a displacement (w) which is directed normally to their planes and varies in some manner from point to point of these planes. We could show that all the conditions of the problem are satisfied by this assumption, provided that the longitudinal displacement (w), considered as a function of the position of a point (x, y) in the cross-section, satisfies the equation

(1)

and the boundary condition

(2)

where τ denotes the amount of the twist, and ν the direction of the normal to the boundary. The solution is known for a great many forms of section. (In the particular case of a circular section w vanishes.) The tangential traction at any point of the cross-section is directed along the tangent to that curve of the family ψ = const. which passes through the point, ψ being the function determined by the equations

The amount of the twist τ produced by terminal couples of magnitude G is G/C, where C is a constant, called the “torsional rigidity” of the prism, and expressed by the formula

the integration being taken over the cross-section. When the coefficient of μ in the expression for C is known for any section, μ can be determined by experiment with a bar of that form of section.

43. The distortion of the cross-sections into curved surfaces is shown graphically by drawing the contour lines (w = const.). In general the section is divided into a number of compartments, and the portions that lie within two adjacent compartments are respectively concave and convex. This result is illustrated in the accompanying figures (fig. 4 for the ellipse, given by x²/b² + y²/c² = 1; fig. 5 for the equilateral triangle, given by (x + 1⁄3a) (x² − 3y² − 4⁄3ax + 4⁄9a²) = 0; fig. 6 for the square).

44. The distribution of the shearing stress over the cross-section is determined by the function ψ, already introduced. If we draw the curves ψ = const., corresponding to any form of section, for equidifferent values of the constant, the tangential traction at any point on the cross-section is directed along the tangent to that curve of the family which passes through the point, and the magnitude of it is inversely proportional to the distance between consecutive curves of the family. Fig. 7 illustrates the result in the case of the equilateral triangle. The boundary is, of course, one of the lines. The “lines of shearing stress” which can thus be drawn are in every case identical with the lines of flow of frictionless liquid filling a cylindrical vessel of the same cross-section as the bar, when the liquid circulates in the plane of the section with uniform spin. They are also the same as the contour lines of a flexible and slightly extensible membrane, of which the edge has the same form as the bounding curve of the cross-section of the bar, when the membrane is fixed at the edge and slightly deformed by uniform pressure.

45. Saint-Venant’s theory shows that the true torsional rigidity is in general less than that which would be obtained by extending Coulomb’s law (G = μτI) to sections which are not circular. For an elliptic cylinder of sectional area ω and moment of inertia I about its central-line the torsional rigidity is μω4 / 4π²I, and this formula is not far from being correct for a very large number of sections. For a bar of square section of side a centimetres, the torsional rigidity in C.G.S. units is (0.1406) μa4 approximately, μ being expressed in dynes per square centimetre. How great the defect of the true value from that given by extending Coulomb’s law may be in the case of sections with projecting corners is shown by the diagrams (fig. 8 especially no. 4). In these diagrams the upper of the two numbers under each figure indicates the fraction which the true torsional rigidity corresponding to the section is of that value which would be obtained by extending Coulomb’s law; and the lower of the two numbers indicates the ratio which the torsional rigidity for a bar of the corresponding section bears to that of a bar of circular section of the same material and of equal sectional area. These results have an important practical application, inasmuch as they show that strengthening ribs and projections, such as are introduced in engineering to give stiffness to beams, have the reverse of a good effect when torsional stiffness is an object, although they are of great value in increasing the resistance to bending. The theory shows further that the resistance to torsion is very seriously diminished when there is in the surface any dent approaching to a re-entrant angle. At such a place the shearing strain tends to become infinite, and some permanent set is produced by torsion. In the case of a section of any form, the strain and stress are greatest at points on the contour, and these points are in many cases the points of the contour which are nearest to the centroid of the section. The theory has also been applied to show that a longitudinal flaw near the axis of a shaft transmitting a torsional couple has little influence on the strength of the shaft, but that in the neighbourhood of a similar flaw which is much nearer to the surface than to the axis the shearing strain may be nearly doubled, and thus the possibility of such flaws is a source of weakness against which special provision ought to be made.

46. Bending of Beams.—As a second example of the application of the general theory we take the problem of the flexure of a beam. In this case also we begin by forming a simple intuition as to the nature of the strain and the stress. On the side of the beam towards the centre of curvature the longitudinal filaments must be contracted, and on the other side they must be extended. If we assume that the cross-sections remain plane, and that the central-line is unaltered in length, we see (at once from fig. 9) that the extensions (or contractions) are given by the formula y/R, where y denotes the distance of a longitudinal filament from the plane drawn through the unstrained central-line at right-angles to the plane of bending, and R is the radius of curvature of the curve into which this line is bent (shown by the dotted line in the figure). Corresponding to this strain there must be traction acting across the cross-sections. If we assume that there is no other stress, then the magnitude of the traction in question is Ey/R, where E is Young’s modulus, and it is tension on the side where the filaments are extended and pressure on the side where they are contracted. If the plane of bending contains a set of principal axes of the cross-sections at their centroids, these tractions for the whole cross-section are equivalent to a couple of moment EI/R, where I now denotes the moment of inertia of the cross-section about an axis through its centroid at right angles to the plane of bending, and the plane of the couple is the plane of bending. Thus a beam of any form of section can be held bent in a “principal plane” by terminal couples of moment M, that is to say by a “bending moment” M; the central-line will take a curvature M/EI, so that it becomes an arc of a circle of radius EI/M; and the stress at any point will be tension of amount My/I, where y denotes distance (reckoned positive towards the side remote from the centre of curvature) from that plane which initially contains the central-line and is at right angles to the plane of the couple. This plane is called the “neutral plane.” The restriction that the beam is bent in a principal plane means that the plane of bending contains one set of principal axes of the cross-sections at their centroids; in the case of a beam of rectangular section the plane would bisect two opposite edges at right angles. In order that the theory may hold good the radius of curvature must be very large.

47. In this problem of the bending of a beam by terminal couples the stress is tension, determined as above, and the corresponding strain consists therefore of longitudinal extension of amount My/EI or y/R (contraction if y is negative), accompanied by lateral contraction of amount σMy/EI or σy/R (extension if y is negative), σ being Poisson’s ratio for the material. Our intuition of the nature of the strain was imperfect, inasmuch as it took no account of these lateral strains. The necessity for introducing them was pointed out by Saint-Venant. The effect of them is a change of shape of the cross-sections in their own planes. This is shown in an exaggerated way in fig. 10, where the rectangle ABCD represents the cross-section of the unstrained beam, or a rectangular portion of this cross-section, and the curvilinear figure A′B′C′D′ represents in an exaggerated fashion the cross-section (or the corresponding portion of the cross-section) of the same beam, when bent so that the centre of curvature of the central-line (which is at right angles to the plane of the figure) is on the line EF produced beyond F. The lines A′B′ and C′D′ are approximately circles of radii R/σ, when the central-line is a circle of radius R, and their centres are on the line FE produced beyond E. Thus the neutral plane, and each of the faces that is parallel to it, becomes strained into an anticlastic surface, whose principal curvatures are in the ratio σ : 1. The general appearance of the bent beam is shown in an exaggerated fashion in fig. 11, where the traces of the surface into which the neutral plane is bent are dotted. The result that the ratio of the principal curvatures of the anticlastic surfaces, into which the top and bottom planes of the beam (of rectangular section) are bent, is Poisson’s ratio σ, has been used for the experimental determination of σ. The result that the radius of curvature of the bent central-line is EI/M is used in the experimental determination of E. The quantity EI is often called the “flexural rigidity” of the beam. There are two principal flexural rigidities corresponding to bending in the two principal planes (cf. § 62 below).

48. That this theory requires modification, when the load does not consist simply of terminal couples, can be seen most easily by considering the problem of a beam loaded at one end with a weight W, and supported in a horizontal position at its other end. The forces that are exerted at any section p, to balance the weight W, must reduce statically to a vertical force W and a couple, and these forces arise from the action of the part Ap on the part Bp (see fig. 12), i.e. from the stresses across the section at p. The couple is equal to the moment of the applied load W about an axis drawn through the centroid of the section p at right angles to the plane of bending. This moment is called the “bending moment” at the section, it is the product of the load W and the distance of the section from the loaded end, so that it varies uniformly along the length of the beam. The stress that suffices in the simpler problem gives rise to no vertical force, and it is clear that in addition to longitudinal tensions and pressures there must be tangential tractions on the cross-sections. The resultant of these tangential tractions must be a force equal to W, and directed vertically; but the direction of the traction at a point of the cross-section need not in general be vertical. The existence of tangential traction on the cross-sections implies the existence of equal tangential traction, directed parallel to the central-line, on some planes or other which are parallel to this line, the two sets of tractions forming a shearing stress. We conclude that such shearing stress is a necessary constituent of the stress-system in the beam bent by terminal transverse load. We can develop a theory of this stress-system from the assumptions (i.) that the tension at any point of the cross-section is related to the bending moment at the section by the same law as in the case of uniform bending by terminal couples; (ii.) that, in addition to this tension, there is at any point shearing stress, involving tangential tractions acting in appropriate directions upon the elements of the cross-sections. When these assumptions are made it appears that there is one and only one distribution of shearing stress by which the conditions of the problem can be satisfied. The determination of the amount and direction of this shearing stress, and of the corresponding strains and displacements, was effected by Saint-Venant and R.F.A. Clebsch for a number of forms of section by means of an analysis of the same kind as that employed in the solution of the torsion problem.

49. Let l be the length of the beam, x the distance of the section p from the fixed end A, y the distance of any point below the horizontal plane through the centroid of the section at A, then the bending moment at p is W (l − x), and the longitudinal tension P or Xx at any point on the cross-section is −W (l − x)y/I, and this is related to the bending moment exactly as in the simpler problem.

50. The expressions for the shearing stresses depend on the shape of the cross-section. Taking the beam to be of isotropic material and the cross-section to be an ellipse of semiaxes a and b (fig. 13), the a axis being vertical in the unstrained state, and drawing the axis z at right angles to the plane of flexure, we find that the vertical shearing stress U or Xy at any point (y, z) on any cross-section is

The resultant of these stresses is W, but the amount at the centroid, which is the maximum amount, exceeds the average amount, W/πab, in the ratio

{4a² (1 + σ) + 2b²} / (3a² + b²) (1 + σ).

If σ = ¼, this ratio is 7⁄5 for a circle, nearly 4⁄3 for a flat elliptic bar with the longest diameter vertical, nearly 8⁄5 for a flat elliptic bar with the longest diameter horizontal.

In the same problem the horizontal shearing stress T or Zx at any point on any cross-section is of amount

The resultant of these stresses vanishes; but, taking as before σ = ¼, and putting for the three cases above a = b, a = 10b, b = 10a, we find that the ratio of the maximum of this stress to the average vertical shearing stress has the values 3⁄5, nearly 1⁄15, and nearly 4. Thus the stress T is of considerable importance when the beam is a plank.

As another example we may consider a circular tube of external radius r0 and internal radius r1. Writing P, U, T for Xx, Xy, Zx, we find