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Rh by Archbishop Parker. Withers had proposed a disputation against vestments, which the university would not allow; his thesis affirming the excommunicating power of the presbytery was sustained. Hence the treatise of Erastus. It was published (1589) by Giacomo Castelvetri, who had married his widow, with the title Explicatio gravissimae quaestionis utrum excommunicatio, quatenus religionem intelligentes et amplexantes, a sacramentorum usu, propter admissum facinus arcet, mandato nitatur divino, an excogitata sit ab hominibus. The work bears the imprint Pesclavii (i.e. Poschiavo in the Grisons) but was printed by John Wolfe in London, where Castelvetri was staying; the name of the alleged printer is an anagram of Jacobum Castelvetrum. In the Stationers’ Register (June 20, 1589) the printing is said to have been “alowed” by Archbishop Whitgift. It consists of seventy-five Theses, followed by a Confirmatio in six books, and an appendix of letters to Erastus by Bullinger and Gualther, showing that his Theses, written in 1568, had been circulated in manuscript. An English translation of the Theses, with brief life of Erastus (based on Melchior Adam’s account), was issued in 1659, entitled The Nullity of Church Censures; it was reprinted as A Treatise of Excommunication (1682), and, as revised by Robert Lee, D.D., in 1844. The aim of the work is to show, on Scriptural grounds, that sins of professing Christians are to be punished by civil authority, and not by withholding of sacraments on the part of the clergy. In the Westminster Assembly a party holding this view included Selden, Lightfoot, Coleman and Whitelocke, whose speech (1645) is appended to Lee’s version of the Theses; but the opposite view, after much controversy, was carried, Lightfoot alone dissenting. The consequent chapter of the Westminster Confession (“Of Church Censures”) was, however, not ratified by the English parliament. “Erastianism,” as a by-word, is used to denote the doctrine of the supremacy of the state in ecclesiastical causes; but the problem of the relations between church and state is one on which Erastus nowhere enters. What is known as “Erastianism” would be better connected with the name of Grotius. The only direct reply made to the Explicatio was the Tractatus de vera excommunicatione (1590) by Theodore Beza, who found himself rather savagely attacked in the Confirmatio thesium; e.g. “Apostolum et Mosen adeoque Deum ipsum audes corrigere.”

See A. Bonnard, Thomas Éraste et la discipline ecclésiastique (1894); Gass, in Allgemeine deutsche Biog. (1877); G.V. Lechler and R. Stähelin, in A. Hauck’s ''Realencyklop. für prot. Theol. u.'' Kirche (1898).

ERATOSTHENES OF ALEXANDRIA (c. 276–c. 194 ), Greek scientific writer, was born at Cyrene. He studied grammar under Callimachus at Alexandria, and philosophy under the Stoic Ariston and the Academic Arcesilaus at Athens. He returned to Alexandria at the summons of Ptolemy III. Euergetes, by whom he was appointed chief librarian in place of Callimachus. He is said to have died of voluntary starvation, being threatened with total blindness. Eratosthenes was one of the most learned men of antiquity, and wrote on a great number of subjects. He was the first to call himself Philologos (in the sense of the “friend of learning”), and the name Pentathlos was bestowed upon him in honour of his varied accomplishments. He was also called Beta as being second in all branches of learning, though not actually first in any. In mathematics he wrote two books On means ( ) which are lost, but appear, from a remark of Pappus, to have dealt with “loci with reference to means.” He devised a mechanical construction for two mean proportionals, reproduced by Pappus and Eutocius (Comm. on Archimedes). His  or sieve (cribrum Eratosthenis) was a device for discovering all prime numbers. He laid the foundation of mathematical geography in his Geographica, in three books. His greatest achievement was his measurement of the earth. Being informed that at Syene (Assuan), on the day of the summer solstice at noon, a well was lit up through all its depth, so that Syene lay on the tropic, he measured, at the same hour, the zenith distance of the sun at Alexandria. He thus found the distance between Syene and Alexandria (known to be 5000 stadia) to correspond to th of a great circle, and so arrived at 250,000 stadia (which he seems subsequently to have corrected to 252,000) as the circumference of the earth. He is credited by Ptolemy and his commentator Theon with having found the distance between the tropics to be 11 ⁄ 83 rds. of the meridian circle, which gives 23° 51’ 20&Prime; for the obliquity of the ecliptic. His astronomical poem Hermes began apparently with the birth and exploits of Hermes, then passed to the legend of his having ordered the heavens, the zones and the stars, and gave a history of the latter. His Erigone, of which a few fragments are also preserved, is sometimes spoken of as a separate poem, but it may have belonged to the Hermes, which appears also to have been known by other names such as Catalogi. The still extant Catasterismi, containing the story of certain stars in prose, is probably not by Eratosthenes.

Eratosthenes was the founder of scientific chronology in his  in which he endeavoured to fix the dates of the chief literary and political events from the conquest of Troy. An important work was his treatise on the old comedy, dealing with theatres and theatrical apparatus generally, and discussing the works of the principal comic poets themselves. Works on moral philosophy, history, and a number of letters were also attributed to him.

There is a complete edition of the fragments of Eratosthenes by Bernhardy (1822); poetical fragments, Hillier (1872); geographical, Seidel (1799) and Berger (1880);, Schaubach (1795) and Robert (1878). See Sandys, ''Hist. Class. Schol.'' i. (1906).

ERBACH, a town of Germany, in the grand-duchy of Hesse-Darmstadt, on the Mümling, 22 m. S.E. of Darmstadt. It has cloth mills and ivory-turning, for which last branch it possesses a technical school. Wool and cattle fairs are held twice a year. Pop. 2800. The castle contains an interesting collection of weapons and pictures, and in the chapel are the coffins of Einhard, the friend and biographer of Charlemagne, and his wife, Emma.

Erbach has long been the residence of the counts of Erbach, who trace their descent back to the 12th century, and who held the office of cupbearer to the electors palatine of the Rhine until 1806. In 1532 the emperor Charles V. made the county a direct fief of the Empire, on account of the services rendered by Count Eberhard during the Peasants’ War. Since 1717 the family has been divided into the three lines of Erbach-Fürstenau, Erbach-Erbach and Erbach-Schönberg, who rank for precedence, not according to the age of their descent, but according to the age of the chief of their line. In 1818 the counts of Erbach-Erbach inherited the county of Wartenberg-Roth, and in 1903 the count of Erbach-Schönberg was granted the title of prince. The county was mediatized in 1806, and is now incorporated with the duchy of Hesse-Darmstadt.

See Simon, Die Geschichte der Dynasten und Grafen zu Erbach (Frankfort, 1858).

ERBIUM (symbol, Er; atomic weight, 165-166), one of the metals of the rare earths. The first of the rare earth minerals was discovered in 1794 by J. Gadolin and was named gadolinite from its discoverer. In 1797 Ekeberg showed that gadolinite contained another rare earth, which was given the name yttria. Yttria is an exceedingly complex mixture, which has been decomposed, yielding as an intermediate product terbia. This latter substance in its turn has been split by J. L. Soret, P. T. Cleve, Lecoq de Boisbaudran and others into erbia, holmia, thulia and dysprosia, but it is still doubtful whether any one of these four splitting products is a single substance. The rare earth metals are found in the minerals gadolinite, samarskite, fergusonite, euxenite and cerite. They are separated from the minerals by converting them into oxalates, which by ignition give the corresponding oxides. The oxides are then converted into double sulphates which are separated from each other by repeated fractional crystallization or by fractional precipitation with ammonia or some other base. Erbium forms rose-coloured salts and a rose-coloured oxide. The oxide dissolves slowly in acids; it is not reduced by hydrogen and is infusible. The salts show a characteristic absorption spectrum.

See J. F. Bahr and R. Bunsen (Ann., 1866, 137, p. 1); A. v. Welsbach (Monats., 1883, 4, p. 641; 1884, 5, p. 508; 1885, 6, p. 477); P. T. Cleve (Comptes rendus, 1879, 89, p. 478; 1880, 91, pp. 328,