Chapter III: Act 1836: , which created two new dioceses (Ripon and Manchester), (2)

DIONYSIUS EXIGUUS, one of the most learned men of the 6th century, and especially distinguished as a chronologist, was, according to the statement of his friend Cassiodorus, a Scythian by birth, "_Scytha natione_." This may mean only that he was a native of the region bordering on the Black Sea, and does not necessarily imply that he was not of Greek origin. Such origin is indicated by his name and by his thorough familiarity with the Greek language. His surname "Exiguus" is usually translated "the Little," but he probably assumed it out of humility. He was living at Rome in the first half of the 6th century, and is usually spoken of as abbot of a Roman monastery. Cassiodorus, however, calls him simply "monk," while Bede calls him "abbot." But as it was not unusual to apply the latter term to distinguished monks who were not heads of their houses, it is uncertain whether Dionysius was abbot in fact or only by courtesy. He was in high repute as a learned theologian, was profoundly versed in the Holy Scriptures and in canon law, and was also an accomplished mathematician and astronomer. We owe to him a collection of 401 ecclesiastical canons, including the apostolical canons and the decrees of the councils of Nicaea, Constantinople, Chalcedon and Sardis, and also a collection of the decretals of the popes from Siricius (385) to Anastasius II. (498). These collections, which had great authority in the West (see CANON LAW), were published by Justel in 1628. Dionysius did good service to his contemporaries by his translations of many Greek works into Latin; and by these translations some works, the originals of which have perished, have been handed down to us. His name, however, is now perhaps chiefly remembered for his chronological labours. It was Dionysius who introduced the method of reckoning the Christian era which we now use (see CHRONOLOGY). His friend Cassiodorus depicts in glowing terms the character of Dionysius as a saintly ascetic, and praises his wisdom and simplicity, his accomplishments and his lowly-mindedness, his power of eloquent speech and his capacity of silence. He died at Rome, some time before A.D. 550.

His works have been published in Migne, _Patrologia Latina_, tome 67;
see especially A. Tardif, _Histoire des sources du droit canonique_
(Paris, 1887), and D. Pitra, _Analecta novissima, Spicilegii
Solesmensis continuatio_, vol. i. p. 36 (Paris, 1885).

DIONYSIUS HALICARNASSENSIS ("of Halicarnassus"), Greek historian and teacher of rhetoric, flourished during the reign of Augustus. He went to Rome after the termination of the civil wars, and spent twenty-two years in studying the Latin language and literature and preparing materials for his history. During this period he gave lessons in rhetoric, and enjoyed the society of many distinguished men. The date of his death is unknown. His great work, entitled [Greek: Romaike archaiologia] (Roman Antiquities), embraced the history of Rome from the mythical period to the beginning of the first Punic War. It was divided into twenty books,--of which the first nine remain entire, the tenth and eleventh are nearly complete, and the remaining books exist in fragments in the excerpts of Constantine Porphyrogenitus and an epitome discovered by Angelo Mai in a Milan MS. The first three books of Appian, and Plutarch's _Life of Camillus_ also embody much of Dionysius. His chief object was to reconcile the Greeks to the rule of Rome, by dilating upon the good qualities of their conquerors. According to him, history is philosophy teaching by examples, and this idea he has carried out from the point of view of the Greek rhetorician. But he has carefully consulted the best authorities, and his work and that of Livy are the only connected and detailed extant accounts of early Roman history.

Dionysius was also the author of several rhetorical treatises, in which he shows that he has thoroughly studied the best Attic models:--_The Art of Rhetoric_ (which is rather a collection of essays on the theory of rhetoric), incomplete, and certainly not all his work; _The Arrangement of Words_ ([Greek: Peri syntheseos onomaton]), treating of the combination of words according to the different styles of oratory; _On Imitation_ ([Greek: Peri mimeseos]), on the best models in the different kinds of literature and the way in which they are to be imitated--a fragmentary work; _Commentaries on the Attic Orators_ ([Greek: Peri ton archaion rhetoron hypomnematismoi]), which, however, only deal with Lysias, Isaeus, Isocrates and (by way of supplement) Dinarchus; _On the admirable Style of Demosthenes_ ([Greek: Peri tes lektikes Demosthenous deinotetos]); and _On the Character of Thucydides_ ([Greek: Peri tou Thoukydidou charakteros]), a detailed but on the whole an unfair estimate. These two treatises are supplemented by letters to Cn. Pompeius and Ammaeus (two).

Complete edition by J. J. Reiske (1774-1777); of the _Archaeologia_ by
A. Kiessling and V. Prou (1886) and C. Jacoby (1885-1891); Opuscula by
Usener and Radermacher (1899); Eng. translation by E. Spelman (1758).
A full bibliography of the rhetorical works is given in W. Rhys
Roberts's edition of the Three Literary Letters (1901); the same
author published an edition of the _De compositione verborum_ (1910,
with trans.); see also M. Egger, _Denys d'Halicarnasse_ (1902), a very
useful treatise. On the sources of Dionysius see O. Bocksch, "De
fontibus Dion. Halicarnassensis" in _Leipziger Studien_, xvii. (1895).
Cf. also J. E. Sandys, _Hist. of Class. Schol._ i. (1906).

DIONYSIUS PERIEGETES, author of a [Greek: Periegesis tes oikoumenes], a description of the habitable world in Greek hexameter verse, written in a terse and elegant style. Nothing certain is known of the date or nationality of the writer, but there is some reason for believing that he was an Alexandrian, who wrote in the time of Hadrian (some put him as late as the end of the 3rd century). The work enjoyed a high degree of popularity in ancient times as a school-book; it was translated into Latin by Rufus Festus Avienus, and by the grammarian Priscian. The commentary of Eustathius is valuable.

The best editions are by G. Bernhardy (1828) and C. Muller (1861) in
their _Geographici Graeci minores_; see also E. H. Bunbury, _Ancient
Geography_ (ii. p. 480), who regards the author as flourishing from
the reign of Nero to that of Trajan, and U. Bernays, _Studien zu Dion.
Perieg._ (1905). There are two old English translations: T. Twine
(1572, black letter), J. Free (1789, blank verse).

DIONYSIUS TELMAHARENSIS ("of Tell-Ma[h.]r[=e]"), patriarch or supreme head of the Syrian Jacobite Church during the years 818-848, was born at Tell-Ma[h.]r[=e] near Ra[k.][k.]a (ar-Ra[k.][k.]ah) on the Bal[=i]kh. He was the author of an important historical work, which has seemingly perished except for some passages quoted by Barhebraeus and an extract found by Assemani in Cod. _Vat._ 144 and published by him in the _Bibliotheca orientalis_ (ii. 72-77). He spent his earlier years as a monk at the convent of [K.]en-neshr[=e] on the upper Euphrates; and when this monastery was destroyed by fire in 815, he migrated northwards to that of Kais[=u]m in the district of Samos[=a]ta. At the death of the Jacobite patriarch Cyriacus in 817, the church was agitated by a dispute about the use of the phrase "heavenly bread" in connexion with the Eucharist. An anti-patriarch had been appointed in the person of Abraham of [K.]artam[=i]n, who insisted on the use of the phrase in opposition to the recognized authorities of the church. The council of bishops who met at Ra[k.][k.]a in the summer of 818 to choose a successor to Cyriacus had great difficulty in finding a worthy occupant of the patriarchal chair, but finally agreed on the election of Dionysius, hitherto known only as an honest monk who devoted himself to historical studies. Sorely against his will he was brought to Ra[k.][k.]a, ordained deacon and priest on two successive days, and raised to the supreme ecclesiastical dignity on the 1st of August. From this time he showed the utmost zeal in fulfilling the duties of his office, and undertook many journeys both within and without his province. The ecclesiastical schism continued unhealed during the thirty years of his patriarchate. The details of this contest, of his relations with the caliph Ma'm[=u]n, and of his many travels--including a journey to Egypt, on which he viewed with admiration the great Egyptian monuments,--are to be found in the _Ecclesiastical Chronicle_ of Barhebraeus.[1] He died in 848, his last days having been especially embittered by Mahommedan oppression. We learn from Michael the Syrian that his _Annals_ consisted of two parts each divided into eight chapters, and covered a period of 260 years, viz. from the accession of the emperor Maurice (582-583) to the death of Theophilus (842-843).

In addition to the lost _Annals_, Dionysius was from the time of Assemani until 1896 credited with the authorship of another important historical work--a _Chronicle_, which in four parts narrates the history of the world from the creation to the year A.D. 774-775 and is preserved entire in _Cod. Vat._ 162. The first part (edited by Tullberg, Upsala, 1850) reaches to the epoch of Constantine the Great, and is in the main an epitome of the Eusebian Chronicle.[2] The second part reaches to Theodosius II. and follows closely the _Ecclesiastical History_ of Socrates; while the third, extending to Justin II., reproduces the second part of the _History_ of John of Asia or Ephesus, and also contains the well-known chronicle attributed to Joshua the Stylite. The fourth part[3] is not like the others a compilation, but the original work of the author, and reaches to the year 774-775--apparently the date when he was writing. On the publication of this fourth part by M. Chabot, it was discovered and clearly proved by Noldeke (_Vienna Oriental Journal_, x. 160-170), and Nau (_Bulletin critique_, xvii. 321-327), who independently reached the same conclusion, that Assemani's opinion was a mistake, and that the chronicle in question was the work not of Dionysius of Tell-Ma[h.]r[=e] but of an earlier writer, a monk of the convent of Zu[k.]n[=i]n near [=A]mid (Diarbekr) on the upper Tigris. Though the author was a man of limited intelligence and destitute of historical skill, yet the last part of his work at least has considerable value as a contemporary account of events during the middle period of the 8th century. (N. M.)

FOOTNOTES:

[1] Ed. Abbeloos and Lamy, i. 343-386; cf. Wright, _Syriac
Literature_, 196-200, and Chabot's introduction to his translation of
the fourth part of the _Chronicle_ of (pseudo) Dionysius.

[2] See the studies by Siegfried and Gelzer, _Eusebii canonum epitome
ex Dionysii Telmaharensis chronico petita_ (Leipzig, 1884), and von
Gutschmid, _Untersuchungen uber die syrische Epitome der Eusebischen
Canones_ (Stuttgart, 1886).

[3] Text and translation by J.-B. Chabot (Paris, 1895).

DIONYSIUS THRAX (so called because his father was a Thracian), the author of the first Greek grammar, flourished about 100 B.C. He was a native of Alexandria, where he attended the lectures of Aristarchus, and afterwards taught rhetoric in Rhodes and Rome. His [Greek: Techne grammatike], which we possess (though probably not in its original form), begins with the definition of grammar and its functions. Dealing next with accent, punctuation marks, sounds and syllables, it goes on to the different parts of speech (eight in number) and their inflections. No rules of syntax are given, and nothing is said about style. The authorship of Dionysius was doubted by many of the early middle-age commentators and grammarians, and in modern times its origin has been attributed to the oecumenical college founded by Constantine the Great, which continued in existence till 730. But there seems no reason for doubt; the great grammarians of imperial times (Apollonius Dyscolus and Herodian) were acquainted with the work in its present form, although, as was natural considering its popularity, additions and alterations may have been made later. The [Greek: Techne] was first edited by J. A. Fabricius from a Hamburg MS. and published in his _Bibliotheca Graeca_, vi. (ed. Harles). An Armenian translation, belonging to the 4th or 5th century, containing five additional chapters, was published with the Greek text and a French version, by M. Cirbied (1830). Dionysius also contributed much to the criticism and elucidation of Homer, and was the author of various other works--amongst them an account of Rhodes, and a collection of [Greek: Meletai] (literary studies), to which the considerable fragment in the _Stromata_ (v. 8) of Clement of Alexandria probably belongs.

Editions, with scholia, by I. Bekker in _Anecdota Graeca_, ii. and G.
Uhlig (1884), reviewed exhaustively by P. Egenolff in Bursian's
_Jahresbericht_, vol. xlvi. (1888); Scholia, ed. A. Hilgard (1901);
see also W. Horschelmann, _De Dionysii Thracis interpretibus
veteribus_ (1874); J. E. Sandys, _Hist. of Classical Scholarship_, i.
(1906).

DIONYSUS (probably = "son of Zeus," from [Greek: Dios] and [Greek: nysos], a Thracian word for "son"), in Greek mythology, originally a nature god of fruitfulness and vegetation, especially of the vine; hence, distinctively, the god of wine. The names Bacchus ([Greek: Bakchos], in use among the Greeks from the 5th century), Sabazius, and Bassareus, are also Thracian names of the god. The two first (like Iacchus, Bromius and Euios) have been connected with the loud "shout" ([Greek: sabazein = bazein = euazein]) of his worshippers, Bassareus with [Greek: bassarai], the fox-skin garments of the Thracian Bacchanals. It has been suggested (J. E. Harrison _Prolegomena to Greek Religion_) that Sabazius and Bromius = "beer-god," "god of a cereal intoxicant" (cf. Illyrian _sabaia_ and modern Greek [Greek: bromi], "oats"), while W. Ridgeway (_Classical Review_, January 1896), comparing Apollo Smintheus, interprets Bassareus as "he who keeps away the foxes from the vineyards" (for various interpretations of these and other cult-titles, see O. Gruppe, _Griechische Mythologie_, ii. pp. 1408, 1532, especially the notes).

In Homer, notwithstanding the frequent mention of the use of wine, Dionysus is never mentioned as its inventor or introducer, nor does he appear in Olympus; Hesiod is the first who calls wine the gift of Dionysus. On the other hand, he is spoken of in the _Iliad_ (vi. 130 foll., a passage belonging to the latest period of epic), as "raging," an epithet that indicates that in those comparatively early times the orgiastic character of his worship was recognized. In fact, Dionysus may be regarded under two distinct aspects: that of a popular national Greek god of wine and cheerfulness, and that of a foreign deity, worshipped with ecstatic and mysterious rites introduced from Thrace. According to the usual tradition, he was born at Thebes--originally the local centre of his worship in Greece--and was the son of Zeus, the fertilizing rain god, and Semele, the daughter of Cadmus, a personification of earth. Before the child was mature, Zeus appeared to Semele at her request in his majesty as god of lightning, by which she was killed, but the infant was saved from the flames by Zeus (or Hermes). The epithet [Greek: perikionios], originally referring to an ivy-crowned, pillar-shaped fetish of the god, afterwards gave rise to the legend of a miraculous growth of ivy "round the pillars" of the royal palace, whereby the infant Dionysus was preserved from the flames. Zeus took him up, enclosed him within his own thigh till he came to maturity, and then brought him to the light, so that he was twice born; it was to celebrate this double birth that the _dithyrambus_ (also used as an epithet of the god) was sung (see _Etym. Mag._ s.v.). It has been suggested that this is an allusion to the _couvade_ of certain barbarous tribes, amongst whom it is customary, when a child is born, for the husband to take to his bed and receive medical treatment, as if he shared the pains of maternity (see COUVADE, and references there). Dionysus was then conveyed by Hermes to be brought up by the nymphs of Nysa, a purely imaginary spot, afterwards localized in different parts of the world, which claimed the honour of having been the birthplace of the god. As soon as Dionysus was grown up, he started on a journey through the world, to teach the cultivation of the vine and spread his worship among men. While so engaged he met with opposition, even in his own country, as in the case of Pentheus, king of Thebes, who opposed the orgiastic rites introduced by Dionysus among the women of Thebes, and, having been discovered watching one of these ceremonies, was mistaken for some animal of the chase, and slain by his own mother (see A. G. Bather, _Journ. Hell. Studies_, xiv. 1894). A similar instance is that of Lycurgus, a Thracian king, from whose attack Dionysus saved himself by leaping into the sea, where he was kindly received by Thetis. Lycurgus was blinded by Zeus and soon died, or became frantic and hewed down his own son, mistaking him for a vine. At Orchomenus, the three daughters of Minyas refused to join the other women in their nocturnal orgies, and for this were transformed into birds (see AGRIONIA). These and similar stories point to the vigorous resistance offered to the introduction of the mystic rites of Dionysus, in places where an established religion already existed. On the other hand, when the god was received hospitably he repaid the kindness by the gift of the vine, as in the case of Icarius of Attica (see ERIGONE).

The worship of Dionysus was actively conducted in Asia Minor, particularly in Phrygia and Lydia. Here, as Sabazius, he was associated with the Phrygian goddess Cybele, and was followed in his expeditions by a _thiasos_ (retinue) of centaurs, and satyrs, with Pan and Silenus. In Lydia his triumphant return from India was celebrated by an annual festival on Mount Tmolus; in Lydia he assumed the long beard and long robe which were afterwards given him in his character of the "Indian Bacchus," the conqueror of the East, who, after the campaigns of Alexander, was reported to have advanced as far as the Ganges. The other incidents in which he appears in a purely triumphal character are his transforming into dolphins the Tyrrhene pirates who attacked him, as told in the Homeric hymn to Dionysus and represented on the monument of Lysicrates at Athens, and his part in the war of the gods against the giants. The former story has been connected with the sailors' custom of hanging vine leaves, ivy and bunches of grapes round the masts of vessels in honour of vintage festivals. The adventure with the pirates occurred on his voyage to Naxos, where he found Ariadne abandoned by Theseus. At Naxos Ariadne (probably a Cretan goddess akin to Aphrodite) was associated with Dionysus as his wife, by whom he was the father of Oenopion (wine-drinker), Staphylus (grape), and Euanthes (blooming), and their marriage was annually celebrated by a festival. Having compelled all the world to recognize his divinity, he descended to the underworld to bring up his mother, who was afterwards worshipped with him under the name of Thyone ("the raging"), he himself being called after her Thyoneus.

Another phase in the myth of Dionysus originated in observing the decay of vegetation in winter, to suit which he was supposed to be slain and to join the deities of the lower world. This phase of his character was developed by the Orphic poets, he having here the name of Zagreus ("torn in pieces"), and being no longer the Theban god, but a son of Zeus and Persephone. The child was brought up secretly, watched over by Curetes; but the jealous Hera discovered where he was, and sent Titans to the spot, who, finding him at play, tore him to pieces, and cooked and ate his limbs, while Hera gave his heart to Zeus. The tearing in pieces is referred by some to the torture experienced by the grape (_Naturschmerz_) when crushed for making into wine (cf. Burns's _John Barleycorn_); but it is better to refer it to the tearing of the flesh of the victim at sacrifices at which the deity or the sacred animal was slain, and sacramentally eaten raw (cf. the title [Greek: omestes] given to Dionysus in certain places, probably pointing to human sacrifice.) To connect this with the myth of the Theban birth of Dionysus, it is said that Zeus gave the child's heart to Semele, or himself swallowed it and gave birth to the new Dionysus (called Iacchus from his worshippers' cry of rejoicing), who was cradled and swung in a winnowing fan ([Greek: liknos]; see J. E. Harrison, _Journ. Hellenic Studies_, xxiii.), the swinging being supposed to act as a charm in awakening vegetation from its winter sleep. The conception of Zagreus, or the winter Dionysus, appears to have originated in Crete, but it was accepted also in Delphi, where his grave was shown, and sacrifice was secretly offered at it annually on the shortest day. The story is in many respects similar to that of Osiris. According to others, Zagreus was originally a god of the chase, who became a hunter of men and a god of the underworld, more akin to Hades than to Dionysus (see also TITANS).

Dionysus further possessed the prophetic gift, and his oracle at Delphi was as important as that of Apollo. Like Hermes, Dionysus was a god of the productiveness of nature, and hence Priapus was one of his regular companions, while not only in the mysteries but in the rural festivals his symbol, the phallus, was carried about ostentatiously. His symbols from the animal kingdom were the bull (perhaps a totemistic attribute and identified with him), the panther, the lion, the tiger, the ass, the goat, and sometimes also the dolphin and the snake. His personal attributes are an ivy wreath, the thyrsus (a staff with pine cone at the end), the laurel, the pine, a drinking cup, and sometimes the horn of a bull on his forehead. Artistically he was represented mostly either as a youth of soft, nearly feminine form, or as a bearded and draped man, but frequently also as an infant, with reference to his birth or to his bringing up in "Nysa." His earliest images were of wood with the branches still attached in parts, whence he was called Dionysus Dendrites, an allusion to his protection of trees generally (according to Pherecydes in C. W. Muller, _Frag. Hist. Graec._ iv. p. 637, the word [Greek: nysa] signified "tree"). It is suggested that the cult of Dionysus absorbed that of an old tree-spirit. He was figured also, like Hermes, in the form of a pillar or term surmounted by his head. For the connexion of Dionysus with Greek tragedy see DRAMA.

See Farnell, _Cults of the Greek States_, v. (1910); also O. Rapp,
_Beziehungen des Dionysuskultus zu Thrakien_ (1882); O. Ribbeck,
_Anfange und Entwickelung des Dionysuskultes in Attica_ (1869); A.
Lang, _Myth, Ritual and Religion_, ii. p. 241; L. Dyer, _The Gods in
Greece_ (1891); J. E. Harrison, _Prolegomena to the Study of Greek
Religion_ (1903); J. G. Frazer, _The Golden Bough_, ii (1900), pp.
160, 291, who regards the bull and goat form of Dionysus as
expressions of his proper character as a deity of vegetation; F. A.
Voigt in Roscher's _Lexikon der Mythologie_; L. Preller, _Griechische
Mythologie_ (4th ed. by C. Robert); F. Lenormant (s.v. "Bacchus") in
Daremberg and Saglio's _Dictionnaire des antiquites_; O. Kern in
Pauly-Wissowa's _Realencyclopadie_ (with list of cult titles); W.
Pater, _Greek Studies_ (1895); E. Rohde, _Psyche_, ii., who finds the
origin of the Hellenic belief in the immortality of the soul in the
"enthusiastic" rites of the Thracian Dionysus, which lifted persons
out of themselves, and exalted them to a fancied equality with the
gods; O. Gruppe, _Griechische Mythologie und Religionsgeschichte_, ii.
(1907), who considers Boeotia, not Thrace, to have been the original
home of Dionysus; P. Foucart, "Le Culte de Dionysos en Attique" in
_Memoires de l'Institut national de France_, xxxvii. (1906), who finds
the prototype of Dionysus in Egypt. _The Great Dionysiak Myth_
(1877-1878) by R. Brown contains a wealth of material, but is weak in
scholarship. For a striking survival of Dionysiac rites in Thrace
(Bizye), see Dawkins, in _J.H.S._ (1906), p. 191.

DIOPHANTUS, of Alexandria, Greek algebraist, probably flourished about the middle of the 3rd century. Not that this date rests on positive evidence. But it seems a fair inference from a passage of Michael Psellus (_Diophantus_, ed. P. Tannery, ii. p. 38) that he was not later than Anatolius, bishop of Laodicea from A.D. 270, while he is not quoted by Nicomachus (fl. c. A.D. 100), nor by Theon of Smyrna (c. A.D. 130), nor does Greek arithmetic as represented by these authors and by Iamblichus (end of 3rd century) show any trace of his influence, facts which can only be accounted for by his being later than those arithmeticians at least who would have been capable of understanding him fully. On the other hand he is quoted by Theon of Alexandria (who observed an eclipse at Alexandria in A.D. 365); and his work was the subject of a commentary by Theon's daughter Hypatia (d. 415). The _Arithmetica_, the greatest treatise on which the fame of Diophantus rests, purports to be in thirteen Books, but none of the Greek MSS. which have survived contain more than six (though one has the same text in seven Books). They contain, however, a fragment of a separate tract on _Polygonal Numbers_. The missing books were apparently lost early, for there is no reason to suppose that the Arabs who translated or commented on Diophantus ever had access to more of the work than we now have. The difference in form and content suggests that the _Polygonal Numbers_ was not part of the larger work. On the other hand the _Porisms_, to which Diophantus makes three references ("we have it in the Porisms that ..."), were probably not a separate book but were embodied in the _Arithmetica_ itself, whether placed all together or, as Tannery thinks, spread over the work in appropriate places. The "Porisms" quoted are interesting propositions in the theory of numbers, one of which was clearly that _the difference between two cubes can be resolved into the sum of two cubes_. Tannery thinks that the solution of a complete quadratic promised by Diophantus himself (I. def. 11), and really assumed later, was one of the Porisms.

Among the great variety of problems solved are problems leading to
determinate equations of the first degree in one, two, three or four
variables, to determinate quadratic equations, and to indeterminate
equations of the first degree in one or more variables, which are,
however, transformed into determinate equations by arbitrarily
assuming a value for one of the required numbers, Diophantus being
always satisfied with a rational, even if fractional, result and not
requiring a solution in integers. But the bulk of the work consists of
problems leading to indeterminate equations of the second degree, and
these universally take the form that one or two (and never more)
linear or quadratic functions of one variable x are to be made
rational square numbers by finding a suitable value for x. A few
problems lead to indeterminate equations of the third and fourth
degrees, an easy indeterminate equation of the sixth degree being
also found. The general type of problem is to find two, three or four
numbers such that different expressions involving them in the first
and second, and sometimes the third, degree are squares, cubes, partly
squares and partly cubes, &c. E.g. _To find three numbers such that
the product of any two added to the sum of those two gives a square_
(III. 15, ed. Tannery); _To find four numbers such that, if we take
the square of their sum [+-] any one of them singly, all the resulting
numbers are squares_ (III. 22); _To find two numbers such that their
product [+-] their sum gives a cube_ (IV. 29); _To find three squares
such that their continued product added to any one of them gives a
square_ (V. 21). Book VI. contains problems of finding rational
_right-angled triangles_ such that different functions of their parts
(the sides and the area) are squares. A word is necessary on
Diophantus' notation. He has only one symbol (written somewhat like a
final sigma) for an unknown quantity, which he calls [Greek: arithmos]
(defined as "an undefined number of units"); the symbol may be a
contraction of the initial letters [alpha][rho], as [Delta]^[Upsilon],
[Kappa]^[Upsilon], [Delta]^[Upsilon][Delta], &c., are for the powers
of the unknown ([Greek: dynamis], square; [Greek: kubos], cube;
[Greek: dynamodynamis], fourth power, &c.). The only other algebraical
symbol is [graphic: /|\] for minus; plus being expressed by merely
writing terms one after another. With one symbol for an unknown, it
will easily be understood what scope there is for adroit assumptions,
for the required numbers, of expressions in the one unknown which are
at once seen to satisfy some of the conditions, leaving only one or
two to be satisfied by the particular value of x to be determined.
Often assumptions are made which lead to equations in x which cannot
be solved "rationally," i.e. would give negative, surd or imaginary
values; Diophantus then traces how each element of the equation has
arisen, and formulates the auxiliary problem of determining how the
assumptions must be corrected so as to lead to an equation (in place
of the "impossible" one) which can be solved rationally. Sometimes his
x has to do duty twice, for different unknowns, in one problem. In
general his object is to reduce the final equation to a simple one by
making such an assumption for the side of the square or cube to which
the expression in x is to be equal as will make the necessary number
of coefficients vanish. The book is valuable also for the propositions
in the theory of numbers, other than the "porisms," stated or assumed
in it. Thus Diophantus knew that _no number of the form 8n + 7 can be
the sum of three squares_. He also says that, if 2n + 1 is to be the
sum of two squares, "n must not be odd" (i.e. _no number of the form
4n + 3, or 4n - 1, can be the sum of two squares_), and goes on to
add, practically, the condition stated by Fermat, "and the double of
it [n] increased by one, when divided by the greatest square which
measures it, must not be divisible by a prime number of the form 4n -
1," except for the omission of the words "when divided ... measures
it."

# AUTHORITIES.--The first to publish anything on Diophantus in Europe
was Rafael Bombelli, who embodied in his Algebra (1572) all the
problems of Books I.-IV. and some of Book V. interspersing them with
his own problems. Next Xylander (Wilhelm Holzmann) published a Latin
translation (Basel, 1575), an altogether meritorious work, especially
having regard to the difficulties he had with the text of his MS. The
Greek text was first edited by C. G. Bachet (_Diophanti Alexandrini
arithmeticorum libri sex, et de numeris multangulis liber unus, nunc
primum graece et latine editi atque absolutissimis commentariis
illustrati_ ... Lutetiae Parisiorum ... MDCXXI.). A reprint of 1670 is
only valuable because it contains P. de Fermat's notes; as far as the
Greek text is concerned it is much inferior to the other. There are
two German translations, one by Otto Schulz (1822) and the other by G.
Wertheim (Leipzig, 1890), and an English edition in modern notation
(T. L. Heath, _Diophantos of Alexandria: A Study in the History of
Greek Algebra_ (Cambridge, 1885)). The Greek text has now been
definitively edited (with Latin translation, Scholia, &c.) by P.
Tannery (Teubner, vol. i., 1893; vol. ii., 1895). General accounts of
Diophantus' work are to be found in H. Hankel and M. Cantor's
histories of mathematics, and more elaborate analyses are those of
Nesselmann (_Die Algebra der Griechen_, Berlin, 1842) and G. Loria
(_Le Scienze esatte nell' antica Grecia_, libro v., Modena, 1902, pp.
95-158). (T. L. H.)

DIOPSIDE, an important member of the pyroxene group of rock-forming minerals. It is a calcium-magnesium metasilicate, CaMg(SiO3)2, and crystallizes in the monoclinic system. Usually some iron is present replacing magnesium, and when this predominates there is a passage to hedenbergite, CaFe(SiO3)2, a closely allied variety of monoclinic pyroxene. These are distinguished from augite by containing little or no aluminium. Diopside is colourless, white, pale green to dark green or nearly black in colour, the depth of the colour depending on the amount of iron present. The specific gravity and optical constants also vary with the chemical composition; the sp. gr. of diopside is 3.2, increasing to 3.6 in hedenbergite, and the angle of optical extinction in the plane of symmetry varies between 38 deg. and 47 deg. in the two extremes of the series. Crystals are usually prismatic in habit with a rectangular cross-section as shown in the figure: the angle between the prism faces m, parallel to which there are perfect cleavages, is 92 deg. 50'.

Several varieties, depending on differences in structure and chemical composition, have been distinguished, viz. coccolite (from [Greek: kokkos], a grain), a granular variety; salite or sahlite, from Sala in Sweden; malacolite; diallage; violane, a lamellar variety of a dark violet-blue colour; chrome-diopside, a bright green variety containing a small amount of chromium; and many others. Belonging to the same series with diopside and hedenbergite is a manganese pyroxene, known as schefierite, which has the composition (Ca, Mg) (Fe, Mn) (Si03)2.

Diopside is the characteristic pyroxene of metamorphic rocks, occurring especially in crystalline limestones, and often in association with garnet and epidote. It is also an essential constituent of some pyroxene-granites, diorites and a few other igneous rocks, but the characteristic pyroxene of this class of rocks is augite. Fine transparent crystals of a pale green colour occur, with crystals of yellowish-red garnet (hessonite) and chlorite, in veins traversing serpentine in the Ala valley near Turin in Piedmont: a crystal of this variety ("alalite") is represented in the accompanying figure. These, as well as the long, transparent, bottle-green crystals from the Zillerthal in the Tyrol, have occasionally been cut as gem-stones. Good crystals have been found also at Achmatovsk near Zlatoust in the Urals, Traversella near Ivrea in Piedmont ("traversellite"), Nordmark in Sweden, Monroe in New York, Burgess in Lanark county, Ontario, and several other places: at Nordmark the large, rectangular black crystals occur with magnetite in the iron mines. (L. J. S.)

DIOPTASE, a rare mineral species consisting of acid copper orthosilicate, H2CuSiO4, crystallizing in the parallel-faced hemihedral class of the rhombohedral system. The degree of symmetry is the same as in the mineral phenacite, there being only an axis of triad symmetry and a centre of symmetry. The crystals have the form of a hexagonal prism m terminated by a rhombohedron r, the alternate edges between these being sometimes replaced by the faces of a rhombohedron s. The faces are striated parallel to the edges between r, s and m. There are perfect cleavages parallel to the faces of a rhombohedron which truncate the polar edges of r: from the cleavage cracks internal reflections are often to be seen in the crystal, and it was on account of this that the mineral was named dioptase, by R. J. Hauy in 1797, from [Greek: diopteuein], "to see into." The crystals vary from transparent to translucent with a vitreous lustre, and are bright emerald-green in colour; they thus have a certain resemblance to emerald, hence the early name emerald-copper (German, _Kupfer-Smaragd_). Hardness 5; sp. gr. 3.3. The mineral is decomposed by hydrochloric acid with separation of gelatinous silica. At a red heat it blackens and gives off water. The fine crystals from Mount Altyn-Tube on the western slopes of the Altai Mountains in the Kirghiz Steppes, Asiatic Russia, line cavities in a compact limestone; they were first sent to Europe in 1785 by Achir Mahmed, a Bucharian merchant, after whom the mineral has been named archirite. More recently, in 1890, good crystals of similar habit, but rather darker in colour, have been found with quartz and malachite near Komba in the French Congo. As drusy crystalline crusts it has been found at Copiapo in Chile and in Arizona.

Dioptase has occasionally been used as a gem-stone, especially in Russia and Persia; it has a fine colour, but a low degree of hardness and the transparency is imperfect. (L. J. S.)

DIORITE (from the Gr. [Greek: diorizein] to distinguish, from [Greek: dia] through, [Greek: oros], a boundary), in petrology, the name given by Hauy to a family of rocks of granitic texture, composed of plagioclase felspar and hornblende. As they are richer in the dark coloured ferromagnesian minerals they are usually grey or dark grey, and have a higher specific gravity than granite. They also rarely show visible quartz. But there are diorites of many kinds, as the name applies rather to a family of rocks than to a single species. Some contain biotite, others augite or hypersthene; many have a small amount of quartz. Orthoclase is rarely entirely absent, and when it is fairly common the rock becomes a tonalite; in this way a transition is furnished between diorites and granites. It is rare to find the pure types of "hornblende-diorite," "augite-diorite," &c., but in most cases the rocks contain two or more ferromagnesian silicates, and such combinations as "hornblende-biotite-diorite" are commonest in nature.

The felspar of the diorites ranges in composition from oligoclase to labradorite, and is often remarkably zonal, the external layers being more alkaline than the internal. Small fluid enclosures and black grains, probably iron oxides, often occur in it in great numbers. Weathering produces epidote, calcite, sericite and kaolin. The biotite is always brown or yellow; the hornblende usually green, but sometimes brown or yellowish brown in those diorites which have affinities to lamprophyres. The augite is nearly always green but sometimes has a reddish tinge; bronzite and hypersthene have their usual green and brown shades. Apatite, iron oxides and zircon are almost invariably present; sphene, garnet and orthite are occasionally observed; calcite, chlorite, muscovite, kaolin, epidote and bastite are secondary. The structure is not essentially different from that of granite. The ferromagnesian minerals crystallize comparatively early and have some idiomorphism; the felspar usually follows and only in part shows good crystalline outlines. Orthoclase and quartz, if present, are last to separate out, and fill the spaces between the other minerals; often they interpenetrate to form micropegmatite. In many diorites the plagioclase felspar has crystallized before the hornblende, which consequently has less perfect outlines and forms irregular plates which enclose sharply formed individuals of felspar. This produces the ophitic structure (very common also in the dolerites). More rarely biotite and augite exhibit the same relations to the plagioclase. Orbicular structure also occasionally appears in these rocks; in fact the orbicular diorite of Corsica (also called "Napoleonite" or "Corsite") was for a long time the best-known example of this structure. The rock seems composed of spheroids, about an inch in diameter, surrounded by a smaller amount of dark-coloured dioritic matrix. The spheroids have a radiate structure and often show concentric dark and pale shells. These consist of hornblende (dark green) and basic plagioclase felspar, labradorite and bytownite (grey or nearly white). Occasionally diorites have a parallel banded or foliated structure, but these must not be confounded with the epidiorites, which are metamorphic rocks and also have a conspicuous foliation.

Diorites must also be distinguished from hornblendic gabbros, which contain more basic felspars, rarely quartz and occasionally olivine; but the boundary lines between diorites and gabbros are admittedly somewhat vague, e.g. some authors would call rocks gabbro which others would regard as augite-diorite. The hornblendites differ from the diorites in containing little felspar, and consist principally of hornblende. Among varietal designations given to rocks of the diorite family are "banatite" for an augite-diorite with or without quartz (from the Schemnitz district), "granodiorite" for a quartz-hornblende-diorite (essentially the same as tonalite) from California, &c., "adamellite" for the quartz-mica-diorite or tonalite of Monte Adamello (Alps), "ornite" for a hornblende-diorite rich in felspar, from Sweden. (J. S. F.)

DIP (Old Eng. _dyppan_, connected with the common Teutonic root seen in "deep"), the angle which the magnetic needle makes with the horizon. A freely suspended magnetic needle will not maintain a horizontal position except at the magnetic equator. Over the N. magnetic pole the north-seeking end of the needle points directly downwards and dips at an intermediate angle at intermediate distances between the magnetic poles and equator. There are secular progressive variations of dip as well as of declination and the maxima are independent of each other. In 1576 the dip at London was 71 deg. 50', in 1720 (max.) 74 deg. 42', in 1900 67 deg. 9'. (For Dip Circle see INCLINOMETER.)

DIPHENYL (phenyl benzene), C6H5.C6H5, a hydrocarbon found in that fraction of the coal-tar distillate boiling between 240-300 deg. C., from which it may be obtained by warming with sulphuric acid, separating the acid layer and strongly cooling the undissolved oil. It may be artificially prepared by passing benzene vapour through a red-hot tube; by the action of sodium on brombenzene dissolved in ether; by the action of stannous chloride on phenyldiazonium chloride; or by the addition of solid phenyldiazonium sulphate to warm benzene (R. Mohlau, _Berichte, 1893, 26_, 1997) C6H5N2.HSO4 + C6H6 = H2SO4 + N2 + C6H5.C6H5. L. Gattermann (_Berichte, 1890, 23_, 1226) has also prepared it by the decomposition of a solution of phenyldiazonium sulphate with alcohol and copper powder. It crystallizes in plates (from alcohol) melting at 70-71 deg. C. and boiling at 254 deg. C. It is oxidized by chromic acid in glacial acetic acid solution to benzoic acid, dilute nitric acid and chromic acid mixture being without effect. It is not reduced by hydriodic acid and phosphorus, but sodium in the presence of amyl alcohol reduces it to tetrahydrodiphenyl C12H14.

Many substitution derivatives are known: the monosubstitution
derivatives being capable of existing in three isomeric forms. Of the
disubstitution derivatives the most important are those derived from
diparadiaminodiphenyl or benzidine (q.v.).

_Orthoaminodiphenyl_,

NH2
__ |__
/ \__/ \ ,
\__/ \__/

is prepared by the action of bromine and caustic soda on
orthophenylbenzamide (R. Hirsch, _Berichte, 1892, 25_, 1974); when its
vapour is passed over heated lime, carbazol (q.v.) is formed.

_Diorthodiaminodiphenyl_,

NH2 NH2
__| |__
/ \__/ \ ,
\__/ \__/

is obtained by the reduction of the corresponding nitro compound
(obtained by the action of ethyl nitrite at 0 deg. C. on
metadinitrobenzidine hydrochloride). Its tetrazo compound on reduction
gives a hydrazine which, on warming with hydrochloric acid at 150 deg.
C., decomposes into ammonium chloride and _phenazone_,

N = N
__| |__
/ \___/ \
\__/ \__/

(C12H8N2). One of the most important derivatives of diphenyl, from the
theoretical point of view, is _diphenic acid_ or diorthodiphenyl
carboxylic acid, which can be obtained from
diparadiaminodiphenyldiorthocarboxylic acid,
__ __
H2N / \__/ \ NH2 ,
\__/ \__/
| |
HOOC COOH

or from phenanthrene (q.v.), the constitution of which it determines.
See BENZIDINE for diparadiaminodiphenyl.

DIPHILUS, of Sinope, poet of the new Attic comedy and contemporary of Menander (342-291 B.C.). Most of his plays were written and acted at Athens, but he led a wandering life, and died at Smyrna. He was on intimate terms with the famous courtesan Gnathaena (Athenaeus xiii. pp. 579, 583). He is said to have written 100 comedies, the titles of fifty of which are preserved. He sometimes acted himself. To judge from the imitations of Plautus. (_Casina_ from the [Greek: Kleroumenoi], _Asinaria_ from the [Greek: Onagos], _Rudens_ from some other play), he was very skilful in the construction of his plots. Terence also tells us that he introduced into the _Adelphi_ (ii. 1) a scene from the [Greek: Synapothneskontes], which had been omitted by Plautus in his adaptation (_Commorientes_) of the same play. The style of Diphilus was simple and natural, and his language on the whole good Attic; he paid great attention to versification, and was supposed to have invented a peculiar kind of metre. The ancients were undecided whether to class him among the writers of the New or Middle comedy. In his fondness for mythological subjects (_Hercules_, _Theseus_) and his introduction on the stage (by a bold anachronism) of the poets Archilochus and Hipponax as rivals of Sappho, he approximates to the spirit of the latter.

Fragments in H. Koch, _Comicorum Atticorum fragmenta_, ii.; see J.
Denis, _La Comedie grecque_ (1886), ii. p. 414; R. W. Bond in
_Classical Review_ (Feb. 1910, with trans. of _Emporos_ fragm.).

DIPHTHERIA (from [Greek: diphthera], a skin or membrane), the term applied to an acute infectious disease, which is accompanied by a membranous exudation on a mucous surface, generally on the tonsils and back of the throat or pharynx.

In general the symptoms at the commencement of an attack of diphtheria are comparatively slight, being those commonly accompanying a cold, viz. chilliness and depression. Sometimes more severe phenomena usher in the attack, such as vomiting and diarrhoea. A slight feeling of uneasiness in the throat is experienced along with some stiffness of the back of the neck. When looked at the throat appears reddened and somewhat swollen, particularly in the neighbourhood of the tonsils, the soft palate and upper part of pharynx, while along with this there is tenderness and swelling of the glands at the angles of the jaws. The affection of the throat spreads rapidly, and soon the characteristic exudation appears on the inflamed surface in the form of greyish-white specks or patches, increasing in extent and thickness until a yellowish-looking false membrane is formed. This deposit is firmly adherent to the mucous membrane beneath or incorporated with it, and if removed leaves a raw, bleeding, ulcerated surface, upon which it is reproduced in a short period. The appearance of the exudation has been compared to wet parchment or washed leather, and it is more or less dense in texture. It may cover the whole of the back of the throat, the cavity of the mouth, and the posterior nares, and spread downwards into the air-passages on the one hand and into the alimentary canal on the other, while any wound on the surface of the body is liable to become covered with it. This membrane is apt to be detached spontaneously, and as it loosens it becomes decomposed, giving a most offensive and characteristic odour to the breath. There is pain and difficulty in swallowing, but unless the disease has affected the larynx no affection of the breathing. The voice acquires a snuffling character. When the disease invades the posterior nares an acrid, fetid discharge, and sometimes also copious bleeding, takes place from the nostrils. Along with these local phenomena there is evidence of constitutional disturbance of the most severe character. There may be no great amount of fever, but there is marked depression and loss of strength. The pulse becomes small and frequent, the countenance pale, the swelling of the glands of the neck increases, which, along with the presence of albumen in the urine, testifies to a condition of blood poisoning. Unless favourable symptoms emerge death takes place within three or four days or sooner, either from the rapid extension of the false membrane into the air-passage, giving rise to asphyxia, or from a condition of general collapse, which is sometimes remarkably sudden. In cases of recovery the change for the better is marked by an arrest in the extension of the false membrane, the detachment and expectoration of that already formed, and the healing of the ulcerated mucous membrane beneath. Along with this there is a general improvement in the symptoms, the power of swallowing returns, and the strength gradually increases, while the glandular enlargement of the neck diminishes, and the albumen disappears from the urine. Recovery, however, is generally slow, and it is many weeks before full convalescence is established. Even, however, where diphtheria ends thus favourably, the peculiar sequelae already mentioned are apt to follow, generally within a period of two or three weeks after all the local evidence of the disease has disappeared. These secondary affections may occur after mild as well as after severe attacks, and they are principally in the form of paralysis affecting the soft palate and pharynx, causing difficulty in swallowing with regurgitation of food through the nose, and giving a peculiar nasal character to the voice. There are, however, other forms of paralysis occurring after diphtheria, especially that affecting the muscles of the eye, which produces a loss of the power of accommodation and consequent impairment of vision. There may be, besides, paralysis of both legs, and occasionally also of one side of the body (hemiplegia). These symptoms, however, after continuing for a variable length of time, almost always ultimately disappear.

Under the name of the _Malum Egyptiacum_, Aretaeus in the 2nd century gives a minute description of a disease which in all its essential characteristics corresponds to diphtheria. In the 16th, 17th and 18th centuries epidemics of diphtheria appear to have frequently prevailed in many parts of Europe, particularly in Holland, Spain, Italy, France, as well as in England, and were described by physicians belonging to those countries under various titles; but it is probable that other diseases of a similar nature were included in their descriptions, and no accurate account of this affection had been published till M. Bretonneau of Tours in 1821 laid his celebrated treatise on the subject before the French Academy of Medicine. By him the term _La Diphtherite_ was first given to the disease.

Great attention has been paid to diphtheria in recent years, with some striking results. Its cause and nature have been definitely ascertained, the conditions which influence its prevalence have been elucidated, and a specific "cure" has been found. In the last respect it occupies a unique position at the present time. In the case of several other zymotic diseases much has been done by way of prevention, little or nothing for treatment; in the case of diphtheria prevention has failed, but treatment has been revolutionized by the introduction of antitoxin, which constitutes the most important contribution to practical medicine as yet made by bacteriology.

Causation.

The exciting cause of diphtheria is a micro-organism, identified by Klebs and Loffler in 1883 (see PARASITIC DISEASES). It has been shown by experiment that the symptoms of diphtheria, including the after-effects, are produced by a toxin derived from the micro-organisms which lodge in the air-passages and multiply in a susceptible subject. The natural history of the organism outside the body is not well understood, but there is some reason to believe that it lives in a dormant condition in suitable soils. Recent research does not favour the theory that it is derived from defective drains or "sewer gas," but these things, like damp and want of sunlight, probably promote its spread, by lowering the health of persons exposed to them, and particularly by causing an unhealthy condition of the throat, rendering it susceptible to the contagion. Defective drainage, or want of drainage, may also act, by polluting the ground, and so providing a favourable soil for the germ, though it is to be noted that "the steady increase in the diphtheria mortality has coincided, in point of time, with steady improvement in regard of such sanitary circumstances as water supply, sewerage, and drainage" (Thorne Thorne). Cats and cows are susceptible to the diphtheritic bacillus, and fowls, turkeys and other birds have been known to suffer from a disease like diphtheria, but other domestic animals appear to be more or less resistant or immune. In human beings the mere presence of the germ is not sufficient to cause disease; there must also be susceptibility, but it is not known in what that consists. Individuals exhibit all degrees of resistance up to complete immunity. Children are far more susceptible than adults, but even children may have the Klebs-Loffler bacillus in their throats without showing any symptoms of illness. Altogether there are many obscure points about this micro-organism, which is apt to assume a puzzling variety of forms. Nevertheless its identification has greatly facilitated the diagnosis of the disease, which was previously a very difficult matter, often determined in an arbitrary fashion on no particular principles.

Diphtheria, as at present understood, may be defined as sore throat in which the bacillus is found; if it cannot be found, the illness is regarded as something else, unless the clinical symptoms are quite unmistakable. One result of this is a large transference of registered mortality from other throat affections, and particularly from croup, to diphtheria. Croup, which never had a well-defined application, and is not recognized by the College of Physicians as a synonym for diphtheria, appears to be dying out from the medical vocabulary in Great Britain. In France the distinction has never been recognized.

Prevalence.

Diphtheria is endemic in all European and American countries, and is apparently increasing, but the incidence varies greatly. It is far more prevalent on the continent than in England, and still more so in the United States and Canada. The following table, compiled from figures collected by Dr Newsholme, shows how London compares with some foreign cities. The figures give the mean death-rate from diphtheria and croup for the term of years during which records have been kept. The period varies in different cases, and therefore the comparison is only a rough one.

_Mean Death-Rates from Diphtheria and Croup per Million living._

New York 1610 | Munich 990
Chicago 1400 | Milan 990
Buenos Aires 1360 | Florence 830
Trieste 1300 | Vienna 770
Dresden 1290 | Stockholm 720
Berlin 1190 | St Petersburg 650
Boston 1160 | Moscow 640
Marseilles 1130 | Paris 630
Christiania 1090 | Hamburg 490
Budapest 1880 | London 386