Chapter M: M. J. SUTHERLAND, D.Sc., F.I.C (3)

DICE, cubical pieces of bone or ivory, marked with dots on each of their six faces, from one to six, according to the number of faces. They are shaken in a small box and then thrown on the table. Dice are often loaded or falsified in some way so as to make the high or the low sides turn down. The origin of dice is ascribed to Palamedes of Greece (1244 B.C.), although Herodotus attributes the invention of knuckle-bones and of dice to the Lydians. Dice were well known amongst the ancient Egyptians and Greeks, and are still very popular in Japan, China, India, and other Asiatic countries.

DICEN'TRA. See _Dielytra_.

DICHASIUM. See _Cyme_.

DICHLAMYDEOUS (d[=i]-klam-id'i-us), in botany, said of plants that have both calyx and corolla.

DICHOGAMY, in flowers, the condition in which anthers and stigmas ripen at different times, whereby self-pollination is effectually prevented. If the anthers ripen first, as in borage, columbine, crocus, Caryophyllaceae, Compositae, Labiatae, &c., the flower is said to be protandrous; protogynous flowers, with stigmas ripening and withering before the pollen is shed, occur, e.g. in Christmas rose, Colchicum, horse-chestnut, and in the majority of wind-pollinated plants.

DICHOTOMY (d[=i]-kot'o-mi), a cutting in two; a division by pairs. Hence, in botany, a mode of branching by constant forking, each branch dividing into two others. See _Branching_.

DICHROIC, or more generally PLEOCHROIC, CRYSTALS (d[=i]-kr[=o]'ik), crystals that have the property of exhibiting different colours, according to the direction in which they are traversed by rays of light. When polarized light is passed through a transparent plate of a pleochroic mineral, the colour will vary with the direction in which the light-vibrations take place. Hence, _face-pleochroism_, the colour of the plate, may be distinguished from the colours given by _axis-pleochroism_, the colours given by light vibrating parallel with certain optical directions in the crystal.

DICHROITE (d[=i]'kro-[=i]t), or IOLITE, a mineral, a silicate of magnesium, iron, and aluminium, which readily undergoes modifications and passes into hydrous silicate. It exhibits marked pleochroism, whence the name.

DICK, Thomas, LL.D., a Scottish author of popular scientific works, born at Dundee in 1774, died 29th July, 1857. He was for many years a teacher at Perth, but subsequently resided at Broughty-Ferry, where he devoted himself to astronomical science, especially in its relations to religion. Some years before his death a small pension was granted to him by the Government. Amongst his works are: _The Christian Philosopher_ (1823), _The Philosophy of Religion_ (1825), _The Philosophy of a Future State (1828)_, and _Celestial Scenery_ (1838).

DICKENS, Charles, one of the greatest English novelists, born 7th Feb., 1812, at Landport, Portsmouth, died 9th June, 1870. His father, John Dickens, was then in the employment of the Navy Pay Department, but subsequently became a newspaper reporter in London. Young Dickens received a somewhat scanty education, was for a time a mere drudge in a blacking warehouse, and subsequently a clerk in an attorney's office. Having perfected himself in shorthand, however, he became a newspaper critic and reporter, was engaged on _The Mirror of Parliament_, and _The True Sun_, and in 1835 on _The Morning Chronicle_. For some time previously he had been contributing humorous pieces to _The Monthly Magazine_; but at length, in 1835, appeared in _The Morning Chronicle_ the first of that series of _Sketches by Boz_ which brought Dickens into fame. It was followed in quick succession by a pamphlet entitled _Sunday under Three Heads, by Timothy Spark_ (1836); _The Tuggs at Ramsgate_ (1836); _The Village Coquette_, a comic opera (1836); and a farce called _The Strange Gentleman_ (1836). In the same year Chapman & Hall engaged the new writer to prepare the letterpress for a series of comic sketches on sporting subjects by Seymour, an artist who had already achieved fame, and suggested as a subject the adventures of an eccentric club. Seymour committed suicide soon after, and H. K. Browne joined Dickens as illustrator, the result being the immortal _Pickwick Papers_. The great characteristics of Dickens's genius were now fully apparent, and his fame rose at once to the highest point it was possible for a writer of fiction to reach. A new class of characters, eccentric indeed, but vital representations of the humours and oddities of life, such as Mr. Pickwick, Sam Weller and his father, Mr. Winkle, and others, was made familiar to the public. Under the name of _The Posthumous Papers of the Pickwick Club_ this work was published in 2 vols. 8vo, in 1837. In the same year Dickens was engaged as editor of _Bentley's Magazine_, to which he contributed _Oliver Twist_, a work which opened up that vein of philanthropic pathos and indignant satire upon institutions which became a distinguishing feature of his works. Before the completion of _Oliver Twist_, _Nicholas Nickleby_ was begun, being issued complete in 1839. As the special object of _Oliver Twist_ was to expose the conduct of workhouses, that of _Nicholas Nickleby_ was to denounce the management of cheap boarding-schools. _Master Humphrey's Clock_, issued in weekly numbers, contained among other matter two other leading tales, _The Old Curiosity Shop_ and _Barnaby Rudge_, the latter a historical tale, going back to the times of the Gordon riots. It was published complete between 1840 and 1841. In 1841 Dickens visited America, and on his return he wrote _American Notes for General Circulation_ (1842). His next novel, _Martin Chuzzlewit_ (1844), dwelt again on his American experiences. This work also added a number of typical figures--Mr. Pecksniff, Mark Tapley, Sarah Gamp, and others--to English literature. The series of _Christmas Tales_, in which a new element of his genius, the power of handling the weird machinery of ghostly legend in subordination to his own peculiar humour, excited a new sensation of wonder and delight. These, enumerated consecutively, were: _A Christmas Carol_ (1843), _The Chimes_ (1844), _The Cricket on the Hearth_ (1845), _The Battle of Life_ (1846), _The Haunted Man_ and _The Ghost's Bargain_ (1847). The extraordinary popularity of these tales created for a time a new department in literature, that of the sensational tale for the Christmas season. In 1845 Dickens went to Italy, and on his return _The Daily News_, started on 1st Jan., 1846, was entrusted to his editorial management; but, despite his early training, this was an occupation uncongenial to his mind, and in a few months the experiment was abandoned. His _Pictures from Italy_ were published the same year. Next followed his novel of _Dombey and Son_ (1848), and _David Copperfield_, a work which has a strong autobiographical element in it (1849-50). In 1850 Dickens became editor of the weekly serial _Household Words_, in which various original contributions from his own pen appeared. In 1853 his _Bleak House_ came out. _A Child's History of England_, commenced in _Household Words_, was published between 1852 and 1854. _Hard Times_ appeared in _Household Words_, and was published in 1854. _Little Dorrit_, commenced in 1856, dealt with imprisonment for debt, the contrasts of character developed by wealth and poverty, and executive imbecility, idealized in the Circumlocution Office. In 1859, in consequence of a disagreement with his publishers, _All the Year Round_ superseded _Household Words_; and in the first number of this periodical, 28th May, was begun _A Tale of Two Cities_. _Great Expectations_ followed in the same paper, on 1st Dec., 1860. In _All the Year Round_ also appeared a series of disconnected sketches called _The Uncommercial Traveller_, published in 1868. _Our Mutual Friend_, completed in 1865, and published in the usual monthly numbers, with illustrations by Marcus Stone, was the last great serial work which Dickens lived to finish. It contained some studies of characters of a breadth and depth unusual with Dickens, and is distinguished among his works by its elaborate plot. The first number of his last work, _The Mystery of Edwin Drood_, was issued on 1st April, 1870, and only three numbers had appeared when he died somewhat suddenly, at his residence, Gad's Hill Place, near Rochester, on 9th June. He had considerably overtaxed his strength during his later years, more especially by his successive series of public readings from his own works, one series being delivered in America between 1867 and 1868. He was buried in Westminster Abbey. Dickens's work as a novelist is firmly based upon a wide and keen observation of men. The essence of his art was caricature, and for comic effect he, therefore, often exaggerated the abuses he attacked. His characters exhibit little more than one trait or quality, but the single trait or quality which they embody is truly conceived, and exhibited with great vitality and humour. His creative power was immense, and his great humour is admitted by all, even by those who consider his pathos as overdrawn. In spite, therefore, of all that is grotesque and overstrained in his work, he has been rightly placed amongst the great artists.--BIBLIOGRAPHY: J. Forster, _Life of Charles Dickens_; George Gissing, _Charles Dickens: a Critical Study_; G. K. Chesterton, _Charles Dickens_; R. H. Shepherd, _The Bibliography of Dickens_; Sir F. T. Marzials, _Life of Charles Dickens_; E. Pugh, _The Charles Dickens Originals_; P. H. Fitzgerald, _Memoirs of Charles Dickens_.

DICKSONIA, a genus of Leptosporangiate ferns, section Gradatae, mostly large tree-ferns, such as _D. antarctica_, a native of Australia and New Zealand, often grown in greenhouses.

B, Bast. B.K., Bark external to the first periderm layer, corresponding to the primary cortex. C, Cambium ring. E, Early wood. J, J, J, Junction of the wood of successive years. L, Late wood. M, Medulla. M.R., Medullary rays, various views. P, Protoxylem. 1, 2, 3, 4, The four successive annual rings.]

DICOTYLEDON (d[=i]-kot-i-le'don), a plant whose seeds are readily recognized by the embryo containing a pair of cotyledons or seed-leaves, which are always opposite to each other. Dicotyledons are further characterized by their netted-veined leaves and their 'open' vascular bundles containing a cambium; the parts of the flower are commonly in fours or fives. In Bentham and Hooker's system the class is divided into four subclasses--Thalamiflorae, Calyciflorae, Corolliflorae, and Monochlamydeae. Engler's system recognizes only two subclasses, viz. Archichlamydeae and Sympetalae.

DICTAPHONE, an adaptation of the gramophone, in which the principle of that invention is applied to the requirements of modern business. Letters or memoranda are spoken into the machine, which 'records' them on waxen cylinders. The machine is then passed on to a shorthand writer or typist (or the cylinder may be transferred to a duplicate machine), and the recorded matter is dictated. The motive power is electricity; the speed of dictation is capable of adjustment to that of the writer; and by means of an accessory machine the records can be scraped and re-used.

DICTA'TOR, an extraordinary magistrate of the Roman Republic, first instituted B.C. 501. The power of naming a dictator, when an emergency arose requiring a concentration of the powers of the State in a single superior officer, was vested by a resolution of the Senate in one of the Consuls. The dictatorship was limited to six months, and the person who held it could not go out of Italy. This rule was laid aside during the first Punic War. The dictator was also forbidden to appear in Rome on horseback without the permission of the people, and he had no control over the public funds without the permission of the Senate. He had the power of life and death, and could punish without appeal to the Senate or people. All the other magistrates were under his orders. Originally the dictator was a patrician, but in 356 B.C. the plebeian Marcius Rutilus was called upon to fill the office of dictator. The term is now often applied to rulers enjoying or exercising extra-constitutional power.--Cf. A. H. J. Greenidge, _Roman Public Life_.

DICTIONARY (from the Lat., _dictio_, a saying, expression, word), a book containing the words, or subjects, which it treats, arranged in alphabetical order. It may be either a vocabulary, or collection of the words in a language, with their definitions; or a special work on one or more branches of science or art prepared on the principle of alphabetical arrangement, such as dictionaries of biography, law, music, medicine, history, or philosophy. Amongst dictionaries of the English language, the earliest seem to have been those of Bullokar (1616) and Cockeram (1623). That of Dr. Johnson, published in 1755, made an epoch in this department of literature. Previous to this the chief English dictionary was that of Bailey, a useful work in its way. An enlarged edition of Johnson's dictionary, by the Rev. H. J. Todd, appeared in 1818; and this, again enlarged and modified, was issued under the editorship of Dr. R. G. Latham (1864-72). The best-known American dictionary of the English language is that by Noah Webster, published in 1828, and since entirely recast. Richardson's dictionary, published during 1836 and 1837, was valuable chiefly for its quotations. Ogilvie's _Imperial English Dictionary_, based on Webster, and first published between 1847 and 1850, has been issued in a remodelled and greatly enlarged form (4 vols. 1881-2 and subsequently, Charles Annandale, LL.D., editor). It is one of the encyclopaedic dictionaries. Cassell's _Encyclopaedic Dictionary_ is another extensive work (1879-88). The largest completed English dictionary is the _Century Dictionary_ (New York, 1889-91, 6 vols. quarto). _The Standard Dictionary_ is another American work. A new English dictionary 'on historical principles', first edited by Sir J. A. H. Murray, LL.D., with the assistance of many scholars, and now edited by Dr. Henry Bradley, is being published at the Clarendon Press since 1884. Among foreign dictionaries are the polyglot dictionary of Calepino (1502), the Latin and Greek _Thesaurus_ of Robert and Henry Stephanus, the Italian _Vocabulario della Crusca_ (1612), &c. The chief etymological dictionary of English words is that by Professor Skeat (1882). Among French dictionaries (for French people) the chief is that of Littr['e]; among German, the dictionary begun by the brothers Grimm.

DICTYOTACEAE, a family of Brown Algae, section Cyclosporeae. _Dictyota dichotoma_, with a delicate, flattened, repeatedly forked thallus, is not uncommon in sandy pools on our coasts. The plants are of three kinds, viz. [male], bearing antheridia; [female], bearing oogonia; and neuter, producing tetraspores. The oospores give rise to neuter plants, the tetraspores to [male] or [female] plants. This is one of the best instances of 'homologous' alternation of generations, i.e. that type in which the different generations are identical in form, differing only in their reproductive organs and in the number of chromosomes in their nuclei. Another genus is Padina.

DIDACTIC POETRY, that kind of poetry which professes to give a kind of systematized instruction on a definite subject or range of subjects. Thus the _Georgics_ of Virgil and the _De Rerum Natura_ of Lucretius profess to give, the one a complete account of agriculture and kindred arts, the other a philosophical explanation of the world. Other examples of purely didactic poetry are Horace's _Ars Poetica_, and Pope's _Essay on Criticism_. In a larger sense of the word most great poems might be called didactic, since they contain a didactic element in the shape of history or moral teaching, Dante's _Divina Commedia_, Milton's _Paradise Lost_, or Goethe's _Faust_, for example. The difference may be said to be this, that in the one case the materials are limited and controlled by nothing but the creative fancy of the poet, while in the other they are much more determined by the actual nature of the subject treated of.

DIDEL'PHIA, one of the three subclasses of the Mammalia (the others being Monodelphia and Ornithodelphia), comprising only one order, that of Marsupials or pouched mammals.

DIDEROT (d[=e]d-r[=o]), Denis, a French writer and philosopher, born in 1713, at Langres, in Champagne, died in 1784. He was educated in the school of the Jesuits, and afterwards at Paris, at the College of Harcourt, but declined to study law, preferring to earn his living by teaching mathematics. His first works were the _Essai sur le M['e]rite et la Vertu_ (1745); and the _Pens['e]es Philosophiques_ (1746), a pamphlet against the Christian religion. His _Lettre sur les Aveugles [`a] l'Usage de Ceux qui Voyent_ is in the same strain. These heterodox publications cost him an imprisonment for some time at Vincennes. Diderot now tried writing for the stage, but his pieces were failures. In 1749 he had begun, along with D'Alembert and some others, the _Encyclopaedia_. At first it was intended to be mainly a translation of one already published in English by Chambers. Diderot and D'Alembert, however, enlarged upon this project, and made the new _Encyclopaedia_ a magnificently comprehensive and bold account of all the thought and science of the time. Diderot, besides revising the whole, undertook at first the mechanical arts, and subsequently made contributions in history, philosophy, and art criticism. But the profits of all his labour were small, and it was only the liberality of the Empress Catherine, who purchased his library for 50,000 livres and made him a yearly allowance of 1000 livres, that saved Diderot from indigence. In 1773 he visited St. Petersburg to thank his benefactress and was received with great honour. On his return to France he lived in retirement, passing the last ten years of his life in writing and conversations, wherein, as Marmontel said, he was at his best. Besides his articles in the _Encyclopaedia_ he wrote numerous works, some of which were published after his death. Among the best known are _Le Neveu de Rameau_, a kind of philosophical dialogue which Goethe thought worthy of translation; _Essai sur la Peinture_, and _Paradoxe sur le Com['e]dien_, suggestive essays on the principles of painting and acting; two lively tales, _La Religieuse_ and _Jacques le Fataliste_. On account of his great interest in almost every branch of human knowledge, Voltaire nicknamed him 'Pantophile Diderot'.--BIBLIOGRAPHY: T. Carlyle, _Essay on Diderot_; F. Bruneti[`e]re, _['E]tudes Critiques_; R. L. Cru, _Diderot as a Disciple of English Thought_.

DIDO, or ELISSA, the reputed founder of Carthage. She was the daughter of a king of Tyre, called by some Belus, by others Metten or Matgenus. After her father's death, her brother Pygmalion murdered her husband Sicharbas, or as Virgil calls him Sychaeus, with the view of obtaining his wealth. But Dido, accompanied by many Tyrians of her party, fled with all the treasure over sea, and, landing on the coast of Africa, founded Carthage about 860 B.C. The story is told by Virgil, with many inventions of his own, in the _Aeneid_ (Books i and ii).

DIDOT (d[=e]-d[=o]), a famous house of printers, booksellers, and typefounders at Paris. The founder was _Francois Didot_, born in 1689, died 1757. Of his sons _Francois-Ambroise_ (born 1720, died 1804) and _Pierre-Francois_ (born 1732, died 1795) the first distinguished himself in the type-founding art as an inventor of new processes and machines, the second was equally eminent for his bibliographical knowledge, and contributed much also to the advancement of printing.--_Pierre_ (born 1761, died 1853) succeeded his father Francois-Ambroise in the printing business. He made himself famous by his magnificent editions of classic authors in folio, amongst which his Virgil (1798) and his Racine (1801) may be particularly mentioned. He did much also for the improvement of types. He is known also as an author.--_Firmin_ (born 1764, died 1836), the brother of Pierre, took charge of the type-founding, was the inventor of a new sort of script, and an improver of the stereotype process.--_Ambroise-Firmin_ (born 1790, died 1876), and _Hyacinthe-Firmin_ (born 1794, died 1880) occupied a distinguished position amongst the publishers of Paris. The former left a collection of MSS. which was worth, at the time of his death, about two million francs. The house has now extended its trade into everything connected with bookselling, paper-making, and bookbinding.

DIDSBURY, a district of Manchester, on the Midland Railway, 4 miles south by east of Manchester, a place of residence of many Manchester business men. There is an important Wesleyan Training College there. Pop. 9234.

DIDUN'CULUS, a genus of birds allied to the pigeons, and comprising only the one species, _D. strigirostris_, native to some of the Samoan Islands. This bird is of special interest as being the nearest living ally of the extinct dodo. It has a length of about 14 inches, with a glossy plumage verging from a velvety black on the back to greenish black on the head, breast, and abdomen. The large beak, which is nearly as long as the head, is greatly arched on the upper half, while the lower is furnished with two or three tooth-like indentations.

DIDYM'IUM, a rare metallic element, occurring along with _lanthanum_ in the mineral cerite as discovered by Mosander in 1842. It has been resolved into two new elements: _Praseodymium_ (Pr, 140.9) and _Neodymium_ (Nd, 144.3).

DIE, a metallic stamp for impressing a design or figure upon coins or other metallic objects. See _Dies_ and _Die-sinking_.

DIE (d[=e]), an ancient town, France, department of Dr[^o]me, 26 miles south-east of Valence; with an ancient cathedral and Roman remains. Pop. 4000.

DI['E] (di-[=a]), ST., a town, France, department of Vosges, on the Meurthe, 25 miles E.N.E. of Epinal. Both iron and copper are worked; there are marble quarries; and numerous manufactures are carried on. Pop. 19,029.

DIEBITSCH-SABALKANSKI, Hans Karl, a Russian general, born at Grossleippe, in Silesia, in 1785, died 9th June, 1831. He was educated at the military school of Berlin, but in 1801 quitted the Prussian service for that of Russia. He was present at the battles of Austerlitz and Friedland, served with distinction in the campaign of 1812, took part in the battles of Dresden and Leipzig, and was made lieutenant-general at the age of twenty-eight. He had the chief command in the Turkish War of 1828-9, stormed Varna, and made the famous passage of the Balkans, for which the surname of Sabalkanski was conferred on him. In 1830 he commanded the army sent against the revolted Poles, but did not distinguish himself in this service.--Cf. Bantych-Kamenski, _Biographies of Russian Field-marshals_.

DIEFFENBACH (d[=e]'fen-b[.a]_h_), Johann Friedrich, German surgeon, born at K[:o]nigsberg in 1792, died in 1847. After having studied at Bonn and Paris, he settled in Berlin, where his talent as an operator soon attracted notice. Surgery is particularly indebted to him for new methods of forming artificial noses, eyelids, and lips, and curing squinting and stammering.

DIEGO GARCIA. See _Chagos_.

DI'ELECTRIC, in electricity, a name applied by Faraday to any medium through or across which electrostatic induction can take place. See _Electricity_ (Electrostatics). Faraday first showed that electrostatic induction was not action at a distance, but took place by means of the insulating medium separating the two conductors. The medium he named a _dielectric_, and measured its specific inductive capacity by taking that of common air as unity.

DIELY'TRA, or DICENTRA, a genus of plants, of the nat. ord. Fumariaceae or Fumitories. The best known is _D. spectabilis_, a native of Northern China and Siberia, now common in European and other gardens. It blossoms in April and May, and its long drooping racemes of purplish-red blossoms present a very graceful appearance. It grows freely in the open air. It is sometimes called bleeding heart or virgin's heart from the shape of the blossoms.

DIEMEN (d[=e]'men), Anton van, Dutch administrator, was born in 1593, died in 1645. Having gone to India, he speedily rose to the highest dignities, and was at length, in 1636, made Governor-General. He administered the government with much ability, and contributed much to the establishment of the Dutch commerce in India. Abel Tasman, whom he sent with a vessel to the South Seas in 1642, gave the name of _Van Diemen's Land_ to the island now called Tasmania.

DIEPPE (d[=e]-ep'), a seaport town, France, department of Seine-Inf['e]rieure, on the English Channel, at the embouchure of the Arques, 93 miles N.N.W. of Paris. Almost the only public edifices worth special notice are the two Gothic churches, St. Jacques, begun in the thirteenth century, and St. R['e]mi, founded in 1522, and the old castle (1433), now a barracks. To the west of Dieppe proper is the suburb La Barre; and on the opposite side of the harbour Le Pollet, inhabited chiefly by sailors and fishermen. The old port is spacious, but a new channel with its own harbour system has been added, and vessels of 20-foot draft can now enter. Dieppe is one of the chief watering-places of France, and is much frequented by visitors in summer and autumn. The great bathing establishment forms a luxurious retreat for bathers and invalids, and includes a ballroom. The manufactures include works in ivory, horn, and bone, lace-making, sugar-refining, and shipbuilding. There is a busy fishery, and the foreign trade is still considerable. There is constant steam intercourse between this port and Newhaven. In early times Dieppe was the chief port of France, but its prosperity diminished after the revocation of the Edict of Nantes (1685). During the European War Dieppe was an important Allied base. Pop. 23,973.

DIERX, L['E]ON, French poet, born in the Island of R['e]union in 1838. Educated in Paris, he became one of the foremost of the Parnassians. His works include: _Aspirations_, _Po[`e]mes et Po['e]sies_, _La rencontre_, and _Les Amants_. His collected poems (1889-90) were crowned by the Acad['e]mie. He died in Paris, 11th June, 1912.

DIES AND DIE-SINKING. Die-sinking is the art of preparing dies, a die being a plate or block, usually of metal, so cut or shaped as to be capable, by means of stamping or pressure, of transferring a given design to some article which is to be manufactured in quantity. The pressure may be applied by any sort of power, from hand to hydraulic.

The steel for the manufacture of steel dies is carefully selected, forged at a high heat into the rough die, softened by careful annealing, and then handed over to the engraver. After the engraver has worked out the design in intaglio, the die is put through the operation of hardening, after which, being cleaned and polished, it is called a _matrix_. This is not, however, generally employed in multiplying impressions, but is used for making a _punch_ or steel impression for relief. For this purpose another block of steel of the same quality is selected, and, being carefully annealed or softened, is compressed by proper machinery upon the matrix till it receives the impression. When this process is complete, the impression is retouched by the engraver, and hardened and collared like the matrix. Any number of dies may now be made from this punch by impressing upon it plugs of soft steel.

There is hardly any article which does not in the course of its manufacture require the use of a die of some kind. For all sorts of metal-work, seals, rings, silverware, moulds and shapes of sheet steel or tin, dies are employed. For this class of work they are usually of steel. For embossing articles of leather, wood, celluloid, rubber, cloth, or clay, dies of brass and phosphor-bronze are commonly used, these being easier media to work in and yet sufficiently strong. The dies for letter headings and company seals are cut, in reverse to the design required, in steel; those for sealing-wax seals in steel or brass; the lettering being usually punched in by hand by separate letter punches, which themselves have been cut in relief on steel. Designs which are unusually ornate may be engraved by hand. Dies for embossing designs on leather, catalogue covers, cardboard articles, cards, and soft materials are usually modelled in brass. The design in reverse is cut out to a depth corresponding to the relief wanted. These dies are usually worked up by hand by the engraver. Dies for the reproduction of rubber stamps for printing on clay are cut in phosphor-bronze or hard brass in relief and reverse, and with an extreme bevel. The dies or blocks are then struck deeply into lead, and melted rubber is poured into the moulds so formed. When set, the rubber is removed and mounted as a hand-stamp ready to impress the clay in ink. Dies for wallpapers are cut on rollers. Steel dies for flower-shapes have a cutting edge, so that they can stamp out and emboss in one action. Of late years machinery has come much into use for relieving the engraver of some of his labour, but the designs are generally kept secret. One machine, called the pantograph or engraving machine, reproduces engravings in all metals and many shapes from patterns. Many of the stamp-duty steel dies made and issued by the Royal Mint are reproduced from this machine in reductions from brass patterns.--BIBLIOGRAPHY: Lucas, _Dies and Die-making_; J. V. Woodworth, _Dies: their Construction and Use_.

DIESEL, Rudolph, German inventor, born in Paris in 1858, died in 1913. Educated in England and at Munich, he proposed in 1893 to utilize directly the energy created by the combustion of fuel, a proposal which led to his invention of the Diesel engine. (See _Internal Combustion Engines_.) In 1913 he was called to England to consult with the Admiralty on the application of his motor, but was drowned in crossing the Channel. In 1894 he published a monograph entitled _Theory and Construction of a Rational Heat Motor_.

DIES FASTI ET NEFASTI, a Roman division of days, with reference to judicial business, into working-days and holidays. A _dies fastus_ was a day on which courts and assemblies could be held and judgments pronounced; a _dies nefastus_, a day on which courts could not be held nor judgments pronounced.

DIES IRAE (d[=i]'es [=i]'r[=e]), one of the great Latin hymns of the Mediaeval Church, generally used as part of the requiem or mass for the souls of the dead. It describes, as its name ('the day of wrath') denotes, the Last Judgment of the world, and seems to have been suggested by the description in _Zephaniah_, i, 15 and 16. It is supposed to have been written by Thomas da Celano, a Franciscan friar of the thirteenth century. It was translated by Crashaw and Dryden in the seventeenth century, and by Macaulay and others in the nineteenth, but none of these translations conveys the solemn force of the original.

DIEST (d[=e]st), a town, Belgium, province of Brabant, 32 miles E.N.E. of Brussels. It has some manufactures, but the chief products of the place are beer and gin, the former being largely exported. The town was occupied by the Germans in 1914, and re-entered by the Belgians in 1918. Pop. 8800.

DIESTERWEG, Friedrich Adolf Wilhelm, German educator, born in 1790, died in 1866. In 1820 he became director of the new Teachers' Seminary at M[:o]rs, and soon gained a reputation as teacher and educator. He was a follower of Pestalozzi, and aimed at making every subject of instruction a means of education. In 1827 he founded the _Rheinische Bl[:a]tter f[:u]r Erziehung und Unterricht_, wherein he advocated his pedagogical views.

DI'ET, a meeting of some body of men held for deliberation or other purposes; a term especially applied to the legislative or administrative assemblies of Austria, Germany, and Poland.

DIETET'ICS (Gr. _diaita_, daily regimen), that part of medicine which relates to the regulation of diet. The ideal diet is clearly that which, without burdening the viscera uselessly, furnishes all necessary nutritive elements, with due consideration for special physiological conditions in any given case. Under the head of _Aliment_ the physiological properties of various foods have already been considered theoretically in respect of their capacity to supply physical waste in nitrogenous and non-nitrogenous matter. (See _Aliment_.) No single substance contains the elements needed to replace this waste in their requisite proportions, and a mixed diet is therefore necessary. For instance, to secure the required amount of carbon a man would need to eat about 4 lb. of lean beef, while 1 lb. would yield all the nitrogen required; thus, apart from the labour of digesting 4 lb. of beef, the body would be compelled to get rid of the excess of nitrogen. Bread, on the other hand, has carbon in abundance, but is deficient in nitrogen; so that by uniting 2 lb. of bread with 3/4 lb. of lean meat, the due proportion of carbon and nitrogen is satisfactorily supplied. Milk and oatmeal taken together also contain nitrogenous and non-nitrogenous substances in nearly the required proportions. A certain proportion of saline matter is also necessary. The nature of the food most suitable for a healthy man is dependent in part upon general conditions, such as climate and season, and in part upon special conditions of individual habit. The inhabitants of the Arctic regions need large quantities of oleaginous food; those of the Tropics live chiefly on starchy products. With increased activity and exertion, as in training, an increase in the nitrogenous foods becomes necessary. In a state of health we need not draw hairbreadth distinctions as to the superior salubrity of the several sorts of diet, the quantity rather than the quality of food being the main consideration. Those persons who have been most remarkable for health and long life have generally been contented with two moderate meals a day, which are certainly quite sufficient during a state of health. In various countries the breakfast generally consists of tea, coffee, or cocoa, with a certain proportion of bread and butter; persons with delicate digestive powers, or who lead a sedentary life, cannot with safety or comfort eat animal food _constantly_ to breakfast. At dinner all made-dishes highly spiced, such as curries, turtle-soup, &c., as provoking appetite, are hurtful; and the custom of late dining is not to be commended. Stewed and boiled meats are more difficult to digest than meat cooked by fire alone. The flesh of young animals seems to be more difficult of digestion than that of old; and the flesh of tame than that of wild animals. All sorts of fat meat must be taken in smaller quantities. Hence, also, ham, bacon, and salted meats cannot be eaten in such quantities as the tender flesh of poultry. Fish has the advantage of being easily soluble. All boiled vegetables are in general easy of digestion; raw vegetables and salads are rather more difficult. Fruit should be taken in the forenoon rather than after a hearty meal. The moderate use of fermented liquors is far from being invariably an evil, but the smaller the quantity habitually used the better in the majority of cases.

In all diseases attended with much fever or quickness of pulse the stomach loathes animal food, and there is generally a great increase of thirst, to quench which water, either quite cold, or iced, or tepid, or rendered acid, may be freely indulged. Infusions, too, of barley, sage, balm, &c., may be taken. In chronic diseases attended with hectic fever, milk is the most proper diet. The best food for infants is, of course, their mother's milk; but whenever they begin to cut teeth a little animal food, such as soft-boiled eggs, beef-tea, and even chicken minced very fine, may be given. Many infants suffer from having too much sugar given them in their food.--BIBLIOGRAPHY: R. H. Chittenden, _Physiological Economy in Nutrition_, and _Nutrition of Man_; Hutchison, _Food and Dietetics_; Lusk, _The Science of Nutrition_.

DIETRICH (d[=e]'tri_h_), Christian Wilhelm Ernst, a German painter and engraver, born in 1712, died in 1774. He studied under his father, and afterwards under Alexander Thiele at Dresden, where he became court-painter and professor in the academy. He adopted several different manners, successfully imitating Raphael and Mieris, Correggio, and Ostade.

DIETRICH OF BERN (d[=e]'tri_h_), the name under which Theodoric the Great, King of the Ostrogoths, appears in the old German legends. Bern stands for Verona, his capital.

DIEU, or D'YEU (dy_eu_; ancient INSULA DEI), an island off the west coast of France, department of Vend['e]e. It is inaccessible on the west side, but on the east has a tolerable harbour defended by batteries. The chief industry is fishing. There are four lighthouses on the island. Pop. 3809.

DIEU ET MON DROIT (dy_eu_ e mo[n.] drw[:a]; 'God and my right'), the battle-cry of Richard I at the battle of Gisors (1198), signifying that he was not subject to France, but owed his power to God alone. The battle-cry was then adopted as the motto of the arms of England, and revived by Edward III in 1340, when he claimed the crown of France. Except during the reigns of Elizabeth and Anne, who used the motto _Semper eadem_, and of William III, who personally used _Je maintiendray_, it has ever since been the royal motto of England.

DIEZ (d[=e]ts), Friedrich Christian, German philologist of the Romance languages, born in 1794, died in 1876. Having qualified himself as a lecturer at Bonn, he was appointed professor of the Romance languages there in 1830. His work stands in much the same relation to the Romance dialects which the researches of Grimm occupy with respect to German dialects. In addition to various works on the poetry of the Troubadours, he published a very valuable _Grammatik der Romanischen Sprachen_ (1836-42, translated into English by Cayley in 1863), and an _Etymologisches W[:o]rterbuch der Romanischen Sprachen_ (1853).

DIFFERENCE, a stock-exchange term. When stock is bought or sold merely as a speculation for the rise or fall, with no intention of the buyer to 'take up' the stock, or of the seller to deliver it, the 'difference' is the movement in price which may take place between the date of the transaction and the following 'settling-day'. If the price falls, the buyer has to pay the difference upon 'carrying over' his purchase to the next account; if it rises, the seller is at the loss. Since the first weeks of the European War all stock-exchange transactions have been made, in theory at least, for cash, and speculative business of this nature has been consequently much reduced.

DIFFERENCES, FINITE, a calculus much used in actuarial work, which deals with a series of numbers by considering the differences of the successive terms.

If u_1, u_2, u_3, ... are the terms of the series, then u_2 - u_1, u_3 - u_2, u_4 - u_3,... form another series called the series of first differences. The notation used is u_2 - u_1 = [Delta]u_1, u_3 - u_2 = [Delta]u_2,...

These first differences may themselves be differenced, giving the second differences [Delta]u_2 - [Delta]u_1, [Delta]u_3 - [Delta]u_2, ..., which are written [Delta]^2u_1, [Delta]^2u_2,...

Similarly, we form the third differences [Delta]^3u_1 = [Delta]^2u_2 - [Delta]^2u_1, and so on.

As an example, let the original series be the cubes of the natural numbers.

1 8 27 64 125 216 / 343 512
7 19 37 61 91 / 127 169
12 18 24 30 / 36 42
6 6 6 / 6 6
0 0 / 0 0

Here we begin by writing down the series of cubes as far, say, as 216; beneath these we write the first differences 8 - 1 = 7, 27 - 8 = 19, &c. We thus obtain the part of the table to the left of the diagonal line.

We observe that the third differences are constant, each being 6. (It is easy to prove generally that the nth differences of the series, 1^n, 2^n, 3^n,..., are constant.) Knowing the third differences, we can now extend the table as far as we wish to the right of the diagonal line. We get first 6 + 30 = 36, 36 + 91 = 127, 127 + 216 = 343. We infer that 7^3 = 343.

Since u_1 - u_0 = [Delta]u_0, we have u_1 = u_0 + [Delta]u_0 = (1 + [Delta])u_0.

Similarly, u_2 = (1 + [Delta])u_1 = (1 + [Delta])^2u_0; and, generally,

u^x = (1 + [Delta])^xu_0
= {1 + x[Delta] + (x(x-1)/(1x2)) x [Delta]^2 + ...}u_0
= u_0 + x[Delta]u_0 + (x(x-1)/(1x2)) x [Delta]^2)u_0 + ...

a formula much used by calculators, and known as Newton's interpolation formula.

The above symbolic method of proof only applies when x is a positive integer, but the result is used in practice even for fractional values of x, as in most cases the high differences become negligible.

If n is a positive integer, it is easy to prove that

[Delta]^nu_x = u_{x+n} - nu_{x+n-1} + ((n(n-1))/(1x2))u_{x+n-2} - ...

If the nth differences vanish, or are negligible, this gives

0 = u_{x+n} - nu_{x+n-1} + ((n(n-1))/(1x2))u_{x+n-2} -... +(-1)^nu_x,

another useful interpolation formula, by which we can calculate any missing term of a series.--BIBLIOGRAPHY: G. Boole, _Finite Differences; Textbook of the Institute of Actuaries_.

DIFFERENTIAL EQUATION, an algebraical relation involving derivatives or differentials. Examples:

d^2z/dt^2 = g: ydx + xdy + zdz = 0.

An _ordinary_ differential equation involves only one independent variable, a _partial_ differential equation involves more than one. Examples of ordinary equations:

d^2y/dx^2 + (1/x)dy/dx + y = 0; d^2x/dt^2 + a(dy/dt) + px + qy = 0.

Examples of partial differential equations:

x(dz/dx) + y(dz/dy) = nz; d^2u/dx^2 + d^2u/dy^2 + d^2u/dz^2 = 0.

Equations, whether ordinary or partial, can also be classified as _linear_ or _non-linear_. A linear equation is a rational integral equation of the first degree in the dependent variable or variables and their derivatives. The equation

x^2 d^2y/dx^2 + x dy/dx + (x^4 + 1)y = 0

is linear, but

(dy/dx)^2 = xy and y dy/dx = x^2

are non-linear. The _order_ of an equation is the order of the highest derivative or differential which it contains. Of the three equations last written, the first is _linear of the second order_, the other two are of the _first order and second degree_. To _integrate_ a differential equation or system of equations is to find a relation or relations among the variables, equivalent to the given equation or equations. Thus the integral of

d^2z/dt^2 = g is z = 1/2gt^2 + At + B,

where A and B are _arbitrary constants_. An ordinary equation of the _n_th order with one dependent variable has exactly _n_ arbitrary constants in its complete integral, or solution. In a practical problem the arbitrary constants are determined by the _initial_, or _boundary_, _conditions_. The solution of d^2z/dt^2 = g, e.g. is completely determinate if the values of z and dz/dt when t = 0 are given. The solution of _partial_ equations may involve arbitrary _functions_, which become definite when proper initial or boundary conditions are assigned. Thus the equation du/dx = du/dt has for its complete solution u = [phi](x + t), where [phi] may be a function of any form whatever; if now we are given that, when t = 0, u = a given function f(x), we obtain f(x) = [phi](x), so that the solution required is u = f(x + t). Certain ordinary linear equations of the second order are specially important, both from the beauty of their theory and from their usefulness in Mathematical Physics. Some of these equations are: Bessel's equation, Legendre's equation, the hypergeometric equation, Mathieu's equation, Lam['e]'s equation. Linear partial equations of the second order are fundamental in Physics. Such are: Laplace's equation,

d^2V/dx^2 + d^2V/dy^2 + d^2V/dz^2= 0;

the wave equation,

d^2V/dt^2 = c^2(d^2V/dx^2 + d^2V/dy^2 + d^2V/dz^2);

the equation of conduction of heat,

dV/dt = k(d^2V/dx^2 + d^2V/dy^2 + d^2V/dz^2).

These involve one dependent variable only. Equations with several dependent variables occur in Elasticity, Electrodynamics, and Hydrodynamics. A notable feature of the hydrodynamical equations is that they are not linear.

No general rules exist enabling us to deal with a differential equation taken at random, and only a few types have been completely solved. Of soluble equations, the most important are those which are _linear with constant coefficients_.

_Example 1._ d^2x/dt^2 - 7dx/dt + 12 = 0. To solve this, try x = e^{mt}. We find e^{mt}(m^2 - 7m + 12) = 0. Thus m = 3 or 4. It is now easy to show that x = Ae^{3t} + Be^{4t} is a solution, where A and B are arbitrary constants. This is the general solution. We can determine A and B if the values of x and dx/dt are given for a definite value of t, say t = 0.

_Example 2._ d^2y/dt^2 = c^2 d^2y/dx^2. Try y = e^{lx + mt}. We find m^2 = c^2l^2, or m = +/-cl. Hence y = Ae^{l(x + ct)} + Be^{l(x - ct)} is a solution for all values of A, B, l; so, also, is the sum of any number of terms of similar forms. We may infer that the general solution is

y = f(x + ct) + F(x - ct),

where f and F are arbitrary functions. It is only in exceptional cases that an equation can be solved, as in these two examples, by an analytical formula; indeed, differential equations are the most fertile source of new functions in analysis. But, as in the analogous cases of algebraic equations and definite integrals, it may be quite possible to find, by methods of approximation, an arithmetical solution which is sufficient for the purpose in hand.--BIBLIOGRAPHY: H. T. H. Piaggio, _Differential Equations_; J. M. Page, _Ordinary Differential Equations_; A. R. Forsyth, _A Treatise on Differential Equations_; E. T. Whittaker and G. N. Watson, _Modern Analysis_.

DIFFRAC'TION, a term applied to the bending that rays of light undergo in passing close to the edge of an opaque body. Thus when a beam of direct sunlight is admitted into a dark room through a narrow slit, and falls upon a screen placed to receive it, there appears a line of white light bordered by coloured fringes; these fringes are produced by diffraction, and in the case given it may be seen that the red or long-wave rays are diffracted more than the blue rays. See _Interference_.

DIFFU'SION, the gradual mixing of gases, liquids, or solids when brought into direct contact. When a block of lead is placed on a block of gold, with their smooth surfaces in close contact, it is found that, after several weeks, gold has diffused into the lead, and lead into the gold. In the case of gases, when a jar of oxygen and a jar of hydrogen are connected together by a tube or opening of any kind, they rapidly become mixed; and their mixture does not depend on gravity, but takes place in opposition to that force, as may be shown by placing the jar of hydrogen gas above the other. Oxygen is sixteen times heavier than hydrogen, bulk for bulk, but the heavier gas moves upwards and the lighter downwards, and the process of intermixture, or _diffusion_, goes on till the two gases are apparently equably distributed throughout the whole space. After that they have no tendency whatever to separate. Similarly, if two vessels, one containing oxygen and the other hydrogen, be connected by a tube which is stuffed with a plug of porous material, such as plaster of Paris, the gases gradually diffuse one into the other through the porous plug. The two gases, however, do not pass through the porous separator at equal rates, but in _inverse proportion to the square roots of the densities of the gases_. Thus in the case of two vessels, one containing hydrogen and the other oxygen, which is sixteen times as heavy as hydrogen, the hydrogen will pass towards the oxygen jar four times as quickly as the oxygen will pass towards the hydrogen jar. Kindred phenomena occur when two liquids that are capable of mixing, such as alcohol and water, are put in contact, the two gradually diffusing one into the other in spite of the action of gravity. In some cases, however, as where ether and water are employed, the diffusion is only partial, this result arising from the fact that these two liquids are not miscible in all proportions. When solutions of various solid bodies are placed in contact, interdiffusion also takes place. On the results of his examination of the phenomena of diffusion of liquids and salts across porous membranes or _septa_, Graham founded a method of separating _colloid_ from _crystalloid_ bodies, which he called _dialysis_.

DIGAM'MA, a letter which once belonged to the Greek alphabet, and which remained longest in use among the Aeolians. It resembled our letter F, and hence was called _digamma_, that is, double [Gamma]. It appears to have had the force of _f_ or _v_. Its existence was first pointed out by Richard Bentley.

DIGBY, Sir Everard, an English gentleman, born of a Roman Catholic family in 1578. He enjoyed some consideration at the court of Elizabeth and James I, by whom he was knighted. Having contributed money to the Guy Fawkes conspiracy, he was tried and hanged in 1606.

DIGBY, Sir Kenelm, eldest son of the preceding, born in 1603, died in 1665. He studied at Oxford, was knighted in 1623, and on the accession of Charles I was created a gentleman of the bedchamber, a Commissioner of the Navy, and a governor of Trinity House. He soon after fitted out at his own expense a small but successful squadron against the French and Venetians. In 1636 he became a Roman Catholic, and was imprisoned as a Royalist during 1642-3, when he was allowed to retire to the Continent. At the Restoration he returned to England, became a member of the Royal Society, and was much visited by men of science. He wrote numerous works: a _Treatise on the Nature of Bodies_, a _Treatise on the Nature and Operation of the Soul_, and _Of the Cure of Wounds by the Powder of Sympathy_.

DI'GEST, a name originally given to a collection or body of Roman laws, digested or arranged under proper titles by order of the Emperor Justinian. Hence applied to any somewhat similar collection.

DIGES'TER, a strong vessel of copper or iron, on which is screwed an air-tight cover with a safety-valve, the object being to prevent loss of heat by evaporation, and to enable boiling to take place at a high pressure. Water may be thus heated to 400degF.; at which temperature its solvent power is so greatly increased that bones are converted into a jelly.

DIGES'TION is that process in the animal body by which the aliments are so acted upon that the nutritive parts are prepared to enter the circulation, and separated from those which cannot afford nourishment to the body. The organs effecting this process are called the _digestive_ organs, and consist of the stomach, the great and small intestines, &c. (see _Intestine_, _Stomach_), the liver, and pancreas. When the aliments, after being properly prepared and mixed with saliva by mastication, have reached the stomach, they are intimately united with a liquid substance called the _gastric juice_, by the motion of the stomach. By this motion the aliments are mechanically separated into their smallest parts, penetrated by the gastric juice, and transformed into a uniform pulpy or fluid mass. The gastric juice acts upon the albuminous parts of the food, converting them into peptones, which can pass through organic membranes and thus enter the blood. This action is aided by the warmth of the stomach. The pulpy mass, called _chyme_, proceeds from the stomach, through the pylorus, into that part of the intestinal canal called the small intestine, where it is mixed with the pancreatic juice, bile, and intestinal juice. The pancreatic juice converts starch into sugar, albumins into peptones, and emulsionizes fats, so that all these kinds of food are rendered capable of absorption. The process is aided by the intestinal juice. The bile also acts upon fats, and thus the food is formed into the _chyle_, which is absorbed into the system by the capillary vessels called _lacteals_ (see _Chyle_; _Chyme_), while the non-nutritious matters pass down the intestinal canal and are carried off.--BIBLIOGRAPHY: F. Hare, _Food Factor in Disease_; Taylor, _Digestion and Metabolism_.

DIGIT (dij'it; Lat. _digitus_, a finger), in arithmetic, any one of the ten numerals, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. Digit is also a measure of a finger's breadth, equal to 3/4 inch.

DIGIT, in astronomy, is the measure by which we estimate the quantity of an eclipse. The diameter of the sun or moon's disk is conceived to be divided into twelve equal parts, called _digits_; and according to the number of those parts or digits which are obscured, so many digits are said to be eclipsed.

DIGITALIN (dij-i-t[=a]'lin), a vegetable alkaloid, the active principle of the _Digit[=a]lis purpur[)e]a_ or foxglove. It has a bitter taste, and is a strong poison, but is used medicinally, especially for the heart. See next article.

DIGITA'LIS (dij-), a genus of plants, nat. ord. Scrophulariaceae, containing about twenty species of tall herbs, natives of Europe and Western Asia. The purple foxglove (_D. purpur[)e]a_) is a common wild flower in Britain, and several species are grown in gardens. Various preparations from the foxglove receive this name, and are used in medicine, principally in cases of heart disease.

DIGITIGRA'DA (_digitus_, finger, toe, and _gradi_, to walk), a section of the Carnivora, so called from their walking on the ends of their toes; as the dog, cat, and their allies. See _Plantigrade_.

DIGITO'RIUM, a small portable dumb instrument having a short keyboard with five keys like those of a piano, used by piano-players for practice, to give strength and flexibility to the fingers.

DIGNE (d[=e]ny), a town, France, capital of the department of Basses-Alpes, picturesquely situated on a mountain slope, 60 miles north-east of Marseilles. In 1629 a plague reduced the population from 20,000 to 1500. Pop. 7317.