CX = AC = AD cos _lat._ = a cos _decl._ cos _lat._
PN = CV = CX cos ACX = a cos _decl._ cos _lat._ cos ACX.
NQ = MH = DH sin MDH = sin _decl._ sin _lat._
(:. the angle MDH = DAC = latitude.)
And since PQ = NQ + PN,
we have, by simple substitution,
a sin _alt._ = a sin _decl._ sin _lat._ + a cos _del._ cos _lat._
cos ACX; or, dividing by a throughout,
sin _alt._ = sin _decl._ sin _lat._ + cos _decl._ cos _lat._
cos ACX ... (1)
which equation determines the hour-angle ACX shown by the bead.
To determine the hour-angle of the sun at the same moment, let fig. 10
represent the celestial sphere, HR the horizon, P the pole, Z the
zenith and S the sun.
From the spherical triangle PZS, we have
cos ZS = cos PS cos ZP + sin PS sin ZP cos ZPS
but ZS = zenith distance = 90° - altitude
ZP = 90° - PR = 90°- latitude
PS = polar distance = 90° - declination,
therefore, by substitution
sin _alt._ = sin _decl._ sin _lat._ + cos _decl._ cos _lat._
cos ZPS ... (2)
and ZPS is the hour-angle of the sun.
A comparison of the two formulae (1) and (2) shows that the hour-angle
given by the bead will be the same as that given by the sun, and
proves the theoretical accuracy of the card-dial. Just at sun-rise or
at sun-set the amount of refraction slightly exceeds half a degree.
If, then, a little cross m (see fig. 8) be made just below the
sun-line, at a distance from it which would subtend half a degree at
c, the time of sun-set would be found corrected for refraction, if the
central line of light were made to fall on cm.
[Illustration: FIG. 10.]
LITERATURE.--The following list includes the principal writers on
dialling whose works have come down, to us, and to these we must refer
for descriptions of the various constructions, some simple and direct,
others fanciful and intricate, which have been at different times
employed: Ptolemy, _Analemma_, restored by Commandine; Vitruvius,
_Architecture_; Sebastian Münster, _Horologiographia_; Orontius
Fineus, _De horologiis solaribus_; Mutio Oddi da Urbino, _Horologi
solari_; Dryander, _De horologiorum compositione_; Conrad Gesner,
_Pandectae_; Andreas Schöner, _Gnomonicae_; F. Commandine,
_Horologiorum descriptio_; Joan. Bapt. Benedictus, _De gnomonum usu_;
Georgius Schomberg, _Exegesis fundamentorum gnomonicorum_; Joan.
Solomon de Caus, _Horologes solaires_; Joan. Bapt. Trolta, _Praxis
horologiorum_; Desargues, _Manière universelle pour poser l'essieu_,
&c.; Ath. Kircher, _Ars magna lucis et Umbrae_; Hallum, _Explicatio
horologii in horto regio Londini_; Joan. Mark, _Tractatus
horologiorum_; Clavius, _Gnomonices de horologiis_. Also among more
modern writers, Deschales, Ozanam, Schottus, Wolfius, Picard, Lahire,
Walper; in German, Paterson, Michael, Müller; in English, Foster,
Wells, Collins, Leadbetter, Jones, Leybourn, Emerson and Ferguson. See
also Hans Löschner, _Über Sonnenuhren_ (2nd ed., Graz, 1906). (H. G.)
[1] In one of the courts of Queens' College, Cambridge, there is an
elaborate sun-dial dating from the end of the 17th or beginning of the
18th century, and around it a series of numbers which make it available
as a moon-dial when the moon's age is known.
[2] Strict equality is not necessary, as the observations made are on
the vertical line through each division-point, without reference to the
others. It is not even requisite that the divisions should go completely
and exactly round the cylinder, although they were always so drawn, and
both these conditions were insisted upon in the directions for the
construction.
DIALECT (from Gr. [Greek: dialektos], conversation, manner of speaking,
[Greek: dialegesthai], to converse), a particular or characteristic
manner of speech, and hence any variety of a language. In its widest
sense languages which are branches of a common or parent language may be
said to be "dialects" of that language; thus Attic, Ionic, Aeolic and
Doric are dialects of Greek, though there may never have at any time
been a separate language of which they were variations; so the various
Romance languages, Italian, French, Spanish, &c., were dialects of
Latin. Again, where there have existed side by side, as in England,
various branches of a language, such as the languages of the Angles, the
Jutes or the Saxons, and the descendant of one particular language, from
many causes, has obtained the predominance, the traces of the other
languages remain in the "dialects" of the districts where once the
original language prevailed. Thus it may be incorrect, from the
historical point of view, to say that "dialect" varieties of a language
represent degradations of the standard language. A "literary" accepted
language, such as modern English, represents the original language
spoken in the Midlands, with accretions of Norman, French, and later
literary and scientific additions from classical and other sources,
while the present-day "dialects" preserve, in inflections, pronunciation
and particular words, traces of the original variety of the language not
incorporated in the standard language of the country. See the various
articles on languages (English, French, &c).
DIALECTIC, or DIALECTICS (from Gr. [Greek: dialektos], discourse,
debate; [Greek: ê dialektikê], sc. [Greek: technê], the art of debate),
a logical term, generally used in common parlance in a contemptuous
sense for verbal or purely abstract disputation devoid of practical
value. According to Aristotle, Zeno of Elea "invented" dialectic, the
art of disputation by question and answer, while Plato developed it
metaphysically in connexion with his doctrine of "Ideas" as the art of
analysing ideas in themselves and in relation to the ultimate idea of
the Good (_Repub._ vii.). The special function of the so-called
"Socratic dialectic" was to show the inadequacy of popular beliefs.
Aristotle himself used "dialectic," as opposed to "science," for that
department of mental activity which examines the presuppositions lying
at the back of all the particular sciences. Each particular science has
its own subject matter and special principles ([Greek: idiai archai]) on
which the superstructure of its special discoveries is based. The
Aristotelian dialectic, however, deals with the universal laws ([Greek:
koinai archai]) of reasoning, which can be applied to the particular
arguments of all the sciences. The sciences, for example, all seek to
define their own species; dialectic, on the other hand, sets forth the
conditions which all definitions must satisfy whatever their subject
matter. Again, the sciences all seek to educe general laws; dialectic
investigates the nature of such laws, and the kind and degree of
necessity to which they can attain. To this general subject matter
Aristotle gives the name "Topics" ([Greek: topoi], loci, communes loci).
"Dialectic" in this sense is the equivalent of "logic." Aristotle also
uses the term for the science of probable reasoning as opposed to
demonstrative reasoning ([Greek: apodeiktikê]). The Stoics divided
[Greek: logikê] (logic) into rhetoric and dialectic, and from their time
till the end of the middle ages dialectic was either synonymous with, or
a part of, logic.
In modern philosophy the word has received certain special meanings. In
Kantian terminology _Dialektik_ is the name of that portion of the
_Kritik d. reinen Vernunft_ in which Kant discusses the impossibility of
applying to "things-in-themselves" the principles which are found to
govern phenomena. In the system of Hegel the word resumes its original
Socratic sense, as the name of that intellectual process whereby the
inadequacy of popular conceptions is exposed. Throughout its history,
therefore, "dialectic" has been connected with that which is remote
from, or alien to, unsystematic thought, with the a priori, or
transcendental, rather than with the facts of common experience and
material things.
DIALLAGE, an important mineral of the pyroxene group, distinguished by
its thin foliated structure and bronzy lustre. The chemical composition
is the same as diopside, Ca Mg (SiO_{3})_{2}, but it sometimes contains
the molecules (Mg, Fe") (Al, Fe"')_{2} SiO_{6} and Na Fe"'
(SiO_{3})_{2}, in addition, when it approaches to augite in composition.
Diallage is in fact an altered form of these varieties of pyroxene; the
particular kind of alteration which they have undergone being known as
"schillerization." This, as described by Prof. J. W. Judd, consists in
the development of a fine lamellar structure or parting due to secondary
twinning and the separation of secondary products along these and other
planes of chemical weakness ("solution planes") in the crystal. The
secondary products consist of mixtures of various hydrated oxides--opal,
göthite, limonite, &c--and appear as microscopic inclusions filling or
partly filling cavities, which have definite outlines with respect to
the enclosing crystal and are known as negative crystals. It is to the
reflection and interference of light from these minute inclusions that
the peculiar bronzy sheen or "schiller" of the mineral is due. The most
pronounced lamination is that parallel to the orthopinacoid; another,
less distinct, is parallel to the basal plane, and a third parallel to
the plane of symmetry; these planes of secondary parting are in addition
to the ordinary prismatic cleavage of all pyroxenes. Frequently the
material is interlaminated with a rhombic pyroxene (bronzite) or with an
amphibole (smaragdite or uralite), the latter being an alteration
product of the diallage.
Diallage is usually greyish-green or dark green, sometimes brown, in
colour, and has a pearly to metallic lustre or schiller on the laminated
surfaces. The hardness is 4, and the specific gravity 3.2 to 3.35. It
does not occur in distinct crystals with definite outlines, but only as
lamellar masses in deep-seated igneous rocks, principally gabbro, of
which it is an essential constituent. It occurs also in some peridotites
and serpentines, and rarely in volcanic rocks (basalt) and crystalline
schists. Masses of considerable size are found in the coarse-grained
gabbros of the Island of Skye, Le Prese near Bornio in Valtellina,
Lombardy, Prato near Florence, and many other localities.
The name diallage, from diallage, "difference," in allusion to the
dissimilar cleavages and planes of fracture, as originally applied by R.
J. Haüy in 1801, included other minerals (the orthorhombic pyroxenes
hypersthene, bronzite and bastite, and the smaragdite variety of
hornblende) which exhibit the same peculiarities of schiller structure;
it is now limited to the monoclinic pyroxenes with this structure. Like
the minerals of similar appearance just mentioned, it is sometimes cut
and polished for ornamental purposes. (L. J. S.)
DIALOGUE, properly the conversation between two or more persons,
reported in writing, a form of literature invented by the Greeks for
purposes of rhetorical entertainment and instruction, and scarcely
modified since the days of its invention. A dialogue is in reality a
little drama without a theatre, and with scarcely any change of scene.
It should be illuminated with those qualities which La Fontaine
applauded in the dialogue of Plato, namely vivacity, fidelity of tone,
and accuracy in the opposition of opinions. It has always been a
favourite with those writers who have something to censure or to impart,
but who love to stand outside the pulpit, and to encourage others to
pursue a train of thought which the author does not seem to do more than
indicate. The dialogue is so spontaneous a mode of expressing and noting
down the undulations of human thought that it almost escapes analysis.
All that is recorded, in any literature, of what pretend to be the
actual words spoken by living or imaginary people is of the nature of
dialogue. One branch of letters, the drama, is entirely founded upon it.
But in its technical sense the word is used to describe what the Greek
philosophers invented, and what the noblest of them lifted to the
extreme refinement of an art.
The systematic use of dialogue as an independent literary form is
commonly supposed to have been introduced by Plato, whose earliest
experiment in it is believed to survive in the _Laches_. The Platonic
dialogue, however, was founded on the mime, which had been cultivated
half a century earlier by the Sicilian poets, Sophron and Epicharmus.
The works of these writers, which Plato admired and imitated, are lost,
but it is believed that they were little plays, usually with only two
performers. The recently discovered mimes of Herodas (Herondas) give us
some idea of their scope. Plato further simplified the form, and reduced
it to pure argumentative conversation, while leaving intact the amusing
element of character-drawing. He must have begun this about the year
405, and by 399 he had brought the dialogue to its highest perfection,
especially in the cycle directly inspired by the death of Socrates. All
his philosophical writings, except the _Apology_, are cast in this form.
As the greatest of all masters of Greek prose style, Plato lifted his
favourite instrument, the dialogue, to its highest splendour, and to
this day he remains by far its most distinguished proficient. In the 2nd
century a.d. Lucian of Samosata achieved a brilliant success with his
ironic dialogues "Of the Gods," "Of the Dead," "Of Love" and "Of the
Courtesans." In some of them he attacks superstition and philosophical
error with the sharpness of his wit; in others he merely paints scenes
of modern life. The title of Lucian's most famous collection was
borrowed in the 17th century by two French writers of eminence, each of
whom prepared _Dialogues des morts_. These were Fontenelle (1683) and
Fénelon (1712). In English non-dramatic literature the dialogue had not
been extensively employed until Berkeley used it, in 1713, for his
Platonic treatise, _Hylas and Philonous_. Landor's _Imaginary
Conversations_ (1821-1828) is the most famous example of it in the 19th
century, although the dialogues of Sir Arthur Helps claim attention. In
Germany, Wieland adopted this form for several important satirical works
published between 1780 and 1799. In Spanish literature, the Dialogues of
Valdés (1528) and those on Painting (1633) by Vincenzo Carducci, are
celebrated. In Italian, collections of dialogues, on the model of Plato,
have been composed by Torquato Tasso (1586), by Galileo (1632), by
Galiani (1770), by Leopardi (1825), and by a host of lesser writers. In
our own day, the French have returned to the original application of
dialogue, and the inventions of "Gyp," of Henri Lavedan and of others,
in which a mundane anecdote is wittily and maliciously told in
conversation, would probably present a close analogy to the lost mimes
of the early Sicilian poets, if we could meet with them. This kind of
dialogue has been employed in English, and with conspicuous cleverness
by Mr Anstey Guthrie, but it does not seem so easily appreciated by
English as by French readers. (E.G.)
DIALYSIS (from the Gr. [Greek: dia], through, [Greek: luein], to
loosen), in chemistry, a process invented by Thomas Graham for
separating colloidal and crystalline substances. He found that solutions
could be divided into two classes according to their action upon a
porous diaphragm such as parchment. If a solution, say of salt, be
placed in a drum provided with a parchment bottom, termed a "dialyser,"
and the drum and its contents placed in a larger vessel of water, the
salt will pass through the membrane. If the salt solution be replaced by
one of glue, gelatin or gum, it will be found that the membrane is
impermeable to these solutes. To the first class Graham gave the name
"crystalloids," and to the second "colloids." This method is
particularly effective in the preparation of silicic acid. By adding
hydrochloric acid to a dilute solution of an alkaline silicate, no
precipitate will fall and the solution will contain hydrochloric acid,
an alkaline chloride, and silicic acid. If the solution be transferred
to a dialyser, the hydrochloric acid and alkaline chloride will pass
through the parchment, while the silicic acid will be retained.
DIAMAGNETISM. Substances which, like iron, are attracted by the pole of
an ordinary magnet are commonly spoken of as magnetic, all others being
regarded as non-magnetic. It was noticed by A. C. Becquerel in 1827 that
a number of so-called non-magnetic bodies, such as wood and gum lac,
were influenced by a very powerful magnet, and he appears to have formed
the opinion that the influence was of the same nature as that exerted
upon iron, though much feebler, and that all matter was more or less
magnetic. Faraday showed in 1845 (_Experimental Researches_, vol. iii.)
that while practically all natural substances are indeed acted upon by a
sufficiently strong magnetic pole, it is only a comparatively small
number that are attracted like iron, the great majority being repelled.
Bodies of the latter class were termed by Faraday _diamagnetics_. The
strongest diamagnetic substance known is bismuth, its susceptibility
being--0.000014, and its permeability 0.9998. The diamagnetic quality of
this metal can be detected by means of a good permanent magnet, and its
repulsion by a magnetic pole had been more than once recognized before
the date of Faraday's experiments. The metals gold, silver, copper,
lead, zinc, antimony and mercury are all diamagnetic; tin, aluminium and
platinum are attracted by a very strong pole. (See MAGNETISM.)
DIAMANTE, FRA, Italian fresco painter, was born at Prato about 1400. He
was a Carmelite friar, a member of the Florentine community of that
order, and was the friend and assistant of Filippo Lippi. The Carmelite
convent of Prato which he adorned with many works in fresco has been
suppressed, and the buildings have been altered to a degree involving
the destruction of the paintings. He was the principal assistant of Fra
Filippo in the grand frescoes which may still be seen at the east end of
the cathedral of Prato. In the midst of the work he was recalled to
Florence by his conventual superior, and a minute of proceedings of the
commune of Prato is still extant, in which it is determined to petition
the metropolitan of Florence to obtain his return to Prato,--a proof
that his share in the work was so important that his recall involved the
suspension of it. Subsequently he assisted Fra Filippo in the execution
of the frescoes still to be seen in the cathedral of Spoleto, which Fra
Diamante completed in 1470 after his master's death in 1469. Fra Filippo
left a son ten years old to the care of Diamante, who, having received
200 ducats from the commune of Spoleto, as the balance due for the work
done in the cathedral, returned with the child to Florence, and, as
Vasari says, bought land for himself with the money, giving but a small
portion to the child. The accusation of wrong-doing, however, would
depend upon the share of the work executed by Fra Diamante, and the
terms of his agreement with Fra Filippo. Fra Diamante must have been
nearly seventy when he completed the frescoes at Spoleto, but the exact
year of his death is not known.
DIAMANTE, JUAN BAUTISTA (1640?-1684?), Spanish dramatist, was born at
Castillo about 1640, entered the army, and began writing for the stage
in 1657. He became a knight of Santiago in 1660; the date of his death
is unknown, but no reference to him as a living author occurs after
1684. Like many other Spanish dramatists of his time, Diamante is
deficient in originality, and his style is riddled with affectations;
_La Desgraciada Raquel_, which was long considered to be his best play,
is really Mira de Amescua's _Judía de Toledo_ under another title; and
the earliest of Diamante's surviving pieces, _El Honrador de su padre_
(1658), is little more than a free translation of Corneille's Cid.
Diamante is historically interesting as the introducer of French
dramatic methods into Spain.
DIAMANTINA (formerly called _Tejuco_), a mining town of the state of
Minas Geraes, Brazil, in the N.E. part of the state, 3710 ft. above
sea-level. Pop. (1890) 17,980. Diamantina is built partly on a steep
hillside overlooking a small tributary of the Rio Jequitinhonha (where
diamond-washing was once carried on), and partly on the level plain
above. The town is roughly but substantially built, with broad streets
and large squares. It is the seat of a bishopric, with an episcopal
seminary, and has many churches. Its public buildings are inconspicuous;
they include a theatre, military barracks, hospitals, a lunatic asylum
and a secondary school. There are several small manufactures, including
cotton-weaving, and diamond-cutting is carried on. The surrounding
region, lying on the eastern slopes of one of the lateral ranges of the
Serra do Espinhaço, is rough and barren, but rich in minerals,
principally gold and diamonds. Diamantina is the commercial centre of an
extensive region, and has long been noted for its wealth. The date of
the discovery of diamonds, upon which its wealth and importance chiefly
depend, is uncertain, but the official announcement was made in 1729,
and in the following year the mines were declared crown property, with a
crown reservation, known as the "forbidden district," 42 leagues in
circumference and 8 to 16 leagues in diameter. Gold-mining was forbidden
within its limits and diamond-washing was placed under severe
restrictions. There are no trustworthy returns of the value of the
output, but in 1849 the total was estimated up to that date at
300,000,000 francs (see DIAMOND). The present name of the town was
assumed (instead of Tejuco) in 1838, when it was made a _cidade_.
DIAMANTINO, a small town of the state of Matto Grosso, Brazil, near the
Diamantino river, about 6 m. above its junction with the Paraguay, in
14° 24' 33" S., 56° 8' 30" W. Pop. (1890) of the municipality 2147,
mostly Indians. It stands in a broken sterile region 1837 ft. above
sea-level and at the foot of the great Matto Grosso plateau. The first
mining settlement dates from 1730, when gold was found in the vicinity.
On the discovery of diamonds in 1746 the settlement drew a large
population and for a time was very prosperous. The mines failed to meet
expectations, however, and the population has steadily declined.
Ipecacuanha and vanilla beans are now the principal articles of export.
DIAMETER (from the Gr. [Greek: dia], through, [Greek: metron], measure),
in geometry, a line passing through the centre of a circle or conic
section and terminated by the curve; the "principal diameters" of the
ellipse and hyperbola coincide with the "axes" and are at ...
(_continued in volume 8, slice 4, page 0158._)
* * * * *
Corrections made to printed original.
DETERMINANT, formula = ab'c" - ab"c' + a'b"c - a'bc" - a"bc' - a"b'c.
changed to = ab'c" - ab"c' + a'b"c - a'bc" + a"bc' - a"b'c.
DETMOLD, added missing comma after 'Detmold possesses a natural history
museum'.
DEVENTER, 'The "Athenaeum" disappeared' corrected from the original
'disappered'.
DEVIL, replaced comma with a period after 'according to 1 Chron. xxi'.
DEVONSHIRE, EARLS AND DUKES OF, 'In November 1684' originally 'Novembr'.
DIAGRAM, 'found to be of use especially' originally 'epsecially'.
DIAL, table angles on the dial, column IX. A.M. III. P.M. bottom entry
corrected from '45 45' to '40 45'.
DIAGRAM, missing closing parenthesis added after 'to mark out by lines'.