[1] The terms applied by different writers to these nitrogenous
compounds are conflicting. For instance, the term "proteid" is
sometimes used as protein is here used, and sometimes to designate
the group here called albuminoids. The classification and terminology
here followed are those tentatively recommended by the Association of
American Agricultural Colleges and Experiment Stations.
[2] Folin, _Festschrift fur Olaf Hammarsten_, iii. (Upsala, 1906).
[3] _Ztschr. Biol._ 30, 73.
[4] In Russian. Cited in United States Department of Agriculture,
Office of Experiment Stations, Bul. No. 45, _A Digest of Metabolism
Experiments_, by W. O. Atwater and C. F. Langworthy.
[5] _Arch. physiol. norm. et path._ (1894) 4.
[6] U.S. Department of Agriculture, Office of Experiment Stations,
Bulletins Nos. 63, 69, 109, 136, 175. For a description of the
respiration calorimeter here mentioned see also publication No. 42 of
the Carnegie Institution of Washington.
[7] _Ztschr. Biol._ 21 (1885), p. 377.
[8] _Connecticut_ (Storrs) _Agricultural Experiment Station Report_
(1899), 73.
[9] One ounce equals 28.35 grams.
[10] As the chief function of both fats and carbohydrates is to
furnish energy, their exact proportion in the diet is of small
account. The amount of either may vary largely according to taste,
available supply, or other condition, as long as the total amount of
both is sufficient, together with the protein to furnish the required
energy.
DIETRICH, CHRISTIAN WILHELM ERNST (1712-1774), German painter, was born
at Weimar, where he was brought up early to the profession of art by his
father Johann George, then painter of miniatures to the court of the
duke. Having been sent to Dresden to perfect himself under the care of
Alexander Thiele, he had the good fortune to finish in two hours, at the
age of eighteen, a picture which attracted the attention of the king of
Saxony. Augustus II. was so pleased with Dietrich's readiness of hand
that he gave him means to study abroad, and visit in succession the
chief cities of Italy and the Netherlands. There he learnt to copy and
to imitate masters of the previous century with a versatility truly
surprising. Winckelmann, to whom he had been recommended, did not
hesitate to call him the Raphael of landscape. Yet in this branch of his
practice he merely imitated Salvator Rosa and Everdingen. He was more
successful in aping the style of Rembrandt, and numerous examples of
this habit may be found in the galleries of St Petersburg, Vienna and
Dresden. At Dresden, indeed, there are pictures acknowledged to be his,
bearing the fictitious dates of 1636 and 1638, and the name of
Rembrandt. Among Dietrich's cleverest reproductions we may account that
of Ostade's manner in the "Itinerant Singers" at the National Gallery.
His skill in catching the character of the later masters of Holland is
shown in candlelight scenes, such as the "Squirrel and the Peep-Show" at
St Petersburg, where we are easily reminded of Godfried Schalcken.
Dietrich tried every branch of art except portraits, painting Italian
and Dutch views alternately with Scripture scenes and still life. In
1741 he was appointed court painter to Augustus III. at Dresden, with an
annual salary of 400 thalers (L60), conditional on the production of
four cabinet pictures a year. This condition, no doubt, accounts for the
presence of fifty-two of the master's panels and canvases in one of the
rooms at the Dresden museum. Dietrich, though popular and probably the
busiest artist of his time, never produced anything of his own; and his
imitations are necessarily inferior to the originals which he affected
to copy. His best work is certainly that which he gave to engravings. A
collection of these at the British Museum, produced on the general lines
of earlier men, such as Ostade and Rembrandt, reveal both spirit and
skill. Dietrich, after his return from the Peninsula, generally signed
himself "Dietericij," and with this signature most of his extant
pictures are inscribed. He died at Dresden, after he had successively
filled the important appointments of director of the school of painting
at the Meissen porcelain factory and professor of the Dresden academy of
arts.
DIETRICH OF BERN, the name given in German popular poetry to Theodoric
the Great. The legendary history of Dietrich differs so widely from the
life of Theodoric that it has been suggested that the two were
originally unconnected. Medieval chroniclers, however, repeatedly
asserted the identity of Dietrich and Theodoric, although the more
critical noted the anachronisms involved in making Ermanaric (d. 376)
and Attila (d. 453) contemporary with Theodoric (b. 455). That the
legend is based on vague historical reminiscences is proved by the
retention of the names of Theodoric (Thiuda-reiks, Dietrich) and his
father Theudemir (Dietmar), by Dietrich's connexion with Bern (Verona)
and Raben (Ravenna). Something of the Gothic king's character descended
to Dietrich, familiarly called the Berner, the favourite of German
medieval saga heroes, although his story did not leave the same mark on
later German literature as did that of the Nibelungs. The cycle of songs
connected with his name in South Germany is partially preserved in the
Heldenbuch (q.v.) in _Dietrich's Flucht_, the _Rabenschlacht_ and
_Alpharts Tod_; but it was reserved for an Icelandic author, writing in
Norway in the 13th century, to compile, with many romantic additions, a
consecutive account of Dietrich. In this Norse prose redaction, known as
the _Vilkina Saga_, or more correctly the _Thidrekssaga_, is
incorporated much extraneous matter from the Nibelungen and Wayland
legends, in fact practically the whole of south German heroic tradition.
There are traces of a form of the Dietrich legend in which he was
represented as starting out from Byzantium, in accordance with
historical tradition, for his conquest of Italy. But this early
disappeared, and was superseded by the existing legend, in which,
perhaps by an "epic fusion" with his father Theudemir, he was associated
with Attila, and then by an easy transition with Ermanaric. Dietrich was
driven from his kingdom of Bern by his uncle Ermanaric. After years of
exile at the court of Attila he returned with a Hunnish army to Italy,
and defeated Ermanaric in the Rabenschlacht, or battle of Ravenna.
Attila's two sons, with Dietrich's brother, fell in the fight, and
Dietrich returned to Attila's court to answer for the death of the young
princes. This very improbable renunciation of the advantages of his
victory suggests that in the original version of the story the
Rabenschlacht was a defeat. In the poem of _Ermenrichs Tod_ he is
represented as slaying Ermanaric, as in fact Theodoric slew Odoacer.
"Otacher" replaces Ermanaric as his adversary in the _Hildebrandslied_,
which relates how thirty years after the earlier attempt he reconquered
his Lombard kingdom. Dietrich's long residence at Attila's court
represents the youth and early manhood of Theodoric spent at the
imperial court and fighting in the Balkan peninsula, and, in accordance
with epic custom, the period of exile was adorned with war-like
exploits, with fights with dragons and giants, most of which had no
essential connexion with the cycle. The romantic poems of _Konig
Laurin_, _Sigenot_, _Eckenlied_ and _Virginal_ are based largely on
local traditions originally independent of Dietrich. The court of Attila
(Etzel) was a ready bridge to the Nibelungen legend. In the final
catastrophe he was at length compelled, after steadily holding aloof
from the combat, to avenge the slaughter of his Amelungs by the
Burgundians, and delivered Hagen bound into the hands of Kriemhild. The
flame breath which anger induced from him shows the influence of pure
myth, but the tales of his demonic origin and of his being carried off
by the devil in the shape of a black horse may safely be put down to the
clerical hostility to Theodoric's Arianism.
Generally speaking, Dietrich of Bern was the wise and just monarch as
opposed to Ermanaric, the typical tyrant of Germanic legend. He was
invariably represented as slow of provocation and a friend of peace, but
once roused to battle not even Siegfried could withstand his onslaught.
But probably Dietrich's fight with Siegfried in Kriemhild's rose garden
at Worms is a late addition to the Rosengarten myth. The chief heroes of
the Dietrich cycle are his tutor and companion in arms, Hildebrand (see
HILDEBRAND, lay of), with his nephews the Wolfings Alphart and Wolfhart;
Wittich, who renounced his allegiance to Dietrich and slew the sons of
Attila; Heime and Biterolf.
The contents of the poems dealing with the Dietrich cycle are
summarized by Uhland in _Schriften zur Geschichte der Dichtung und
Sage_ (Stuttgart, 1873). The _Thidrekssaga_ (ed. C. Unger,
Christiania, 1853) is translated into German by F. H. v. der Hagen in
_Altdeutsche und altnordische Heldensagen_ (vols. i. and ii. 3rd ed.,
Breslau, 1872). A summary of it forms the concluding chapter of T.
Hodgkin's _Theodoric the Goth_ (1891). The variations in the Dietrich
legend in the Latin historians, in Old and Middle High German
literature, and in the northern saga, can be studied in W. Grimm's
_Deutsche Heldensage_ (2nd ed., Berlin, 1867). There is a good account
in English in F. E. Sandbach's _Heroic Saga-cycle of Dietrich of Bern_
(1906), forming No. 15 of Alfred Nutt's _Popular Studies in
Mythology_, and another in M. Bentinck Smith's translation of Dr O. L.
Jiriczek's _Deutsche Heldensage_ (_Northern Legends_, London, 1902).
For modern German authorities and commentators see B. Symons,
"Deutsche Heldensage" in H. Paul's _Grd. d. german. Phil._
(Strassburg, new ed., 1905); also Goedeke, _Geschichte der deutschen
Dichtung_ (i. 241-246).
DIEZ, FRIEDRICH CHRISTIAN (1794-1876), German philologist, was born at
Giessen, in Hesse-Darmstadt, on the 15th of March 1794. He was educated
first at the gymnasium and then at the university of his native town.
There he studied classics under Friedrich Gottlieb Welcker (1784-1868)
who had just returned from a two years' residence in Italy to fill the
chair of archaeology and Greek literature. It was Welcker who kindled in
him a love of Italian poetry, and thus gave the first bent to his
genius. In 1813 he joined the Hesse corps as a volunteer and served in
the French campaign. Next year he returned to his books, and this short
taste of military service was the only break in a long and uneventful
life of literary labours. By his parents' desire he applied himself for
a short time to law, but a visit to Goethe in 1818 gave a new direction
to his studies, and determined his future career. Goethe had been
reading Raynouard's _Selections from the Romance Poets_, and advised the
young scholar to explore the rich mine of Provencal literature which the
French savant had opened up. This advice was eagerly followed, and
henceforth Diez devoted himself to Romance literature. He thus became
the founder of Romance philology. After supporting himself for some
years by private teaching, he removed in 1822 to Bonn, where he held the
position of privatdocent. In 1823 he published his first work, _An
Introduction to Romance Poetry_; in the following year appeared _The
Poetry of the Troubadours_, and in 1829 _The Lives and Works of the
Troubadours_. In 1830 he was called to the chair of modern literature.
The rest of his life was mainly occupied with the composition of the two
great works on which his fame rests, the _Grammar of the Romance
Languages_ (1836-1844), and the _Lexicon of the Romance
Languages--Italian, Spanish and French_ (1853); in these two works Diez
did for the Romance group of languages what Jacob Grimm did for the
Teutonic family. He died at Bonn on the 29th of May 1876.
The earliest French philologists, such as Perion and Henri Estienne,
had sought to discover the origin of French in Greek and even in
Hebrew. For more than a century Menage's _Etymological Dictionary_
held the field without a rival. Considering the time at which it was
written (1650), it was a meritorious work, but philology was then in
the empirical stage, and many of Menage's derivations (such as that of
"rat" from the Latin "mus," or of "haricot" from "faba") have since
become bywords among philologists. A great advance was made by
Raynouard, who by his critical editions of the works of the
Troubadours, published in the first years of the 19th century, laid
the foundations on which Diez afterwards built. The difference between
Diez's method and that of his predecessors is well stated by him in
the preface to his dictionary. In sum it is the difference between
science and guess-work. The scientific method is to follow implicitly
the discovered principles and rules of phonology, and not to swerve a
foot's breadth from them unless plain, actual exceptions shall justify
it; to follow the genius of the language, and by cross-questioning to
elicit its secrets; to gauge each letter and estimate the value which
attaches to it in each position; and lastly to possess the true
philosophic spirit which is prepared to welcome any new fact, though
it may modify or upset the most cherished theory. Such is the
historical method which Diez pursues in his grammar and dictionary. To
collect and arrange facts is, as he tells us, the sole secret of his
success, and he adds in other words the famous apophthegm of Newton,
"hypotheses non fingo." The introduction to the grammar consists of
two parts:--the first discusses the Latin, Greek and Teutonic elements
common to the Romance languages; the second treats of the six dialects
separately, their origin and the elements peculiar to each. The
grammar itself is divided into four books, on phonology, on flexion,
on the formation of words by composition and derivation, and on
syntax.
His dictionary is divided into two parts. The first contains words
common to two at least of the three principal groups of
Romance:--Italian, Spanish and Portuguese, and Provencal and French.
The Italian, as nearest the original, is placed at the head of each
article. The second part treats of words peculiar to one group. There
is no separate glossary of Wallachian.
Of the introduction to the grammar there is an English translation by
C. B. Cayley. The dictionary has been published in a remodelled form
for English readers by T. C. Donkin.
DIEZ, a town of Germany, in the Prussian province of Hesse-Nassau,
romantically situated in the deep valley of the Lahn, here crossed by an
old bridge, 30 m. E. from Coblenz on the railway to Wetzlar. Pop. 4500.
It is overlooked by a former castle of the counts of Nassau-Dillenburg,
now a prison. Close by, on an eminence above the river, lies the castle
of Oranienstein, formerly a Benedictine nunnery and now a cadet school,
with beautiful gardens. There are a Roman Catholic and two Evangelical
churches. The new part of the town is well built and contains numerous
pretty villa residences. In addition to extensive iron-works there are
sawmills and tanneries. In the vicinity are Fachingen, celebrated for
its mineral waters, and the majestic castle of Schaumburg belonging to
the prince of Waldeck-Pyrmont.
DIFFERENCES, CALCULUS OF (_Theory of Finite Differences_), that branch
of mathematics which deals with the successive differences of the terms
of a series.
1. The most important of the cases to which mathematical methods can be
applied are those in which the terms of the series are the values, taken
at stated intervals (regular or irregular), of a continuously varying
quantity. In these cases the formulae of finite differences enable
certain quantities, whose exact value depends on the law of variation
(i.e. the law which governs the relative magnitude of these terms) to be
calculated, often with great accuracy, from the given terms of the
series, without explicit reference to the law of variation itself. The
methods used may be extended to cases where the series is a double
series (series of double entry), i.e. where the value of each term
depends on the values of a pair of other quantities.
2. The _first differences_ of a series are obtained by subtracting from
each term the term immediately preceding it. If these are treated as
terms of a new series, the first differences of this series are the
_second differences_ of the original series; and so on. The successive
differences are also called _differences of the first, second, ...
order_. The differences of successive orders are most conveniently
arranged in successive columns of a table thus:--
+-----+----------+-----------+-----------------+----------------------+
|Term.| 1st Diff.| 2nd Diff. | 3rd Diff. | 4th Diff. |
+-----+----------+-----------+-----------------+----------------------+
| | | | | |
| a | | | | |
| | b - a | | | |
| b | | c - 2b +a | | |
| | c - b | | d - 3c + 3b - a | |
| c | | d - 2c +b | | e - 4d + 6c - 4b + a |
| | d - c | | e - 3d + 3c - b | |
| d | | e - 2d +c | | |
| | e - d | | | |
| e | | | | |
+-----+----------+-----------+-----------------+----------------------+
_Algebra of Differences and Sums._
[Illustration: FIG. 1.]
3. The formal relations between the terms of the series and the
differences may be seen by comparing the arrangements (A) and (B) in
fig. 1. In (A) the various terms and differences are the same as in S
2, but placed differently. In (B) we take a new series of terms
[alpha], [beta], [gamma], [delta], commencing with the same term
[alpha], and take the successive sums of pairs of terms, instead of
the successive differences, but place them to the left instead of to
the right. It will be seen, in the first place, that the successive
terms in (A), reading downwards to the right, and the successive terms
in (B), reading downwards to the left, consist each of a series of
terms whose coefficients follow the binomial law; i.e. the
coefficients in b - a, c - 2b + a, d - 3c + 3b - a, ... and in [alpha]
+ [beta], [alpha] + 2[beta] + [gamma], [alpha] + 3[beta] + 3[gamma] +
[delta], ... are respectively the same as in y - x, (y - x)^2, (y -
x)^3, ... and in x + y, (x + y)^2, (x + y)^3,.... In the second place,
it will be seen that the relations between the various terms in (A)
are identical with the relations between the similarly placed terms in
(B); e.g. [beta] + [gamma] is the difference of [alpha] + 2[beta] +
[gamma] and [alpha] + [beta], just as c - b is the difference of c and
b: and d - c is the sum of c - b and d - 2c + b, just as [beta] +
2[gamma] + [delta] is the sum of [beta] + [gamma] and [gamma] +
[delta]. Hence if we take [beta], [gamma], [delta], ... of (B) as
being the same as b - a, c - 2b + a, d -3c + 3b - a, ... of (A), all
corresponding terms in the two diagrams will be the same.
Thus we obtain the two principal formulae connecting terms and
differences. If we provisionally describe b - a, c - 2b + a, ... as
the first, second, ... differences of the particular term a (S 7),
then (i.) the nth difference of a is
n.n - 1
l - nk + ... + (-1)^(n-2) ------- c + (-1)^(n-1) nb + (-1)^n a,
1.2
where l, k ... are the (n + 1)th, nth, ... terms of the series a, b,
c, ...; the coefficients being those of the terms in the expansion of
(y -x)^n: and (ii.) the (n + 1)th term of the series, i.e. the nth
term after a, is
n.n - 1
a + n[beta] + ------- [gamma] + ...
1.2
where [beta], [gamma], ... are the first, second, ... differences of
a; the coefficients being those of the terms in the expansion of (x +
y)^n.
4. Now suppose we treat the terms a, b, c, ... as being themselves the
first differences of another series. Then, if the first term of this
series is N, the subsequent terms are N + a, N + a + b, N + a + b + c,
...; i.e. the difference between the (n + 1)th term and the first term
is the sum of the first n terms of the original series. The term N, in
the diagram (A), will come above and to the left of a; and we see, by
(ii.) of S 3, that the sum of the first n terms of the original series
is
/ n.n - 1 \ n.n - 1 n.n - 1.n - 2
( N + na + ------- [beta] + ...) - N = na + ------- [beta] + ------------- [gamma] + ...
\ 1.2 / 1.2 1 . 2 . 3