A determinant of the order n is the sum of the 1.2.3...n products which
can be formed with n elements out of n² elements arranged in the form of
a square, no two of the n elements being in the same line or in the same
column, and each such product having the coefficient ± unity.
The products in question may be obtained by permuting in every possible
manner the columns (or the lines) of the determinant, and then taking
for the factors the n elements in the dexter diagonal. And we thence
derive the rule for the signs, viz. considering the primitive
arrangement of the columns as positive, then an arrangement obtained
therefrom by a single interchange (inversion, or derangement) of two
columns is regarded as negative; and so in general an arrangement is
positive or negative according as it is derived from the primitive
arrangement by an even or an odd number of interchanges. [This implies
the theorem that a given arrangement can be derived from the primitive
arrangement only by an odd number, or else only by an even number of
interchanges,--a theorem the verification of which may be easily
obtained from the theorem (in fact a particular case of the general
one), an arrangement can be derived from itself only by an even number
of interchanges.] And this being so, each product has the sign belonging
to the corresponding arrangement of the columns; in particular, a
determinant contains with the sign + the product of the elements in its
dexter diagonal. It is to be observed that the rule gives as many
positive as negative arrangements, the number of each being = ½ 1.2...n.
The rule of signs may be expressed in a different form. Giving to the
columns in the primitive arrangement the numbers 1, 2, 3 ... n, to
obtain the sign belonging to any other arrangement we take, as often as
a lower number succeeds a higher one, the sign -, and, compounding
together all these minus signs, obtain the proper sign, + or - as the
case may be.
Thus, for three columns, it appears by either rule that 123, 231, 312
are positive; 213, 321, 132 are negative; and the developed expression
of the foregoing determinant of the third order is
= ab'c" - ab"c' + a'b"c - a'bc" + a"bc' - a"b'c.
3. It further appears that a determinant is a linear function[1] of the
elements of each column thereof, and also a linear function of the
elements of each line thereof; moreover, that the determinant retains
the same value, only its sign being altered, when any two columns are
interchanged, or when any two lines are interchanged; more generally,
when the columns are permuted in any manner, or when the lines are
permuted in any manner, the determinant retains its original value, with
the sign + or - according as the new arrangement (considered as derived
from the primitive arrangement) is positive or negative according to the
foregoing rule of signs. It at once follows that, if two columns are
identical, or if two lines are identical, the value of the determinant
is = 0. It may be added, that if the lines are converted into columns,
and the columns into lines, in such a way as to leave the dexter
diagonal unaltered, the value of the determinant is unaltered; the
determinant is in this case said to be _transposed_.
4. By what precedes it appears that there exists a function of the n²
elements, linear as regards the terms of each column (or say, for
shortness, linear as to each column), and such that only the sign is
altered when any two columns are interchanged; these properties
completely determine the function, except as to a common factor which
may multiply all the terms. If, to get rid of this arbitrary common
factor, we assume that the product of the elements in the dexter
diagonal has the coefficient +1, we have a complete definition of the
determinant, and it is interesting to show how from these properties,
assumed for the definition of the determinant, it at once appears that
the determinant is a function serving for the solution of a system of
linear equations. Observe that the properties show at once that if any
column is = 0 (that is, if the elements in the column are each = 0),
then the determinant is = 0; and further, that if any two columns are
identical, then the determinant is = 0.
5. Reverting to the system of linear equations written down at the
beginning of this article, consider the determinant
|ax + by + cz - d , b , c |;
|a'x + b'y + c'z - d', b', c'|
|a"x + b"y + c"z - d", b", c"|
it appears that this is
= x|a , b , c | + y|b , b , c | + z|c , b , c | - |d , b , c |;
|a', b', c'| |b', b', c'| |c', b', c'| |d', b', c'|
|a", b", c"| |b", b", c"| |c", b", c"| |d", b", c"|
viz. the second and third terms each vanishing, it is
= x|a , b , c | - |d , b , c |.
|a', b', c'| |d', b', c'|
|a", b", c"| |d", b", c"|
But if the linear equations hold good, then the first column of the
original determinant is = 0, and therefore the determinant itself is = 0;
that is, the linear equations give
x|a , b , c | - |d , b , c | = 0;
|a', b', c'| |d', b', c'|
|a", b", c"| |d", b", c"|
which is the result obtained above.
We might in a similar way find the values of y and z, but there is a
more symmetrical process. Join to the original equations the new
equation
[alpha]x + [beta]y + [gamma]z = [delta];
a like process shows that, the equations being satisfied, we have
|[alpha], [beta], [gamma], [delta]| = 0;
| a , b , c , d |
| a' , b' , c' , d' |
| a" , b" , c" , d" |
or, as this may be written,
|[alpha], [beta], [gamma] | - [delta]| a , b , c | = 0:
| a , b , c , d | | a', b', c'|
| a' , b' , c' , d'| | a", b", c"|
| a" , b" , c" , d"| | |
which, considering [delta] as standing herein for its value [alpha]x +
[beta]y + [gamma]z, is a consequence of the original equations only: we
have thus an expression for [alpha]x + [beta]y + [gamma]z, an arbitrary
linear function of the unknown quantities x, y, z; and by comparing the
coefficients of [alpha], [beta], [gamma] on the two sides respectively,
we have the values of x, y, z; in fact, these quantities, each
multiplied by
|a , b , c |,
|a', b', c'|
|a", b", c"|
are in the first instance obtained in the forms
|1 |, | 1 |, | 1 |;
|a , b , c , d | |a , b , c , d | |a , b , c , d |
|a', b', c', d'| |a', b', c', d'| |a', b', c', d'|
|a", b", c", d"| |a", b", c", d"| |a", b", c", d"|
but these are
= |b , c , d |, - |c , d , a |, |d , a , b |,
|b', c', d'| |c', d', a'| |d', a', b'|
|b", c", d"| |c", d", a"| |d", a", b"|
or, what is the same thing,
= |b , c , d |, |c , a , d |, |a , b , d |
|b', c', d'| |c', a', d'| |a', b', d'|
|b", c", d"| |c", a", d"| |a", b", d"|
respectively.
6. _Multiplication of two Determinants of the same Order._--The theorem
is obtained very easily from the last preceding definition of a
determinant. It is most simply expressed thus--
([alpha], [alpha]', [alpha]"),
([beta],[beta]',[beta]"),
([gamma],[gamma]',[gamma]")
+---------------------------------------+
(a , b , c )| " " " | =
(a', b', c')| " " " |
(a", b", c")| " " " |
= |a , b , c |. |[alpha] , [beta] , [gamma] |,
|a', b', c'| |[alpha]', [beta]', [gamma]'|
|a", b", c"| |[alpha]", [beta]", [gamma]"|
where the expression on the left side stands for a determinant, the
terms of the first line being (a, b, c)([alpha], [alpha]', [alpha]"),
that is, a[alpha] + b[alpha]' + c[alpha]", (a, b, c)([beta], [beta]',
[beta]"), that is, a[beta] + b[beta]' + c[beta]", (a, b, c)([gamma],
[gamma]', [gamma]"), that is a[gamma] + b[gamma]' + c[gamma]"; and
similarly the terms in the second and third lines are the life functions
with (a', b', c') and (a", b", c") respectively.
There is an apparently arbitrary transposition of lines and columns; the
result would hold good if on the left-hand side we had written ([alpha],
[beta], [gamma]), ([alpha]', [beta]', [gamma]'), ([alpha]", [beta]",
[gamma]"), or what is the same thing, if on the right-hand side we had
transposed the second determinant; and either of these changes would, it
might be thought, increase the elegance of the form, but, for a reason
which need not be explained,[2] the form actually adopted is the
preferable one.
To indicate the method of proof, observe that the determinant on the
left-hand side, _qua_ linear function of its columns, may be broken up
into a sum of (3³ =) 27 determinants, each of which is either of some
such form as
= [alpha][beta][gamma]'|a , a , b |,
|a', a', b'|
|a", a", b"|
where the term [alpha][beta][gamma]' is not a term of the
[alpha][beta][gamma]-determinant, and its coefficient (as a determinant
with two identical columns) vanishes; or else it is of a form such as
= [alpha][beta]'[gamma]"|a , b , c |,
|a', b', c'|
|a", b", c"|
that is, every term which does not vanish contains as a factor the
abc-determinant last written down; the sum of all other factors ±
[alpha][beta]'[gamma]" is the [alpha][beta][gamma]-determinant of the
formula; and the final result then is, that the determinant on the
left-hand side is equal to the product on the right-hand side of the
formula.
7. _Decomposition of a Determinant into complementary
Determinants._--Consider, for simplicity, a determinant of the fifth
order, 5 = 2 + 3, and let the top two lines be
a , b , c , d , e
a', b', c', d', e'
then, if we consider how these elements enter into the determinant, it
is at once seen that they enter only through the determinants of the
second order |a , b |, &c., which can be formed by selecting any two
|a', b'|
columns at pleasure. Moreover, representing the remaining three lines by
a" , b" , c" , d" , e"
a"', b"', c"', d"', e"'
a"", b"", c"", d"", e""
it is further seen that the factor which multiplies the determinant
formed with any two columns of the first set is the determinant of the
third order formed with the complementary three columns of the second
set; and it thus appears that the determinant of the fifth order is a
sum of all the products of the form
= |a , b | |c" , d" , e" |,
|a', b"| |c"', d"', e"'|
|c"", d"", e""|
the sign ± being in each case such that the sign of the term ±
ab'c"d'"e"" obtained from the diagonal elements of the component
determinants may be the actual sign of this term in the determinant of
the fifth order; for the product written down the sign is obviously +.
Observe that for a determinant of the n-th order, taking the
decomposition to be 1 + (n - 1), we fall back upon the equations given
at the commencement, in order to show the genesis of a determinant.
8. Any determinant |a , b | formed out of the elements of the original
|a', b'|
determinant, by selecting the lines and columns at pleasure, is termed a
_minor_ of the original determinant; and when the number of lines and
columns, or order of the determinant, is n-1, then such determinant is
called a _first minor_; the number of the first minors is = n², the
first minors, in fact, corresponding to the several elements of the
determinant--that is, the coefficient therein of any term whatever is
the corresponding first minor. The first minors, each divided by the
determinant itself, form a system of elements _inverse_ to the elements
of the determinant.
A determinant is _symmetrical_ when every two elements symmetrically
situated in regard to the dexter diagonal are equal to each other; if
they are equal and opposite (that is, if the sum of the two elements be
= 0), this relation not extending to the diagonal elements themselves,
which remain arbitrary, then the determinant is _skew_; but if the
relation does extend to the diagonal terms (that is, if these are each =
0), then the determinant is _skew symmetrical_; thus the determinants
|a, h, g|; | a , [nu], - [mu]|; | 0, [nu], - [mu]|
|h, b, f| |- [nu], b,[lambda]| |- [nu], 0,[lambda]|
|g, f, c| | [mu],-[lambda], c | | [mu],- [lambda], 0|
are respectively symmetrical, skew and skew symmetrical:
The theory admits of very extensive algebraic developments, and
applications in algebraical geometry and other parts of mathematics. For
further developments of the theory of determinants see ALGEBRAIC FORMS.
(A. CA.)
9. _History._--These functions were originally known as "resultants,"
a name applied to them by Pierre Simon Laplace, but now replaced by
the title "determinants," a name first applied to certain forms of
them by Carl Friedrich Gauss. The germ of the theory of determinants
is to be found in the writings of Gottfried Wilhelm Leibnitz (1693),
who incidentally discovered certain properties when reducing the
eliminant of a system of linear equations. Gabriel Cramer, in a note
to his _Analyse des lignes courbes algébriques_ (1750), gave the rule
which establishes the sign of a product as _plus_ or _minus_ according
as the number of displacements from the typical form has been even or
odd. Determinants were also employed by Étienne Bezout in 1764, but
the first connected account of these functions was published in 1772
by Charles Auguste Vandermonde. Laplace developed a theorem of
Vandermonde for the expansion of a determinant, and in 1773 Joseph
Louis Lagrange, in his memoir on _Pyramids_, used determinants of the
third order, and proved that the square of a determinant was also a
determinant. Although he obtained results now identified with
determinants, Lagrange did not discuss these functions systematically.
In 1801 Gauss published his _Disquisitiones arithmeticae_, which,
although written in an obscure form, gave a new impetus to
investigations on this and kindred subjects. To Gauss is due the
establishment of the important theorem, that the product of two
determinants both of the second and third orders is a determinant. The
formulation of the general theory is due to Augustin Louis Cauchy,
whose work was the forerunner of the brilliant discoveries made in the
following decades by Hoëné-Wronski and J. Binet in France, Carl Gustav
Jacobi in Germany, and James Joseph Sylvester and Arthur Cayley in
England. Jacobi's researches were published in _Crelle's Journal_
(1826-1841). In these papers the subject was recast and enriched by
new and important theorems, through which the name of Jacobi is
indissolubly associated with this branch of science. The far-reaching
discoveries of Sylvester and Cayley rank as one of the most important
developments of pure mathematics. Numerous new fields were opened up,
and have been diligently explored by many mathematicians.
Skew-determinants were studied by Cayley; axisymmetric-determinants by
Jacobi, V. A. Lebesque, Sylvester and O. Hesse, and centro-symmetric
determinants by W. R. F. Scott and G. Zehfuss. Continuants have been
discussed by Sylvester; alternants by Cauchy, Jacobi, N. Trudi, H.
Nagelbach and G. Garbieri; circulants by E. Catalan, W. Spottiswoode
and J. W. L. Glaisher, and Wronskians by E. B. Christoffel and G.
Frobenius. Determinants composed of binomial coefficients have been
studied by V. von Zeipel; the expression of definite integrals as
determinants by A. Tissot and A. Enneper, and the expression of
continued fractions as determinants by Jacobi, V. Nachreiner, S.
Günther and E. Fürstenau. (See T. Muir, _Theory of Determinants_,
1906).
[1] The expression, a linear function, is here used in its narrowest
sense, a linear function without constant term; what is meant is that
the determinant is in regard to the elements a, a', a", ... of any
column or line thereof, a function of the form Aa + A'a' + A"a" + ...
without any term independent of a, a', a" ...
[2] The reason is the connexion with the corresponding theorem for the
multiplication of two matrices.
DETERMINISM (Lat. _determinare_, to prescribe or limit), in ethics, the
name given to the theory that all moral choice, so called, is the
determined or necessary result of psychological and other conditions. It
is opposed to the various doctrines of Free-Will, known as voluntarism,
libertarianism, indeterminism, and is from the ethical standpoint more
or less akin to necessitarianism and fatalism. There are various degrees
of determinism. It may be held that every action is causally connected
not only externally with the sum of the agent's environment, but also
internally with his motives and impulses. In other words, if we could
know exactly all these conditions, we should be able to forecast with
mathematical certainty the course which the agent would pursue. In this
theory the agent cannot be held responsible for his action in any sense.
It is the extreme antithesis of Indeterminism or Indifferentism, the
doctrine that a man is absolutely free to choose between alternative
courses (the _liberum arbitrium indifferentiae_). Since, however, the
evidence of ordinary consciousness almost always goes to prove that the
individual, especially in relation to future acts, regards himself as
being free within certain limitations to make his own choice of
alternatives, many determinists go so far as to admit that there may be
in any action which is neither reflex nor determined by external causes
solely an element of freedom. This view is corroborated by the
phenomenon of remorse, in which the agent feels that he ought to, and
could, have chosen a different course of action. These two kinds of
determinism are sometimes distinguished as "hard" and "soft"
determinism. The controversy between determinism and libertarianism
hinges largely on the significance of the word "motive"; indeed in no
other philosophical controversy has so much difficulty been caused by
purely verbal disputation and ambiguity of expression. How far, and in
what sense, can action which is determined by motives be said to be
free? For a long time the advocates of free-will, in their eagerness to
preserve moral responsibility, went so far as to deny all motives as
influencing moral action. Such a contention, however, clearly defeats
its own object by reducing all action to chance. On the other hand, the
scientific doctrine of evolution has gone far towards obliterating the
distinction between external and internal compulsion, e.g. motives,
character and the like. In so far as man can be shown to be the product
of, and a link in, a long chain of causal development, so far does it
become impossible to regard him as self-determined. Even in his motives
and his impulses, in his mental attitude towards outward surroundings,
in his appetites and aversions, inherited tendency and environment have
been found to play a very large part; indeed many thinkers hold that the
whole of a man's development, mental as well as physical, is determined
by external conditions.
In the Bible the philosophical-religious problem is nowhere discussed,
but Christian ethics as set forth in the New Testament assumes
throughout the freedom of the human will. It has been argued by
theologians that the doctrine of divine fore-knowledge, coupled with
that of the divine origin of all things, necessarily implies that all
human action was fore-ordained from the beginning of the world. Such an
inference is, however, clearly at variance with the whole doctrine of
sin, repentance and the atonement, as also with that of eternal reward
and punishment, which postulates a real measure of human responsibility.
For the history of the free-will controversy see the articles, WILL,
PREDESTINATION (for the theological problems), ETHICS.
DETINUE (O. Fr. _detenue_, from _detenir_, to hold back), in law, an
action whereby one who has an absolute or a special property in goods
seeks to recover from another who is in actual possession and refuses to
redeliver them. If the plaintiff succeeds in an action of detinue, the
judgment is that he recover the chattel or, if it cannot be had, its
value, which is assessed by the judge and jury, and also certain damages
for detaining the same. An order for the restitution of the specific
goods may be enforced by a special writ of execution, called a writ of
delivery. (See CONTRACT; TROVER.)
DETMOLD, a town of Germany, capital of the principality of
Lippe-Detmold, beautifully situated on the east slope of the Teutoburger
Wald, 25 m. S. of Minden, on the Herford-Altenbeken line of the Prussian
state railways. Pop. (1905) 13,164. The residential château of the
princes of Lippe-Detmold (1550), in the Renaissance style, is an
imposing building, lying with its pretty gardens nearly in the centre of
the town; whilst at the entrance to the large park on the south is the
New Palace (1708-1718), enlarged in 1850, used as the dower-house.
Detmold possesses a natural history museum, theatre, high school,
library, the house in which the poet Ferdinand Freiligrath (1810-1876)
was born, and that in which the dramatist Christian Dietrich Grabbe
(1801-1836), also a native, died. The leading industries are
linen-weaving, tanning, brewing, horse-dealing and the quarrying of
marble and gypsum. About 3 m. to the south-west of the town is the
Grotenburg, with Ernst von Bandel's colossal statue of Hermann or
Arminius, the leader of the Cherusci. Detmold (Thiatmelli) was in 783
the scene of a conflict between the Saxons and the troops of
Charlemagne.
DETROIT, the largest city of Michigan, U.S.A., and the county-seat of
Wayne county, on the Detroit river opposite Windsor, Canada, about 4 m.
W. from the outlet of Lake St Clair and 18 m. above Lake Erie. Pop.
(1880) 116,340; (1890) 205,876; (1900) 285,704, of whom 96,503 were
foreign-born and 4111 were negroes; (1910 census) 465,766. Of the
foreign-born in 1900, 32,027 were Germans and 10,703 were German Poles,
25,403 were English Canadians and 3541 French Canadians, 6347 were
English and 6412 were Irish. Detroit is served by the Michigan Central,
the Lake Shore & Michigan Southern, the Wabash, the Grand Trunk, the
Père Marquette, the Detroit & Toledo Shore Line, the Detroit, Toledo &
Ironton and the Canadian Pacific railways. Two belt lines, one 2 m. to 3
m., and the other 6 m. from the centre of the city, connect the factory
districts with the main railway lines. Trains are ferried across the
river to Windsor, and steamboats make daily trips to Cleveland,
Wyandotte, Mount Clemens, Port Huron, to less important places between,
and to several Canadian ports. Detroit is also the S. terminus for
several lines to more remote lake ports, and electric lines extend from
here to Port Huron, Flint, Pontiac, Jackson, Toledo and Grand Rapids.
The city extended in 1907 over about 41 sq. m., an increase from 29 sq.
m. in 1900 and 36 sq. m. in 1905. Its area in proportion to its
population is much greater than that of most of the larger cities of the
United States. Baltimore, for example, had in 1904 nearly 70% more
inhabitants (estimated), while its area at that time was a little less
and in 1907 was nearly one-quarter less than that of Detroit. The ground
within the city limits as well as that for several miles farther back is
quite level, but rises gradually from the river bank, which is only a
few feet in height. The Detroit river, along which the city extends for
about 10 m., is here ½ m. wide and 30 ft. to 40 ft. deep; its current is
quite rapid; its water, a beautiful clear blue; at its mouth it has a
width of about 10 m., and in the river there are a number of islands,
which during the summer are popular resorts. The city has a 3 m.
frontage on the river Rouge, an estuary of the Detroit, with a 16 ft.
channel. Before the fire by which the city was destroyed in 1805, the
streets were only 12 ft. wide and were unpaved and extremely dirty. But
when the rebuilding began, several avenues from 100 ft. to 200 ft. wide
were--through the influence of Augustus B. Woodward (c. 1775-1827), one
of the territorial judges at the time and an admirer of the plan of the
city of Washington--made to radiate from two central points. From a half
circle called the Grand Circus there radiate avenues 120 ft. and 200 ft.
wide. About ¼ m. toward the river from this was established another
focal point called the Campus Martius, 600 ft. long and 400 ft. wide, at
which commence radiating or cross streets 80 ft. and 100 ft. wide.
Running north from the river through the Campus Martius and the Grand
Circus is Woodward Avenue, 120 ft. wide, dividing the present city, as
it did the old town, into nearly equal parts. Parallel with the river is
Jefferson Avenue, also 120 ft. wide. The first of these avenues is the
principal retail street along its lower portion, and is a residence
avenue for 4 m. beyond this. Jefferson is the principal wholesale street
at the lower end, and a fine residence avenue E. of this. Many of the
other residence streets are 80 ft. wide. The setting of shade trees was
early encouraged, and large elms and maples abound. The intersections of
the diagonal streets left a number of small, triangular parks, which, as
well as the larger ones, are well shaded. The streets are paved mostly
with asphalt and brick, though cedar and stone have been much used, and
kreodone block to some extent. In few, if any, other American cities of
equal size are the streets and avenues kept so clean. The Grand
Boulevard, 150 ft. to 200 ft. in width and 12 m. in length, has been
constructed around the city except along the river front. A very large
proportion of the inhabitants of Detroit own their homes: there are no
large congested tenement-house districts; and many streets in various
parts of the city are faced with rows of low and humble cottages often
having a garden plot in front.
Of the public buildings the city hall (erected 1868-1871), overlooking
the Campus Martius, is in Renaissance style, in three storeys; the
flagstaff from the top of the tower reaches a height of 200 ft. On the
four corners above the first section of the tower are four figures, each
14 ft. in height, to represent Justice, Industry, Art and Commerce, and
on the same level with these is a clock weighing 7670 lb--one of the
largest in the world. In front of the building stands the Soldiers' and
Sailors' monument, 60 ft. high, designed by Randolph Rogers (1825-1892)
and unveiled in 1872. At each of the four corners in each of three
sections rising one above the other are bronze eagles and figures
representing the United States Infantry, Marine, Cavalry and Artillery,
also Victory, Union, Emancipation and History; the figure by which the
monument is surmounted was designed to symbolize Michigan. A larger and
more massive and stately building than the city hall is the county
court house, facing Cadillac Square, with a lofty tower surmounted by a
gilded dome. The Federal building is a massive granite structure, finely
decorated in the interior. Among the churches of greatest architectural
beauty are the First Congregational, with a fine Byzantine interior, St
John's Episcopal, the Woodward Avenue Baptist and the First
Presbyterian, all on Woodward Avenue, and St. Anne's and Sacred Heart of
Mary, both Roman Catholic. The municipal museum of art, in Jefferson
Avenue, contains some unusually interesting Egyptian and Japanese
collections, the Scripps' collection of old masters, other valuable
paintings, and a small library; free lectures on art are given here
through the winter. The public library had 228,500 volumes in 1908,
including one of the best collections of state and town histories in the
country. A large private collection, owned by C. M. Burton and relating
principally to the history of Detroit, is also open to the public. The
city is not rich in outdoor works of art. The principal ones are the
Merrill fountain and the soldiers' monument on the Campus Martius, and a
statue of Mayor Pingree in West Grand Circus Park.
The parks of Detroit are numerous and their total area is about 1200
acres. By far the most attractive is Belle Isle, an island in the river
at the E. end of the city, purchased in 1879 and having an area of more
than 700 acres. The Grand Circus Park of 4½ acres, with its trees,
flowers and fountains, affords a pleasant resting place in the busiest
quarter of the city. Six miles farther out on Woodward Avenue is Palmer
Park of about 140 acres, given to the city in 1894 and named in honour
of the donor. Clark Park (28 acres) is in the W. part of the city, and
there are various smaller parks. The principal cemeteries are Elmwood
(Protestant) and Mount Elliott (Catholic), which lie adjoining in the E.
part of the city; Woodmere in the W. and Woodlawn in the N. part of the
city.
_Charity and Education._--Among the charitable institutions are the
general hospitals (Harper, Grace and St Mary's); the Detroit Emergency,
the Children's Free and the United States Marine hospitals; St Luke's
hospital, church home, and orphanage; the House of Providence (a
maternity hospital and infant asylum); the Woman's hospital and
foundling's home; the Home for convalescent children, &c. In 1894 the
mayor, Hazen Senter Pingree (1842-1901), instituted the practice of
preparing, through municipal aid and supervision, large tracts of vacant
land in and about the city for the growing of potatoes and other
vegetables and then, in conjunction with the board of poor
commissioners, assigning it in small lots to families of the unemployed,
and furnishing them with seed for planting. This plan served an
admirable purpose through three years of industrial depression, and was
copied in other cities; it was abandoned when, with the renewal of
industrial activity, the necessity for it ceased. The leading penal
institution of the city is the Detroit House of Correction, noted for
its efficient reformatory work; the inmates are employed ten hours a
day, chiefly in making furniture. The house of correction pays the city
a profit of $35,000 to $40,000 a year. The educational institutions, in
addition to those of the general public school system, include several
parochial schools, schools of art and of music, and commercial colleges;
Detroit College (Catholic), opened in 1877; the Detroit College of
Medicine, opened in 1885; the Michigan College of Medicine and Surgery,
opened in 1888; the Detroit College of law, founded in 1891, and a city
normal school.
_Commerce._--Detroit's location gives to the city's shipping and
shipbuilding interests a high importance. All the enormous traffic
between the upper and lower lakes passes through the Detroit river. In
1907 the number of vessels recorded was 34,149, with registered tonnage
of 53,959,769, carrying 71,226,895 tons of freight, valued at
$697,311,302. This includes vessels which delivered part or all of their
cargo at Detroit. The largest item in the freights is iron ore on
vessels bound down. The next is coal on vessels up bound. Grain and
lumber are the next largest items. Detroit is a port of entry, and its
foreign commerce, chiefly with Canada, is of growing importance. The
city's exports increased from $11,325,807 in 1896 to $37,085,027 in
1909. The imports were $3,153,609 in 1896 and $7,100,659 in 1909.
As a manufacturing city, Detroit holds high rank. The total number of
manufacturing establishments in 1890 was 1746, with a product for the
year valued at $77,351,546; in 1900 there were 2847 establishments with
a product for the year valued at $100,892,838; or an increase of 30.4%
in the decade. In 1900 the establishments under the factory system,
omitting the hand trades and neighbourhood industries, numbered 1259 and
produced goods valued at $88,365,924; in 1904 establishments under the
factory system numbered 1363 and the product had increased 45.7% to
$128,761,658. In the district subsequently annexed the product in 1904
was about $12,000,000, making a total of $140,000,000. The output for
1906 was estimated at $180,000,000. The state factory inspectors in 1905
visited 1721 factories having 83,231 employees. In 1906 they inspected
1790 factories with 93,071 employees. Detroit is the leading city in the
country in the manufacture of automobiles. In 1904 the value of its
product was one-fifth that for the whole country. In 1906 the city had
twenty automobile factories, with an output of 11,000 cars, valued at
$12,000,000. Detroit is probably the largest manufacturer in the country
of freight cars, stoves, pharmaceutical preparations, varnish, soda ash
and similar alkaline products. Other important manufactures are ships,
paints, foundry and machine shop products, brass goods, furniture, boots
and shoes, clothing, matches, cigars, malt liquors and fur goods; and
slaughtering and meat packing is an important industry.
The Detroit Board of Commerce, organized in 1903, brought into one
association the members of three former bodies, making a compact
organization with civic as well as commercial aims. The board has
brought into active co-operation nearly all the leading business men of
the city and many of the professional men. Their united efforts have
brought many new industries to the city, have improved industrial
conditions, and have exerted a beneficial influence upon the municipal
administration. Other business organizations are the Board of Trade,
devoted to the grain trade and kindred lines, the Employers'
Association, which seeks to maintain satisfactory relations between
employer and employed, the Builders' & Traders' Exchange, and the Credit
Men's Association.
_Administration._--Although the city received its first charter in 1806,
and another in 1815, the real power rested in the hands of the governor
and judges of the territory until 1824; the charters of 1824 and 1827
centred the government in a council and made the list of elective
officers long; the charter of 1827 was revised in 1857 and again in 1859
and the present charter dates from 1883. Under this charter only three
administrative officers are elected,--the mayor, the city clerk and the
city treasurer,--elections being biennial. The administration of the
city departments is largely in the hands of commissions. There is one
commissioner each, appointed by the mayor, for the parks and boulevards,
police and public works departments. The four members of the health
board are nominated by the governor and confirmed by the state senate.
The school board is an independent body, consisting of one elected
member from each ward holding office for four years, but the mayor has
the veto power over its proceedings as well as those of the common
council. In each case a two-thirds vote overrules his veto. The other
principal officers and commissions, appointed by the mayor and confirmed
by the council, are controller, corporation counsel, board of three
assessors, fire commission (four members), public lighting commission
(six members), water commission (five members), poor commission (four
members), and inspectors of the house of correction (four in number).
The members of the public library commission, six in number, are elected
by the board of education. Itemized estimates of expenses for the next
fiscal year are furnished by the different departments to the controller
in February. He transmits them to the common council with his
recommendations. The council has four weeks in which to consider them.
It may reduce or increase the amounts asked, and may add new items. The
budget then goes to the board of estimates, which has a month for its
consideration. This body consists of two members elected from each ward
and five elected at large. The mayor and heads of departments are
advisory members, and may speak but not vote. The members of the board
of estimates can hold no other office and they have no appointing power,
the intention being to keep them as free as possible from all political
motives and influences. They may reduce or cut out any estimates
submitted, but cannot increase any or add new ones. No bonds can be
issued without the assent of the board of estimates. The budget is
apportioned among twelve committees which have almost invariably given
close and conscientious examination to the actual needs of the
departments. A reduction of $1,000,000 to $1,500,000, without impairing
the service, has been a not unusual result of their deliberations.
Prudent management under this system has placed the city in the highest
rank financially. Its debt limit is 2% on the assessed valuation, and
even that low maximum is not often reached. The debt in 1907 was only
about $5,500,000, a smaller _per capita_ debt than that of any other
city of over 100,000 inhabitants in the country; the assessed valuation
was $330,000,000; the city tax, $14.70 on the thousand dollars of
assessed valuation. Both the council and the estimators are hampered in
their work by legislative interference. Nearly all the large salaries
and many of those of the second grade are made mandatory by the
legislature, which has also determined many affairs of a purely
administrative character.
Detroit has made three experiments with municipal ownership. On account
of inadequate and unsatisfactory service by a private company, the city
bought the water-works as long ago as 1836. The works have been twice
moved and enlargements have been made in advance of the needs of the
city. In 1907 there were six engines in the works with a pumping
capacity of 152,000,000 gallons daily. The daily average of water used
during the preceding year was 61,357,000 gallons. The water is pumped
from Lake St Clair and is of exceptional purity. The city began its own
public lighting in April 1895, having a large plant on the river near
the centre of the city. It lights the streets and public buildings, but
makes no provision for commercial business. The lighting is excellent,
and the cost is probably less than could be obtained from a private
company. The street lighting is done partly from pole and arm lights,
but largely from steel towers from 100 ft. to 180 ft. in height, with
strong reflected lights at the top. The city also owns two portable
asphalt plants, and thus makes a saving in the cost of street repairing
and resurfacing. With a view of effecting the reduction of street car
fares to three cents, the state legislature in 1899 passed an act for
purchasing or leasing the street railways of the city, but the Supreme
Court pronounced this act unconstitutional on the ground that, as the
constitution prohibited the state from engaging in a work of internal
improvement, the state could not empower a municipality to do so.
Certain test votes indicated an almost even division on the question of
municipal ownership of the railways.
_History._--Detroit was founded in 1701 by Antoine Laumet de la Mothe
Cadillac (c. 1661-1730), who had pointed out the importance of the place
as a strategic point for determining the control of the fur trade and
the possession of the North-west and had received assistance from the
French government soon after Robert Livingston (1654-1725), the
secretary of the Board of Indian Commissioners in New York, had urged
the English government to establish a fort at the same place. Cadillac
arrived on the 24th of July with about 100 followers. They at once built
a palisade fort about 200 ft. square S. of what is now Jefferson Avenue
and between Griswold and Shelby streets, and named it Fort Pontchartrain
in honour of the French colonial minister. Indians at once came to the
place in large numbers, but they soon complained of the high price of
French goods; there was serious contention between Cadillac and the
French Canadian Fur Company, to which a monopoly of the trade had been
granted, as well as bitter rivalry between him and the Jesuits. After
the several parties had begun to complain to the home government the
monopoly of the fur trade was transferred to Cadillac and he was
exhorted to cease quarrelling with the Jesuits. Although the
inhabitants then increased to 200 or more, dissatisfaction with the
paternal rule of the founder increased until 1710, when he was made
governor of Louisiana. The year before, the soldiers had been withdrawn;
by the second year after there was serious trouble with the Indians, and
for several years following the population was greatly reduced and the
post threatened with extinction. But in 1722, when the Mississippi
country was opened, the population once more increased, and again in
1748, when the settlement of the Ohio Valley began, the governor-general
of Canada offered special inducements to Frenchmen to settle at Detroit,
with the result that the population was soon more than 1000 and the
cultivation of farms in the vicinity was begun. In 1760, however, the
place was taken by the British under Colonel Robert Rogers and an
English element was introduced into the population which up to this time
had been almost exclusively French. Three years later, during the
conspiracy of Pontiac, the fort first narrowly escaped capture and then
suffered from a siege lasting from the 9th of May until the 12th of
October. Under English rule it continued from this time on as a military
post with its population usually reduced to less than 500. In 1778 a new
fort was built and named Fort Lernault, and during the War of
Independence the British sent forth from here several Indian expeditions
to ravage the frontiers. With the ratification of the treaty which
concluded that war the title to the post passed to the United States in
1783, but the post itself was not surrendered until the 11th of January
1796, in accordance with Jay's Treaty of 1794. It was then named Fort
Shelby; but in 1802 it was incorporated as a town and received its
present name. In 1805 all except one or two buildings were destroyed by
fire. General William Hull (1753-1825), a veteran of the War of American
Independence, governor of Michigan territory in 1805-1812, as commander
of the north-western army in 1812 occupied the city. Failing to hear
immediately of the declaration of war between the United States and
Great Britain, he was cut off from his supplies shipped by Lake Erie. He
made from Detroit on the 12th of July an awkward and futile advance into
Canada, which, if more vigorous, might have resulted in the capture of
Malden and the establishment of American troops in Canada, and then
retired to his fortifications. On the 16th of August 1812, without any
resistance and without consulting his officers, he surrendered the city
to General Brock, for reasons of humanity, and afterwards attempted to
justify himself by criticism of the War Department in general and in
particular of General Henry Dearborn's armistice with Prevost, which had
not included in its terms Hull, whom Dearborn had been sent out to
reinforce.[1] After Perry's victory on the 14th of September on Lake
Erie, Detroit on the 29th of September was again occupied by the forces
of the United States. Its growth was rather slow until 1830, but since
then its progress has been unimpeded. Detroit was the capital of
Michigan from 1805 to 1847.
AUTHORITIES.--Silas Farmer, _The History of Detroit and Michigan_
(Detroit, 1884 and 1889), and "Detroit, the Queen City," in L. P.
Powell's _Historic Towns of the Western States_ (New York and London,
1901); D. F. Wilcox, "Municipal Government in Michigan and Ohio," in
_Columbia University Studies_ (New York, 1896); C. M. Burton,
_"Cadillac's Village" or Detroit under Cadillac_ (Detroit, 1896);
Francis Parkman, _A Half Century of Conflict_ (Boston, 1897); and _The
Conspiracy of Pontiac_ (Boston, 1898); and the annual _Reports_ of the
Detroit Board of Commerce (1904 sqq.).
[1] Hull was tried at Albany in 1814 by court martial, General Dearborn
presiding, was found guilty of treason, cowardice, neglect of duty and
unofficerlike conduct, and was sentenced to be shot; the president
remitted the sentence because of Hull's services in the Revolution.
DETTINGEN, a village of Germany in the kingdom of Bavaria, on the Main,
and on the Frankfort-on-Main-Aschaffenburg railway, 10 m. N.W. of
Aschaffenburg. It is memorable as the scene of a decisive battle on the
27th of June 1743, when the English, Hanoverians and Austrians (the
"Pragmatic army"), 42,000 men under the command of George II. of
England, routed the numerically superior French forces under the duc de
Noailles. It was in memory of this victory that Handel composed his
_Dettingen Te Deum_.
DEUCALION, in Greek legend, son of Prometheus, king of Phthia in
Thessaly, husband of Pyrrha, and father of Hellen, the mythical ancestor
of the Hellenic race. When Zeus had resolved to destroy all mankind by a
flood, Deucalion constructed a boat or ark, in which, after drifting
nine days and nights, he landed on Mount Parnassus (according to others,
Othrys, Aetna or Athos) with his wife. Having offered sacrifice and
inquired how to renew the human race, they were ordered to cast behind
them the "bones of the great mother," that is, the stones from the
hillside. The stones thrown by Deucalion became men, those thrown by
Pyrrha, women.
See Apollodorus i. 7, 2; Ovid, _Metam._ i. 243-415; Apollonius Rhodius
iii. 1085 ff.; H. Usener, _Die Sintflutsagen_ (1899).
DEUCE (a corruption of the Fr. _deux_, two), a term applied to the "two"
of any suit of cards, or of dice. It is also a term used in tennis when
both sides have each scored three points in a game, or five games in a
set; to win the game or set two points or games must then be won
consecutively. The earliest instances in English of the use of the slang
expression "the deuce," in exclamations and the like, date from the
middle of the 17th century. The meaning was similar to that of "plague"
or "mischief" in such phrases as "plague on you," "mischief take you"
and the like. The use of the word as an euphemism for "the devil" is
later. According to the _New English Dictionary_ the most probable
derivation is from a Low German _das daus_, i.e. the "deuce" in dice,
the lowest and therefore the most unlucky throw. The personification,
with a consequent change of gender, to _der daus_, came later. The word
has also been identified with the name of a giant or goblin in Teutonic
mythology.
DEUS, JOÃO DE (1830-1896), the greatest Portuguese poet of his
generation, was born at San Bartholomeu de Messines in the province of
Algarve on the 8th of March 1830. Matriculating in the faculty of law at
the university of Coimbra, he did not proceed to his degree but settled
in the city, dedicating himself wholly to the composition of verses,
which circulated among professors and undergraduates in manuscript
copies. In the volume of his art, as in the conduct of life, he
practised a rigorous self-control. He printed nothing previous to 1855,
and the first of his poems to appear in a separate form was _La Lata_,
in 1860. In 1862 he left Coimbra for Beja, where he was appointed editor
of _O Bejense_, the chief newspaper in the province of Alemtejo, and
four years later he edited the _Folha do Sul_. As the pungent satirical
verses entitled _Eleições_ prove, he was not an ardent politician, and,
though he was returned as Liberal deputy for the constituency of Silves
in 1869, he acted independently of all political parties and promptly
resigned his mandate. The renunciation implied in the act, which cut him
off from all advancement, is in accord with nearly all that is known of
his lofty character. In the year of his election as deputy, his friend
José Antonio Garcia Blanco collected from local journals the series of
poems, _Flores do campo_, which is supplemented by the _Ramo de flores_
(1869). This is João de Deus's masterpiece. _Pires de Marmalada_ (1869)
is an improvisation of no great merit. The four theatrical
pieces--_Amemos o nosso proximo_, _Ser apresentado_, _Ensaio de
Casamento_, and _A Viúva inconsolavel_--are prose translations from
Méry, cleverly done, but not worth the doing. _Horacio e Lydia_ (1872),
a translation from Ronsard, is a good example of artifice in
manipulating that dangerously monotonous measure, the Portuguese
couplet. As an indication of a strong spiritual reaction three prose
fragments (1873)--_Anna, Mãe de Maria_, _A Virgem Maria_ and _A Mulher
do Levita de Ephrain_--translated from Darboy's _Femmes de la Bible_,
are full of significance. The _Folhas soltas_ (1876) is a collection of
verse in the manner of _Flores do campo_, brilliantly effective and
exquisitely refined. Within the next few years the writer turned his
attention to educational problems, and in his _Cartilha maternal_ (1876)
first expressed the conclusions to which his study of Pestalozzi and
Fröbel had led him. This patriotic, pedagogical apostolate was a
misfortune for Portuguese literature; his educational mission absorbed
João de Deus completely, and is responsible for numerous controversial
letters, for a translation of Théodore-Henri Barrau's treatise, _Des
devoirs des enfants envers leurs parents_, for a prosodic dictionary
and for many other publications of no literary value. A copy of verses
in Antonio Vieira's _Grinalda de Maria_ (1877), the _Loas á Virgem_
(1878) and the _Proverbios de Salomão_ are evidence of a complete return
to orthodoxy during the poet's last years. By a lamentable error of
judgment some worthless pornographic verses entitled _Cryptinas_ have
been inserted in the completest edition of João de Deus's poems--_Campo
de Flores_ (Lisbon, 1893). He died at Lisbon on the 11th of January
1896, was accorded a public funeral and was buried in the National
Pantheon, the Jeronymite church at Belem, where repose the remains of
Camoens, Herculano and Garrett. His scattered minor prose writings and
correspondence have been posthumously published by Dr Theophilo Braga
(Lisbon, 1898).
Next to Camoens and perhaps Garrett, no Portuguese poet has been more
widely read, more profoundly admired than João de Deus; yet no poet in
any country has been more indifferent to public opinion and more
deliberately careless of personal fame. He is not responsible for any
single edition of his poems, which were put together by pious but
ill-informed enthusiasts, who ascribed to him verses that he had not
written; he kept no copies of his compositions, seldom troubled to write
them himself, and was content for the most part to dictate them to
others. He has no great intellectual force, no philosophic doctrine, is
limited in theme as in outlook, is curiously uncertain in his touch,
often marring a fine poem with a slovenly rhyme or with a misplaced
accent; and, on the only occasion when he was induced to revise a set of
proofs, his alterations were nearly all for the worse. And yet, though
he never appealed to the patriotic spirit, though he wrote nothing at
all comparable in force or majesty to the restrained splendour of _Os
Lusiadas_, the popular instinct which links his name with that of his
great predecessor is eminently just. For Camoens was his model; not the
Camoens of the epic, but the Camoens of the lyrics and the sonnets,
where the passion of tenderness finds its supreme utterance. Braga has
noted five stages of development in João de Deus's artistic life--the
imitative, the idyllic, the lyric, the pessimistic and the devout
phases. Under each of these divisions is included much that is of
extreme interest, especially to contemporaries who have passed through
the same succession of emotional experience, and it is highly probable
that _Caturras_ and _Gaspar_, pieces as witty as anything in Bocage but
free from Bocage's coarse impiety, will always interest literary
students. But it is as the singer of love that João de Deus will delight
posterity as he delighted his own generation. The elegiac music of
_Rachel_ and of _Marina_, the melancholy of _Adeus_ and of _Remoinho_,
the tenderness and sincerity of _Meu casta lirio_, of _Lagrima celeste_,
of _Descalça_ and a score more songs are distinguished by the large,
vital simplicity which withstands time. It is precisely in the quality
of unstudied simplicity that João de Deus is incomparably strong. The
temptations to a display of virtuosity are almost irresistible for a
Portuguese poet; he has the tradition of virtuosity in his blood, he has
before him the example of all contemporaries, and he has at hand an
instrument of wonderful sonority and compass. Yet not once is João de
Deus clamorous or rhetorical, not once does he indulge in idle ornament.
His prevailing note is that of exquisite sweetness and of reverent
purity; yet with all his caressing softness he is never sentimental,
and, though he has not the strength for a long fight, emotion has seldom
been set to more delicate music. Had he included among his other gifts
the gift of selection, had he continued the poetic discipline of his
youth instead of dedicating his powers to a task which, well as he
performed it, might have been done no less well by a much lesser man,
there is scarcely any height to which he might not have risen.
See also Maxime Formont, _Le Mouvement poétique contemporain en
Portugal_ (Lyon, 1892). (J. F.-K.)
DEUTERONOMY, the name of one of the books of the Old Testament. This
book was long the storm-centre of Pentateuchal criticism, orthodox
scholars boldly asserting that any who questioned its Mosaic authorship
reduced it to the level of a pious fraud. But Biblical facts have at
last triumphed over tradition, and the non-Mosaic authorship of
Deuteronomy is now a commonplace of criticism. It is still instructive,
however, to note the successive phases through which scholarly opinion
regarding the composition and date of his book has passed.
In the 17th century the characteristics which so clearly mark off
Deuteronomy from the other four books of the Pentateuch were frankly
recognized, but the most advanced critics of that age were inclined to
pronounce it the earliest and most authentic of the five. In the
beginning of the 19th century de Wette startled the religious world by
declaring that Deuteronomy, so far from being Mosaic, was not known till
the time of Josiah. This theory he founded on 2 Kings xxii.; and ever
since, this chapter has been one of the recognized foci of Biblical
criticism. The only other single chapter of the Bible which is
responsible for having brought about a somewhat similar revolution in
critical opinion is Ezek. xliv. From this chapter, some seventy years
after de Wette's discovery, Wellhausen with equal acumen inferred that
Leviticus was not known to Ezekiel, the priest, and therefore could not
have been in existence in his day; for had Leviticus been the recognized
Law-book of his nation Ezekiel could not have represented as a
degradation the very position which that Law-book described as a special
honour conferred on the Levites by Yahweh himself. Hence Leviticus, so
far from belonging to an earlier stratum of the Pentateuch than
Deuteronomy, as de Wette thought, must belong to a much later stratum,
and be at least exilic, if not post-exilic.
The title "Deuteronomy" is due to a mistranslation by the Septuagint of
the clause in chap. xvii. 18, rendered "and he shall write out for
himself this Deuteronomy." The Hebrew really means "and he [the king]
shall write out for himself a copy of this law," where there is not the
slightest suggestion that the author intended to describe "this law"
delivered on the plains of Moab as a second code in contradistinction to
the first code given on Sinai thirty-eight years earlier. Moreover the
phrase "this law" is so ambiguous as to raise a much greater difficulty
than that caused by the Greek mistranslation of the Hebrew word for
"copy." How much does "this law" include? It was long supposed to mean
the whole of our present Deuteronomy; indeed, it is on that supposition
that the traditional view of the Mosaic authorship is based. But the
context alone can determine the question; and that is often so ambiguous
that a sure inference is impossible. We may safely assert, however, that
nowhere need "this law" mean the whole book. In fact, it invariably
means very much less, and sometimes, as in xxvii. 3, 8, so little that
it could all be engraved in large letters on a few plastered stones set
up beside an altar.
Deuteronomy is not the work of any single writer but the result of a
long process of development. The fact that it is legislative as well as
hortatory is enough to prove this, for most of the laws it contains are
found elsewhere in the Pentateuch, sometimes in less developed,
sometimes in more developed forms, a fact which is conclusive proof of
prolonged historical development. According to the all-pervading law of
evolution, the less complex form must have preceded the more complex.
Still, the book does bear the stamp of one master-mind. Its style is as
easily recognized as that of Deutero-Isaiah, being as remarkable for its
copious diction as for its depths of moral and religious feeling.
The original Deuteronomy, D, read to King Josiah, cannot have been so
large as our present book, for not only could it be read at a single
sitting, but it could be easily read twice in one day. On the day it was
found, Shaphan first read it himself, and then went to the king and read
it aloud to him. But perhaps the most conclusive proof of its brevity is
that it was read publicly to the assembled people immediately before
they, as well as their king, pledged themselves to obey it; and not a
word is said as to the task of reading it aloud, so as to be heard by
such a great multitude, being long or difficult.
The legislative part of D consists of fifteen chapters (xii.-xxvi.),
which, however, contain many later insertions. But the impression made
upon Josiah by what he heard was far too deep to have been produced by
the legislative part alone. The king must have listened to the curses as
well as the blessings in chap, xxviii., and no doubt also to the
exhortations in chaps. v.-xi. Hence we may conclude that the original
book consisted of a central mass of religious, civil and social laws,
preceded by a hortatory introduction and followed by an effective
peroration. The book read to Josiah must therefore have comprised most
of what is found in Deut. v.-xxvi., xxvii. 9, 10 and xxviii. But
something like two centuries elapsed before the book reached its present
form, for in the closing chapter, as well as elsewhere, e.g. i. 41-43
(where the joining is not so deftly done as usual) and xxxii. 48-52,
there are undoubted traces of the Priestly Code, P, which is generally
acknowledged to be post-exilic.