ded
other events in the military history of his country: the "Sortie of the
Garrison of Huningue" (now in the Luxemburg), the "Vincendon Brigade,"
and "Bizerte," reminiscences of the expedition to Tunis. After a visit
to Russia, Detaille exhibited "The Cossacks of the Ataman" and "The
Hereditary Grand Duke at the Head of the Hussars of the Guard." Other
important works are: "Victims to Duty," "The Prince of Wales and the
Duke of Connaught" and "Pasteur's Funeral." In his picture of "Chalons,
9th October 1896," exhibited in the Salon, 1898, Detaille painted the
emperor and empress of Russia at a review, with M. Felix Faure. Detaille
became a member of the French Institute in 1898.

See Marius Vachon, _Detaille_ (Paris, 1898); Frederic Masson,
_Edouard Detaille and his work_ (Paris and London, 1891); J. Claretie,
_Peintres et sculpteurs contemporains_ (Paris, 1876); G. Goetschy,
_Les Jeunes peintres militaires_ (Paris, 1878).

DETAINER (from _detain_, Lat. _detinere_), in law, the act of keeping a
person against his will, or the wrongful keeping of a person's goods, or
other real or personal property. A writ of detainer was a form for the
beginning of a personal action against a person already lodged within
the walls of a prison; it was superseded by the Judgment Act 1838.

DETERMINANT, in mathematics, a function which presents itself in the
solution of a system of simple equations.

1. Considering the equations

ax + by + cz = d,
a'x + b'y + c'z = d',
a"x + b"y + c"z = d",

and proceeding to solve them by the so-called method of cross
multiplication, we multiply the equations by factors selected in such a
manner that upon adding the results the whole coefficient of y becomes =
0, and the whole coefficient of z becomes = 0; the factors in question
are b'c" - b"c', b"c - bc", bc' - b'c (values which, as at once seen,
have the desired property); we thus obtain an equation which contains on
the left-hand side only a multiple of x, and on the right-hand side a
constant term; the coefficient of x has the value

a(b'c" - b"c') + a'(b"c - bc") + a"(bc' - b'c),

and this function, represented in the form

|a, b, c |,
|a', b', c'|
|a", b", c"|

is said to be a determinant; or, the number of elements being 3 squared, it is
called a determinant of the third order