molluscs were studied and
classified according to the shell formation; the word is chiefly now
used for the collection of shells (see MOLLUSCA, and such articles as
GASTROPODA, MALACOSTRACA, &c.). Large spiral conchs have been from early
times used as a form of trumpet, emitting a very loud sound. They are
used in the West Indies and the South Sea Islands. The Tritons of
ancient mythology are represented as blowing such "wreathed horns." In
anatomy, the term _concha_ or "conch" is used of the external ear, or of
the hollowed central part leading to the meatus; and, in architecture,
it is sometimes given to the half dome over the semicircular apse of the
basilica. In late Roman work at Baalbek and Palmyra and in Renaissance
buildings shells are frequently carved in the heads of circular niches.
A low class of the negro or other inhabitants of the Bahamas and the
Florida Keys are sometimes called "Conches" or "Conks" from the
shell-fish which form their staple food.

CONCHOID (Gr. [Greek: konche], shell, and [Greek: eidos], form), a plane
curve invented by the Greek mathematician Nicomedes, who devised a
mechanical construction for it and applied it to the problem of the
duplication of the cube, the construction of two mean proportionals
between two given quantities, and possibly to the trisection of an angle
as in the 8th lemma of Archimedes. Proclus grants Nicomedes the credit
of this last application, but it is disputed by Pappus, who claims that
his own discovery was original. The conchoid has been employed by later
mathematicians, notably Sir Isaac Newton, in the construction of various
cubic curves.

[Illustration]

The conchoid is generated as follows:--Let O be a fixed point and BC a
fixed straight line; draw any line through O intersecting BC in P and
take on the line PO two points X, X', such that PX = PX' = a constant
quantity. Then the locus of X and X' is the conchoid. The conchoid is
also the locus of any point on a rod which is constrained to move so
that it always passes through a fixed point, while a fixed point on the
rod travels along a straight line. To obtain the equation to the curve,
draw AO perpendicular to BC, and let AO = a; let the constant quantity
PX = PX' = b. Then taking O as pole and a line through O parallel to BC
as the initial line, the polar equation is r = a cosec [theta] [+-] b,
the upper sign referring to the branch more distant from O. The
cartesian equation with A as origi