This funambulatory track.
Sir T. Browne.
Fu*nam"bu*list (?), n. A ropewalker or ropedancer.
{ ||Fu*nam"bu*lo (?), ||Fu*nam"bu*lus (?) } n. [Sp. funambulo, or It.
funambolo, fr. L. funambulus; funis rope (perh. akin to E. bind) +
ambulare to walk. See Amble, and cf. Funambulist.] A ropewalker or
ropedancer. [Obs.] Bacon.
Func"tion (?), n. [L. functio, fr. fungi to perform, execute, akin to
Skr. bhuj to enjoy, have the use of: cf. F. fonction. Cf. Defunct.] 1.
The act of executing or performing any duty, office, or calling;
performance. "In the function of his public calling." Swift.
2. (Physiol.) The appropriate action of any special organ or part of an
animal or vegetable organism; as, the function of the heart or the
limbs; the function of leaves, sap, roots, etc.; life is the sum of the
functions of the various organs and parts of the body.
3. The natural or assigned action of any power or faculty, as of the
soul, or of the intellect; the exertion of an energy of some
determinate kind.
As the mind opens, and its functions spread.
Pope.
4. The course of action which peculiarly pertains to any public officer
in church or state; the activity appropriate to any business or
profession.
Tradesmen . . . going about their functions.
Shak.
The malady which made him incapable of performing his regal
functions.
Macaulay.
5. (Math.) A quantity so connected with another quantity, that if any
alteration be made in the latter there will be a consequent alteration
in the former. Each quantity is said to be a function of the other.
Thus, the circumference of a circle is a function of the diameter. If x
be a symbol to which different numerical values can be assigned, such
expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
Algebraic function, a quantity whose connection with the variable is
expressed by an equation that involves only the algebraic operations of
addition, subtraction, multiplication, division, raising to a given
power, and extracting a given root; -- opposed to transcendental
function. -- Arbitrary function. See under Arbitrary. -- Calculus of
functions. See under Calculus. -- Carnot's function (Thermo-dynamics),
a relation between the amount of heat given off by a source of heat,
and the work which can be done by it. It is approximately equal to the
mechanical equivalent of the thermal unit divided by the number
expressing the temperature in degrees of the air thermometer, reckoned
from its zero of expansion. -- Circular functions. See Inverse
trigonometrical functions (below). -- Continuous function, a quantity
that has no interruption in the continuity of its real values, as the
variable changes between any specified limits. -- Discontinuous
function. See under Discontinuous. -- Elliptic functions, a large and
important class of functions, so called because one of the forms
expresses the relation of the arc of an ellipse to the straight lines
connected therewith. -- Explicit function, a quantity directly
expressed in terms of the independently varying quantity; thus, in the
equations y = 6x2, y = 10 - x3, the quantity y is an explicit function
of x. -- Implicit function, a quantity whose relation to the variable
is expressed indirectly by an equation; thus, y in the equation x2 + y2
= 100 is an implicit function of x. -- Inverse trigonometrical
functions, or Circular function, the lengths of arcs relative to the
sines, tangents, etc. Thus, AB is the arc whose sine is BD, and (if the
length of BD is x) is written sin -1x, and so of the other lines. See
Trigonometrical function (below). Other transcendental functions are
the exponential functions, the elliptic functions, the gamma functions,
the theta functions, etc. -- One- valued function, a quantity that has
one, and only one, value for each value of the variable. --
Transcendental functions, a quantity whose connection with the variable
cannot be expressed by algebraic operations; thus, y in the equation y
= 10x is a transcendental function of x. See Algebraic function
(above). -- Trigonometrical function, a quantity whose relation to the
variable is the same as that of a certain straight line drawn in a
circle whose radius is unity, to the length of a corresponding are of
the circle. Let AB be an arc in a circle, whose radius OA is unity let
AC be a quadrant, and let OC, DB, and AF be drawnpependicular to OA,
and EB and CG parallel to OA, and let OB be produced to G and F. E Then
BD is the sine of the arc AB; OD or EB is the cosine, AF is the
tangent, CG is the cotangent, OF is the secant OG is the cosecant, AD
is the versed sine, and CE is the coversed sine of the are AB. If the
length of AB be represented by x (OA being unity) then the lengths of
Functions. these lines (OA being unity) are the trigonometrical
functions of x, and are written sin x, cos x, tan x (or tang x), cot x,
sec x, cosec x, versin x, coversin x. These quantities are also
considered as functions of the angle BOA.
{ Func"tion (?), Func"tion*ate (?), } v. i. To execute or perform a
function; to transact one's regular or appointed business.
Func"tion*al (?), a. 1. Pertaining to, or connected with, a function or
duty; official.
2. (Physiol.) Pertaining to the function of an organ or part, or to the
functions in general.
Functional disease (Med.), a disease of which the symptoms cannot be
referred to any appreciable lesion or change of structure; the
derangement of an organ arising from a cause, often unknown, external
to itself opposed to organic disease, in which the organ itself is
affected.