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 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 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 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 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
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.
(Func"tion*al*ize) v. t. To assign to some function or office. [R.]
(Func"tion*al*ly), adv. In a functional manner; as regards normal or appropriate activity.
The organ is said to be functionally disordered.Lawrence.
(Func"tion*a*ry) n.; pl. Functionaries [Cf. F. fonctionnaire.] One charged with the performance
of a function or office; as, a public functionary; secular functionaries.
(Func"tion*less), a. Destitute of function, or of an appropriate organ. Darwin.
(Fund) n. [OF. font, fond, nom. fonz, bottom, ground, F. fond bottom, foundation, fonds fund,
fr. L. fundus bottom, ground, foundation, piece of land. See Found to establish.]