fun 
TO be great fun, to lie v. TV amusing or funny. (Colloq. ] 
He 'tl rjreat fun, loan tell yon. . . . \Ve had such a.uatnc 
witll him last half. T. Ifttiflii'x, Tom I'.rou n at KiiL:M . ii. ::. 
To make fun of, to ridicule. 
fun (fun), p. i. ; pret. and pp. fiinnrrl, ppr. fuii- 
iiiiui. [</,.] To make fuii ; jest ; joke : as, 
I was only funning. [Colloq.] 
funambulant (i'u-nam'bu-lant), u. [< L.J'iaiix, 
a rope, + ambnln>i(t-)x, ppr. of ambulare, walk: 
see amble. Ct. fnnambulate,"} A rope-walker ; 
a funambulist. [Bare.] 
He's fain tostaiul like the h'ltnambulant, 
Who seems to trend the air. and fall he must, 
Save his Self's waight him counter-poyseth iust. 
Sylvester, tr. of Du Bartas's Weeks, ii., The Decay. 
funambulate (fu-nam'bu-lat), r. i. ; pret. ami 
pp. fuiidinlniliilcil, jipv. j'/iiiiiinliulaliiitj. [< L. 
fuiiis, a rope, + ambulatus, pp. of anibultin; 
walk: see amble, v. Cf. funambulus.'] To walk 
on a rope. [Rare.] 
funambulation(fu-uana-bu-la'shon), . [</- 
itawbuliite + -ion.] Rope-walking. [Rare.] 
funambulatory (fu-nam'bu-la-to-ri), . [< /- 
iiambulate + -ori/.] 1. Performing like a rope- 
walker. 2. Pertaining to or characteristic of 
rope-walking. [Rare in both uses.] 
Tread softly and circumspectly iti this funambulatory 
track and narrow path of goodness. 
Sir T. Brotme, Christ. Mor., i. 1. 
funambulist (fu-nam'bu-list), n. [< ~L.funam- 
buluK, a rope-dancer, +' -ist.] A performer on 
a stretched rope; a rope-walker or rope-dancer. 
He [Mr. Pitt] described his situation at the end [of his 
attempt to read an act of Parliament] with the simplicity 
natural to one who was no charlatan, and sought for no 
reputation by the tricks of & funambulist. 
De Quincey, Style. 
funambulof (fu-nam'bu-16), n. [= F. funam- 
bule = Sp. fundmbiilo = Pg. funambulo = It. 
fuititmbolo, funanbulo, < L. funambulus, a rope- 
walker: see funambulus.] Same as funambu- 
list. 
We see the industry and practice of tumblers and/- 
nantbulos. Baton. 
funambulust (fu-nam'bu-lus), . [L., a rope- 
dancer, rope-walker, < funis, a rope, + ambu- 
lare, walk: see amble, v.] Same as funam bulist. 
I see him walking, not, like a funambulus, upon a cord, 
but upon the edge of a razor. 
Sir II. Wotton, Reliquiie, p. 367. 
Funaria (fu-na'ri-a), . [NL., fern, of LL./w- 
narius, of or belonging to a rope, < funis, a rope, 
a cord.] A genus of terminal-fruited mosses 
with an inflated calyptra and an oblique and 
(usually) double peristome. F. hysrrometrica is 
very common and widely distributed, growing in spring 
by waysides, on bare ground, wet sand, and rocks. It has 
received its specific name from the hygroscopic character 
of the fruit-stalk, which twists in drying and untwists 
again when wet. There are 3 other British and 8 other 
North American species. 
function (fungk'shon), n. [< OF. function, F. 
f auction = Sp.funcion = Pg. funq So, fancy So = 
It. funzione, < L. fu>ictio(n-), performance, exe- 
cution, < fungi, pp. fiinctus, perform, execute, 
discharge. Cf.de/wxtf.] 1 . Fulfilment or dis- 
charge of a set duty or requirement ; exercise 
of a faculty or office. 
And all the ceremony of this compact 
Seal'd in my function, by my testimony. 
Shak., T. N., v. 1. 
There is hardly a greater difference between two things 
than there is between a representing commoner in the 
function of his publick calling and the same person ill 
common life. Swift. 
2. Activity in general; action of any kind; be- 
havior. 
My thought, whose murder yet is but fantastical, 
Shakes so my single state of man, that function 
Is smother'd in surmise. Shak., Macbeth, i. 3. 
Function carries pleasure witli it as its psychical ac- 
companiment, but what determines, makes, and is good 
or bad, is in the end function. 
f. 11. Bradley, Ethical Studies, p. 123. 
3. Power of acting; faculty; that power of 
acting in a specific way which appertains to a 
thing by virtue of its special constitution; that 
mode of action or operation which is proper to 
any organ, faculty, office, structure, etc. [This 
is the most usual signification of the term.] 
Dark night, that from the eye We function takes, 
The ear more quick of apprehension makes. 
Shale., M. N. D., iii. 2. 
So slow th' unprofitable moments roll. 
That lock up all the functions of my soul. 
Pope, Imit. of Horace, I. i. 40. 
I think, articulate, I laugh and weep, 
And exercise a\\ function* of a man. 
Cowper, Task, ill. 199. 
Functions dwell in beast and bird that sway 
The reasoning mind, or with the fancy play. 
Wordtworth, Humanity. 
2407 
All these various fiinrtiottx [of living beings], however, 
may be considered under three heads : (1) f-'uni-tions of 
.\ nt, -in mi. divisible i i ill i J'u ni-l /I//A.V nl alisitrptii.ii and meta- 
morphosis, and comprising all those fnnrtiiinx by which 
an organism is enabled to In e. ^rn', and maintain its ex- 
istence as an individual. (2) Function* of ]{rj>ri><iin-li<n,, 
comprising all tlmse t'u m'timi* whereby fresh individuals 
are produced and the perpetuation of the species is se- 
cured. (a) I''t'ni-tiniix at' lfi'titfii',1 nr fjin-i-i'liitinn. compris- 
ing all those f inn-till, ix (such as sensation and voluntary 
motion) wherehy the outer world is Ill-might into relation 
\\ ith tin organism, and the organism in turn is enabled to 
act upon the outer world. //. .1. Xicli/.<n,i. 
The very idea nf an organ is that of an apparatus for the 
doing of some definite work, which is its function. 
Argyll, Nineteenth Century, XXIII. 102. 
The normal operations of each of these faculties are 
called its functions. The term is taken from the action 
of the bodily organs. From these it is transferred to or- 
gans in the metaphysical sense, as the "organs of govern- 
ment," and the functions which they perform. In both 
these applications it has come to mean, first, the appro- 
priate operations of each, and then the activities to which 
they are appointed, set apart, or destined. 
N. Porter, Human Intellect, 37. 
4. That which one is bound or which is one's 
business to do; business; office; duty; em- 
ployment. 
You have paid the heavens your function, and the pris- 
oner the very debt of your calling. 
Shak., M. for SI., iii. 2. 
The king being dead, and his death concealed, he, under 
colour of executing the function of another, gathereth 
strength to himselfe. Holland, tr. of Livy, p. 30. 
His [Washington's] function was to create an army and 
administer the government, both of which he did with 
self-devotion, ability, and faithfulness. 
Theodore Parker, Historic Americans, p. 15. 
5. All official ceremony, (a) Eccles., a religious 
service witli elaborate rittfal and music. 
I ... kept fasts and feasts innumerable, 
Matins and vespers,/tmcft'os to no end. 
Browning, Ring and Book, I. 212. 
On the whole, the music was good, and the function 
sufficiently impressive what with the gloom of the tem- 
ple everywhere starred with tapers, and the grand altar 
lighted to the mountain-top. 
W. D. Ilowelli, Venetian Life, xviii. 
(&) Any important occasion marked by elaborate cere- 
monial : extended in recent use to cover social entertain- 
ments, as operas, balls, and receptions. 
The other great annual function is the burning of Guy 
Fawkes on the 5th of November. 
Fortnightly Ren., N. S., XXXIX. 181. 
On the first occasion when Robert could be induced to 
attend one of these functions [breakfast-parties], he saw 
opposite to him what lie supposed to be a lad of twenty. 
Mrs. Ward, Robert Elsmere, xxxiii. 
6. In math., a mathematical quantity whose 
value depends upon the values of other quanti- 
ties, called the arguments or independent varia- 
bles of the function ; a mathematical quantity 
whose changes of value depend on those of 
other quantities called its variables. Thus, if the 
diameter of a circle be conceived to vary in length, the 
length of the circumference will also vary with it, in ac- 
cordance with a fixed geometrical law, and is therefore a 
function of the diameter, the latter being regarded as the 
independent variable. So ill the equation y = ax + b, if a; 
be conceived to vary independently, y will be its function, 
since its value will vary witli each successive value of x, 
The common algebraic notation is y = f(x), to be read 
"y is a function of x." F, <$>, and other letters are often 
used in place of/. It is not the special value of fx, but 
this quantity considered as variable and as depending 
upon x, which is called the function. It is even called 
the same function irrespective of the special values of 
certain parameters upon which it may depend, and which 
are considered not as variables, but as constants. The 
earlier analysts used function to mean merely a power, 
or continued product of a quantity into itself. The pres- 
ent mathematical meaning first appears in the Latin cor- 
respondence between Leibnitz and John Bernoulli. Mathe- 
matical usage is not precisely settled as to the meaning, 
and this in two respects. First, as some writers use the 
word, the possible values of the function depend upon the 
values of the variables; so that, if v is a function of x, 
there must be some value which y caii take for some value 
of Z, which it cannot take for some other value of z. But 
other writers hold that two quantities which are func- 
tions of a third are functions of each other. For exam- 
ple, if x = tan t and y = tan (t y 2) + i tan (t y 3), they 
hold that y is a function of x, although it can take every 
value for every value of a: ; for there is even here a con- 
nection between the values of z and ;/, so that in the course 
of any continuous change of x the mode of change of y is 
somewhat restricted. Secondly, according to the usage 
of Cauchy and his followers, if an imaginary quantity, 
X + Yi, be so connected with another, x + yi, that X and 
Y are each of them functions of x and u, say X = F(x, y) 
and Y=f(x, /), then the former imaginary is a function 
of the other; but the'majority of mathematicians have 
restricted the mne^toMtionto what the school of Cauchy 
would term monogenous and differentiable functions, al- 
though such a restriction is impossible where the variable 
does not vary continuously. The tendency of recent writ- 
ers is to give the greatest possible breadth to the applica- 
tion of trie term. 
7. Hence, anything which is dependent for its 
value, significance, etc., upon something else. 
Abelian function. See Abelianv. Adjunct spherical 
function, a higher differential ci.etticient of one of the 
spherical functions PM or Qn multiplied by certain con- 
stants depending on m and n and by (1 o:2)*/2, where 
function 
M is the order of differentiation. Algebraic function. 
see uiifi-braic. Alternating function, see iin.>,-n<it, . 
i'. <". Analytic function, a function which can be per- 
fectly represented by a series proceeding according to 
lUOMHta integral positive powers of the variable, or of 
the variable plus a constant, or by a multitude of such 
series, some one of which is convergent for each value of 
t he \ariable which does not correspond to an infinite value 
of the function. [This term was introduced hv l.agrange 
in 17D7. ] Animal function, arbitrary function, etc. 
Wee the adjectives. Appell'S functions, h.vperjjeomet- 
rical functions of t\vo variables. Associated function. 
Same &a adjunct tt/'hi-rirrilfii/ii-iion.- Bernoullian func- 
tion. See Hei-ntinilinn.- Bessel's <>r Besselian func- 
tions, functions defined by the equation 
J||X = 
,--4 
But some writers substitute everywhere in this equation 
2x for x. There are, besides, associated functions called 
Besselian functions of the second order. Binet's func- 
tion, the function defined by the integral 
<(>) =^(l/(e 1) -l + j)e-M"/a;. ds. 
Biquadratic function, an integral function of the fourth 
degree. Borchardt's function, the generating func- 
tion of symmetric functions of the roots of an equation. 
Calculus of functions. See calculus. Camot's func- 
tion, a function of the temperature in Carnot's theory 
of heat, which is now known to be the reciprocal of the 
absolute temperature. Characteristic function of a 
moving system, the time-integral of the vis viva, or the 
space-integral of the momentum. Circular function. 
See circular. Circulating function. Same as circula- 
tor, 3. Class of functions with reference to a group 
Of operations, such a collection of functions that any 
operation of the group performed on any function of the 
class produces another function of the class : the class of 
a function is used in another sense by Vivanti. Com- 
plementary function. See complementary. Complex 
function, an imaginary function. Conical function, a 
special kind of spherical function adapted to calculating 
the distribution of electricity upon a cone. Conjugate 
functions, two functions, , ti, of rectangular coordi- 
nates, x, y, such that + v y^l is a monogenous function 
of * + ?/ y^i. Continuous, critical, curvital, etc., 
function. See the adjectives. Cyclic function, a func- 
tion of more than one variable which experiences a con- 
stant addition to its value every time the variables are 
made to vary continuously from a given set of values 
through some cycle of values back to the same primitive set 
of values. Thomson and Tail. CyclOtomiC function, 
an irreducible function forming a divisor of an equation 
for the division of the circle into a number of equal parts. 
Cylindrical function, a Besselian function of the first 
or second order. [So first called by Heine, on account of 
the connection of these functions with the potential of 
a cylinder.] Derivative function. See derivative. 
Derived function, a differential coefficient. Differen- 
tiable function, a function having a determinate finite 
differential coefficient for every value of the variable with- 
in a certain limit. Du Boijt-Rfumond, 1874. See Weier- 
strastfian function (b), under Weierstrassian. Dihedral 
function. See polyhedral function, under polyhedral. 
Dirichletian function, a function occurring in the the- 
ory of the numbers of classes of binary quadratic forms. 
It is represented by the expression S I \ except when 
V n / n 
D=l (mod. 4), when this expression is to be divided by 
D i i /m 
!(!) 5~^' In this expression I I is the Legen- 
i Irian symbol in its Jacobian sense, and the summation ex- 
tends to all values of n which are positive, integer, and rela- 
tively prime to 2D. Discontinuous function. See dis- 
conlimious, 3. Dissipation or dissipative function, 
disslpativity ; half the rate at which the energy of a system 
is dissipated by forces like viscosity, etc. It forms one of the 
terms of the Lagrangian function. Distributive func- 
tion. See distributive. Doubly periodic functions, 
functions which return to the same values when the variable 
is increased by either one of two values the ratio of which 
is imaginary. Elliptic function. See elliptic. Entire 
or integral function, or rational and integral func- 
tion, a function which is expressible as a polynomial or 
infinite series containing only positiveintegralpowersof its 
variable. Equivalence of functions, a communistic 
term implyingthat no man's labor ought to be remunerated 
at a higher rate than that of any other man, whatever be the 
difference of capacity or production. Euler's function, 
the simplest function which becomes 1 2" + 3". . ,(2x 
l)n, when 1 is a positive integer and vanishes for x = . e. 
This is not to be confounded with the Evlerian function, 
for which see the adjective. Even function, a function 
whose value is not changed by reversing the sign of the 
variable. Explicit, exponential, fluctuating, etc., 
function. See the adjectives.- Factorial function, an 
integral function which can be put in the form (x a) 
(x 6) (z e), etc., where a, b, c, etc., are in arithmetical 
progression. Force function, the function expressing 
the potential of a force. See force-function. Fraction- 
ary function. Same as meromorphic function. This is 
the older phrase, and is still preferred by some writers. 
Fuchsian function, a one-valued function which remains 
unaltered by the transformations of a Fuchsian group, 
and in the interior of a certain curvilinear polygon has the 
same value only for a finite number of values of the vari- 
able. Function Of judgment, in the Kantian philos., 
the particular mode of judging which determines a par- 
ticular logical form of proposition, as universal, particu- 
lar, or singular in quantity; affirmative, negative, or in- 
flnitated in quality; categorical, conditional, or disjunc- 
tive in relation ; assertory, problematic, or apodictic in 
modality.- Function of limited domain, a lacunary 
function. Function of limited variation, a function 
such that the sum, without regard to signs of all its changes 
of value between given values of the variable, is finite. 
Gamma function. See <iatn ma. Gaussian function, 
the same as the hypergeometric function of the second 
order. Generating function, a function which, when 
developed according to powers of its variable, gives as 
