FUN 
2. Funaria tmihleabergii; leaves obovate, awned, 
concave, ferrulate, fpread ; capfiile obovate, oblique. 
3. Funaria anguflata : leaves clofely fheathing j cap- 
fule narrowed at the bafe. 
PUNCH, or Funcius (John), a German lutheran 
divine in the fixteentli century, born at Werden, near 
Nuremberg, in 1518. He married a daughter of Oftander, 
profefTor of divinity at Konigfberg, and became tlie fe- 
cond to that fanciful divine in the difputes which he 
introduced into the lutheran church. Punch was after¬ 
wards chofen'couri preacher to Albert duke of Pruflia, 
and, unfortunately for himfelf, was perfuaded to turn 
politician, and engage in cabals unfavotirable to the in- 
terefls of the Polifli nation. For this conduft he was 
profecuted in the name of the province, and was con¬ 
demned to be put to death as a diiHtrber of the public 
peace. He was beheaded at Konigfberg, in 1566, in th.e 
forty-ninth year of his age. He was the author of a 
Chronology, very favourably received by the learned 
world; in writing which he is laid to have been adilled 
by his father-in-law Ofiander, who was no mean hiftorian. 
The firft part of it, reaching from Adam to the birth of 
Chrilf, was printed in 1544. In 1554 the whole of the 
Chronology was publiOied, beginning with the creation 
of the world, and ending with the year of Chrift 1552. 
In a third edition, he brought it down as far as the year 
1560. He was alfo the author of Cimiinentaries upon the 
Apocalypfe; the Life of Andrew Ofiander; the Life of 
Vitus Theodorus, &c. 
FUNCHAL', or Funchial, a feaport town and capi¬ 
tal of the ifland of Maderia, fituated in a valley jon the 
fouth coaft of the ifland : faid to be fo called from the 
quantity of fennel (funcha in Portuguefe) which grew on 
the fpot. The harbour is deiended by feveral batteries, 
and a caftle. It contains fix parilhes, feveral chapels, 
and fix convents, wjth feveral hofpitals. When Funchal 
was fortified, it would feem the engineer had nothing in 
view befides rendering it flrong on the fea fide ; for there 
all tlie works, except a fingle wall, are direfted. This 
was certainly a great overfight, as there are feveral bays 
not far diftant from the land lide, wlieic an enemy might 
fafely di!'embark, and march to the very walls without 
oppofition. Tlie Portuguele, though numerous, do not 
conftitute the bu'k of the inhabitants, the Englifh and 
French Roman Catholics, who live in the Portuguefe 
manner, arejullly fuppol'ed to exceed the others in num¬ 
ber and wealth ; befides thefe, there is an infinity of mu¬ 
latto and negro freemen. The fireets of Funchal are 
drawn by a line, all the houfes neat, and the windows 
fafhed with lath-work, but with openings wide enough 
for thofe within to fee and be feen. The principal trade 
of the inhabitants confifts in wine and fweetnieais. Lat. 
32. 32. N. Ion. 16 49. W. Greenwich. 
On the night of the 9th of Oftober, 1803, a torrent 
riifiled down from the mountains on the town of Funchal, 
with irrefiftible violence, bearing every thing before it in 
its paffage to the fea. The bed of the river, not being 
capable of containing this increafe of water, overflowed 
on each fide to a confiderable extent, and fwept away 
three of its bridges, and a magnificent church, Maii- 
fions, warehutifes, inhabitants, cattle, and effects of all 
forts, were i-difcnminately involved in this refiftlefs ele¬ 
ment, and hurried to the ocean. The fireetsof two-thirds 
of the town were completely inundated : in mod places 
the water re.iched to the firft floor. The darknefs of 
the night, the rufli and roar of the waters, the cries of 
the fufferers, the terror of all, formed fuch a feeue as 
mocks ail powers of defeription. Towards morning, 
however, the violence of the torrent abated, and towards 
the noon of next day h: d nearly fubfided. The vaft ag- 
gregare of water is conjectured to have been produced 
by the builting of a water-fpout in the mountains, (an 
accident not iinfrequent;) for, although it had rained on 
the day of, and on that preceding, the event, yet the 
quantity which had fallen was not at all fufficient to pro. 
F U N 115 
duce fuch a flood. The village of Santa Cruz and Ma- 
chico were more than half fwept away, At the former 
three or four, and at the latter twenty-three, perfons pe- 
rifiied. Two hundred perfons at leafi loft their lives in the 
ifland. The effects of this difafler extended to the north 
eaft part of the ifland, but to tlie vveflward was not much 
felt beyond Magdalenar. Betwixt that place and Funchal 
the rivers did much damage, but only nine perfons were 
drowned. The friary at Serros de Deos wascairied away, 
but the church flood. 
FUN'CHEON, a river of Ireland, wliich runs into 
Blackwater river, five miles north Rathcormuck, in the 
county of Cork. 
FUNC'TION.yi \_funElio, orfungor, Lat. to perform. J 
Difchargc ; performance.—There is hardly a greater dif- 
ference between two things than there is between a re- 
prefenting commoner in the funftion of his public call¬ 
ing, and the fame perfon in common life. Swift —Em¬ 
ployment; office—The minifiry is not now bound to any 
one tribe : now none is fecluded from that funEiion of any 
degree, ftate, or calling. Whitgifu. —Let not thefe indig¬ 
nities dlfcourage us from aflening the juft privileges and 
pre-eminence of our holy funSion and character. Atter- 
bury. —Single aft of any office.—They have feveral offices 
and prayers againft fire, ternpefts, and efpecially for the 
dead, in which funBions they ufe facerdotal garments. 
StiUingJLcct.—Trside ■, occupation.—Follow your funEiion\ 
go, and batten on cold bits. Shahe/peare. —Office of any 
particular part of the body.—The bodies of men, and 
other animals, are excellently well fitted for life and mo¬ 
tion ; and the feveral parts of them well adapted to their 
particular fuvElions. BerUUy, —Power; faculty: either 
animal or i n tell eft ual.—Though every human conftitu- 
tion is morbid, yet are their difeafes confiftent with the 
common funSions of life. Arbuthnot. 
Whatever warms the heart, or fills the head, 
As the mind opens, and its funBions fpread,.. 
Imagination plies her dang’rcus art, 
And pours it all upon the peccant part. Pope^ 
FUNCTION, ill mathematics, a term ufed in analy¬ 
tics, for an algebraical expreffion any how compounded 
of a certain letter or quantity with other quantities or 
numbers: and the expreffion is laid to be a funfVion of 
that letter or quantity. Thus, tz — i,x, or ax-f 3^^, or 
2x —a 3/ — X-, or x', or c'', is each of them a funftion 
of the quantity x. 
In a memoir inferted in the Berlin Affs for the year 
1772, M. La Grange, who has made many important dif- 
coveries in pure analyfis, and has contributed very largely 
to the prefent opulence of aftronomiral fcience, alferted 
that the theory of the developement of funffions con¬ 
tained the true principles of the differential calculus, 
freed from all confideration of infinitely fmall quantities, 
or of limits. To eftablifii this pofition more fully and 
particularly was the exprefs objeft of a treatife on the 
Tfteory of Analytical Funftions, which he publifhed at 
Paris in 1798, 410. His definition of a funffion is as fol¬ 
lows:—A funffion, of one or more quantities, is every 
expreffion in which thefe quantities enter after any manner 
whatever, combined or not with other quantities of given 
or invariable values, while the quantities of the funffion 
may receive all poffible values. Thus: fx defignates a 
funftion of x-,f {a-^-bx) fundtions of x* and a -j-^x. 
Let, then, fx delignate a function of any variable quan¬ 
tity X. If, inftead uf x, x-f-z be fubftituted, z being any 
indeterminate quantity, fx becomes/(x+ i) ; which, by 
the method of feries, may be expanded into this form : 
Jxpi + qi'^+ri^ &c. in which, p, q, r, &c. the 
coefficients of the powers of z, are new fundlions of x, 
derived from the primitive furiStion fx, and independent 
of the quantity i. 
Having eftabliflied the general form of the develope¬ 
ment of the function J (x-^-z), the author proceeds to 
examine more particularly in what this developement 
a confifts« 
