FRU
F U S
FRUsTtfM of tin hyperbolic conoid. In the hyperbolic conoid ttois excels is the Tame as in the cone generated by the tri- angle OCf, (fig. II.) formed by the axis QC, the alym- ptotcOtfj and the perpendicular Ce t the altitude of the fruf
Fig. II.
turn and the inclination of the axis to their bafes being the fame in both. TkuSTVM of afpheroid. In the fpheroid ABkh, (fig. III.) the cylinder exceeds the frujium; and the difference between them is the fame as in the cone CDrrf, the plane Drd, or Bkb, being fuppofed parallel to thole which terminate the frujium. In different inclinations of thofe planes, when the altitude of the frujium is given, that difference is reciprocally as the cube of the diameter Bb, which is the conjugate of C A, the axis of the frujium. But if the altitude of the frujium be alfo varied fo as to be reciprocally proportional to the dia- meter Bb, then the difference between the frujium and cy- linder will be always of the fame magnitude in the fame fphe- roid or conoid.
Fig. III.
When the inclination of the axis of the folid to the plane* that terminate the frujium is given, the difference between the frujium and cylinder, in the fame, or in fimilar bodies, is as the cube of their common altitude. Mac Laurin's Fluxions, Introd. p. 24, 25.
Thefe proportions Concerning fruflums are of ufe in gaug- ing. See the article Gauging, SuppL
FUMAGE, a term ufed in feme parts of the kingdom for dung, or manuring with dung.
FUMER, in zoology, a name given to the pole-cat. See the article Putorius, SuppL
FUMET, among fportfmen, a term ufed for the ordure or dung of harts, otherwife called fewmets.
FUNCTION (Cycl.) — The term funclion is ufed in algebra, for an analytical expreffion any way compounded of a vari- able quantity, and of numbers, or confiant quantities. There- fore every analytical expreffion, in which, befides a variable
quantity .v^ there are confiant quantities, is a fuuclion of ft Thus fl+3A-, ax — 4-va', ax -\-bs/aa — xx, c *, &c. are functions of x.
The difference of funthoks confifls in the manner in which they are compounded ; and depends, therefore, upon the opera- tions by which quantities may be compounded and mixed. Thefe operations arc, addition, fubtraction, multiplication, and divifion, the raffing to powers, and extraction of roots, to which the resolution of equations ought to be referred. Bcfide thefe operations, which are called algebraical, there are other tranfcendental ones, fuch as exponential, logarith- mic, and many others arifing from the inverfe method of fluxions.
Functions may arife from the moft firnple and analytical ope- rations : thus we have the multiple funclions 2z, 3%, jz,
- pow
5 of
s z t z ',C5V. are
az, fcf>. and the
called funclions. Functions are divided into algebraical and tranfcendental : al- gebraical or algebraic funclions, are thofe formed by algebraic operations only; fuch are thofe above Specified, except c*, which belongs to the following (pedes,
Tranfcendental funclions are thofe formed by tranfcendental operations : fuch are exponential quantities or powers, the exponents of which are variable quantities ; whereas in alge- braic funclions the exponents are always confiant quantities. It is to be obferved as to tranfcendental funclions , that thofe funclions only of a variable quantity are to be deemed tranfcen- dental, which not only enter the compofition with, but alfo affect the variable quantity : thus if z fignifies a circular arc, or a logarithm, then will ca x , and the like expremons, be tranfcendental funclions of z. But if the tranfcendental oper- ation appertains only to confiant quantities, the funclion is no more than algebraic : thus if c denote the circumference of a circle, the radius of which is =: x, e will be a tranfcen- dental quantity, and yet the expreffions c-\-z, cz% 4a*, are but algebraic funclions of z. Some indeed have doubted whether % c ought to be ranked among algebraic funclions, or not ; but the doubt is of fmall weight. And fome choofe to call the powers of 2, the exponents of which are irra- tional numbers, hit erf cendmt funclions : thus 7* is an inter* fcendent funclion of z.
On the fubject of funclions, their divifions, transformations, explication by infinite feries, fiifa Mr. Euler fhould be con- fulted, who has treated this matter very fully in the firfl chap- ter of his Analyf. infinitorum.
FURCA cs" flagellum, in our old writers, denotes the meaneft of all fervile tenures, when the bondman was at the difpofal of his lord for life and limb. — Ipfe tenet in villenagio ad furcam & flagellum de domino fuo, &c.
FURROW, among gardeners, demotes a ridge or fwelling on the fide of a tree, flalk, fruit.
Fwrrow is alfo ufed for the deep trench left between ridges, to drain off the fuperfluous moiflure.
FURZE, in botany, the Englifh name of a genus of plants called by authors gen'jla Jpartium. See the article Genista fpartium, SuppL
FUSTIC-//W, in botany. See the article Fustuc, SuppL
GAL
G.
GAS
AELOCK.S, the name by which the artificial fpurs of "Y game cocks are called. See the article Cock, SuppL
J GADDS, among miners. See the article Digging,
SuppL GAFFS, a name fometimes ufed for the gablocks of cocks.
See the article G ablock, fttpra. GALANGAL, the name by which the root of a genus of
plants called by Linnaeus Kampfiria, is commonly known.
See the article Kjep-ipferia, Append. GALANTHUS, in the Linnaean fyftem of botany, the name
of a diflinct genus of plants, which Toumefort makes only
a fpecies of ^NarciJJo-lcucoium, See the article Narcisso-
leucoium, SuppL GALE, in botany, the name of a genus of plants defcribed
by Linnaeus under that of myrica. See the article Myrica,
Append. Ghhh-ftcknefs, a name fometimes given to bilious and inter- mitting fevers. See the article Bilious fever, Append. GALLi , on fhip-board, a place in the cook-room, where the
grates are put up, fires lighted, and the victuals boiled or
reailed. Blandley, Nav. Expofitor, p. 62.
GAMMER-Iamb. See the article GiMMZR-lamb, Append.
GAMMONING, on fhip-board, are feveral turns of rope
' taken round the bow-fprit, and reeved through holes in the knees of the head, for the greater fecurity of the bow-fprit. Blandley, Nav. Exp. p. 62.
GANDER, the popular name for a male goofe : one of thefe will ferve five geefe.
GAR-jfjft, in ichthyology, a name ufed in feveral parts of the kingdom for the cfox. See the article Esox, SuppL
GARGET, a difeafe of cattle, confuting in a fwelling of the throat and the neighbouring parts ; to prevent which, bleed- ing in the fpring is recommended.
GARGIL, a diflemper in geefe, which by flopping the head frequently proves mortal. Three or four cloves of garlick, beaten in a mortar with fweet butter, and made into little balls, and given the creature faffing, is the ordinary cure. Diet. Ruft. in voc.
GARLICK (SuppL)— ffild-GA.Ki.icvL, a name by which fome call a fpecies of onion. See the article Onion, SuppL
GASKETS, on fhip-board, the fmall cords ufed for fattening fails to the yards when furled up, Bjanckley, Nav. Exp. p. 63.
- GAST-
