HYP 
continually increasing equally, ordinates to 
the curve being drawn parallel to the other 
asymptote; the abscisses will represent an 
infinite series of natural numbers, and the 
corresponding hyperbolic, or asymptotic 
spaces, will represent the series of loga- 
rithms of the same number. Hence differ- 
ent hyperbolas will furnish different series 
of logarithms ; so that to determine any 
particular series of logarithms, choice must 
be made of some particular hyperbola. 
Now the most simple of all hyperbolas is 
the equilateral one, i. e. that whose asymp- 
totes make a right angle between them- 
selves. 
Equilateral hyperbola is that wherein the 
conjugate axes are equal. 
Apollonian hyperbola is the common hy- 
perbola, or the hyperbola of the first kind : 
thus called in contradistinction to the hy- 
perbolas of the higher kinds, or infinite 
hyperbolas: for the hyperbola of the first 
kind, or order, has two asymptotes ; that 
of the second order has three; that of the 
third, four, &c. 
HYPERBOLE, in rhetoric, a figure, 
whereby the truth and reality of things are 
excessively either enlarged, or diminished. 
See Rhetoric. 
HYPERBOLIC, or hyperbolical, some- 
thing relating either to an hyperbole, or an 
hyperbola. 
Hyperbolic cylindroid, is a solid figure, 
whose generation is given by Sir Christo- 
pher Wren, in the “ Philosophical Transac- 
tions.” Thus, two opposite hyperbolas being 
joined by the transverse axis, and through 
the centre a right line being drawn at right 
angles to that axis ; and about that, as an 
axis, the hyperbolas being supposed to 
revolve; by such revolution, a body will 
be generated, which is called the hyper- 
bolic cylindroid, whose bases, and all sec- 
tions parallel to them, will be circles. In 
a subsequent transaction, the same author 
applies it to the grinding of hyperbolical 
glasses: affirming, that they must be form- 
ed this way or not at all. Hyperbolic leg 
of a curve, is that which approaches infi- 
nitely near to some asymptote. Sir Isaac 
Newton, reduces all curves, both of the 
first and higher kinds, into those with 
hyperbolic legs, and those with parabolic 
ones. 
Hyperbolic line is used by some au- 
thors for what we call the hyperbola itself. 
In this sense, the plane surface, termi- 
nated by the curve line, is called the hy- 
perbola, or hyperbolic space; and the 
HYP 
curve line that terminates it the hyperbolic 
line. 
HYPERICUM, in botany, St. John's 
wort, a genus of the Polyadelphia Polyan- 
dria class and order. Natural order of 
Rotaceae. Hyperica, Jussieu. Essential 
character : calyx five parted ; petals five ; 
filaments many, connected at the base in 
five bundles. There are fifty-seven species. 
These are principally shrubs or under 
shrubs, with cylindrical, ancipital, or quad- 
rangular stems ; leaves frequently with 
pellucid dots ; flowers sometimes in cymes, 
frequently in corymbs, with the peduncles 
often trichotomous and three flowered. 
HYPHYDRA, in botany, a genus of the 
Monoecia Gy nandria class and order. Essen- 
tial character : male, calyx one-leafed, three 
parted ; corolla none ; stamens six, insert- 
ed above the germ : female, calyx and 
corolla none; style triangular, with three 
stigmas ; capsule one celled, three valved ; 
seed single. There is but one species, viz. 
H. fluviatilis, a little plant which grows 
three or four feet under water ; it is a native 
of Guiana. 
HYPNUM, in botany, a genus of the 
Cryptogamia Musci class and order. Na- 
tural order of Musci or Mosses. Generic 
character : capsule oblong ; peristomium 
double, outer with sixteen broadish teeth, 
inner membranaceous, equally laciniated ; 
segments broadish with capillary ones in- 
terposed. Males germaceous on different 
plants. Botanists differ greatly as to the num- 
ber of species, some reckon forty, others 
fifty, and Dr. Withering enumerates seventy, 
and to facilitate the investigation of the 
species he has thrown them into seven 
divisions. 
HYPOCHOERIS, in botany, a genus 
of the Syngenesia Polygamia JEqualis class 
and order. Natural order of Compositae 
Semiflosculosi. Ciclioraceae, Jussieu. Es- 
sential character : calyx subimbricate ; down 
feathered; receptacle chaffy- There are 
five species. 
HYPOTHECATE, in law, to hypothe- 
cate a ship, is to pawn the same for neces- 
saries ; and a master may hypothecate 
either ship or goods for relief, when in 
distress at sea ; for he represents the trad- 
ers as well as owners ; and in whose hands 
soever a ship or goods hypothecated come, 
they are liable. But it has been recently 
held in the Court of King’s Bench, that if 
the master pay for the repairs' himself, and 
do not hypothecate the ship, he has no 
lien upon the ship for his debt. 
