CUR 
is any small piece that slides, as the piece 
in an equinoctial ring-dial that slides to the 
day of the month ; the little label of brass 
divided like a line of sines, and sliding in a 
groove along the middle of another label, 
representing the horizon in the analenima ; 
and likewise a brass point screwed on the 
beam-compasses, which may be moved 
along the beam for the striking of greater 
or less circles. 
. CURTATE distance, in astronomy, the 
distance of a planet from the sun to that 
point where a perpendicular let fell from the 
planet meets with the ecliptic. 
CURTATION, in astronomy, is the in- 
terval between a planet’s distance from the 
sun, and the curtate distance. 
CURTIN, Curtain, or Courtin, in 
fortification, is that part of the rampart of 
a place which is betwixt the flanks of two 
bastions bordered with a parapet five feet 
high, behind which the soldiers stand to 
fire upon the covered way, and into the 
moat. 
CURTISIA, in botany, so named from 
.William Curtis, teacher of botany in Lon- 
don, author of “ Flora Londinensis,” a ge- 
nus of the Tetrandria Monogynia class and 
order. Essential character : calyx four- 
parted ; petals four ; drupe superior, round- 
ish, succulent, with a four or five-celled nut. 
There is but one species, viz. C. feginea, 
beech-leaved Curtisia, or hassagay-tree. 
This is one of the largest trees in tlie Afri- 
can woods, with very diminutive flowers. 
The Hottentots and Cafties make the shafts 
of their javelins, or assagays, from the wood 
of this tree. They always carry one or two 
of these with them on their journies. They 
consist of an iron spear hollowed out on 
each side, about six inches long, with an 
iron shaft. It is fastened with thongs of 
leather to a slender round stick, five feet 
long, tapering towards the end. With these 
.lances, which they throw with great dex- 
terity to the distance of a hundred paces, 
.tlie Hottentots and CafFres defend them- 
selves, and kill buffaloes and other wild 
animals. 
CURVATURE of a line, is the peculiar 
manner of its bending or flexure by which 
it becomes a curve of such and such peculiar 
properties. Any two arches of curve lines 
touch each other when the same right line 
is tlie tangent of both at the same point ; 
.but when they are applied upon each other 
,in this manner, they never perfectly coin- 
cide, unless they are similar arches of equal 
and similar figures ; and the curvature of 
CUR 
lines admit of indefinite variety. Because 
the curvature is uniform in a given circle, 
and may be varied at pleasure in them, by 
enlarging or diminishing their diameters: 
the curvature of circles serves for measur- 
ing that of other lines. 
Of all the circles that touch a curve in 
any given point, that is said to have the 
same curvature with it, which touches it so 
closely, that no circle can be drawn through 
the point of contact between them. And 
tills circle is called tlie circle of curvature ; 
its centre," the centre of curvature ; and its 
semidiameter, the ray of curvature belong- 
ing to the point of contact. As in all figures, 
rectilinear ones excepted, the position of 
the tangent is continually varying ; so the 
curvature is continually varying in all cur- 
vilinear figures, the circle only excepted. 
As the cm’ve is separated from its tangent 
by its curvature, so it is separated from the 
circle of curvature in consequence of the 
increase or decrease of its curvature; and 
as its curvature is greater or less, according 
as it is more or less inflected from the tan- 
genlfso the variation of curvature is greater 
or less, according as it is more or less sepa- 
rated from the circle of curvature. 
When any two curve lines touch each 
other in such a manner that no circle can 
pass between them, they must have the 
same curvature ; for the circle that touches 
the one so closely that no circle can pass 
between them, must touch the other in the 
same manner. And it can be made appeal-, 
that circles may touch curve lines in this 
manner ; that there may be indefinite de- 
grees of more or less intimate contact be- 
tween the curve and the circle of curvature ; 
and that a conic section may be described 
that sliall have the same curvature with a 
given line at a given point, and the same 
varfetion of a curvature, or a contact of 
the same kind with the circle of curvature. 
The rays of curvature of similar arches, in 
similar figures, arc in the same ratio as ivny 
homologous lines of these figures, and the 
variation of curvature is the same. , See 
Curve. 
CUR'VE, in geometry, a line which run- 
ning on continually in all directions, may 
be cut by one right line in more points than 
one. Curves are divided into algebraical 
or geometrical and transcendental. Geo- 
metrical or algebraical curves are those 
whose ordinates and abscisses being right 
lines, the nature thereof can be expressed 
by a finite equation having those ‘ordinate* 
and abscisses in it. 
