curvature 
ed by the length of the curve or the area of the surface. 
Center of curvature, of principal curvature, of 
spherical curvature. See center!.- Chord of curva- 
ture. See chord. Circle of curvature. See circle. 
Curvature Of concussion, in but. , curvature in a grow- 
ing internode which follows upon a sharp blow, the curva- 
ture being concave on the side which receives the stroke : 
a phrase derived from Sachs. Curve of curvature. See 
euror. Curve of double curvature. See cu roe. Dar- 
winian curvature, the curvature observed by Darwin as 
occurring in roots in response to stimulation. It is pecu- 
liar in being convex on the side to which the stimulus is 
applied. Double curvature, a term applied to the cur- 
vature of a line which twists, so that all the parts of it do 
not lie in the same plane, as the rhumb-line or loxodromic 
curve. Geodesic curvature, the ratio of the angle be- 
tween two successive geodesic tangents to a curve drawn 
upon a curved surface to the length of the infinitesimal 
arc between those tangents. Hyperbolic curvature. 
See antKlastic curvature. Indeterminate curvature, 
the curvature of a curve or surface at a node, where the 
usual expression for the curvature becomes indeterminate. 
Integral curvature. See whole curvature. Lateral 
curvature of the spine, in pathol., abnormal curvature 
of the spinal column in a lateral direction, caused by a 
relaxation of the ligaments and muscles which normally 
keep the spine erect. Also called scoliosis. Line of cur- 
vature, in geom., a curve traced upon a surface so as to 
lie constantly in the plane of the section of maximum or 
of minimum curvature of the surface at the point. Mea- 
sure Of curvature, at any point of a curve or surface, the 
average curvature in the immediate neighborhood of that 
point. Also simply curvature. Pott's curvature. Same 
as angular curvature of the spine. Radius of curva- 
ture, the radius of the circle of curvature. Second cur- 
vature. torsion ; the rate of rotation of the osculating 
plane 01 a curve, relatively to the increment of the arc. 
Spherical curvature of a twisted curve, (a) The recip- 
rocal of the radius of the osculating sphere. (6) Plane cur- 
vature existing in any part of a twisted curve ; that kind 
of curvature which exists at any part of a surface where 
the osculating quadric surface reduces to a sphere. Syn- 
clastic curvature, that kind of curvature which belongs 
to a surface not cutting its tangent-plane in a real locus. 
Whole, total, or Integral curvature, the angle be- 
tween the normals at the extremities of an arc of a plane 
curve ; as applied to a portion of a surface, the area on 
the surface of a unit-sphere described by a radius which 
moves parallel to the normal to the contour of the por- 
tion of surface whose curvature is spoken of ; as applied 
to an arc of a twisted curve, the length of the curve de- 
scribed on the surface of a unit-sphere by a radius moving 
parallel to the normal to the curve. 
curve (kerv), a. and n. [In earlier use curb, < 
ME. combe, < OF. courbe, corbe (see curb), F. 
courbe = Pr. corb = Sp. Pg. It. curvo, < L. cur- 
vus, bent, curved, = OBulg. kriru, bent, = Lith. 
kreivas, crooked, akin to Gr. /ti'prrff, bent, and 
prob. to Kpmoc, KipKof, L. circus, a ring, circle: 
see circle.] I. a. Bending; crooked; curved. 
A curve line is that which is neither a straight line nor 
composed of straight lines. Ogilvie. 
II. . 1. A continuous bending; a flexure 
without angles ; usually, as a concrete noun, a 
one-way geometrical locus which may be gen- 
erated by the continuous turning of a line and 
motion of a point along the line. All the positions 
of the point, taken together, make the curve, which is also 
the envelop of all the positions of the line. Geometers 
understand a curve as something capable of being denned 
by an equation or equations, or otherwise described in 
general terms. It may thus have nodes, cusps, and other 
singularities, but must not be broken in a way which can- 
not be precisely denned without the use of special num- 
bers. Curves are often employed in physics and statistics 
to represent graphically the changes in value of certain 
physical or statistical quantities : as, the energy curve of 
the solar spectrum ; the isothermal line or curve ; the curve 
of population. 
Nor pastoral rivulet that swerves 
To left and right thro' meadowy curves. 
Tennyson, In Memoriam, c. 
2. Anything continuously bent. 3. A drafts- 
man's instrument for forming curved figures. 
4. In base-ball, the course of a ball so 
E itched that it does not pass in a straight line 
rom the pitcher to the catcher, but makes a 
deflection in the air other than the ordinary 
one caused by the force of gravity : as, it was 
difficult to gage the curves of the pitcher. An in 
curve is one that deflects from the straight line toward 
the batter ; an out curve, away from the batter. A drop 
deflects downward, and a rise or up curve upward _ 
Adiabatic curve. See adiabatic. Algebraic curve a 
curve whose equations in linear coordinates contain only 
algebraic functions of the coordinates. Anaclastic 
curves, anallagmatic curves. See the adjectives. 
Anticlinal and synclinal curves, in geol., terms ap- 
plied to the elevations and depressions of undulating sur- 
faces of strata. See anticlinal and synclinal Asymp- 
totical curves. See asymptotical. Axis of a curve 
Seeazwfi. Bicursal curve, a curve which cannot be de- 
scribed by the continuous motion of one point, even if it 
passes through Infinity, but can be so described by two 
points. Bipartite curve, bitaugential curve. See the 
adjectives. Cartesian curve. SameasCartm'an,.,2. 
Catenary or catenarian curve. See catenary. Caus- 
tic curve. Same as caustic, n., 3. Center of a curve 
See center!. Characteristic angle of a curve See 
characteristic. Class of a curve. See class, 6. Closed 
curve. See closei, v. Contact of two curves, see 
contact. Cubic curve, a curve of the third order cut- 
ting every plane (or else every line in the plane) in three 
ints. A cubic curve in a plane is one which is cut 
every line in the plane in three points, real or imagi- 
poi 
by 
1410 
nary. Such curves are of three genera : nodal cubics, 
which have either a crunode or an acnode ; cuspidal cu- 
bics, which have a cusp; and non-singular cubics, which 
are bicursal, though one branch may be imaginary. 
Curve coordinates. See coordinate. Curve of beau- 
ty, a gentle curve of double or contrary flexure, in which 
it has been sought to trace the foundation of all beauty of 
form. Also called line of beauty. Curve of curvature, 
a curve drawn ujwn a surface in such a manner that at 
every point normals to the surface at consecutive points 
of the curve intersect one another. Curve Of double 
curvature, a curve not contained in one plane. Curve 
of elastic resistance, in gun., a curve whose ordinates 
give the elastic resistance of a built-up gun at the different 
points along the bore. Curve of equal or equable ap- 
proach. See approach. Curve of probability, a curve 
whose equation is 
representing the probabilities of different numbers of re- 
currences of an event. Curve Of pursuit, the curve de- 
scribed by a point representing a dog which runs with 
constant velocity toward another point representing a 
hare, this second point also moving, generally in a straight 
line, with constant velocity. After the dog passes the 
hare, he runs away from it according to the same law. 
Curve of sines, cosines, tangents, secants, etc., 
curves in which the abscissa is proportional to the angle, 
and the ordinate to a trigonometric function of the angle. 
Cuspidal Curve, a curve on a surface along which the 
surface so touches itself that on cutting the surface by an 
arbitrary plane at every intersection of this plane with 
the cuspidal curve the intersection of the plane with the 
surface has a cusp. Deficiency of an algebraical 
curve, the number by which the number of its double 
points nodes and cusps falls short of the highest num- 
ber which a curve of the same order can have. Diano- 
dal curve. See a ianodal. Distribution of a curve, i n 
geom., twice the number of double points increased by 
three times the number of cusps. Elastic curve, the 
figure assumed by a thin elastic plate acted upon by a 
force and a couple. Equation to a curve. See equa- 
tion. Equitangential curve, a curve upon whose tan- 
gents a fixed line (called the directrix) intercepts equal 
distances from the points of tangency. Exponential 
curve. See exponential. Family Of curves, a singly 
infinite series of curves differing from one another only 
by the different values assumed by one constant. Flex- 
ure of a curve, in math., the bending of the curve to- 
ward or from a straight line. Focal curve, the locus of 
foci of a surface. Foliate curve, Newton's 41st species 
of cubic curves, a plane cubic having a crunode and a 
point of inflection at infinity, the inflectional tangent being 
an ordinary line. It is supposed to resemble a leaf. For 
a figure, see cissoid. Geodesic curve. See geodesic. 
Geometric curve. See geometric. Harmonic curve, 
a curve whose ordinates are a simple harmonic func- 
tion of the abscissas; a curve of sines. Lemniscatic 
curve, a plane curve whose polar equation is of the form 
i" = A sin n. Lissaj ous curves (so named from the 
French physicist Jules Antoine Lissajous, who observed 
them first in 1855), figures produced by the composition 
of two simple harmonic motions, as the curve formed on 
a screen by a ray of light reflected first from a mirror at- 
tached to one vibrating tuning-fork, and then from a mir- 
ror on another fork which is placed, for example, at right 
angles to the first. The form of the curve traced out by 
the point of light depends upon the difference of pitch 
between the two forks, and also upon the difference of 
phase. Loxodromic curve. See loxodromic. Mag- 
netic curves. See magnetic. Mechanical curve, a 
curve of such a nature that the relation between the ab- 
scissa and the ordinate cannot be expressed by an algebraic 
equation. Such curves are now generally called transcen- 
dental curves : opposed to algebraic curve. Order Of an 
algebraic curve, the numberof points, real or imaginary, 
in which it cuts every plane (or every line in that plane). 
Organic description of curves, in geom. , the description 
of curves on a plane by means of instrumenta. Periodic 
curve, a curve which represents a periodic function. 
Plane curve, a curve lying in a plane. Quartic curve, 
a curve of the fourth order. Radical curve, a spiral hav- 
ing several branches through the origin. Range curve, 
a curve employed to determine the approximate ranges 
for different angles of elevation of a projectile fired from a 
given piece with a given charge of powder. It is con- 
structed by tracing a line through the points of intersec- 
tion of the ordinates and abscissas representing respec- 
tively the angles of elevation given and the corresponding 
ranges obtained from practice. It gives a rapid method 
for interpolating intermediate ranges. The tabulation of 
these elevations with their corresponding ranges taken 
from the curve constitutes a range table,. Rank of a 
curve. See rank. Sextic curve, a curve of the sixth 
order. Skew, twisted, or tortuous curve, a curve not 
lying in a plane. Transcendental curve, a curve whose 
equation contains transcendental functions of one or more 
of the coordinates. Twisted cubic curve. Same as 
twisted cubic (which see, under cubic, n.). 
curve (kerv), v. ; pret. and pp. curved, ppr. 
cur ring. [In earlier use curb (now with de- 
flected senses: see curb, v.), < OF. curber, 
corber, courbcr, F. courber = Pr. corbar OSp. 
corvar (Sp. encorvar) = Pg. curvar = It. cur- 
rare, corvare, < L. curvare, bend, curve, < curvus, 
bent, curved: see curve, a.] I. trans. To bend; 
cause to take the shape of a curve ; crook ; 
inflect. 
And lissome Vivien . . . 
. . . curved an arm about his neck. 
Tennyson, Merlin and Vivien. 
Brunelleschi curved the dome which Michel Angelo 
hung in air on St. Peter's. 
Lowell, Among my Books, 2d ser., p. 2. 
II. intrans. To have or assume a curved or 
flexed form : as, to curve inward. 
Out again I curve and flow. Tennyson, The Brook. 
curviserial 
Through the dewy meadow's breast, fringed with shade, 
but touched on one side with the sun-smile, ran the crys- 
tal river, curving in its brightness, like diverted hope. 
JK. D. Ulackmorf, Lorna Doone, xxxiii. 
curvedness (ker'ved-nes), . The state of be- 
ing curved. [Bare.] 
curvet (ker'vet or ker-vet'), n. [Formerly 
carpet, < It. corvetta (= F. courbette), a curvet, 
leap, bound, < corvare, curvare, bow, bend, 
stoop, < L. curvare, bend, curve : see curve, B.I 
1. In the manege, a leap of a horse in which 
both the fore legs are raised at once and 
equally advanced, the haunches lowered, and 
the hind legs brought forward, the horse spring- 
ing as the fore legs are falling, so that all his 
legs are in the air at once. 
The bound and high curvet 
Of Main's fiery steed. Shak., All's Well, ii. 3. 
2. Figuratively, a prank ; a frolic. Johnson. 
curvet (ker'vet or ker-vet'), v. ; pret. and pp. 
curveted or curvetted, ppr. curveting or curvet- 
ting. [Formerly corvet; = It. corvettare = F. 
courbetter ; from the noun.] I. intrans. 1. To 
leap in a curvet ; prance. 
Anon he rears upright, curvets and leaps. 
Shak., Venus and Adonis, 1. 279. 
He ruled his eager courser's gait ; 
Forced him, with chastened fire, to prance, 
And, high curvetting, slow advance. 
Scott, L. of L. M., iv. 18. 
The huge steed . . . plunged and curveted, with re- 
doubled fury, down the long avenue. Poe t Tales, I. 480. 
2. To leap and frisk. 
Cry, holla ! to the tongue, I prithee ; it curvets unsea- 
sonably. Shak., As you Like it, iii. 2. 
A gang of merry roistering devils, frisking and curvet- 
ing on a flat rock. Irving, Knickerbocker, p. 348. 
II. trans. To cause to make a curvet ; cause 
to make an upward spring. 
The upright leaden spout curvetting its liquid filament 
into it. Landor. 
curvicaudate (ker-vi-ka'dat), a. [< L. curvus, 
curved, + cauda, tail: see caudate.] Having 
a curved or crooked tail. 
CUTVicostate (ker-vi-kos'tat), a. [< L. curvus, 
curved, + costa, a rib: see costate."] Having 
small curved ribs. 
CUTVidentate (ker-vi-den'tat), a. [< L. cur- 
vus, curved, + den(t-)s = E. tooth : see den- 
tate."] Having curved teeth. 
CUrvifoliate (ker-vi-fo'H-at), a. [< L. curvus, 
curved, + folium, a leaf: see foliate.'] Having 
curved leaves. 
curyiform (ker' vi-f orm), a. [< L. curvus, curved, 
+ forma, shape.] Having a curved form. 
curvilinead (ker-vi-lin'e-ad), n. [As curvi- 
line-ar + -ad^.] An instrument for delineat- 
ing curves. 
curvilinear (ker-vi-lin'e-ar), a. [Also curvi- 
lineal (after linear, lineafj; cf. F. curviligne = 
Sp. Pg. It. curvilineo; < L. curvus, bent, + linea, 
line: see line 2 .] Having a curved line; con- 
sisting of or bounded by curved lines : as, a cur- 
vilinear figure Curvilinear angle. See angles, i. 
Curvilinear coordinates. See coordinate. 
curvilinearity (ker-vi-lin-e-ar'i-ti), n. [< cur- 
vilinear + -ity.] The state of being curvilin- 
ear, or of consisting in curved lines. 
CUrvilinearly (ker-vi-lin'e-jjr-li), adv. In a 
curvilinear manner. 
curvinervate (ker-vi-ner'vat), a. [< L. curvus, 
curved, + nervtts, nerve: see nervate.] Hav- 
ing the veins or nervures curved. 
curvinerved (ker'vi-nervd), a. Same as cur- 
vinervate. 
Ourvirostra (ker-vi-ros'tra), n. [NL., < L. 
curvus, curved, + rostrum, lieak.] A genus of 
birds ; the crossbills : synonymous with Loxia 
(which see). Scopoli, 1777. Also called Cru- 
cirostra. 
CUTVirostral (ker-vi-ros'tral), a. [< L. curvus, 
bent, + rostrum, a beak, + -a?.] 1. In gen- 
eral, having a decurved bill, as a curlew or 
creeper. 2. Specifically, having a crooked, 
cruciate bill, as the crossbills ; metagnathous. 
See cut under crossbill. 
Curvirostres (ker-vi-ros'trez), w. pi. [NL., < L. 
ciirrus, curved, + rostrum, a beak.] luernlth., 
a group of laminiplantar oscine Passeres, nearly 
the same as the Certliiomorplia; of Sundevall. 
Sclater, 1880. 
curviserial (ker-vi-se'ri-al), a. [< L. curvit.*, 
curved, 4- scries, series, + -a!.] Arranged in 
curved or spiral ranks: in bot., applied byBra- 
vais to a theoretical form of leaf-arrangement 
in which the angle of divergence is incommen- 
surable with the circumference, and conse- 
