curvation (kervashon)

[L. curvatio ( n- ), curvature (ker'va-tūr), п. [= Sp. It. curva tura = Pg. curvadura, In a curve, the curvature is the angle through which the tangent sweeps round per unit of length of the curve. A. Daniell , Prin. of Physics, p. 74. ed by the length of the curve or the area of the surface. Center of curvature, of principal curvature, of spherical curvature. See center1. - Chord of curvature. See chord. - Circle of curvature. See circle. Curvature of concu ion, in bot., curvature in a growing internode which follows upon a sharp blow, the curvature being concave on the side which receives the stroke: a phrase derived from Sachs. - Curve of curvature. See curve. Curve of double curvature. See curve. - Darwin i an curvature, the curvature observed by Darwin as occurring in roots in response to stimulation. It is peculiar in being convex on the side to which the stimulus is applied. Double curvature, a term applied to the curvature 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 between two succe ive geodesic tangents to a curve drawn upon a curved surface to the length of the infinitesimal arc between those tangents. - Hyperbolic curvature. See anticlastic curvature. Indeterminate curvature, the curvature of a curve or surface at a node, where the usual expre ion 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 curvature, 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. - Measure 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 curvature, the radius of the circle of curvature. - Second curvature, torsion; the rate of rotation of the osculating plane of a curve, relatively to the increment of the arc. Spherical curvature of a twisted curve. (a) The reciprocal of the radius of the osculating sphere. (6) Plane curvature 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. - Synclastic 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 between 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.