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conjugate axis

Axis Ax"is, n.; pl. Axes. [L. axis axis, axle. See Axle.] A straight line, real or imaginary, passing through a body, on which it revolves, or may be supposed to revolve; a line passing through a body or system around which the parts are symmetrically arranged. 2. (Math.) A straight line with respect to which the different parts of a magnitude are symmetrically arranged; as, the axis of a cylinder, i. e., the axis of a cone, that is, the straight line joining the vertex and the center of the base; the axis of a circle, any straight line passing through the center. 3. (Bot.) The stem; the central part, or longitudinal support, on which organs or parts are arranged; the central line of any body. --Gray. 4. (Anat.) (a) The second vertebra of the neck, or vertebra dentata. (b) Also used of the body only of the vertebra, which is prolonged anteriorly within the foramen of the first vertebra or atlas, so as to form the odontoid process or peg which serves as a pivot for the atlas and head to turn upon. 5. (Crystallog.) One of several imaginary lines, assumed in describing the position of the planes by which a crystal is bounded. 6. (Fine Arts) The primary or secondary central line of any design. Anticlinal axis (Geol.), a line or ridge from which the strata slope downward on the two opposite sides. Synclinal axis, a line from which the strata slope upward in opposite directions, so as to form a valley. Axis cylinder (Anat.), the neuraxis or essential, central substance of a nerve fiber; -- called also axis band, axial fiber, and cylinder axis. Axis in peritrochio, the wheel and axle, one of the mechanical powers. Axis of a curve (Geom.), a straight line which bisects a system of parallel chords of a curve; called a principal axis, when cutting them at right angles, in which case it divides the curve into two symmetrical portions, as in the parabola, which has one such axis, the ellipse, which has two, or the circle, which has an infinite number. The two axes of the ellipse are the major axis and the minor axis, and the two axes of the hyperbola are the transverse axis and the conjugate axis. Axis of a lens, the straight line passing through its center and perpendicular to its surfaces. Axis of a telescope or microscope, the straight line with which coincide the axes of the several lenses which compose it. Axes of co["o]rdinates in a plane, two straight lines intersecting each other, to which points are referred for the purpose of determining their relative position: they are either rectangular or oblique. Axes of co["o]rdinates in space, the three straight lines in which the co["o]rdinate planes intersect each other. Axis of a balance, that line about which it turns. Axis of oscillation, of a pendulum, a right line passing through the center about which it vibrates, and perpendicular to the plane of vibration. Axis of polarization, the central line around which the prismatic rings or curves are arranged. --Brewster. Axis of revolution (Descriptive Geom.), a straight line about which some line or plane is revolved, so that the several points of the line or plane shall describe circles with their centers in the fixed line, and their planes perpendicular to it, the line describing a surface of revolution, and the plane a solid of revolution. Axis of symmetry (Geom.), any line in a plane figure which divides the figure into two such parts that one part, when folded over along the axis, shall coincide with the other part. Axis of the equator, ecliptic, horizon (or other circle considered with reference to the sphere on which it lies), the diameter of the sphere which is perpendicular to the plane of the circle. --Hutton. Axis of the Ionic capital (Arch.), a line passing perpendicularly through the middle of the eye of the volute. Neutral axis (Mech.), the line of demarcation between the horizontal elastic forces of tension and compression, exerted by the fibers in any cross section of a girder. Optic axis of a crystal, the direction in which a ray of transmitted light suffers no double refraction. All crystals, not of the isometric system, are either uniaxial or biaxial. Optic axis, Visual axis (Opt.), the straight line passing through the center of the pupil, and perpendicular to the surface of the eye. Radical axis of two circles (Geom.), the straight line perpendicular to the line joining their centers and such that the tangents from any point of it to the two circles shall be equal to each other. Spiral axis (Arch.), the axis of a twisted column drawn spirally in order to trace the circumvolutions without. Axis of abscissas and Axis of ordinates. See Abscissa.

Axis Ax"is, n.; pl. Axes. [L. axis axis, axle. See Axle.] A straight line, real or imaginary, passing through a body, on which it revolves, or may be supposed to revolve; a line passing through a body or system around which the parts are symmetrically arranged. 2. (Math.) A straight line with respect to which the different parts of a magnitude are symmetrically arranged; as, the axis of a cylinder, i. e., the axis of a cone, that is, the straight line joining the vertex and the center of the base; the axis of a circle, any straight line passing through the center. 3. (Bot.) The stem; the central part, or longitudinal support, on which organs or parts are arranged; the central line of any body. --Gray. 4. (Anat.) (a) The second vertebra of the neck, or vertebra dentata. (b) Also used of the body only of the vertebra, which is prolonged anteriorly within the foramen of the first vertebra or atlas, so as to form the odontoid process or peg which serves as a pivot for the atlas and head to turn upon. 5. (Crystallog.) One of several imaginary lines, assumed in describing the position of the planes by which a crystal is bounded. 6. (Fine Arts) The primary or secondary central line of any design. Anticlinal axis (Geol.), a line or ridge from which the strata slope downward on the two opposite sides. Synclinal axis, a line from which the strata slope upward in opposite directions, so as to form a valley. Axis cylinder (Anat.), the neuraxis or essential, central substance of a nerve fiber; -- called also axis band, axial fiber, and cylinder axis. Axis in peritrochio, the wheel and axle, one of the mechanical powers. Axis of a curve (Geom.), a straight line which bisects a system of parallel chords of a curve; called a principal axis, when cutting them at right angles, in which case it divides the curve into two symmetrical portions, as in the parabola, which has one such axis, the ellipse, which has two, or the circle, which has an infinite number. The two axes of the ellipse are the major axis and the minor axis, and the two axes of the hyperbola are the transverse axis and the conjugate axis. Axis of a lens, the straight line passing through its center and perpendicular to its surfaces. Axis of a telescope or microscope, the straight line with which coincide the axes of the several lenses which compose it. Axes of co["o]rdinates in a plane, two straight lines intersecting each other, to which points are referred for the purpose of determining their relative position: they are either rectangular or oblique. Axes of co["o]rdinates in space, the three straight lines in which the co["o]rdinate planes intersect each other. Axis of a balance, that line about which it turns. Axis of oscillation, of a pendulum, a right line passing through the center about which it vibrates, and perpendicular to the plane of vibration. Axis of polarization, the central line around which the prismatic rings or curves are arranged. --Brewster. Axis of revolution (Descriptive Geom.), a straight line about which some line or plane is revolved, so that the several points of the line or plane shall describe circles with their centers in the fixed line, and their planes perpendicular to it, the line describing a surface of revolution, and the plane a solid of revolution. Axis of symmetry (Geom.), any line in a plane figure which divides the figure into two such parts that one part, when folded over along the axis, shall coincide with the other part. Axis of the equator, ecliptic, horizon (or other circle considered with reference to the sphere on which it lies), the diameter of the sphere which is perpendicular to the plane of the circle. --Hutton. Axis of the Ionic capital (Arch.), a line passing perpendicularly through the middle of the eye of the volute. Neutral axis (Mech.), the line of demarcation between the horizontal elastic forces of tension and compression, exerted by the fibers in any cross section of a girder. Optic axis of a crystal, the direction in which a ray of transmitted light suffers no double refraction. All crystals, not of the isometric system, are either uniaxial or biaxial. Optic axis, Visual axis (Opt.), the straight line passing through the center of the pupil, and perpendicular to the surface of the eye. Radical axis of two circles (Geom.), the straight line perpendicular to the line joining their centers and such that the tangents from any point of it to the two circles shall be equal to each other. Spiral axis (Arch.), the axis of a twisted column drawn spirally in order to trace the circumvolutions without. Axis of abscissas and Axis of ordinates. See Abscissa.

- e^{2}-1}.} The transverse axis of a hyperbola coincides with the major axis. In a hyperbola, a conjugate axis or minor axis of length 2 b {\displaystyle...

- In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude, but opposite...

- prin****l axes are the transverse axis (containing the segment of length 2a with endpoints at the vertices) and the conjugate axis (containing the segment of...

- parabola subtends a right angle. The transverse axis of a hyperbola is perpendicular to the conjugate axis and to each directrix. The product of the perpendicular...

- phase-conjugate beam, Ξ4. Its direction is given by k4 = k1 + k2 − k3, and so if the two pump beams are counterpropagating (k1 = −k2), then the conjugate and...

- contributions by Cayley and others. In his memoir on the theory of the conjugate axis and of the moment of inertia of bodies he enumerated the principle now...

- the optical axis are conjugate to image planes perpendicular to the axis. The image of an object confined to a plane normal to the axis is geometrically...

- equivalently: the foci and the semi-major axis). If this presumption is not fulfilled one has to know at least two conjugate diameters. With help of Rytz's construction...

- for a given system can be defined (ignoring orientation) by its semi major axis and the eccentricity. However, with a hyperbolic orbit other parameters may...

- rotation axis (/ˈæksiːz/ AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes. If the rotation axis p****es...

- In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude, but opposite...

- prin****l axes are the transverse axis (containing the segment of length 2a with endpoints at the vertices) and the conjugate axis (containing the segment of...

- parabola subtends a right angle. The transverse axis of a hyperbola is perpendicular to the conjugate axis and to each directrix. The product of the perpendicular...

- phase-conjugate beam, Ξ4. Its direction is given by k4 = k1 + k2 − k3, and so if the two pump beams are counterpropagating (k1 = −k2), then the conjugate and...

- contributions by Cayley and others. In his memoir on the theory of the conjugate axis and of the moment of inertia of bodies he enumerated the principle now...

- the optical axis are conjugate to image planes perpendicular to the axis. The image of an object confined to a plane normal to the axis is geometrically...

- equivalently: the foci and the semi-major axis). If this presumption is not fulfilled one has to know at least two conjugate diameters. With help of Rytz's construction...

- for a given system can be defined (ignoring orientation) by its semi major axis and the eccentricity. However, with a hyperbolic orbit other parameters may...

- rotation axis (/ˈæksiːz/ AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes. If the rotation axis p****es...

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