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Prin·ci·pal a.

1. Highest in rank, authority, character, importance, or degree; most considerable or important; chief; main; as, the principal officers of a Government; the principal men of a state; the principal productions of a country; the principal arguments in a case.

*Wisdom is the principal thing.* --*Prov. iv. 7.*

2. Of or pertaining to a prince; princely. [A Latinism] [Obs.]

**Principal axis**. See Axis of a curve, under Axis.

**Principal axes of a quadric** Geom., three lines in which the principal planes of the solid intersect two and two, as in an ellipsoid.

**Principal challenge**. Law See under Challenge.

**Principal plane**. See Plane of projection (a), under Plane.

**Principal of a quadric** Geom., three planes each of which is at right angles to the other two, and bisects all chords of the quadric perpendicular to the plane, as in an ellipsoid.

**Principal point** Persp., the projection of the point of sight upon the plane of projection.

**Principal ray** Persp., the line drawn through the point of sight perpendicular to the perspective plane.

**Principal section** Crystallog., a plane passing through the optical axis of a crystal.

Ax·is n.; *pl.* Axes 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.

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 microscope** *or* **Axis of a telescope**, the straight line with which coincide the axes of the several lenses which compose it.

**Axes of coördinates 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 coördinates in space**, the three straight lines in which the coördinate 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.

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Curve, n.

1. A bending without angles; that which is bent; a flexure; as, a curve in a railway or canal.

2. Geom. A line described according to some low, and having no finite portion of it a straight line.

**Axis of a curve**. See under Axis.

**Curve of quickest descent**. See Brachystochrone.

**Curve tracing** Math., the process of determining the shape, location, singular points, and other peculiarities of a curve from its equation.

**Plane curve** Geom., a curve such that when a plane passes through three points of the curve, it passes through all the other points of the curve. Any other curve is called a curve of double curvature, or a twisted curve.