Principal Prin"ci*pal, a. [F., from L. principalis. See Prince.] 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.] --Spenser. 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.
Principal Prin"ci*pal, a. [F., from L. principalis. See Prince.] 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.] --Spenser. 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.
Principal Prin"ci*pal, a. [F., from L. principalis. See Prince.] 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.] --Spenser. 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., 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.
Principal Prin"ci*pal, a. [F., from L. principalis. See Prince.] 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.] --Spenser. 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., Challenge Chal"lenge, n. [OE. chalenge claim, accusation, challenge, OF. chalenge, chalonge, claim, accusation, contest, fr. L. calumnia false accusation, chicanery. See Calumny.] 1. An invitation to engage in a contest or controversy of any kind; a defiance; specifically, a summons to fight a duel; also, the letter or message conveying the summons. A challenge to controversy. --Goldsmith. 2. The act of a sentry in halting any one who appears at his post, and demanding the countersign. 3. A claim or demand. [Obs.] There must be no challenge of superiority. --Collier. 4. (Hunting) The opening and crying of hounds at first finding the scent of their game. 5. (Law) An exception to a juror or to a member of a court martial, coupled with a demand that he should be held incompetent to act; the claim of a party that a certain person or persons shall not sit in trial upon him or his cause. --Blackstone 6. An exception to a person as not legally qualified to vote. The challenge must be made when the ballot is offered. [U. S.] Challenge to the array (Law), an exception to the whole panel. Challenge to the favor, the alleging a special cause, the sufficiency of which is to be left to those whose duty and office it is to decide upon it. Challenge to the polls, an exception taken to any one or more of the individual jurors returned. Peremptory challenge, a privilege sometimes allowed to defendants, of challenging a certain number of jurors (fixed by statute in different States) without assigning any cause. Principal challenge, that which the law allows to be sufficient if found to be true.
Principal Prin"ci*pal, a. [F., from L. principalis. See Prince.] 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.] --Spenser. 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.
Focus Fo"cus, n.; pl. E. Focuses, L. Foci. [L. focus hearth, fireplace; perh. akin to E. bake. Cf. Curfew, Fuel, Fusil the firearm.] 1. (Opt.) A point in which the rays of light meet, after being reflected or refrcted, and at which the image is formed; as, the focus of a lens or mirror. 2. (Geom.) A point so related to a conic section and certain straight line called the directrix that the ratio of the distace between any point of the curve and the focus to the distance of the same point from the directrix is constant. Note: Thus, in the ellipse FGHKLM, A is the focus and CD the directrix, when the ratios FA:FE, GA:GD, MA:MC, etc., are all equal. So in the hyperbola, A is the focus and CD the directrix when the ratio HA:HK is constant for all points of the curve; and in the parabola, A is the focus and CD the directrix when the ratio BA:BC is constant. In the ellipse this ratio is less than unity, in the parabola equal to unity, and in the hyperbola greater than unity. The ellipse and hyperbola have each two foci, and two corresponding directrixes, and the parabola has one focus and one directrix. In the ellipse the sum of the two lines from any point of the curve to the two foci is constant; that is: AG+GB=AH+HB; and in the hyperbola the difference of the corresponding lines is constant. The diameter which passes through the foci of the ellipse is the major axis. The diameter which being produced passes through the foci of the hyperbola is the transverse axis. The middle point of the major or the transverse axis is the center of the curve. Certain other curves, as the lemniscate and the Cartesian ovals, have points called foci, possessing properties similar to those of the foci of conic sections. In an ellipse, rays of light coming from one focus, and reflected from the curve, proceed in lines directed toward the other; in an hyperbola, in lines directed from the other; in a parabola, rays from the focus, after reflection at the curve, proceed in lines parallel to the axis. Thus rays from A in the ellipse are reflected to B; rays from A in the hyperbola are reflected toward L and M away from B. 3. A central point; a point of concentration. Aplanatic focus. (Opt.) See under Aplanatic. Conjugate focus (Opt.), the focus for rays which have a sensible divergence, as from a near object; -- so called because the positions of the object and its image are interchangeable. Focus tube (Phys.), a vacuum tube for R[oe]ntgen rays in which the cathode rays are focused upon the anticathode, for intensifying the effect. Principal, or Solar, focus (Opt.), the focus for parallel rays.
Principal Prin"ci*pal, a. [F., from L. principalis. See Prince.] 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.] --Spenser. 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.