Spherical excess

Spherical \Spher"ic*al\, Spheric \Spher"ic\, a. [L. sphaericus,
   Gr. ???: cf. F. sph['e]rique.]
   1. Having the form of a sphere; like a sphere; globular;
      orbicular; as, a spherical body.
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   2. Of or pertaining to a sphere.
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   3. Of or pertaining to the heavenly orbs, or to the sphere or
      spheres in which, according to ancient astronomy and
      astrology, they were set.
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            Knaves, thieves, and treachers by spherical
            predominance.                         --Shak.
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            Though the stars were suns, and overburned
            Their spheric limitations.            --Mrs.
                                                  Browning.
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   {Spherical angle}, {Spherical coordinate}, {Spherical
   excess}, etc. See under {Angle}, {Coordinate}, etc.

   {Spherical geometry}, that branch of geometry which treats of
      spherical magnitudes; the doctrine of the sphere,
      especially of the circles described on its surface.

   {Spherical harmonic analysis}. See under {Harmonic}, a.

   {Spherical lune},portion of the surface of a sphere included
      between two great semicircles having a common diameter.

   {Spherical opening}, the magnitude of a solid angle. It is
      measured by the portion within the solid angle of the
      surface of any sphere whose center is the angular point.
      

   {Spherical polygon},portion of the surface of a sphere
      bounded by the arcs of three or more great circles.

   {Spherical projection}, the projection of the circles of the
      sphere upon a plane. See {Projection}.

   {Spherical sector}. See under {Sector}.

   {Spherical segment}, the segment of a sphere. See under
      {Segment}.

   {Spherical triangle},re on the surface of a sphere, bounded
      by the arcs of three great circles which intersect each
      other.

   {Spherical trigonometry}. See {Trigonometry}.
      [1913 Webster] -- {Spher"ic*al*ly}, adv. --
      {Spher"ic*al*ness}, n.
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Excess \Ex*cess"\, n. [OE. exces, excess, ecstasy, L. excessus a
   going out, loss of self-possession, fr. excedere, excessum,
   to go out, go beyond: cf. F. exc[`e]s. See {Exceed}.]
   1. The state of surpassing or going beyond limits; the being
      of a measure beyond sufficiency, necessity, or duty; that
      which exceeds what is usual or proper; immoderateness;
      superfluity; superabundance; extravagance; as, an excess
      of provisions or of light.
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            To gild refined gold, to paint the lily,
            To throw a perfume on the violet, . . .
            Is wasteful and ridiculous excess.    --Shak.
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            That kills me with excess of grief, this with excess
            of joy.                               --Walsh.
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   2. An undue indulgence of the appetite; transgression of
      proper moderation in natural gratifications; intemperance;
      dissipation.
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            Be not drunk with wine, wherein is excess. --Eph. v.
                                                  18.
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            Thy desire . . . leads to no excess
            That reaches blame.                   --Milton.
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   3. The degree or amount by which one thing or number exceeds
      another; remainder; as, the difference between two numbers
      is the excess of one over the other.
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   {Spherical excess} (Geom.), the amount by which the sum of
      the three angles of a spherical triangle exceeds two right
      angles. The spherical excess is proportional to the area
      of the triangle.
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