Spherical harmonic analysis

Harmonic \Har*mon"ic\ (h[aum]r*m[o^]n"[i^]k), Harmonical
\Har*mon"ic*al\ (-[i^]*kal), a. [L. harmonicus, Gr. "armoniko`s;
   cf. F. harmonique. See {Harmony}.]
   1. Concordant; musical; consonant; as, harmonic sounds.
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            Harmonic twang! of leather, horn, and brass. --Pope.
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   2. (Mus.) Relating to harmony, -- as melodic relates to
      melody; harmonious; esp., relating to the accessory sounds
      or overtones which accompany the predominant and apparent
      single tone of any string or sonorous body.
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   3. (Math.) Having relations or properties bearing some
      resemblance to those of musical consonances; -- said of
      certain numbers, ratios, proportions, points, lines,
      motions, and the like.
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   {Harmonic interval} (Mus.), the distance between two notes of
      a chord, or two consonant notes.

   {Harmonical mean} (Arith. & Alg.), certain relations of
      numbers and quantities, which bear an analogy to musical
      consonances.

   {Harmonic motion}, the motion of the point A, of the foot of
      the perpendicular PA, when P moves uniformly in the
      circumference of a circle, and PA is drawn perpendicularly
      upon a fixed diameter of the circle. This is simple
      harmonic motion. The combinations, in any way, of two or
      more simple harmonic motions, make other kinds of harmonic
      motion. The motion of the pendulum bob of a clock is
      approximately simple harmonic motion.

   {Harmonic proportion}. See under {Proportion}.

   {Harmonic series} or {Harmonic progression}. See under
      {Progression}.

   {Spherical harmonic analysis}, a mathematical method,
      sometimes referred to as that of {Laplace's Coefficients},
      which has for its object the expression of an arbitrary,
      periodic function of two independent variables, in the
      proper form for a large class of physical problems,
      involving arbitrary data, over a spherical surface, and
      the deduction of solutions for every point of space. The
      functions employed in this method are called spherical
      harmonic functions. --Thomson & Tait.

   {Harmonic suture} (Anat.), an articulation by simple
      apposition of comparatively smooth surfaces or edges, as
      between the two superior maxillary bones in man; -- called
      also {harmonia}, and {harmony}.

   {Harmonic triad} (Mus.), the chord of a note with its third
      and fifth; the common chord.
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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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