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Definition: Spherical harmonic analysis
(-[i^]*kal), a. [L. harmonicus, Gr. "armoniko`s;
cf. F. harmonique. See Harmony
1. Concordant; musical; consonant; as, harmonic sounds.
Harmonic twang! of leather, horn, and brass. --Pope.
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.
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.
(Mus.), the distance between two notes of
a chord, or two consonant notes.
(Arith. & Alg.), certain relations of
numbers and quantities, which bear an analogy to musical
, 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.
. See under Proportion
or Harmonic progression
. See under
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.
(Anat.), an articulation by simple
apposition of comparatively smooth surfaces or edges, as
between the two superior maxillary bones in man; -- called
, and harmony
(Mus.), the chord of a note with its third
and fifth; the common chord.
, 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.
2. Of or pertaining to a sphere.
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.
Knaves, thieves, and treachers by spherical
Though the stars were suns, and overburned
Their spheric limitations. --Mrs.
, Spherical co["o]rdinate
, Spherical excess
, etc. See under Angle
, 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
,portion of the surface of a sphere included
between two great semicircles having a common diameter.
, 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.
,portion of the surface of a sphere
bounded by the arcs of three or more great circles.
, the projection of the circles of the
sphere upon a plane. See Projection
. See under Sector
, the segment of a sphere. See under
,re on the surface of a sphere, bounded
by the arcs of three great circles which intersect each
. See Trigonometry
[1913 Webster] -- Spher"ic*al*ly
, adv. --