Variation \Va`ri*a"tion\, n. [OE. variatioun, F. variation, L.
   variatio. See Vary.]
   1. The act of varying; a partial change in the form,
      position, state, or qualities of a thing; modification;
      alteration; mutation; diversity; deviation; as, a
      variation of color in different lights; a variation in
      size; variation of language.
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            The essences of things are conceived not capable of
            any such variation.                   --Locke.
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   2. Extent to which a thing varies; amount of departure from a
      position or state; amount or rate of change.
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   3. (Gram.) Change of termination of words, as in declension,
      conjugation, derivation, etc.
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   4. (Mus.) Repetition of a theme or melody with fanciful
      embellishments or modifications, in time, tune, or
      harmony, or sometimes change of key; the presentation of a
      musical thought in new and varied aspects, yet so that the
      essential features of the original shall still preserve
      their identity.
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   5. (Alg.) One of the different arrangements which can be made
      of any number of quantities taking a certain number of
      them together.
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   Annual variation (Astron.), the yearly change in the right
      ascension or declination of a star, produced by the
      combined effects of the precession of the equinoxes and
      the proper motion of the star.

   Calculus of variations. See under Calculus.

   Variation compass. See under Compass.

   Variation of the moon (Astron.), an inequality of the
      moon's motion, depending on the angular distance of the
      moon from the sun. It is greater at the octants, and zero
      at the quadratures.

   Variation of the needle (Geog. & Naut.), the angle included
      between the true and magnetic meridians of a place; the
      deviation of the direction of a magnetic needle from the
      true north and south line; -- called also declination of
      the needle.
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   Syn: Change; vicissitude; variety; deviation.
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