\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;
   alternation; mutation; diversity; deviation; as, a
   variation of color in different lights; a variation in
   size; variation of language.
         The essences of things are conceived not capable of
         any such variation.                   --Locke.
2. Extent to which a thing varies; amount of departure from a
   position or state; amount or rate of change.
3. (Gram.) Change of termination of words, as in declension,
   conjugation, derivation, etc.
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.
5. (Alg.) One of the different arrangements which can be made
   of any number of quantities taking a certain number of
   them together.
{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}.
Syn: Change; vicissitude; variety; deviation.