Source : Webster's Revised Unabridged Dictionary (1913)

Arbitrary \Ar"bi*tra*ry\, a. [L. arbitrarius, fr. arbiter: cf.
   F. arbitraire. See {Arbiter}.]
   1. Depending on will or discretion; not governed by any fixed
      rules; as, an arbitrary decision; an arbitrary punishment.

            It was wholly arbitrary in them to do so. --Jer.
                                                  Taylor.

            Rank pretends to fix the value of every one, and is
            the most arbitrary of all things.     --Landor.

   2. Exercised according to one's own will or caprice, and
      therefore conveying a notion of a tendency to abuse the
      possession of power.

            Arbitrary power is most easily established on the
            ruins of liberty abused licentiousness.
                                                  --Washington.

   3. Despotic; absolute in power; bound by no law; harsh and
      unforbearing; tyrannical; as, an arbitrary prince or
      government.                                 --Dryden.

   {Arbitrary constant}, {Arbitrary function} (Math.), a
      quantity of function that is introduced into the solution
      of a problem, and to which any value or form may at will
      be given, so that the solution may be made to meet special
      requirements.

   {Arbitrary quantity} (Math.), one to which any value can be
      assigned at pleasure.

Constant \Con"stant\, n.
   1. That which is not subject to change; that which is
      invariable.

   2. (Math.) A quantity that does not change its value; -- used
      in countradistinction to {variable}.

   {Absolute constant} (Math.), one whose value is absolutely
      the same under all circumstances, as the number 10, or any
      numeral.

   {Arbitrary constant}, an undetermined constant in a
      differential equation having the same value during all
      changes in the values of the variables.