arbitrary constant

Constant \Con"stant\, n.
   1. That which is not subject to change; that which is
      invariable.
      [1913 Webster]

   2. (Math.) A quantity that does not change its value; -- used
      in countradistinction to {variable}.
      [1913 Webster]

   3. (Astron.) A number whose value, when ascertained (as by
      observation) and substituted in a general mathematical
      formula expressing an astronomical law, completely
      determines that law and enables predictions to be made of
      its effect in particular cases.
      [Webster 1913 Suppl.]

   4. (Physics) A number expressing some property or condition
      of a substance or of an instrument of precision; as, the
      dielectric constant of quartz; the collimation constant of
      a transit instrument.
      [Webster 1913 Suppl.]

   5. (Computers) a data structure that does not change during
      the course of execution of a program. It may be a number,
      a string, or a more complex data structure; -- contrasted
      with {variable}.
      [PJC]

   {Aberration constant}, or {Constant of aberration} (Astron.),
      a number which by substitution in the general formula for
      aberration enables a prediction to be made of the effect
      of aberration on a star anywhere situated. Its value is
      20[sec].47.

   {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.

   {Gravitation constant} (Physics), the acceleration per unit
      of time produced by the attraction of a unit of mass at
      unit distance. When this is known the acceleration
      produced at any distance can be calculated.

   {Solar constant} (Astron.), the quantity of heat received by
      the earth from the sun in a unit of time. It is, on the C.
      G. S. system, 0.0417 small calories per square centimeter
      per second. --Young. [Webster 1913 Suppl.]

   {Constant of integration} (Math.), an undetermined constant
      added to every result of integration.
      [1913 Webster + Webster 1913 Suppl.]
    

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.
      [1913 Webster]

            It was wholly arbitrary in them to do so. --Jer.
                                                  Taylor.
      [1913 Webster]

            Rank pretends to fix the value of every one, and is
            the most arbitrary of all things.     --Landor.
      [1913 Webster]

   2. Exercised according to one's own will or caprice, and
      therefore conveying a notion of a tendency to abuse the
      possession of power.
      [1913 Webster]

            Arbitrary power is most easily established on the
            ruins of liberty abused licentiousness.
                                                  --Washington.
      [1913 Webster]

   3. Despotic; absolute in power; bound by no law; harsh and
      unforbearing; tyrannical; as, an arbitrary prince or
      government.                                 --Dryden.
      [1913 Webster]

   {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.
      [1913 Webster]