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2 definitions found

From: Webster's Revised Unabridged Dictionary (1913)

 Ar·bi·tra·ry a.
 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.
 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.

From: Webster's Revised Unabridged Dictionary (1913)

 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.
 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.
 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.
 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˝.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.
 Constant of integration Math., an undetermined constant added to every result of integration.