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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.

--*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.

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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.

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