Equational box

Equation \E*qua"tion\, n. [L. aequatio an equalizing: cf. F.
   ['e]quation equation. See {Equate}.]
   1. A making equal; equal division; equality; equilibrium.
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            Again the golden day resumed its right,
            And ruled in just equation with the night. --Rowe.
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   2. (Math.) An expression of the condition of equality between
      two algebraic quantities or sets of quantities, the sign =
      being placed between them; as, a binomial equation; a
      quadratic equation; an algebraic equation; a
      transcendental equation; an exponential equation; a
      logarithmic equation; a differential equation, etc.
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   3. (Astron.) A quantity to be applied in computing the mean
      place or other element of a celestial body; that is, any
      one of the several quantities to be added to, or taken
      from, its position as calculated on the hypothesis of a
      mean uniform motion, in order to find its true position as
      resulting from its actual and unequal motion.
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   {Absolute equation}. See under {Absolute}.

   {Equation box}, or {Equational box}, a system of differential
      gearing used in spinning machines for regulating the twist
      of the yarn. It resembles gearing used in equation clocks
      for showing apparent time.

   {Equation of the center} (Astron.), the difference between
      the place of a planet as supposed to move uniformly in a
      circle, and its place as moving in an ellipse.

   {Equations of condition} (Math.), equations formed for
      deducing the true values of certain quantities from others
      on which they depend, when different sets of the latter,
      as given by observation, would yield different values of
      the quantities sought, and the number of equations that
      may be found is greater than the number of unknown
      quantities.

   {Equation of a curve} (Math.), an equation which expresses
      the relation between the co["o]rdinates of every point in
      the curve.

   {Equation of equinoxes} (Astron.), the difference between the
      mean and apparent places of the equinox.

   {Equation of payments} (Arith.), the process of finding the
      mean time of payment of several sums due at different
      times.

   {Equation of time} (Astron.), the difference between mean and
      apparent time, or between the time of day indicated by the
      sun, and that by a perfect clock going uniformly all the
      year round.

   {Equation clock} or {Equation watch}, a timepiece made to
      exhibit the differences between mean solar and apparent
      solar time. --Knight.

   {Normal equation}. See under {Normal}.

   {Personal equation} (Astron.), the difference between an
      observed result and the true qualities or peculiarities in
      the observer; particularly the difference, in an average
      of a large number of observation, between the instant when
      an observer notes a phenomenon, as the transit of a star,
      and the assumed instant of its actual occurrence; or,
      relatively, the difference between these instants as noted
      by two observers. It is usually only a fraction of a
      second; -- sometimes applied loosely to differences of
      judgment or method occasioned by temperamental qualities
      of individuals.

   {Theory of equations} (Math.), the branch of algebra that
      treats of the properties of a single algebraic equation of
      any degree containing one unknown quantity.
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