\E*qua"tion\, n. [L. aequatio an equalizing: cf. F.
['e]quation equation. See {Equate}.]
1. A making equal; equal division; equality; equilibrium.
         Again the golden day resumed its right, And ruled in
         just equation with the night.         --Rowe.
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.
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.
{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 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.