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The Collaborative International Dictionary of English v.0.48 (gcide)

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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