equation

Definitions:

  • The act or process of equating or of being equated.
  • The state of being equal.
  • A statement asserting the equality of two expressions, usually written as a linear array of symbols that are separated into left and right sides and joined by an equal sign.
  • A representation of a chemical reaction, usually written as a linear array in which the symbols and quantities of the reactants are separated from those of the products by an arrow or a set of opposing arrows.
  • A complex of variable elements or factors.
  • None
  • In the <em>calculus</em>, an equation which contains no differentials.
  • A making equal, or an equal division; equality.
  • In <em>mathematics</em>, a proposition asserting the equality of two quantities, and expressed by the sign = between them; or an expression of the same quantity in two terms dissimilar but of equal value: as, 3 lb. = 48 oz.; <em>x</em> = <em>b</em> + <internalXref urlencoded="m">m</internalXref> − <em>r.</em>
  • In <em>astronomy</em>, the correction or quantity to be added to or subtracted from the mean position of a heavenly body to obtain the true position; also, in a more general sense, the correction arising from any erroneous supposition whatever.
  • In <em>chem.</em>, a collection of symbols used to indicate that two or more definite bodies, simple or compound, having been brought within the sphere of chemical action, a reaction will take place, and new bodies be produced.
  • An equation for the steady motion of a liquid, namely, where <em>p</em> is the pressure, <bt>ρ</bt> the density, V the potential of the impressed forces, <em>q</em> the velocity, and C a constant for each stream-line and vortex-line, and in the case of irrotational motion a constant for all space.
  • with modern writers, a solution which is a particular case of the general solution;
  • with older writers, any solution not general. A <em>singular solution</em> is one which is neither general nor implied in the general solution. The <em>complete integral of a partial differential equation</em> is a solution containing the full number of arbitrary constants or functions.
  • In modern writings, the correction to be applied to the position of a planet or to the time of an eclipse, etc., owing to the finite velocity of light.
  • In <em>modern astron.</em>, the excess of the true over the mean anomaly. (<em>Gauss</em>, Theoria Motus, I. 7.)
  • The equation of the argument. (<em>Kepler</em>, De Motibus Martis, I. iv.)
  • Any one of the usual equations of hydrodynamics, where the components of the velocity at fixed points of space are taken as variables: so called in contradistinction to the Lagrangian equations where the coordinates of a definite particle are taken as variables; these equations, though also discovered by Euler, having been used by Lagrauge.
  • A general equation of hydrodynamics, in which, instead of considering the velocity at each fixed point of space, the motion of each particle is followed out. This is called a Lagrangian equation because used by Lagrange in his “Méchanique Analitique,” though invented by Euler.
  • An equation of analytical geometry in which certain curves are represented by single letters. Thus, if U = 0, V = 0, W = 0, represent the equations of three circles, UV = W is the symbolic equation of a bicircular quartic
  • A making equal; equal division; equality; equilibrium.
  • An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them
  • 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.
  • See under <er>Absolute</er>.
  • 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.
  • None
  • 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 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.
  • an equation which expresses the relation between the coördinates of every point in the curve.
  • the difference between the mean and apparent places of the equinox.
  • the process of finding the mean time of payment of several sums due at different times.
  • 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.
  • a timepiece made to exhibit the differences between mean solar and apparent solar time.
  • None
  • See under <er>Normal</er>.
  • 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.
  • the branch of algebra that treats of the properties of a single algebraic equation of any degree containing one unknown quantity.
  • An <xref>assertion</xref> that two <xref>expressions</xref> are equal, expressed by writing the two expressions separated by an <xref>equal sign</xref>; from which one is to determine a particular quantity.
  • A small <xref>correction</xref> to <xref>observed</xref> <xref>values</xref> to <xref>remove</xref> the effects of <xref>systematic</xref> <xref>errors</xref> in an <xref>observation</xref>.
  • the act of regarding as equal
  • a state of being essentially equal or equivalent; equally balanced
  • a mathematical statement that two expressions are equal
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