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# Equation

## tions, true, anomaly, motion and orbit

EQUATION, a term based on the idea of equality, in general use throughout the various branches of calculus. (1) In mathematics it is the statement in algebraic expressions of the identity of two or other mathematical expres sions. The assertion of equality is made by writing the sign --(read equal or aequals” between the expressions. Thus: 5x + 7 = 32, and ax' bx t c = 0, are equa tions, each of which indicates the equality of the quantity written on the left of the sign (=----) to that written on the right of the sign. Usu ally the object of writing down an algebraic equation is to express in symbols known rela tions between given and unknown quantities, so that by algebraic processes the latter may be determined in terms of the former. Such equa tions are designated conditional, while equa tions which are true for all values of the vari ables they involve or which involve no variables, are called identities. (See ALGEBRA, DEFINI TIONS AND FUNDAMENTAL CONCEPTS). (2) In astronomy, is the correction by addition to or subtraction from the mean motion of any heavenly body in order to determine its true place at any given time. The angular motion of a planet around the sun will not be uniform if its orbit is not circular, regardless of any per turbations. Furthermore, the mutual attraction among the planets renders each one capable of producing a perturbation in the orbits of all the others. An equation it required for every such perturbation before It is possible to calcu late accurately the course of the planet. Thus we have the equation of the centre, a quantity to be added to or subtracted from the anomaly, in order to determine the true position of a heavenly body. For instance, let the curve

E c F represent the earth's orbit (which is an ellipse), t F the line of the aspides, andA the position of the sun. When the earth is in any position as c, the line A c drawn from the sun to the planet is the radius vector, then will the angle c A ir be the anomaly, or the angular distance from the perihelion. Were the earth's angular motion uniform the increase i or de crease of this angle would be equal n equal times, and the mean anomaly would be the true anomaly; but the earth's motion is retarded as it advances from F to c, is slowest at E, and is accelerated from that point, the aphelion, through the other half of its orbit till it arrives at F, the perihelion. The quantity to be added to the mean angular motion, during one por tion of the orbit, or subtracted from it in the other, in order to find that true anomaly, is called the equation of the centre. (3) In chemistry, is a collection of symbols to denote that two or more definite bodies— simple or compound — have been brought within the sphere of chemical action, that a reaction has taken place, and that new bodies are produced. It is called an equation because the total weight of the substances concerned remains the same. Equations may also involve the energy con sumed or given off in a reaction. See CHEM ISTRY.