EQUATION, a term based on the idea of equality.
Algebra.—Two algebraic expressions which are equal to one another, and are connected by the sign—. Thus 6x-13= ami +19.
is an equation; and, since the equality of the members depends on the value assigned to x, it is called an equation of condition. The two quantities separated by the sign= are called the members of the equation; the quantity to the left of—being the first member, and that to the right the second. The quantities separated by the signs and — are called the terms of the equation. Of the quan tities some are known and the others unknown. The known quantities are gen erally represented by numbers. If letters be used, then those employed are gen erally a, b, c, d, etc.—i. e., letters at or near the beginning of the alphabet. Un known quantities are represented by let ters toward the conclusion of the alpha bet. If there be one unknown quantity it is generaly represented by x; if two, by x and y; and if three, by x, y, and z. Sometimes a statement that two expres sions are equal for all numerical values that can be assigned to the letters in volved, provided that the same value be given to the same letter in each member, e. (x f ±2ax-Fce.
Such a statement is called an identical equation, or briefly, an identity. The solution of an equation is the process which ultimately results in discovering and stating the value of the unknown quantity, which value is the root of the equation. Equations are classified accord ing to the highest power of the unknown quantity sought. When that quantity exists only in the first power we have a simple equation, or one of the first degree; if there be a square or second power of the unknown quantity, the equation becomes a quadratic, or one of the second degree; if the third power be present a cubic equation, or of the third degree. It is rarely that a higher power than the cube of the unknown quantity has to be dealt with. When such cases occur the equation is biquadratic, or one of the fourth degree, an equation of the fifth, of the sixth, of any degree.
Astrononiy.—Any sum to be added or subtracted to allow for an anomaly or a special circumstance affecting the exact ness of a calculation. If, for instance, the orbit of a planet were calculated on the supposition that its orbit was circular when in reality it is elliptical a small number would require to be added or sub tracted to make the calculations accurate.
That small sum would be the astronom ical equation. If the movements of the planets calculated on the supposition that the only attraction operating on them is that of the sun, error, though not of a considerable magnitude, will be the re sult. There is a mutual attraction among all the planets; each is capable of pro ducing a perturbation in the orbits of all the rest. An equation is required for every such perturbation before it is pos sible to calculate accurately the course of the planet.
Chemistry.—A chemical equation rep resents symbolically a chemical reaction, the symbols of the reacting substances being placed on the left hand, and the symbols of the new substances formed by the reaction being placed on the right hand. In a chemical equation the number of atoms of each element must be the same on each side of the equation, thus, 3AgNO3+ Na2HPO, = Ag,P00- 2NaNO3+ HNO,. Three molecules of argentic nitrate and one molecule of disodium-hy drogen-phosphate equal (that is, form when added together) one molecule of triargentic phosphate, and two molecules of sodium nitrate, and one molecule of hydrogen nitrate (nitric acid). Chemical equations are imperfect, as they do not show the amount of heat liberated, or absorbed, during the reaction.
Annual, Personal, Etc.—Annual equa tion, in astronomy, one of the numer ous equations requisite in determing the moon's true longitude; equation of the center; the equation required to fix the place or orbit of a planet calculated as if it were moving in a circle when it is doing so really in an ellipse; equa tion of the equinoxes; the equation re quired to calculate the real position of the equinoxes from its mean one, the dis turbing element being the movement called precession of the equinoxes; equa tion of time, the difference between mean and apparent time; personal equation, the difference between the time at which an astronomical occurrence takes place and that at which a fallible observer notes that it does so; also, the correction of personal differences between particu lar individuals as to exactness in obser vations with astronomical instruments; equation of payments, a rule for ascer Lining at what time a person should in equity pay the whole of a debt contracted in different portions to be repaid at different times.