Also 4 equacion, equacioun, 6–7 æquation. [ad. L. æquātiōn-em, f. æquā-re: see EQUANT.] The action of equalling.
I. The action of making equal.
† 1. spec. in Astrol. Equal partition. Equations of houses: the method of dividing the sphere equally into ‘houses’ for astrological purposes. Obs.
c. 1386. Chaucer, Frankl. T., 551. And hise proporcioneles conuenientz ffor hise equacions in euery thyng. Ibid. (c. 1391), Astrol., I. § 22. With the smale point of the forseide label, shaltow kalcule thyne equaciouns in the bordure of thin Astrolabie.
1393. Gower, Conf., III. 67. He loketh his equacions And eke the constellacions.
2. gen. The action of making equal or balancing; the state of being equally balanced, equilibrium, equality. Now chiefly in phrases like equation of demand and supply, equation of trade, etc.
1656. Blount, Glossogr., Equation, making equal, even or plain.
1677. Hale, Prim. Orig. Man., I. ix. 216. The very Redundance it self of Mankind seeming by a natural consecution to yield and subminister this Remedy, for its Reduction and Equation.
1718. Rowe, trans. Lucan, IV. 94 (1719), 116 (R.).
| Again the golden Day resum’d its Right, | |
| And rul’d in just Equation with the Night. |
1726. Shelvocke, Voy. round World, 140. It would be difficult to determine the different values of the dollars and the candlesticks, so as to come to a nice equation of the matter.
1848. Mill, Pol. Econ., III. xxi. § 1 (1876), 375. An excess of imports over exports, arising from the fact that the equation of international demand is not yet established.
1850. Grote, Greece, II. lx. VII. 481. If his personal suffering could … be … set in equation against the mischief brought by himself both on his army and his country.
1876. Fawcett, Pol. Econ., III. vii. 399. These prices would adjust the equation of international trade.
II. Reduction to a normal value or position.
3. Astr. The action of adding to or subtracting from any result of observation or calculation such a quantity as will compensate for a known cause of irregularity or error. Chiefly concr. the quantity added or subtracted for this purpose.
Annual equation: see ANNUAL 2 b.
Equation of the center: the difference between the mean and the true anomaly of a heavenly body.
† Eccentric equation: = Equation to the center.
Equation of the equinoxes: the difference between the mean and apparent places of the equinoxes, arising from the phenomenon known as Procession of the equinoxes.
Equation of time: the difference between the time shown by a clock (mean time) and that shown by a sundial.
Personal equation: the correction required in astronomical observations in consequence of greater or less inaccuracy habitual to individual observers. Also transf.
1666. Evelyn, Mem. (1857), II. 11. To the Royal Society, where one Mercator … produced his rare clock, and new motion to perform the equations.
1726. trans. Gregory’s Astron., I. III. 421. When both these Causes of the Equation of Time hold.
1812. Woodhouse, Astron., xxxiv. 320. Corrections, or, as they are astronomically called, equations.
1834. Nat. Philos., Astron., x. 193/1 (Usef. Knowl. Soc.). The equation of the centre [of the sun] is subject to a very slow secular variation.
1853. Lardner, Handbk. Astron., § 3200. If we suppose an imaginary moon to move from perihelion through aphelion back to perihelion, with a uniform angular velocity … the distance between this imaginary moon and the true moon is called the equation of the centre.
1854. Moseley, Astron., xxi. (ed. 4), 96. The difference between true and mean solar time … is called the equation of time.
1881. Lockyer, in Nature, No. 614. 318. Photography has no personal equation.
1881. New York Nation, XXXII. 430. The scientific genealogists of the more advanced school, who settle the problem off-hand, often in accordance with their personal equation.
4. Equation of payments: the process of finding a mean time for the equitable payment in one amount of several sums due at different times.
1677. Cocker, Arith., xxix. 309. Equation of payments is that Rule … whereby to reduce the times for payment of several sums of money to an equated time for payment of the whole debt without dammage to the Debtor or Creditor.
III. Statement of equality.
† 5. Math. The action of stating the identity in value of two quantities or expressions. Obs.
1570. Dee, Math. Pref., *ij b. That great Arithmeticall Arte of Æquation: commonly called … Algebra.
1579. Digges, Stratiot., 44. Æquation is nothing else but a certain conference of two numbers being in value Equal, and yet in multitude and Denomination different.
1664. Power, Exp. Philos., III. 187. Thus came they to upbraid … Algebra with the Æquation of three discontinued Numbers.
1673. Kersey, Algebra, I. xi. 51. An Equation in the Algebraical Art is a mutual comparing of two equal Quantities or Things of different Denominations.
6. concr. A formula affirming the equivalence of two quantitative expressions, which are for this purpose connected by the sign =.
The two chief kinds of equations are: (1) Those that contain symbols denoting one or more unknown quantities; to discover the numerical values of these is called ‘solving’ the equation; the numbers that will ‘satisfy’ an equation, i.e., that may be substituted for the symbol of unknown quantity without rendering the statement incorrect, are called its ‘roots.’ (2) Those that indicate a constant relation existing between variables; as Equation to a curve, an equation expressing a relation between coordinates or the like, which is constant for every point in the curve; equation of motions, etc. Equations are distinguished as simple, quadratic, cubic, biquadratic, etc. (or as of the 1st, 2nd, 3rd, 4th, etc., degree) according to the highest power that they contain of any unknown or variable.
1570. Billingsley, Euclid, II. Introd. 60. Many rules … of Algebra, with the equations therein vsed.
1657. Hobbes, Absurd Geom., Wks. 1845, VII. 366. You mean that … the lowermost to the lowermost in the first equation are equal.
1750. Phil. Trans., XLVII. 62. Mr. de Buffon mention’d … we should … resolve the equation.
1807. Hutton, Course Math., II. 322. The equation to the curve being ax = y2.
1816. Playfair, Nat. Phil., II. 227. This method of determining the co-efficients of a given function, or correcting them from observation, by means of what are called Equations of Condition, is said to have been invented by Tobias Mayer of Göttingen.
1838. De Morgan, Ess. Probab., 29. An investigation of the method of solving an equation.
1853. Sir H. Douglas, Mil. Bridges (ed. 3), 11. Hence there is obtained the following equation of motion: a V2 = g sin. θ.
1871. B. Stewart, Heat, § 62. From this equation we derive at once the relation between the temperature and the density of air.
1879. Thomson & Tait, Nat. Phil., I. I. § 191. What is called the ‘equation of continuity’ [for fluids], an unhappily chosen expression.
b. transf.
1860. Abp. Thomson, Laws Th., § 68. 110. Every affirmative judgment may be regarded as an equation of subject and predicate.
c. A formula that represents a chemical reaction by stating the equality between the symbols representing the original and those that represent the resulting substances.
1807. T. Thomson, Chem. (ed. 3), II. 132. We have therefore this equation, Carbon 28 + Oxygen 72 = Carb. Ox. 69 + Oxygen 31.
1844–57. G. Bird, Urin. Deposits (ed. 5), 245. In the following equation this decomposition of the allantoin is assumed to have occurred.
1853. W. Gregory, Inorg. Chem. (ed. 3), 90. The following equation explains the change. (KO, NO5)+2 (HO,SO3) = (KO,HO,2SO3)+(HO,NO5).
