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equation|iːˈkweɪʃən, -ʒən|
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.
c1386Chaucer Frankl. T. 551 And hise proporcioneles conuenientz ffor hise equacions in euery thyng. c1391― Astrol. i. §22 With the smale point of the forseide label, shaltow kalcule thyne equaciouns in the bordure of thin Astrolabie. 1393Gower 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.
1656Blount Glossogr., Equation, making equal, even or plain. 1677Hale Prim. Orig. Man. ii. 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. 1718Rowe tr. Lucan ii. (R.), Again the golden day resum'd its right, And rul'd in just equation with the night. 1726G. 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. 1848Mill 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. 1850Grote 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. 1876Fawcett Pol. Econ. iii. vii. 399 These prices would adjust the equation of international trade.
II. Reduction to a normal value or position.
3. a. 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 centre: the difference between the mean and the true anomaly of a heavenly body.
† eccentric equation: = equation to the centre.
equation of the equinoxes: the difference between the mean and apparent places of the equinoxes, arising from the phenomenon known as precession 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.
1666Evelyn Mem. (1857) II. 11 To the Royal Society, where one Mercator. produced his rare clock, and new motion to perform the equations. 1726tr. Gregory's Astron. I. iii. 421 When both these Causes of the Equation of Time hold. 1812Woodhouse Astron. xxxiv. 320 Corrections, or, as they are astronomically called, equations. 1834Nat. Philos., Astron. x. 193/1 (Usef Knowl. Soc.) The equation of the centre [of the sun] is subject to a very slow secular variation. 1845Penny Cycl. Suppl. I. 535/2 If A and B are severally in the habit of noting events 3-tenths of a second after and 4-tenths of a second before they take place, their personal equations may be described as being + 0s.3 and 0s.4. 1853Lardner 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. 1854Moseley Astron. xxi. (ed. 4) 96 The difference between true and mean solar time..is called the equation of time. 1865Brande & Cox Dict. Sci. (ed. 3) I. 800/2 The term personal equation has of late been introduced into Astronomy. 1881Lockyer in Nature No. 614. 318 Photography has no personal equation. 1881New 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.
b. human equation: transf. sense from personal equation.
1938Reader's Digest Apr. 77/2 The Oakland Bridge suffers from such a simple, unpredictable human equation as the preference of truck drivers to loaf on a ferry. 1964F. Bowers Bibliogr. & Textual Criticism III. ii. 71 We must throw out the human equation as much as we can in our search to find an explanation for seeming aberrancies.
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.
1677Cocker 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.
1570Dee Math. Pref. 6 That great Arithmeticall Arte of æquation: commonly called..Algebra. 1579Digges Stratiot. 44 æquation is nothing else but a certain conference of two numbers being in value Equal, and yet in multitude and Denomination different. 1664Power Exp. Philos. iii. 187 Thus came they to upbraid..Algebra with the æquation of three discontinued Numbers. 1673Kersey Algebra I. xi. 51 An Equation in the Algebraical Art is a mutual comparing of two equal Quantities or Things of different Denominations.
6. a. 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 which contain symbols denoting one or more unknown quantities; to discover the numerical values of these is called ‘solving’ the equation; the numbers which will ‘satisfy’ an equation, i.e. which may be substituted for the symbol of unknown quantity without rendering the statement incorrect, are called its ‘roots’. (2) Those which 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 which they contain of any unknown or variable.
1570Billingsley Euclid ii. Introd 60 Many rules..of Algebra, with the equations therein vsed. 1657Hobbes Absurd Geom. Wks. 1845 VII. 366 You mean that..the lowermost to the lowermost in the first equation are equal. 1750Phil. Trans. XLVII. 62 Mr. de Buffon mention'd..we should..resolve the equation. 1807Hutton Course Math. II. 322 The equation to the curve being ax = y2. 1816Playfair 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. 1838De Morgan Ess. Probab. 29 An investigation of the method of solving an equation. 1853Sir H. Douglas Mil. Bridges (ed. 3) 11 Hence there is obtained the following equation of motion: a V2 = g sin. θ. 1871B. Stewart Heat §62 From this equation we derive at once the relation between the temperature and the density of air. 1879Thomson & Tait Nat. Phil. I. i. §191 What is called the ‘equation of continuity’ [for fluids], an unhappily chosen expression.
b. transf.
1860Abp. Thomson Laws Th. §68. 110 Every affirmative judgment may be regarded as an equation of subject and predicate.
c. A formula which represents a chemical reaction by stating the equality between the symbols representing the original and those which represent the resulting substances.
1807T. Thomson Chem. (ed. 3) II. 132 We have therefore this equation, Carbon 28 + Oxygen 72 = Carb. Ox. 69 + Oxygen 31. 1844–57G. Bird Urin. Deposits (ed. 5) 245 In the following equation this decomposition of the allantoin is assumed to have occurred. 1853W. Gregory Inorg. Chem. (ed. 3) 90 The following equation explains the change. (KO,NO5) + 2 (HO,SO3) = (KO,HO,2SO3) + (HO,NO5).
7. equation box = equational box (see next); equation table, a table showing the time a clock should indicate when the sun is on the meridian.
1893Funk's Stand. Dict. s.v. Equational, Equation box.
1731(title) An explanation of the nature of equation of time, and use of the equation table for adjusting watches and clocks to the motion of the sun. 1850Denison Clock & Watch-m. 19 This [sundial]..with the equation-table will give the means of correcting a clock on any fine day. |