Forms: 5 varyacyoune, -cio(u)n, 6 -cyon; 5 variacioun, 5–6 -cion, 6 -cyon, -tioun, 6– variation. [a. OF. variation, -acion (F. variation, Sp. variacion, Pg. variação, It. variazione), a. L. variātiōn-, variātio, n. of action f. variāre to VARY.]
I. † 1. Difference, divergence or discrepancy between two or more things or persons. Obs.
c. 1386. Chaucer, Knt.’s T., 1730. In al the world … So even withoute variacioun Ther nere suche companyes tweye.
1426. Lydg., De Guil. Pilgr., 20066. I sey also … That ther be … Many constellaciouns And many varyaciouns.
1460. Capgrave, Chron. (Rolls), 48. Here is for to noten that their is grete variacion amongst auctoures, both of ȝeres and of Kyngis names.
1480. Caxton, Myrr., II. i. 65. This present fygure is … demonstraunce certayne and trewe, without ony variacion ne doubtaunce.
1553. Eden, Treat. New Ind. (Arb.), 42. A clyme is a porcion of the worlde betwene South and North, wherein is variacion in length of the daye, the space of halfe an houre.
1628. T. Spencer, Logick, 68. Health … dissenteth from a man that is sicke, by reason of that distance, or variation, which ariseth from sicknes.
a. 1637. B. Jonson, Discoveries, Wks. 1640, II. 106. There is a great variation betweene him, that is rais’d to the soveraignity by the favour of his Peeres, and him that comes to it by the suffrage of the people.
† 2. Discord, variance, dissension; an instance of this. Obs. rare.
c. 1485. Digby Myst. (1882), III. 923. Be-twyx yow and me be never varyacyounes.
1523. Ld. Berners, Froiss., I. cccxlvi. 548. Thus the Christen realmes were in variacyon, and the churches in great dyfference, bycause of the popes.
† 3. a. Uncertainty, doubt. Obs.–1
1471. Caxton, Recuyell (Sommer), 28. In this sorow and in this payne and varyacion … Vesca, Abell and the damoysel were a longe tyme.
† b. Inconstancy: variableness.
1509. Hawes, Past. Pleas., XIX. (Percy Soc.), 88. My heart shall be without variacion Wyth you present, in perfite sykernes.
c. 1530. Crt. of Love, 1340. I … depely swere as mine power to bene Faithful deuoide of variacion.
II. 4. The fact of varying in condition, character, degree or other quality; the fact of undergoing modification or alteration, especially within certain limits.
1502. Ord. Crysten Men (W. de W., 1506), V. vi. In shynynge varyacyon of dyuers coloures.
1513. Bradshaw, St. Werburge, I. 1340. This present lyfe … How dredefull it is, full of varyacyon.
1555. Eden, Decades (Arb.), 45. Paralleles, are lines whereby the sonne passynge causeth variation of tyme.
1579. Fenton, Guicciard., I. (1599), 15. Let vs looke somewhat into the variation of times and things of the world.
1637. Nabbes, Microcosmus, II. Two kisses more will cloy me; nought can relish But variation.
1674. Boyle, Excell. Theol., II. v. 214. According to the varying gravity of the atmosphere; which variation has … a very considerable influence on the weather-glass.
1750. trans. Leonardus’ Mirr. Stones, 53. As is held by many learned men who have written of the variation of the air.
1785. G. A. Bellamy, Apology (ed. 3), I. 67. Lest you accuse me of a want of variation in the conclusion of my letters, I shall end this in the good old-fashion way.
1822. [Mary A. Kelty], Osmond, I. 36. In this variation of feeling the morning and the afternoon wore away.
1845. G. E. Day, trans. Simon’s Anim. Chem., I. 246. From these data, it appears, that … the variation is the most striking with regard to the fibrin and globulin.
1885. Watson & Burbury, Math. Th. Electr. & Magn., I. 96. In order to effect this object the charge upon the conductor must be capable of variation.
b. The action of making some change or alteration.
a. 1704. T. Brown, Satire Antients, Wks. 1730, I. 14. They used in other words the same variation of the letter u into i, as maxumus, maximus.
1711. in Nairne Peerage Evidence (1874), 133. The said parties having in order therto agreed … in the terms of the two former contracts … without change or variation.
1885. Law Rep. 29 Chanc. Div. 542. The powers reserved to Wilson Lomer … to control the variation of investments.
1913. Act 3 Geo. V., c. 3 § 1. Where a resolution is passed … providing for the variation of any existing tax.
5. Variation of the compass, († lodestone,) or needle, the deviation or divergence of the magnetic needle from the true north and south line; the amount or angular measure of this; = DECLINATION 8 b.
1556. Burrough, in Hakluyt (1886), III. 126. I went on shoare and obserued the variation of the Compasse, which was three degrees.
1571. Digges, Pantom., I. xxix. I ij b. Drawing a right line making an angle … equall to the variation of the compasse in your region.
1613. Purchas, Pilgrimage (1614), 49. Cabot first found out the variation of the Compasse.
1679. Moxon, Math. Dict., 160. Variation of the Needle, the Turning or Deviation of the Needle in the Mariners Compass [etc.].
1687. A. Lovell, trans. Thevenot’s Trav., II. 156. The variation of the Loadstone.
1774. M. Mackenzie, Maritime Surv., 62. How to find the Sun’s Azimuth, and from thence to find the Variation of the Needle.
1834. Mrs. Somerville, Connex. Phys. Sci. (1810), xxix. 338. The variation of the compass.
1851. Greenwell, Coal-trade Terms, Northumb. & Durh., 16. The diurnal variation of the needle being far from inconsiderable.
b. ellipt. in the same sense.
1594. Davis, Seaman’s Secrets (1601), 17. If your Compasse be good and without variation.
1597. W. Barlowe, Navigator’s Supply, A 2. By the Variation is vnderstood the difference in the Horizon betweene the true and the magneticall Meridian.
1627. Capt. Smith, Seaman’s Gram., ii. 12. There is also … a Compasse for the variation.
1669. Sturmy, Mariner’s Mag., IV. i. 138. The Points of the Needle … are subject to be drawn aside by the Guns…, or any Iron neer it, and liable to Variation, and doth not show the true North.
1703. Dampier, Voy., III. I. 100. I found that the Variation did not always increase or decrease in proportion to the Degrees of Longitude East or West.
1769. Falconer, Dict. Marine (1780), s.v., The highest variation … appears to be 17°1/4 W. and the least 16°1/2 W.
1846. A. Young, Naut. Dict., 81. The variation is in practice ascertained by comparing the sun’s true and magnetic amplitude or azimuths.
1878. [see DECLINATION 8].
c. Variation of the variation (see last quot.).
1706. Phillips (ed. Kersey), Variation of the Variation, is so call’d, because the Variation of the Needle is not always the same in the same Place.
1839. Noad, Electricity, 201. The variation of the variation, that is, the fact that the variation was not a constant quantity, but varied in different latitudes, was first noticed by the discoverer of America.
1867. Smyth, Sailor’s Word-bk., 710. Variation of the Variation, is the change in the declination of the needle observed at different times in the same place.
6. The fact, on the part of the mercury, of standing higher or lower in the tube of a barometer or thermometer; the extent or range of this.
1719. Quincy, Phys. Dict. (1722), 11. The greatest Variation of the Height of the Mercury being 3 Inches.
1748. Anson’s Voy., II. v. 183. The variation of the thermometer at Petersburgh is at least five times greater … than … at St. Catherine’s.
1815. J. Smith, Panorama Sci. & Art, II. 28. Had the tube been straight, Q would have been the limit of the scale of variation.
1858. Lardner, Hand-bk. Nat. Phil., 168. A rise or fall of the mercury in the tube, within the usual limits of barometric variation.
7. Astr. a. The libration of the moon; = LIBRATION 2.
1704. J. Harris, Lex. Techn., I. Variation is, according to Tycho, the third Inequality in the Motion of the Moon.
1728. Pemberton, Newton’s Philos., 199. This inequality of the moon’s motion about the earth is called by astronomers its variation.
1812. Woodhouse, Astron. (1823), I. II. 682. The Variation is occasioned by the other resolved part, that which acts in the direction of the tangent to the Moon’s orbit.
1879. Newcomb & Holden, Astron., 163. The disturbing action of the sun [upon the moon] produces a great number of other inequalities, of which the largest are the evection and the variation.
b. (See quot.)
1867. Smyth, Sailor’s Word-Bk., 43. Annual Variation, the change produced in the right ascension or declination of a star by the precession of the equinoxes and proper motion of the star taken together.
8. Math. † a. = PERMUTATION 3 b. Obs.
1710. J. Harris, Lex. Techn., II. Variation, or Permutation of Quantities, is the changing any number of given Quantities, with respect to their Places.
1728. Chambers, Cycl., s.v. Combination, Suppose the Quantities 3, and the Exponent of Variation 3; the Number of Changes is found 27 = 33.
b. Change in a function or functions of an equation due to an indefinitely small increase or decrease in the value of the constants.
1743. W. Emerson, Fluxions, 3. The Velocity, Variation, or Quickness of Increase (or Decrease) of any Fluxion is called the second Fluxion.
1843. Penny Cycl., XXVI. 136/3. Variation. Under this head comes the explanation of a part of the language of proportion which is much used…. We refer to such phrases as the following:—A varies as B.—A varies inversely as B.
1885. Watson & Burbury, Math. Th. Electr. & Magn., I. 6. Then … u will, on arriving again at O, have assumed by continuous variation the value u0 + H.
c. Variation of curvature: (see quot. 1842).
a. 1727. Newton, Meth. Fluxions & Inf. Ser. (1736), 76. The Inequability or Variation of Curvature is required at any Point of a Curve.
1842. Francis, Dict. Arts, Variation of curvature, the change made on a curve, so as to occasion it to be flatter or sharper in each succeeding part.
d. Algebra. The following of a + sign after a – sign, or vice versa, in a row of signs.
1891. in Cent. Dict.
9. Mus. (See quot.)
1730. Treat. Harmony, 34. There is another sort of Division called Variation, which may also be upon a Division.
10. Biol. Deviation or divergence in the structure, character or function of an organism from those typical of or usual in the species or group.
1859. Darwin, Orig. Spec., i. 11. There are many laws regulating variation, some few of which can be dimly seen.
1867–8. Lyell, Princ. Geol., III. xliii. (ed. 10), II. 488. If some modification of an organ, or instinct, be produced by what is called ‘Spontaneous Variation.’
1871. Tyndall, Fragm. Sci. (1879), II. ix. 176. No naturalist could tell how far this variation could be carried.
1882. Vines, trans. Sachs’ Bot., 925. The characters of many of these varieties are perfectly hereditary, and all the organs show the greatest degree of variation.
III. 11. An instance of varying or changing; an alteration or change in something, esp. within certain limits.
Sometimes in specific senses: cf. 5–10 above.
1611. Cotgr., Muance, change, alteration; and particularly, a variation, or change of notes in singing.
1659. Pearson, Creed (1839), 525. The natural course of variations in the creature.
1665. Phil. Trans., I. 31. A Baroscope, or an instrument to show all the Minute Variations in the Pressure of the Air.
1719. De Foe, Crusoe, II. (Globe), 486. Variations of the Compass.
1758. Johnson, Idler, No. 11, ¶ 11. The most variable of all variations: the changes of the weather.
1786. Mrs. A. M. Bennett, Juvenile Indiscr., IV. 231. They … contrived to fill a long summer’s day, or winter’s evening, by an agreeable variation of female amusements.
1832. Ht. Martineau, Weal & Woe, vii. 94. Seasons are sometimes stormy and our commerce liable to variations.
1844. Proc. Philol. Soc., I. 196. We may therefore be disposed to consider all marked variations of dialect as evidences of difference of date.
1874. trans. Lommel’s Light, 181. The variations of light and shade are alone visible.
b. A difference due to the introduction or intrusion of some change or alteration.
1699. Bentley, Phal., 36. We have the firmer ground to go upon for this little Variation.
1727. T. Innes, Anc. Inhab. Scot. (1879), 87. Variations which the negligence as well as the ignorance of transcribers is ordinarily the cause of.
1861. Paley, Æschylus (ed. 2), Supplices, 842, note. The other MSS. present only slight variations.
1869. Tozer, Highl. Turkey, II. 272. The … stories have evidently come from the same original, but present curious variations in the form under which the youth is born.
1878. Huxley, Physiogr., 192. In different specimens … the lava exhibits great variations.
c. Biol. A slight departure or divergence from a type. (Cf. 10.)
1835. Lyell, Princ. Geol., III. ii. (ed. 4), II. 428. The phenomenon, that some individuals are made to deviate widely from the ordinary type…. How far … may such variations extend in the course of indefinite periods of time?
1859. Darwin, Orig. Spec., Introd. 4. We shall see how great is the power of man in accumulating by his Selection successive slight variations.
1871. R. H. Hutton, Ess., I. 65. An accidental variation only means a variation of which you cannot determine the direction.
1882. Vines, trans. Sachs’ Bot., 777. Changes in these hereditary peculiarities, or variations, are never brought about by direct external influences.
d. A different form or species; a variety, variant.
1863. Huxley, Knowl. Org. Nat., 99. If, by crossing a variation with the original stock, you multiply that variation, and then take care to keep that variation distinct from the original stock, and make them breed together.
1868. Boy’s own Bk., 593. The Matadore Game … is a variation of All Fives.
1878. Browning, Poets Croisic, 5. Try a variation of the game!
12. A deviation or departure from something.
1647. Clarendon, Hist. Reb., I. § 178. Besides that any Variation from it … would make the Uniformity the less.
a. 1662. Heylin, Laud, I. 223. It was best to take the English Liturgie, without any variation from it.
1782. J. Brown, Nat. & Rev. Relig., III. ii. 246. There often befalls it a deforming variation from the original happy constitution.
1818. Cruise, Digest (ed. 2), I. 208. He did not think fit to make any variation from what was then determined.
13. Math. a. (Cf. 8 a.)
1728. Chambers, Cycl., s.v. Combination, Suppose two Quantities, a and b; their Variations will be 2; consequently, as each of those may be combined, even with it self, to these there must be added two Variations.
b. Calculus of variations, a form of calculus applicable to expressions or functions in which the law relating the quantities is liable to variation.
1810. Woodhouse (title), A Treatise on Isoperimetrical Problems, and the Calculus of Variations.
1855. Brewster, Newton, I. xiii. 349. The calculus of variations discovered by Lagrange in 1760, was the greatest step in the improvement of the infinitesimal calculus which was made in the last century.
1861. Todhunter (title), A History of the Progress of the Calculus of Variations during the Nineteenth Century.
14. Mus. A modification with regard to the tune, time and harmony of a theme, by which on repetition it appears in a new but still recognizable form; esp. in pl., embellishments in an air for giving variety on repetition after playing it in its simple form.
1801. Busby, Dict. Mus. (1811), Variations, or Var, the name given to certain ornamented repetitions, in which, while the original notes, harmony, and modulation, are … so far preserved as to sustain the parent subject, the passages are branched out in flourishes.
1820. Scott, Lett., in Lockhart (1837), IV. xi. 371. She ran a set of variations on ‘Kenmure’s on and awa’,’ which I told her were enough to raise a whole country-side.
1873. H. C. Banister, Music, 216. In some Sonatas, etc., one of the Movements is a Theme with Variations.
15. attrib. in sense 5 b, as variation-chart, compass, instrument.
1669. Sturmy, Mariner’s Mag., II. vi. 67. The Use of the Quadrant and Variation-Compass.
1727. Bailey (vol. II.), Variation Chart, a Chart design’d by Dr. Halley.
1748. Anson’s Voy., Introd. A new variation-chart lately published.
1769. Phil. Trans., LIX. 483. The variation compass was … a very good one.
1837. Lloyd, in Rep. Brit. Assoc., VI. App. 21. The variation instrument will be placed in the magnetic meridian, with respect to the theodolite.
1867. Smyth, Sailor’s Word-bk., 710. The admiralty variation chart has been brought to great perfection.
