variationn.
/ˌvɛːrɪˈeɪʃn/, U.S. /ˌvɛriˈeɪʃən/ I. Senses relating to discrepancy, dissension, or doubt.† 1. Difference, divergence, or discrepancy between two or more things or persons. Obsolete.† 2. Discord, variance, dissension; an instance of this. Obsolete. rare.† 3. † b. Inconstancy; variableness.
ΘΚΠ
the world > relative properties > relationship > difference > [noun]
diversitya1340
difference1340
variancec1374
distancea1382
unlikenessa1387
variationc1405
discrepation?a1425
distinction1435
severaltyc1449
unlikelinessc1450
dissemblance1463
unlikelihood1483
alteritya1500
indifferencec1503
discrepancea1522
dissimilitude1532
differency1542
variety1552
discernment1570
disparitya1575
discrepancy1579
otherness1587
discernance1592
imparity1608
disanalogy1610
disresemblance1622
dislikeness1623
diff1624
inconformity1625
irresemblance1628
variousness1628
odds1642
disparation1654
aliety1656
disparility1656
disparateness1659
severality1664
nonconformity1672
unconformableness1712
dissimilarity1715
differentness1727
differ1787
allogeneitya1834
otherwiseness1890
otherliness1937
diversion-
c1405 (c1385) G. Chaucer Knight's Tale (Hengwrt) (2003) l. 1730 In al the world..So euene with outen variacioun Ther nere swiche compaignyes tweye.
1426 J. Lydgate tr. G. de Guileville Pilgrimage Life Man 20066 I sey also..That ther be..Many constellaciouns And many varyaciouns.
a1464 J. Capgrave Abbreuiacion of Cron. (Cambr. Gg.4.12) (1983) 39 Here is for to noten þat þere is grete variacioun amongis auctouris both of ȝeres and of kyngis names.
1481 W. Caxton tr. Myrrour of Worlde ii. i. 65 This present fygure is..demonstraunce certayne and trewe, without ony variacion ne doubtaunce.
1553 R. Eden tr. S. Münster Treat. Newe India sig. Mvv 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 Art of Logick 68 Health..dissenteth from a man that is sicke, by reason of that distance, or variation, which ariseth from sicknes.
a1637 B. Jonson Timber 1139 in Wks. (1640) III 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.
ΘΚΠ
society > society and the community > dissent > [noun]
unsibeOE
unsaughta1122
un-i-sibc1275
conteckc1290
discordingc1325
distancec1325
discordance1340
dissensionc1384
batea1400
discordc1425
variancec1425
variationc1485
disgreement?1504
distinction1520
factiona1538
jar1546
variety1546
disagreeance1548
disagreeing1548
disagreement1548
misliking1564
odds1567
mislikea1586
discordancy1587
disagree1589
distancy1595
dissent1596
dislike1598
secting1598
dichostasy1606
fraction1609
dissentation1623
ill blood1624
misintelligence1632
clashing1642
misunderstanding1642
discomposure1659
disjointinga1715
uneasiness1744
friction1760
misunderstand1819
unharmony1866
inharmony1867
trouble at (the or t') mill1967
the mind > emotion > hatred > state of variance or disunion > [noun]
unsaughtnessa1000
unsaughta1122
schismc1425
variancec1425
variationc1485
variety1546
breach1745
strain1884
c1485 Digby Myst. (1882) iii. 923 Be-twyx yow and me be never varyacyounes.
1523 Ld. Berners tr. J. Froissart Cronycles I. cccxlvi. 548 Thus the Christen realmes were in variacyon, and the churches in great dyfference, bycause of the popes.
a. Uncertainty, doubt. Obsolete. rare.
ΘΚΠ
the mind > mental capacity > belief > uncertainty, doubt, hesitation > [noun]
studyinglOE
orrathnessc1175
doubta1225
balance1297
were1303
doubtancec1325
unsickernessc1340
wilsomenessa1400
wonda1400
scriple?a1425
ambiguityc1425
diswerec1440
dubitationc1450
variation?1473
incertainty1483
doubting1486
doubtfulness1526
scrupulousness1526
scruple1548
uncertainty1548
disputation1549
irresolution1592
swithering1597
hesitance1601
incertitude1601
unpersuadedness1612
inassurance1614
hesitancy1617
unsettledness1619
hesitation1622
unsatisfaction1643
unsatisfiedness1646
dubitancy1649
insecurity1649
dispersuasion1653
unassuredness1660
scrupling1665
unconfidencea1670
swither1719
dubietyc1750
mank1808
suspense1816
dubitating1837
doubtingness1840
?1473 W. Caxton tr. R. Le Fèvre Recuyell Hist. Troye (1894) I. lf. 13v In this sorow and in this payne and varyacion..Vesca, Cibell and the damoysel were a longe tyme.
ΘΚΠ
the mind > will > decision > irresolution or vacillation > inconstancy > [noun]
unsteadfastnessa1300
falsenessc1330
unstablenessc1380
varyingc1380
inconstancec1386
variance1390
geriness1412
instabilityc1422
changeability?a1425
mutabilitya1425
changec1425
changeableness1447
unconstancec1449
unstabilitya1470
mutableness1481
unsureness1481
instableness1483
variation1509
inconstancy1526
shittleness1530
fickleness1548
unconstancy1548
unconstantness1551
inconstantness?a1562
pliableness1562
fast and loose1575
volubility1603
levity1604
unconstability1611
flexibleness1623
vagrancy1642
self-inconsistency1655
inconsistency1665
flittingnessa1680
easiness1705
inconsistence1713
versatility1755
contrariety1762
vibration1785
changefulness1791
girouettism1825
pirouettism1839
weathercockism1843
pirouettiveness1844
volatileness1849
unfixity1856
ficklety1888
1509 S. Hawes Pastime of Pleasure (1845) xix. 88 My heart shall be without variacion Wyth you present, in perfite sykernes.
c1530 Court of Love 1340 I..depely swere as mine power to bene Faithful deuoide of variacion.
II. Senses relating to modification or change.
4.
a. The fact of varying in condition, character, degree, or other quality; the fact of undergoing modification or alteration, especially within certain limits.
ΘΚΠ
the world > time > change > [noun] > change within limits, variation, or modification
variation1502
diversification1603
flexion1603
divisiona1616
amendment1653
variating1653
sophistication1664
modulation1674
vacillation1769
modification1775
variorum1776
modifyinga1853
tropicalization1893
mod1943
1502 tr. Ordynarye of Crysten Men (de Worde) v. vi. sig. rr.v v In shynynge varyacyon of dyuers colours.
a1513 H. Bradshaw Lyfe St. Werburge (1521) i. xiii. sig. e.iiv This present lyfe..How dredefull it is, full of varyacyon.
1555 R. Eden in tr. Peter Martyr of Angleria Decades of Newe Worlde sig. biiij Paralleles, are lines whereby the sonne passynge causeth variation of tyme.
1579 G. Fenton tr. F. Guicciardini Hist. Guicciardin i. 19 Let vs looke somewhat into the variacion of times and thinges of the worlde.
1637 T. Nabbes Microcosmus 11 Two kisses more will cloy me; nought can relish But variation.
1674 R. Boyle Excellency Theol. ii. v. 214 According to the varying gravity of the atmosphere; which variation has..a very considerable influence on the weather-glass.
1750 tr. C. Leonardus Mirror of Stones 53 As is held by many learned men who have written of the variation of the air.
1785 G. A. Bellamy Apol. Life (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 M. A. Kelty Osmond I. 36 In this variation of feeling the morning..wore away.
1845 G. E. Day tr. J. F. Simon Animal Chem. I. 246 From these data, it appears, that..the variation is the most striking with regard to the fibrin and globulin.
1885 H. W. Watson & S. H. Burbury Math. Theory 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.
ΘΚΠ
the world > time > change > [noun] > change within limits, variation, or modification > making variations
variation1691
1691 in Further Evid. Nairne Peerage (1874) 133 in Sessional Papers House of Lords (H.L. D) XII. 199 The s[ai]d parties having in order therto agreed..the terms of the two former contracts..without change or variation.
a1704 T. Brown Ess. Satire Ancients in Wks. (1730) I. 14 They used in other words the same variation of the letter u into i, as maxumus, maximus.
1885 Law Rep.: Chancery Div. 29 542 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.
a. 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 n. 8(b).
ΘΚΠ
society > travel > travel by water > vessel, ship, or boat > equipment of vessel > navigational aids > [noun] > compass > variation
north-easting1555
variation of the compass, (lodestone,) or needle?a1560
norwesting1561
north-westing1571
variation1595
declination1625
magnetic variation1696
variation of the variation1706
magnetic declination1787
?a1560 L. Digges Geom. Pract.: Pantometria (1571) i. xxix. sig. I ij v Drawing a right line making an angle..equall to the variation of the compasse in your region.
a1584 S. Borough in R. Hakluyt Princ. Navigations (1589) ii. 312 The variation of the compasse, from North to East [was] almost 13. degrees.
1613 S. Purchas Pilgrimage 49 Cabot first found out the variation of the Compasse.
1679 J. Moxon Math. made Easie 160 Variation of the Needle, the Turning or Deviation of the Needle in the Mariners Compass [etc.].
1687 A. Lovell tr. J. de Thévenot Trav. into Levant ii. 156 The variation of the Loadstone.
1774 M. Mackenzie Treat. Maritim Surv. 62 How to find the Sun's Azimuth, and from thence to find the Variation of the Needle.
1834 M. Somerville On Connexion Physical Sci. (1849) xxix. 338 The variation of the compass.
1849 G. C. Greenwell Gloss. Terms Coal Trade Northumberland & Durham 16 The diurnal variation of the needle being far from inconsiderable.
b. elliptical in the same sense.
ΘΚΠ
society > travel > travel by water > vessel, ship, or boat > equipment of vessel > navigational aids > [noun] > compass > variation
north-easting1555
variation of the compass, (lodestone,) or needle?a1560
norwesting1561
north-westing1571
variation1595
declination1625
magnetic variation1696
variation of the variation1706
magnetic declination1787
1595 J. Davis Seamans Secrets i. sig. C1 If your Compasse be good and without variation.
1597 W. Barlow Navigator's Supply sig. A2 By the Variation is vnderstood the difference in the Horizon betweene the true and the magneticall Meridian.
1627 J. Smith Sea Gram. ii. 12 There is also..a Compasse for the variation.
1669 S. Sturmy Mariners 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 shew the true North.
1703 W. Dampier Voy. New Holland iii. 100 I found that the Variation did not always increase or decrease in proportion to the Degrees of Longitude East or West.
1769 W. Falconer Universal Dict. Marine (at cited word) 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 T. H. Huxley Physiography (ed. 2) i. 10 The divergence of the position of the magnetic needle from the true north-and-south line is called its declination, or by nautical men, its variation.
c. variation of the variation (see last quot.).
ΘΚΠ
society > travel > travel by water > vessel, ship, or boat > equipment of vessel > navigational aids > [noun] > compass > variation
north-easting1555
variation of the compass, (lodestone,) or needle?a1560
norwesting1561
north-westing1571
variation1595
declination1625
magnetic variation1696
variation of the variation1706
magnetic declination1787
1706 Phillips's New World of Words (new ed.) Variation of the Variation, is so call'd, because the Variation of the Needle is not always the same in the same Place.
1839 H. M. Noad Course Eight Lect. 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 W. H. Smyth & E. Belcher 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.
ΘΚΠ
the world > matter > properties of materials > temperature > measurement of temperature > [noun] > instrument > variation of level of mercury
variation1719
the world > the earth > weather and the atmosphere > weather > study or science of weather > meteorological instruments > [noun] > barometer > height of mercury in > (proportional) rise and fall
variation1719
gradient1870
1719 J. Quincy Lexicon Physico-medicum (1722) 11 The greatest Variation of the Height of the Mercury being 3 Inches.
1748 B. Robins & R. Walter Voy. round World by Anson 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 D. Lardner Hand-bk. Nat. Philos.: Hydrostatics, Pneumatics, & Heat (new ed.) 168 A rise or fall of the mercury in the tube, within the usual limits of barometric variation.
7. Astronomy.
a. The libration of the moon; = libration n. 2.
ΘΚΠ
the world > the universe > planet > primary planet > moon > movement of moon > [noun] > libration
libration1670
evection1704
reflection1704
variation1704
1704 J. Harris Lexicon Technicum I Variation is, according to Tycho, the third Inequality in the Motion of the Moon.
1728 H. Pemberton View Sir I. Newton's Philos. 199 This inequality of the moon's motion about the earth is called by astronomers its variation.
1812 R. Woodhouse Elem. Treat. 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 S. Newcomb & E. S. Holden Astron. for Schools & Coll. 163 The disturbing action of the sun [upon the moon] produces a great number of the other inequalities, of which the largest are the evection and the variation.
b. (See quot. 1867.)
ΚΠ
1867 W. H. Smyth & E. Belcher 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. Mathematics.† a. = permutation n. 3b. Obsolete.
ΘΚΠ
the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements > changing order
permutation1645
transposition1664
alternation1685
transmutationa1690
variation1710
commutation1852
substitution1854
logical shift1946
1710 J. Harris Lexicon Technicum II Variation, or Permutation of Quantities, is the changing any number of given Quantities, with respect to their Places.
1728 E. Chambers Cycl. at 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.
ΘΚΠ
the world > relative properties > number > algebra > [noun] > expression > function > value or set of values of > change in values
variation1743
1743 W. Emerson Doctr. Fluxions 3 The Velocity, Variation, or Quickness of Increase (or Decrease) of any Fluxion is called the second Fluxion.
1810 R. Woodhouse Treat. Isoperimetrical Probl. ii. 23 If problems involving merely one property, the maximum, require the variation of two, and those involving two properties, the variation of three elements [etc.].
1843 Penny Cycl. XXVI. 136/2 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.
1847 Cambr. & Dublin Math. Jrnl. 1 264 We have, in this case, by Lagrange's theory of the variation of the arbitrary constants, the formulæ da/dt = [etc.].
1885 H. W. Watson & S. H. Burbury Math. Theory Electr. & Magn. I. 6 Then..u will, on arriving again at O, have assumed by continuous variation the value u0 + H.
1918 H. C. Plummer Introd. Treat. Dynamical Astron. xii. 134 This is the foundation of Lagrange's method of the variation of arbitrary constants.
1966 H. Pollard Math. Introd. Celestial Mech. iv. 91 We shall begin with the undisturbed system x̄1 = − x2, ẋ2 = k2x1, and apply the method of variation of parameters.
c. variation of curvature n. (see quot. 1842).
ΘΚΠ
the world > relative properties > number > geometry > curve > [noun] > change in
evolution1673
variation of curvaturea1727
a1727 I. Newton Method of Fluxions (1736) 76 The Inequability or Variation of Curvature is required at any Point of a Curve.
1842 G. W. 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.
ΘΚΠ
the world > relative properties > number > mathematical notation or symbol > [noun] > collection or sequence of
expression1796
type1891
variation1891
plussage1918
string1932
substring1947
1891 in Cent. Dict.
e. The difference between the values of a function at either end of a subinterval; the sum of such differences for all the non-overlapping subintervals into which a given interval is divided; the upper bound (if any) of this sum when all possible modes of subdividing the interval are considered.
ΘΚΠ
the world > relative properties > number > algebra > [noun] > expression > function > value or set of values of > difference or interval between values
period1879
oscillation1893
variation1905
1905 J. Pierpont Lect. Theory Functions Real Variables I. xii. 349 An important class of limited integrable functions is formed by functions with limited variation.
1911 Q. Jrnl. Pure & Appl. Math. 42 57 Although in forming the positive (negative) variation over (a, b) we considered all possible sets of non-overlapping intervals, we may without loss of generality confine ourselves to sets consisting of a finite number of intervals only.
1946 H. Jeffreys & B. S. Jeffreys Methods Math. Physics i. 23 The total variation is of interest since it is related to the condition for existence of a Stieltjes integral..and to the determination of the total length of a curve.
1971 E. R. Phillips Introd. Anal. & Integration Theory ix. 251 Let us assume that the set of nonnegative variations..is bounded from above.
9. Music. (See quot. 1730.)
ΘΚΠ
society > leisure > the arts > music > piece of music > section of piece of music > ornament > [noun] > flourish
passagec1570
division1590
flourish1646
variation1730
fioritura1841
floriation1895
1730 Short Treat. Harmony v. 34 There is another sort of Division called Variation, which may also be upon a Division.
10. Biology. Deviation or divergence in the structure, character, or function of an organism from those typical of or usual in the species or group.
ΘΚΠ
the world > life > biology > taxonomy > [noun] > variation from a type
variability1832
variation1859
1859 C. Darwin Origin of Species i. 11 There are many laws regulating variation, some few of which can be dimly seen.
1867–8 C. Lyell Princ. Geol. (ed. 10) II. iii. xliii. 488 If some modification of an organ, or instinct, be produced by what is called ‘Spontaneous Variation’.
1871 J. Tyndall Fragm. Sci. (1879) II. ix. 176 No naturalist could tell how far this variation could be carried.
1882 S. H. Vines tr. J. von Sachs Text-bk. Bot. (ed. 2) 925 The characters of many of these varieties are perfectly hereditary, and all the organs show the greatest degree of variation.
III. An instance of difference or change, and related uses.
11.
a. An instance of varying or changing; an alteration or change in something, esp. within certain limits.Sometimes in specific senses: cf. 5 – 10 above.
ΘΚΠ
the world > time > change > [noun] > change within limits, variation, or modification > instance of
discrepance1568
vary1600
variation1611
modification1669
1611 R. Cotgrave Dict. French & Eng. Tongues Muance, change, alteration; and particularly, a variation, or change of notes in singing.
1659 J. Pearson Expos. Creed (1839) 525 The natural course of variations in the creature.
1665 Philos. Trans. (Royal Soc.) 1 31 A Baroscope, or an instrument to show all the Minute Variations in the Pressure of the Air.
1719 D. Defoe Farther Adventures Robinson Crusoe 220 Variations of the Compass.
1758 S. Johnson Idler 24 June 89 The most variable of all variations, the changes of the weather.
1786 A. M. Bennett Juvenile Indiscretions IV. 231 They..contrived to fill a long summer's day, or winter's evening, by an agreeable variation of female amusements.
1832 H. Martineau Weal & Woe vii. 94 Seasons are sometimes stormy and our commerce liable to variations.
1844 Proc. Philol. Soc. 1 196 We may therefore be disposed to consider all marked variations of dialect as evidences of difference of date.
1874 tr. E. Lommel Nature of Light (ed. 4) 181 The variations of light and shade are alone visible.
b. A difference due to the introduction or intrusion of some change or alteration.
ΘΚΠ
the world > relative properties > relationship > variety > [noun] > a variant or variation
variance1497
vary1600
variousness1628
varying1628
variegation1668
modification1669
diversificationa1676
variation1699
variant1849
1699 R. Bentley Diss. Epist. Phalaris (new ed.) 36 We have the firmer ground to go upon for this little Variation.
1729 T. Innes Crit. Ess. Anc. Inhabitants Scotl. I. 130 Variations which the negligence, as well as the ignorance of transcribers is ordinarily the cause of.
1861 F. A. Paley Æschylus' Supplices (ed. 2) 842 (note) The other MSS. present only slight variations.
1869 H. F. Tozer Res. Highlands of 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 T. H. Huxley Physiography (ed. 2) 192 In different specimens..the lava exhibits great variations.
c. Biology. A slight departure or divergence from a type. (Cf. sense 10.)
ΘΚΠ
the world > life > biology > taxonomy > [noun] > variation from a type > slight variation
variation1835
1835 C. Lyell Princ. Geol. (ed. 4) II. iii. 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 C. Darwin Origin of Species 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 S. H. Vines tr. J. von Sachs Text-bk. Bot. (ed. 2) 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.
ΘΚΠ
the world > relative properties > kind or sort > [noun] > a kind, sort, or class > a variety or particular form
form1543
edition1598
variety1617
mode1661
version1835
variation1863
phylum1945
1863 T. H. Huxley Knowl. Org. Nature 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. (new ed.) 593 The Matadore Game..is a variation of All Fives.
1878 R. Browning La Saisiaz in La Saisiaz: Two Poets of Croisic 5 Try a variation of the game!
12. A deviation or departure from something.
ΘΚΠ
the world > action or operation > inaction > not doing > abstaining or refraining from action > [noun] > avoiding an action or condition > turning aside from a course of action
divagation1560
swaya1586
deviation1603
deflection1605
recess1605
recession1614
exit1615
non-residence1615
exorbitancy1623
exorbitancea1628
exorbitationa1628
aberrancy1646
aberrance1661
variationa1662
departurea1694
resilience1838
a1662 P. Heylyn Cyprianus Anglicus (1668) i. 223 It was best to take the English Liturgie, without any variation from it.
1702 Clarendon's Hist. Rebellion I. i. 66 Besides that any Variation from it..would make the Uniformity the less.
1782 J. Brown Compend. View Nat. & Revealed Relig. iii. ii. 246 There often befalls it a deforming variation from the original happy constitution.
1818 W. Cruise Digest Laws Eng. Real Prop. (ed. 2) I. 208 He did not think fit to make any variation from what was then determined.
13. Mathematics.
a. (Cf. sense 8a.)
ΚΠ
1728 E. Chambers Cycl. at 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. The amount by which some quantity changes in value, or the addition made to the quantity; esp. the change in a function when there is a small change in the variables or constituent functions of the function; calculus of variations, a form of calculus applicable to expressions or functions in which the law relating the quantities is liable to variation.In the calculus of variations the function concerned is usually an integral, and the aim is to find what relation between the variables in the integrand makes the integral a maximum or a minimum.
ΘΚΠ
the world > relative properties > number > calculus > [noun] > other forms of
calculus of variations1810
predicate calculus1938
the world > relative properties > number > algebra > [noun] > expression > function > value or set of values of > change in values > specific amount
increment1721
variation1810
1810 Woodhouse (title) A Treatise on Isoperimetrical Problems, and the Calculus of Variations.
1810 Woodhouse Treat. Isoperimetrical Problems iii. 45 The general form of these equations is, P.bg − Q.ci + R.dδ, dδ being a variation of the ordinate similar to the variations bg and ci.
1814 J. Toplis tr. P. S. de Laplace Treat. Analyt. Mech. ii. 46 Of all the curves along which a moving body, subjected to the forces P, Q, and R, can pass from one given point to another given point, it will describe that in which the variation of the integral ∫vds is nothing, and in which, consequently this integral is a minimum.
a1832 Encycl. Metrop. (1845) II. 209 To obtain the variation of a function of y we must write y + δy for y, and having expanded the new function according to the powers of δy, subtract from it the original function, and the first term of the difference will be the variation required.
1834 W. R. Hamilton in Philos. Trans. (Royal Soc.) 124 252 Although Lagrange and others, in treating of the motion of a system, have shown that the variation of this definite integral vanishes when the extreme coordinates and the constant H are given, they appear to have deduced from this result only the well known law of least action.
1855 D. Brewster Mem. Life I. Newton (new ed.) 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.
1934 W. V. Houston Princ. Math. Physics v. 56 The variation of the integral is defined as its value when α has the infinitesimal value δα, minus its value when α is zero.
1972 M. Kline Math. Thought xxiv. 578 By equating the variation of the integral to zero and by using a crude limiting process to transform the resulting difference equation, he obtained the differential equation which must be satisfied by the minimizing arc.
14.
a. Music. 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 plural, embellishments in an air for giving variety on repetition after playing it in its simple form.
ΘΚΠ
society > leisure > the arts > music > piece of music > section of piece of music > [noun] > theme > variation
figuration1597
winding1664
variation1786
double1806
paraphrase1880
1786 T. Busby Compl. Dict. Music Variations, 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 W. Scott Let. 3 Apr. (1934) VI. 169 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.
b. Ballet. A solo dance.
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society > leisure > dancing > ballet > [noun] > dance > types of
character dance1757
demi-caractère1776
ballabile1831
variation1912
1912 Dancing Times Aug. 420/2 [Grahn's] career was interrupted by an accident while rehearsing a variation which she was to perform at [a] benefit.
1948 Ballet Ann. 2 49 She attacks the formidable difficulties of the variation and adagio with an ease and confidence.
1980 ‘M. Fonteyn’ Magic of Dance 65 He makes the preparation for his ‘variation’, or solo, with utmost care and accuracy.
Compounds
C1. General attributive in sense 5b.
variation-chart n.
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society > travel > travel by water > vessel, ship, or boat > equipment of vessel > navigational aids > [noun] > chart > types of
plain chart1614
plane chart1696
variation-chart1727
1727 N. Bailey Universal Etymol. Eng. Dict. II Variation Chart, a Chart design'd by Dr. Halley.
1748 B. Robins & R. Walter Voy. round World by Anson Introd. sig. c4v A new variation-chart lately published.
1867 W. H. Smyth & E. Belcher Sailor's Word-bk. 710 The admiralty variation chart has been brought to great perfection.
variation compass n.
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society > travel > travel by water > vessel, ship, or boat > equipment of vessel > navigational aids > [noun] > compass > types of
paradoxal compass1558
steering compass1669
variation compass1669
correcting compass1821
telltale1828
pelorus1854
liquid compass1865
gyroscope-compass1909
gyro-compass1910
radio compass1912
gyro1914
gyroscopic compass1920
inductor compass1922
gyro-pilot1923
induction compass1925
astrocompass1942
flux gate compass1946
1669 S. Sturmy Mariners Mag. ii. vi. 67 The Use of the Quadrant and Variation-Compass.
1770 Philos. Trans. 1769 (Royal Soc.) 59 483 The variation compass..was..a very good one.
variation instrument n.
ΚΠ
1837 Lloyd in Rep. Brit. Assoc. VI. App. 21 The variation instrument will be placed in the magnetic meridian, with respect to the theodolite.
C2.
variation method n. Physics a method for finding an approximate solution to Schrödinger's equation by varying the trial solutions to find which gives the lowest value for the energy and is therefore closest to the true solution.
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the world > matter > physics > quantum theory > quantum mechanics > wave mechanics > [noun] > wave function > equation producing > method of finding solution to
variation method1935
WKB1935
1935 L. Pauling & E. B. Wilson Introd. Quantum Mech. vii. 182 The variation method is..very frequently used to obtain approximate wave functions as well as approximate energy values.
1960 McGraw-Hill Encycl. Sci. & Technol. XI. 145/2 The most useful of these methods, the variation method, has produced most of the important quantum-chemical concepts.
1974 P. W. Atkins Quanta 96/2 With these approximations in hand the variation method is applied to determine the best linear combination of atomic π-orbitals to describe the structure of the molecule.
variation order n. an order authorizing a change in an original order or contract (see quots.).
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society > law > administration of justice > court proceedings or procedure > judging > [noun] > judgement or decision of court > decision in writing or court order > other court orders
restraining order1780
administration order1848
restraint order1883
fraud order1905
possession order1920
variation order1940
Anton Piller order1978
1940 Chambers's Techn. Dict. 886 Variation order,..a document giving authority for some alteration in work being done under contract.
1975 E. B. Ceadel in Barr & Line Essays on Information & Libraries iv. 58 Where a change is made in the contract arrangements, it is listed by the architect as a variation order, which is subsequently costed by the quantity surveyors.
1977 Daily Tel. 19 Nov. 3/2 An order was prepared..requiring him to leave by Nov. 17... The Home Secretary..had considered whether, instead of issuing a ‘variation order’, he should proceed under another provision of the Immigration Act 1971 with a view to deportation.
variation principle n. Physics the principle (employed in the variation method) that the energy corresponding to an arbitrary wave function cannot be less than the actual lowest energy of the system under consideration.
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the world > matter > physics > quantum theory > quantum mechanics > wave mechanics > [noun] > wave function > equation producing > method of finding solution to > principle employed in
variation principle1923
1923 Physical Rev. 22 547 This variation principle includes formally in a single equation the results of classical dynamics and the Sommerfeld quantum conditions.
1975 H. F. Hameka Quantum Theory Chem. Bond i. 28 We shall discuss the two methods of approximation that are most widely used in quantum chemistry, namely the variation principle and perturbation theory.
This entry has not yet been fully updated (first published 1916; most recently modified version published online June 2022).
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