单词 | variation |
释义 | variationn. I. Senses relating to discrepancy, dissension, or doubt. 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. 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. ΘΚΠ 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. ΘΚΠ 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. ΘΚΠ 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. ΘΚΠ 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.). ΘΚΠ 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. ΘΚΠ 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). < n.c1405 |
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