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单词 residual
释义 I. residual, n.|rɪˈzɪdjuːəl|
[See next.]
1. Math.
a. A residual quantity.
1557Recorde Whetst. V j b, We maie comprehende vnder the same name..all other residualles Cossike, whiche be made by subtraction.Ibid. P p 4, The nombers..that be compounde with - be named Residualles.1673Kersey Algebra ii. ix. I. 239 When the Root of a Residual is to be added unto, or subtracted from the Root of its correspondent Binomial.1764Landen Residual Analysis Pref. 3 Such quantities, and algebraic expressions, as by Mathematicians are denominated residuals.1796Stokes in Trans. R. Irish Acad. (1797) VI. 229 It is expedient to remove the surds out of the denominator by multiplication; this is usually done by the multiplication of the demoninator taken as a binomial or residual.1841Penny Cycl. XIX. 413/1 Residual, an expression which gives the remainder of a subtraction.
b. (See quots.)
1867Sylvester in Educ. Times May 42 A residuum of the second or any even order in such series, may be made to consist of a single point, which I call residual of the original µ points.1873Salmon Higher Plane Curves (ed. 2) 136 If two systems of points α, β, together make up the complete intersection with the cubic of a curve of any order, one of these systems is said to be the residual of the other.
c. The difference between an observed or measured value of a quantity and its true, theoretical, or notional value.
1868J. C. Watson Theoret. Astron. vii. 370 In the case of a limited number of observed values of x, the residuals given by comparing the arithmetical mean with the several observations will not..give the true errors.1872Mem. R. Astron. Soc. XXXIX. 100 The usual treatment of equations, by rendering a minimum the sum of the squares of the residuals, not only assumes equal weights for the observations, but also that positive and negative errors are equally probable.1906Wright & Hayford Adjustment of Observations (ed. 2) ii. 12 The sum of the positive residuals is equal to the sum of the negative residuals.1923Glazebrook Dict. Appl. Physics III. 647/2 The distribution of 174 residuals in a certain case is shown in Fig. 1. The residuals are the differences between observed and calculated monthly sea levels at three tidal observatories.1932Human Biol. IV. 478 Departures from the average arm girth and calf girth of children of the given four skeletal dimensions, we have termed residuals and have regarded them as indices of muscular development.1967Oceanogr. & Marine Biol. V. 12 When the residuals at a port are evaluated at say hourly intervals and then plotted against time, a graphical representation of the variations in the surge component at that port is obtained.1972Nature 17 Mar. 96/1 A major contribution to understanding of the seismic velocity variation necessarily comes from travel time residuals (these are differences between observed arrival times of P-waves at seismometers and the theoretical arrival time from a standard set of tables).
2. a. A remainder; an amount still remaining after the main part is subtracted or accounted for.
1860Maury Phys. Geogr. ix. §445 These feeble forces in the water received one of the quantities of small value—residuals of compensation—with which the astronomer has to deal.1878Newcomb Pop. Astron. iii. iv. 338 The moon..is always held in that position by a minute residual of the earth's attraction.1967Economist 28 Oct. p. xxxiii/2 According to the recorded items on the balance of payments Sweden should by now be dead broke. The one thing that has kept it afloat is an unexplained positive ‘residual’ in the balance of payments.1973‘E. McBain’ Let's hear It iii. 42 His first impression was one of total harmony... Her face and figure came as residuals to his brief course in art appreciation.
b. The part of a gravity anomaly or magnetic anomaly that remains after subtraction of the regional. Also attrib.
1949Geophysics XIV. 45 Since the density of salt is less than that of the surrounding sediments, its residual is negative.Ibid. 516 Residual maps have been used extensively by geophysicists to bring into focus local features which tend to be obscured by the broad features of the field.1965Krumbein & Graybill Introd. Statistical Models in Geol. xiii. 325 Many residual maps contain geological information of value in exploration for natural resources.1978Nature 13 July 146/1 After removing the mean values we projected the residuals on to profiles transverse and parallel to the plate motion and averaged the values over 0·5° intervals.
3. A substance or product of the nature of a residuum. Also transf.
1885G. H. Taylor Pelv. & Hern. Therap. 29 The blood, with its residuals and products of waste.1886York Her. 6 Aug. 3/4 Gas-lime was another residual, and when used properly was a most valuable fertiliser.1899Daily News 24 June 4/1 The casual docker is often a residual—the driftwood of society.
4. A royalty paid to an actor, musician, etc., for a repeat of a play, television commercial, etc.
1966Guardian 14 May 7/1 The ‘residuals’, or BBC fringe benefits, lie chiefly in adoption by the Transcription Service.1971Daily Tel. 25 Mar. 21/4 He [sc. Frank Sinatra] will continue to receive money from..record royalties, residuals of his television programmes and a share in the profits of his films.1972D. Ramsay Little Murder Music 78 ‘What makes a jingle date such an important affair?.. The money?’ ‘And how. I could wind up making more in residuals alone.’1977Rolling Stone 13 Jan. 19/1, I love doing jingles because I get residuals.
5. Geomorphol. A portion of rocky or high ground remaining after erosion.
1968R. W. Fairbridge Encycl. Geomorphol. 587/1 Normal fluvial erosion begins to be established, and eventually, only residuals of limestone..are left standing.1970R. J. Small Study of Landforms v. 162 Above the peneplain, a few isolated hills..would remain. Such residuals were referred to by Davis as ‘monadnocks’.
II. residual, a.|rɪˈzɪdjuːəl|
[ad. med. or mod.L. *residuāl-is, f. residuum. Cf. It. residuale, F. résiduel.]
1. Math.
a. Resulting from, formed by, the subtraction of one quantity from another.
1570Billingsley Euclid x. prop. 73. 283 If from a rationall line be taken away a rationall line commensurable in power onely to the whole line: the residue is an irrationall line, and is called a residuall line.1673Kersey Algebra ii. i. I. 138 The Powers from the Residual Root a - e differ only in the signs + and - from like Powers formed from the Binomial Root a + e.1700Moxon Math. Dict. 142 Residual Figure, the remaining Figure after Subtraction of a less from a greater.1704J. Harris Lex. Techn. I, Residual Root, in Mathematicks, is one composed of two Parts or Members only connected together with the Sign -.1734J. Ward Introd. Math. (ed. 6) 172 From thence will arise Surds either Binomial, or Residual.1798Hutton Course Math. (1827) I. 167 A Residual Quantity, is a binomial having one of the terms negative. As a - 2b.
b. residual analysis or residual calculus (see quots.).
1758Landen Disc. Residual Analysis 5 Which method I call the Residual Analysis; because, in all the enquiries wherein it is made use of, the conclusions are obtained by means of residual quantities.1801Encycl. Brit. (ed. 3) Suppl. II. 401/1 Residual analysis, a calculus proposed by the inventor, Mr. Landen, as a substitute for the method of fluxions. [Account follows.]1890Cent. Dict. s.v., Residual calculus, the calculus of residuals or residues.
2. a. Remaining; still left; left over. residual legatee = residuary legatee s.v. residuary a. 1 b; also fig.; residual powers = residuary powers s.v. residuary a. 2 b.
1609[Bp. W. Barlow] Answ. Nameless Cath. 73 Whose Manes, that is, whose residuall memorie, will both Manare and Manere by diffusion and duration.1801W. Taylor in Monthly Mag. XII. 576 It becomes the few residual friends of toleration and humanity to rally with closer union.1822T. Taylor Apuleius 172 The remaining space of the year is completed by the residual months.1860Tyndall Glac. 124 The sky was now for the most part overcast, but through the residual blue spaces the sun at intervals poured light.1881Westcott & Hort Grk. N.T. Introd. §184 The residual Pre-Syrian text which is neither Western nor Alexandrian.1919G. B. Shaw in Irish Statesman 25 Oct. 428/1 When the enfranchisement of the Dominions began with Canada, the question on which freedom depends: namely, which party is to have residual powers, was hardly raised. Those were early days for democracy; and the residual powers were left technically to England.1963Listener 21 Feb. 334/1 The Liberals cash in..by claiming to be the residual legatees of the radical tradition.1967Boston Sunday Herald 30 Apr. iii. 10/1 A specially interesting use of this guide's table of ‘Life Expectancy’ and ‘residual values’ of textiles is in evaluating garments and other textile items donated to charity.1969F. Halliday in Cockburn & Blackburn Student Power 296 The dominant ‘mainstream’ faction..was labelled as ‘Trotskyite’, a residual term meaining that the group was Marxist but opposed to the official Japan Communist Party line.1976National Observer (U.S.) 3 July 8/6 ‘There shouldn't be any wholesale dumping of what we think are good risks into the residual market,’ says the Insurance Information Institute spokesman.1979Jrnl. R. Soc. Arts Jan. 97/2 Alice was the residual legatee and executrix.
b. In the physical sciences: Left as a residuum, esp. at the end of some process.
1757Phil. Trans. L. 351 These..serve to bring back the residual blood from the tumors.1799Sir H. Davy in Beddoes Contrib. Phys. & Med. Knowl. 187 More hydrogen and residual carbon.1807Phil. Trans. XCVII. 252 The united quantities give the sum of the residual gas.1871B. Stewart Heat (ed. 2) §387 The pressure of the residual air which remained in the vacuum chamber.1896Pop. Sci. Jrnl. L. 242 The heat referred to is mainly..the residual heat of a cooling globe.
c. Left unexplained or uncorrected.
1830Herschel Study Nat. Phil. ii. vi. §158 Leaving, as it were, a residual phenomenon to be explained.Ibid., The residual facts are constantly appearing in the form of phenomena altogether new.1867J. Hogg Microsc. i. ii. 58 There will always be residual terms in the general expression for the aberration.1871B. Stewart Heat (ed. 2) §141 These irregularities..are merely due to the residual error in our observations.
d. Applied to magnetism which is retained after the removal of the magnetizing force or in the absence of a magnetizing current.
1837Phil. Mag. X. 195 If the interrupted keeper be applied to a compound magnet, it will be attracted only with a force equal to the quantity of residual magnetism, which being very small the attraction will be comparatively feeble.1874Tyer's Block Telegraph & Electric Locking Signals (ed. 5) 14 There is also..an electro-magnet fitted with ‘homs’ or ‘keepers’.., so arranged as to..retain for an indefinite period the residual magnetism produced on the passage of each signal.1886[see retentiveness 6].1902Encycl. Brit. XXX. 430/2 If a bar of hard steel is placed in a strong magnetic field, a certain intensity of magnetization is induced in the bar, but when the strength of the field is afterward reduced to zero, the magnetization does not entirely disappear. That portion which is permanently retained, and which may amount to considerably more than one-half, is called the residual magnetization.1912, etc. [see retentivity 1].1917, etc. [see remanence 3].
e. Applied to the small charge which some capacitors remain capable of delivering after ‘discharge’.
1838Faraday in Phil. Trans. R. Soc. CXXVIII. 24 It is the assumption for a time of this charged state of the glass between the coatings in the Leyden jar, which gives origin to a well-known phenomenon, usually referred to the diffusion of electricity over the uncoated portion of the glass, namely, the residual charge.1878Encycl. Brit. VIII. 39/2 Kohlrausch called attention to the close analogy between the residual discharge and the ‘elastic recovery’..of strained bodies... The instantaneous strain which follows the application of a stress is analogous to the initial charge of the jar, and the gradually increasing strain which follows to the gradual formation of the latent or residual charge.1921T. F. Wall Electr. Engin. iv. 62 The successive charges after the first discharge are known as residual charges.1938H. G. Mitchell Textbk. Electr. iv. 64 The residual discharge of the condenser can easily be explained if we assume that the charge penetrates the glass and cannot all reach the conducting plates when these are connected.
f. Physical Geogr. Applied to a deposit or feature formed in situ by the weathering of rock, and to a soil largely composed of such material.
1895Geogr. Jrnl. V. 140 Most of the peneplains that I have examined..still possess residual elevations,..evidently to be regarded as unconsumed remnants of the denudation of the former cycle.1906E. W. Hilgard Soils i. 11 When soils have been formed without removal from the site of the original rock, by simple weathering, they are designated as sedentary, or residual soils.1933[see peneplain n.].1937Wooldridge & Morgan Physical Basis Geogr. xi. 150 While its origin has given rise to considerable controversy, all are agreed that it [sc. laterite] is essentially a residual deposit.1944A. Holmes Princ. Physical Geol. viii. 119 Ultimately the angular block is transformed into an onion-like structure of concentric shells of rusty and thoroughly rotted residual material.1954W. D. Thornbury Princ. Geomorphol. iv. 74 Soils were commonly divided into two major groups, residual and transported. Residual soils were classified according to the type of rock from which they were derived.1972J. G. Cruickshank Soil Geogr. ii. 57 Parent materials may be classified by their mode of formation as follows: 1 Weathered rock in place which produces residual soils.
g. residual stress, stress present in an object in the absence of any external load or force.
1931A. Nádai Plasticity xxxviii. 259 Stresses of this kind, remaining after partial plastic flow, may be called residual stresses.1958Engineering 18 Apr. 498/1 The operation of welding gives rise to residual stresses, i.e. stresses which exist independently of the external loading.1976Lindberg & Braton Welding & Other Joining Processes xii. 454 A weldment heated to a temperature at which the yield strength is low..will relieve the residual stresses and increase fatigue life.

Add: Hence reˈsidually adv., to a residual extent; in a residual degree.
1957Proc. London Math. Soc. VII. 29 Mal'cev..proved an even more general result, giving sufficient conditions, and also necessary ones, for a free product of residually nilpotent groups to be itself residually nilpotent.1963Proc. Cambr. Philos. Soc. LIX. 555 The theorem of Gruenberg that a free product of residually finite groups is itself residually finite.1980Christian Science Monitor 24 Jan. 7/2 The council's powers and responsibilities would fall into three categories: those exercised unilaterally, those ‘shared’ with Israel, and those to remain ‘residually’ with Israel.1987A. S. Byatt Sugar 114 Their country, the guide book said, was Confucian, Buddhist, Catholic, residually shamanistic.
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