reciprocal, a. and n.
(rɪˈsɪprəkəl)
Also 6–7 -all.
[f. L. reciproc-us reciproque + -al1.]
A. adj.
† 1. a. Having, or of the nature of, an alternate backward and forward motion. (Said esp. of tides.) Obs.
Used by Chapman Iliad xviii. 355 to render Gr. ἀψόρροος.
| 1601 Holland Pliny II. 400 Amid the reciprocall tides of the sea, ebbing and flowing in their alternatiue turnes. 1631 Milton Epit. Hobson ii. 30 Obedient to the Moon he spent his date In cours reciprocal. 1662 Hobbes Seven Prob. Wks. 1845 VII. 26 The reciprocal and contrary motions of the two pieces of wood. 1726 tr. Gregory's Elem. Astron. vi. 843 The reciprocal Tide arising from the four moons [of Jupiter]..is various and uncertain. |
† b. Of actions: Alternate, alternating. Obs.
| 1667 Hooke in Phil. Trans. II. 539 The Dog being kept alive by the Reciprocal blowing up of his Lungs with Bellowes, and they suffered to subside. 1758 Borlase Nat. Hist. Cornwall 283 The pigeon (whose reciprocal contraction and dilation in those parts is well known). |
† c. (See quot.) Obs.— 0
| 1727–41 Chambers Cycl. s.v., Reciprocal, in poetry, is applied to verses which run the same both backwards and forwards; called also recurrents. |
2. a. Of the nature of, pertaining to, a return made for something; given, felt, shown, etc., in return; correspondent.
| 1596 Drayton Legends iv. 523 And shew in how reciprocall a sort My thankes did with his Courtesie agree. 1647 N. Bacon Disc. Govt. Eng. i. lviii. (1739) 107 After that Royalty sprung up, the influence thereof upon them exhaled..a reciprocal interest back again. 1711 Harley in Ellis Orig. Lett. Ser. ii. IV. 266 This the Queen has done without any reciprocal obligation or promise from her Majesty to France. 1770 Junius' Lett. xxxviii. 187 He had a right to expect from them a reciprocal demonstration of firmness. 1883 H. Drummond Nat. Law in Spir. W. Pref. (1884) 22 No science contributes to another without receiving a reciprocal benefit. |
b. Existing on both sides; felt or shared by both parties; mutual. (Cf. 4 a.)
reciprocal defence, in Fortification, a form of flanking defence (Voyle & Stevenson Milit. Dict. 1876).
| 1579 Lyly Euphues (Arb.) 130 If the Mother nourysh the childe, and the childe sucke the Mother, that there be as it were a relation and reciprocall order of affection. 1607 J. Norden Surv. Dial. i. 37, I know there is a kind of reciprocall bond of duty each to the other, and may be broken of either side. 1652 Earl of Monmouth tr. Bentivoglio's Hist. Relat. 66 Spain and..Flanders..may be said to joyn in one common and reciprocall Government. 1751 Johnson Rambler No. 166 ¶7 Kindness is generally reciprocal. 1785 J. Trusler Mod. Times III. 106 We were as happy as matrimony, reciprocal affection, and good circumstances could render us. 1804 Wellington in Gurw. Desp. III. 157 This treaty of general defensive alliance, for the reciprocal protection of their respective territories. 1879 Farrar St. Paul (1883) 636 A reciprocal recognition of honest convictions. |
3. a. Inversely correspondent or related; correlative, complementary; † opposed. Now chiefly Math. (cf. 4 d).
| 1570 Billingsley Euclid xi. xxxiv. 347 In equall Parallelipipedons the bases are reciprokall to their altitudes. 1632 Lithgow Trav. x. 488 With shrew'd Acerbious speech, you Anathematize My will Reciprocall to yours. 1690 Locke Hum. Und. ii. xxv. §2 Relative Terms that have others answering them with a reciprocal Intimation, as Father and Son,..Cause and Effect. 1852 Mulcahy Princ. Mod. Geom. 39 This is the required reciprocal theorem. 1860 Tyndall Glac. i. xv. 103, I first thought it [a chamois] was a man... It evidently made the reciprocal mistake to my own. 1861 Ferrers Trilinear Co-ordinates vi. 108 Hence, if the Conic..be a parabola, the point (a, b, c) must lie in the reciprocal Conic. |
b. Math. Based upon an inverse relationship.
reciprocal equation, reciprocal proportion, reciprocal ratio (see quots.). reciprocal spiral, a spiral in which the radius vector varies inversely as the angle through which it is turned.
| 1823 Mitchell Dict. Math. & Phys. Sci. 411 *Reciprocal equations are those which contain several pairs of roots, which are the reciprocal of each other. |
| 1656 tr. Hobbes' Elem. Philos. (1839) 171 If there be three continual proportionals, and again, three other continual proportions, which have the same middle term, their extremes will be in *reciprocal proportion. 1709 J. Ward Introd. Math. i. vii. §2 If More require Less, or Less require More..then the Terms will be in Reciprocal Proportion. 1823 Mitchell Dict. Math. & Phys. Sci. 412 Reciprocal proportion is when the reciprocals of the two last terms have the same ratio as the quantities of the first terms. |
| Ibid., *Reciprocal ratio is the ratio of the reciprocals of two quantities. |
| 1743 Emerson Fluxions ii. 144 To draw a Tangent to the *reciprocal spiral. 1886 Carr Synopsis Math. I. ii. 725 The Hyperbolic or Reciprocal Spiral. |
c. reciprocal innervation or reciprocal inhibition (Physiol.): an arrangement of nerve stimulation as a result of which contraction of one muscle or group of muscles to produce movement is accompanied by simultaneous inhibition of an antagonistic muscle or group of muscles, whose contraction would tend to produce the opposite movement.
| 1897 C. S. Sherrington in Jrnl. Physiol. XXII. 327 It has revealed to me an almost unexpectedly significant number of examples of depressor effect generally, perhaps always, in combination with pressor effects, that is to say, in the form of reciprocal innervations. 1906 ― Integrative Action Nervous Syst. iii. 83 (heading) Reciprocal inhibition. 1942 Johnston & Whillis Gray's Anat. (ed. 28) 942 Experimental evidence shows that all the fundamental reflexes of posture.., the reciprocal innervation of antagonists, and the elementary combination of synergists, can still occur without the cerebellum. 1960 W. B. Crow Synopsis of Biol. lxv. 445 Neurons connect up two or more efferent paths so that two or more muscles come into action together, or one is inhibited when another comes into operation (reciprocal innervation). 1971 Sci. Amer. Aug. 75/1 One principle Sherrington discovered was ‘reciprocal innervation’. 1977 G. H. Sage Introd. Motor Behav. (ed. 2) viii. 157 The flexion reflex consists of a contraction of the flexor muscles while reciprocal connections with the antagonistic extensor muscles cause reciprocal inhibition. |
d. Genetics. Of each of a pair of crosses: complementary to another in that the male parent in each is of the same kind as the female parent in the other.
| 1902 W. Bateson Rep. Evolution Comm. R. Soc. I. 21 Reciprocal crosses..showed clearly that of the two pairs of antagonistic characters, the violet colour is dominant. 1909 ― Mendel's Princ. Heredity xi. 203 When the cross is in the form pure single {female} × double-throwing {male}, all the F1 plants give a mixture of doubles and singles in F2; but when the reciprocal cross is made, namely double-thrower used as {female} × pure single used as {male}, it is found that the F1 plants are of two kinds. 1948 H. P. Riley Genetics & Cytogenetics vi. 88 The cross curved × wild type is known technically as the reciprocal of the cross wild type × curved. Ibid. vii. 96 When genes are in autosomes reciprocal crosses normally give identical results, but when genes located in the X chromosome are dealt with, the results of reciprocal crosses are different. 1971 D. J. Cove Genetics viii. 111 If some genetical information is also carried in the cytoplasm, the unequal contribution of cytoplasm to the zygote by the two gametes should provide a way of detecting it. The technique used for this is the reciprocal cross. |
e. Physics. In the names of quantities defined as reciprocals of standard physical units, as reciprocal centimetre, reciprocal ohm, reciprocal second (see quots.).
| 1934 H. E. White Introd. Atomic Spectra i. 6 Wave numbers..are units with the dimensions of reciprocal centimeters, abbreviated cm-1. 1960 Brand & Speakman Molecular Struct. i. 8 The passage of energy between matter and radiation occurs in quanta of magnitude ΔΕ, where ΔΕ = hν. When ΔΕ is expressed in terms of the erg and ν as reciprocal seconds, Planck's constant, h, has the value 6.6256 × 10-27 erg sec. 1960 A. D. Cross Introd. Pract. Infra-Red Spectroscopy i. 2 Band positions are quoted in units of wave number (ν) which are expressed in reciprocal centimetres (cm-1)... However, the true unit of frequency (ν) is given in reciprocal seconds (sec-1). 1978 Sci. Amer. Dec. 66/1 The maximum conductivity is somewhat greater than 2,000 reciprocal ohms per centimeter (equivalent to a resistivity of less than .0005 ohm per centimeter). |
f. reciprocal course: a path followed by a person or craft which is opposite in direction to one with which it stands in relation, e.g., to the one desired or the one which was followed immediately before.
| 1946 Happy Landings (Air Ministry) July 5/3 The immediate action is to turn on the reciprocal course. 1958 ‘N. Shute’ Rainbow & Rose ii. 57, I..flew out to sea..on the reciprocal course, and then turned in again and flew towards the coast on 110°. 1961 B. Fergusson Watery Maze ii. 49 All these craft had lately been ‘degaussed’..with unexpected effects on their compasses, and some of the shoreward-bound parties were steering on a reciprocal course. |
4. Corresponding or answering to each other, as being either similar or complementary. a. of acts, feelings, duties, etc. (Cf. 2 b.)
| 1605 Shakes. Lear iv. vi. 267 Let our reciprocall vowes be remembred. 1632 Lithgow Trav. ix. 405 Leauing our reciprocall loues behind vs, wee diuided our bodies East and West. 1741 Richardson Pamela (1824) I. 210 The highest civilities..and reciprocal good wishes all around. 1781 Gibbon Decl. & F. xix. II. 134 After so many reciprocal injuries, Gallus had reason to fear and to distrust. 1856 Froude Hist. Eng. (1858) II. vii. 138 Their relations were already embittered by many reciprocal acts of hostility. 1872 Yeats Growth Comm. 160 Barcelona and Cadiz..also entered into like alliances for reciprocal privileges. |
† b. of things or persons sent by one party to another. Obs.
| 1633 Prynne 1st Pt. Histrio-m. 20 Pagans, who Consecrated this day,..and sent reciprocall Newyeeres-gifts to their friends vpon it. 1641 Earl of Monmouth tr. Biondi's Civil Warres iii. 142 Reciprocall Embassadors..had already accorded all differences with the Dolphin. 1716 M. Davies Athen. Brit. II. 30 Some of King Henry the 8th's and Queen Anne Bolen's reciprocal letters were printed. 1783 Prelim. Art. Peace w. Spain viii. 21 The necessary orders shall be sent by each of the high Contracting parties, with reciprocal passports for the Ships. |
c. of things in themselves. Somewhat rare.
| 1661 Boyle Style of Script. (1675) 75 The Books of Scripture illustrate and expound each other: Genesis and the Apocalypse are in some things reciprocal commentaries. 1718 Freethinker No. 40 ¶5 Allegiance and Protection are reciprocal in all Countries. 1839–48 Bailey Festus xxv. 312 The world and man are just reciprocal Yet contrary. 1884 tr. Lotze's Metaph. 27 Each will continue to exercise influences on others or to be affected by their influence. These reciprocal agencies [etc.]. |
d. Math. in reciprocal curves, reciprocal figures, reciprocal polars, reciprocal quantities, reciprocal triangles, etc. (Cf. quots.)
| 1570 Billingsley Euclid vi. def. ii. 153 b, Reciprocall figures are those, when the termes of proportion are both antecedentes and consequentes in either figure. 1797 Encycl. Brit. (ed. 3) XVI. 29/1 Reciprocal, in mathematics, is applied to quantities which multiplied together produce unity. 1848 Solutions Camb. Senate-Ho. Problems (1851) 119 This theorem may also be proved by the method of Reciprocal Polars. 1852 Mulcahy Princ. Mod. Geom. 145 The theory of reciprocal curves on the sphere. 1857 Cayley in Q. Jrnl. Math. 7 On a Theorem relating to Reciprocal Triangles. |
† 5. a. Convertible, synonymous, equivalent in meaning or force. Obs.
| 1621 Burton Anat. Mel. To Rdr. (1676) 26 Aristotle, in his Ethicks, holds..to be wise and happy are reciprocal termes. 1681 R. L'Estrange Tully's Offices 139 Make Profit and Honesty Reciprocal. 1733 Shaw tr. Bacon's De Sapientia, Sphinx (1803) 61 note, Knowledge and power are reciprocal. |
† b. Logic. = convertible a. 1 b. Obs.
| 1697 tr. Burgersdicius his Logic i. xxxi. 123 Terms are said to be Reciprocal, when there may be a Conversion of the Predicate into the Place of the Subject, and on the contrary. 1725 Watts Logic ii. ii. §3 These are the Propositions which are properly convertible, and they are called reciprocal Propositions. 1727–41 Chambers Cycl. s.v. Theorem, Reciprocal Theorem is one whose converse is true. |
6. Gram. Of pronouns and verbs, or their signification: a. Reflexive.
| 1611 Florio Rules Ital. Tongue in Dict. 631 It [si] makes the Verbe to which it is affixed to be sometimes directly Actiue..and other times Passiue or Reciprocall. 1727 Boyer Dict. Royal II. s.v., A Pronoun or a Verb reciprocal. 1766 Del Pino New Span. Gram. 27 The two first serve for the Active, Neuter, and Reciprocal Verbs. Ibid. 171 Estarse, reciprocal, signifies to stay long. 1797 Encycl. Brit. (ed. 3) VIII. 50/2 The word self subjoined to a personal pronoun forms also the reciprocal pronoun. 1837 G. Phillips Syriac Gram. 41 The Demonstrative pronouns..become reciprocal by being joined to the personal pronouns. Ibid. 114 The ordinary method of expressing a reciprocal or reflexive sense. 1879 Lewis & Short Lat. Dict. s.v. Reciprocus, A reciprocal pronoun, as sibi, se. |
b. Expressing mutual action or relationship.
| [1727–41 Chambers Cycl. s.v., The abbé de Dangeau defines reciprocal verbs to be those whose nominative is plural, and denotes persons acting mutually on one another.] 1844 Latham in Proc. Philolog. Soc. I. 232 (heading) On the Reciprocal Pronouns, and on the Reciprocal Power of the Reflective Verb. Ibid., Too often the terms Reciprocal and Reflective have been made synonymous. 1872 Morris Eng. Accidence 150 One another, each other, are sometimes called reciprocal pronouns. |
7. Phonetics. reciprocal assimilation (see quot. 1972).
| 1915 G. Noël-Armfield General Phonetics ix. 32 If the adjacent sounds act upon each other more or less equally the influence may be called reciprocal. Ibid. 33 Reciprocal assimilation is common in diphthongs. 1939 L. H. Gray Foundations Lang. iii. 68 It [sc. assimilation] may be reciprocal, when the modification is mutual. 1972 Hartmann & Stork Dict. Lang. & Linguistics 21/2 If two sounds influence each other mutually the term reciprocal assimilation (alternative term: coalescent assimilation) is used, e.g. English seven pronounced as [seb{mfrown}] where the labio-dental [v] has become bilabial [b] which in turn influences the alveolar nasal [n] changing it to the bilabial nasal [m]. |
B. n.
† 1. One who is sent back. Obs. rare—1.
| 1616 Chapman Homer's Hymn Apollo 734 No more Yee must be made, your own Reciprocalls To your lou'd Cittie. |
2. A thing corresponding in some way to another; a return, equivalent, counterpart, etc.
| 1570 in Digges Compl. Ambass. (1655) 12 Offering to deliver unto her the reciprocal of our part under our Great Seal. 1622 Bacon Hen. VII (1876) 205 After he had received the King of Castile into the fraternity of the Garter, and for a reciprocal had his son the prince admitted to the order of the Golden Fleece. 1626 ― Sylva §329 Corruption is a Reciprocall to Generation. 1750 Chesterfield Lett. (1792) III. 42 Pleasure is a necessary reciprocal; no one feels who does not at the same time give it. 1852 Mulcahy Princ. Mod. Geom. 37 By means of the theory of polars, every Proposition..leads immediately to another, called its reciprocal. 1885 J. Martineau Types Eth. Th. (1886) II. i. i. 31 The two cognitions are, therefore, independent reciprocals. |
3. Gram. † a. A reflexive verb. Obs.
| 1659 Hammond On Ps. lxxvi. 5 The reciprocal from [šll] prædatus est. 1766 Del Pino New Span. Gram. 177 Verbs Passive, and the greatest part of the Reciprocals, require the Ablative. |
b. A noun, pronoun, or verb that expresses mutual action or relationship.
| 1961 R. B. Long Sentence & its Parts xvi. 357 Reciprocals can refer only to plural nouns, pronouns, or nounal units; reflexives can refer to singulars as well. 1965 Canad. Jrnl. Linguistics Spring 175 Especially reflexives, reciprocals, iteratives, passives, and the Eyak progressive almost always take the vocalic forms. |
4. Math. a. A function or expression so related to another that their product is unity; the inverse.
| 1782 Hutton in Phil. Trans. LXXIV. 33 The reciprocal of the cosine will be the secant. 1797 Encycl. Brit. (ed. 3) XVI. 29/1 Likewise 1 / x is said to be the reciprocal of x, which is again the reciprocal of 1 / x . 1831 Brewster Optics xvii. 151 The radius O a of the ellipse will be what is called the reciprocal of the index of refraction at a. 1882 Minchin Unipl. Kinemat. 185 Their combined resistance is found from the fact that its reciprocal is equal to the sum of the reciprocals of their separate resistances. |
b. polar reciprocal: (see quot. 1885).
| 1852 Mulcahy Princ. Mod. Geom. 38 The two figures are, therefore, properly called polar reciprocals. 1885 C. Leudesdorf Cremona's Proj. Geom. 240 Two curves..such that each is the locus of the poles of the tangents of the other, and at the same time also the envelope of the polars of the points of the other, are said to be polar reciprocals one of the other with respect to the auxiliary conic. |