[a. F. continuité (16th c.), ad. L. continuitāt-em, f. continu-us: see -ITY.] The state or quality of being continuous.
1. Of material things: The state or quality of being uninterrupted in extent or substance, of having no interstices or breaks; uninterrupted connection of parts; connectedness, unbrokenness.
1543. [see 5].
1570. Dee, Math. Pref., D j. Fyre and Ayre … will descend, when … their Continuitie should be dissolued.
1607. Topsell, Four-f. Beasts (1673), 38. Inflaming the body, loosing the continuity of the parts.
1615. Crooke, Body of Man, 307. Now there is no continuity betweene the vmbilicall veine and the hollow veine.
1646. Sir T. Browne, Pseud. Ep., II. i. 55. Continuity of parts is the cause of perspicuity.
1727–51. Chambers, Cycl., Continuity is usually defined, among schoolmen, the immediate cohesion of parts in the same quantum.
1804. Wellington, in Gurw., Disp., III. 59. The continuity of the frontier.
1813. Bakewell, Introd. Geol. (1815), 52. Sometimes the continuity of rocks and strata is … broken.
1855. Bain, Senses & Int., I. ii. § 17 (1864), 46. The continuity of the cord with the brain is necessary.
2. Of immaterial things, actions, processes, etc.: The state or quality of being uninterrupted in sequence or succession, or in essence or idea; connectedness, coherence, unbrokenness.
1603. Holland, Plutarch’s Mor., 1356. All that shall be, hath a stint and dependance of that which is, by a certeine continuitie, which proceedeth from the beginning to the end.
1751. Harris, Hermes, vii. (1786), 101. We may gain some idea of Time, by considering it under the notion of a transient continuity.
1820. W. Irving, Sketch Bk., I. 10. In travelling by land there is a continuity of scene, a connected succession of incidents that carry on the story of life.
1842. W. Grove, Corr. Phys. Forces, Pref. (ed. 6), 16. The continuity of attention necessary for the proper evolution of a train of thought.
b. Law or principle of continuity: the principle that all change, sequence, or series in nature is continuous, and that nothing passes from one state to another per saltum.
The phrase originated with Leibnitz. In 1687 he laid down as a general principle, that where there is continuity between data, such that one case continually approaches and at length loses itself in another, there will be a corresponding continuity in results or properties. For example, it is a property of the ellipse that all rays from the one focus are reflected from the curve to the other; in the parabola all such rays reflected at the curve are parallel; if there be given a series of ellipses continually approaching the parabola by the continuous increase of distance between the foci, the focal radii of these will continuously approach the relation of parallelism, so as at length to differ from it by less than any assignable amount. This was according to Leibnitz ‘a principle of general order,’ having its origin in the mathematical infinite, absolutely necessary in Geometry, but holding good also in Physics, because the Sovereign Wisdom, the source of all things, acts as a perfect Geometer, and according to a harmony that admits of no addition. In 1702 he referred to this principle as ‘the law of continuity,’ and claimed that it operates in all natural phenomena; and in his Nouveaux Essais, he declared it to be part of his ‘Law of Continuity’ that everything in nature goes by degrees, and nothing per saltum.
[1687. Leibnitz, Lettre à Mr. Bayle, Wks. Erdm. 104. Ibid. (1690), Lettre à Mr. Arnauld, ibid., 107. Chacune de ces substances contient dans sa nature legem continuationis seriei suarum operationum. Ibid. (1702), Repl. aux Refl. de Bayle, ibid., 189/2. Qu’il ne se rencontre jamais rien, où la loi de la continuité (que j’ai introduite, et dont j’ai fait la première mention dans les Nouvelles de la République des Lettres de Mr. Bayle), et toutes les autres règles les plus exactes des Mathématiques soient violées. Ibid. (a. 1716), Nouv. Ess., IV. xvi. Tout va par degrés dans la nature et rien par saut, et cette règle, à l’égard des changements, est une partie de ma loi de la continuité.]
1753. Chambers, Cycl., Suppl. s.v., An eminent mathematician has supposed what he calls a law of continuity to obtain in the universe, by which law every thing that is executed or done in nature, is done by infinitely small degrees.
1812–6. Playfair, Nat. Phil. (1819), I. 271. When bodies, whether solid or fluid, act on one another by impulse or percussion, in such a manner that their action is subject to the law of continuity.
1830. Herschel, Stud. Nat. Phil., 189. It prevents a breach of the law of continuity between transparent and opake bodies.
1841. J. R. Young, Math. Dissert., ii. 74. That the angle changes at once from 90° to zero, is to admit so palpable a violation of the principle of continuity … that, etc.
1862. Mulcahy, Mod. Geom. (ed. 2).
1878. Tait & Stewart, Unseen Univ. (1820), p. xii. We endeavour to show … that immortality is strictly in accordance with the principle of Continuity (rightly viewed).
c. Equation of continuity, in Hydrodynamics: the equation connecting the rate of change of density of a fluid within any closed surface constantly full of fluid with the flow of fluid through the surface.
1836. T. Webster, Equilibr. & Motion of Fluids.
1880. Haughton, Phys. Geog., iii. 141.
1882. Minchin, Unipl. Kinemat., § 93.
3. The state or quality of being continuous in time; uninterrupted duration. rare.
1646. Sir T. Browne, Pseud. Ep., IV. xiii. Wee need not have recourse unto any starre but the Sunne and the continuity of its action.
1840. Mrs. Browning, Drama of Exile, Poems 1850, I. 27. Their stedfast continuity of gaze.
1841. Brewster, Mart. Sc., II. iv. (1856), 146. A painful disease, which had its origin in the severity and continuity of his studies.
4. quasi-concr. A continuous or connected whole; a continuous or unbroken course or series. (Of material or immaterial things.)
1601. Holland, Pliny, II. 423. Running throughout one continuity without interruption.
a. 1619. Fotherby, Atheom., II. ix. § 3 (1622), 296. All magnitudes and continuities are deduced from one originall prick.
1644. Milton, Areop. (Arb.), 70. When every stone is laid artfully together, it cannot be united into a continuity, it can but be contiguous in this world.
1809–10. Coleridge, Friend (1865), 219. A chain that ascends in a continuity of links.
b. A part continuous with something else. rare.
1809. W. Irving, Knickerb. (1861), 248. The New-Netherlands … a continuity of the territory taken possession of … by the Pilgrims, when they landed on Plymouth Rock.
5. Solution of continuity: the fact or condition of being or becoming discontinuous; fracture, rupture, breakage, ‘break.’ Orig. used of wounds, etc., in an animal body; thence also in other senses.
1543. Traheron, trans. Vigo’s Chirurg. (1586), 12. The heart can not suffer solution of continuitie without death.
1661. Bramhall, Just Vind., ii. 14. Schisme is an exteriour breach, or a solution of continuity in the body Ecclesiastick.
1707. Curios. in Husb. & Gard., 77. The Solution of Continuity may hinder the Juice from mounting.
1790. Burke, Fr. Rev., 24. With what address this temporary solution of [historical] continuity is kept from the eye.
1877. Tyndall, in Daily News, 2 Oct., 2/5. We are brought without solution of continuity into the presence of problems, which … lie entirely outside the domain of physics.
