fluxion
(ˈflʌkʃən)
Also, 6 fluxione, -yon.
[a. Fr. fluxion, ad. L. fluxiōn-em, f. flux- ppl. stem of fluĕre to flow; see -ion1.]
1. The action of flowing; a flowing or issuing forth (of water, vapour, etc.). Also, continuous or progressive motion; continual change. Now rare.
| 1599 Hakluyt Voy. II. ii. 333 Whirlepooles, and fluxions are caused..in the middest of the sea. 1603 Holland Plutarch's Mor. 962 The fluxion of the odour comming from the beast. 1606 J. Davies Sel. Sec. Husb. &c. Wks. (Grosart) II. 14 If the fluxion of this instant Now Effect not That, noght wil, that Time doth know. 1635 Swan Spec. M. v. §2 (1643) 165 That [water]..which..hath some certain beginning of fluxion. 1656 T. Stanley Hist. Philos. v. 10 In Sensibles neither magnitude nor quality is permanent, but in continuall fluxion and mutation. 1660 Ibid. ix. 550/1 The point by fluxion makes a Line. 1880 Blackmore M. Anerley I. viii. 92 Their bodies continually going up and down upon perpetual fluxion. |
| fig. 1829 Gen. P. Thompson Exerc. (1842) I. 31 The Catholics know that the fluxion of public opinion is in their favour. |
† b. = effluvium 2 a. Obs.
| 1603 Holland Plutarch's Mor. 725 Those fluxions which rest upon waters, looking-glasses, or any such mirrors. 1655 Stanley Hist. Philos. ii. (1701) 65/1 Falling Stars are not fluxions of the æther extinguisht in the Air almost as soon as lighted. 1748 Hartley Observ. Man. i. iii. 352 The Rays of Light may be considered as a kind of Fluxions in respect of the biggest component Particles of Matter. |
2. An excessive flow of blood, ‘humour,’ serum, etc. to any organ or part of the body. Also concr., the matter which flows.
| 1541 R. Copland Galyen's Terap. 2 B j, Yf the flux or rennynge wyll nat stop with salues, seke the cause of the sayde fluxyon. c 1550 Lloyd Treas. Health (1585) A iij, Horsnesse, and continuall fluxion of snevill in old men. 1601 Holland Pliny II. 559 It is the better for to represse the fluxion of humors into the eies. 1612 Woodall Surg. Mate Wks. (1653) 75 Galles..cure fluxions of the gums. 1746 Lady M. W. Montagu Let. to W. Montagu 23 Aug., I had so bad a fluxion on my eyes, I was really afraid of losing them. 1874 Roosa Dis. Ear 75 A fluxion towards the labyrinth with serous exudation in the nerve structure. |
| fig. 1796 Burney Metastasio II. 351 To attempt the cure of the eloquent fluxion to which he is subject. |
3. = flux n. 1.
| 1563 W. Fulke Meteors (1640) 53 b, The common dew drunke of cattell..bringing them to a fluxion. 1599 A. M. tr. Gabelhouer's Bk. Physicke 217/2 It præventeth also..superfluous fluxione [of the menstrualles]. 1657 Tomlinson Renou's Disp. 165* This cures eroding fluxions. 1760–72 tr. Juan & Ulloa's Voy. (ed. 3) II. 67 At Lima it occasioned constipations and fluxions. |
† 4. = fusion. Obs.
| 1731 Bailey, Fluxion (among Chymists), signifies the running of Metals or any other Bodies, into a Fluid, by Fire or otherwise. 1848 in Craig. |
5. Math. In the Newtonian form of the infinitesimal calculus: ‘The rate or proportion at which a flowing or varying quantity increases its magnitude’ (Hutton Math. Dict.).
This is Newton's own use of the word; but the 18th c. writers on the Newtonian calculus used fluxion for what Newton called the ‘moment’ of a fluent, and modern analysts call the ‘differential’.
corresponding fluxions, rates at which two interdependent quantities may change simultaneously. second fluxion, the rate of change of the fluxion of a variable quantity; the second differential coefficient with respect to the time.
| 1704 [see differential B 1]. 1706 W. Jones Syn. Palmar. Matheseos 174 Let x. be a Ratiuncula, or Fluxion of the Ratio of 1 to 1 + x. 1806 Hutton Course Math. II. 287 Rules..for finding the fluxions of all sorts of quantities. 1828 Ibid. II. 323 The fluxion found from a given fluent is always perfect and complete. |
b. Hence (the method or † doctrine of) fluxions is used as a name for the Newtonian calculus.
The direct and inverse method of fluxions are (apart from differences of notation) essentially identical with the differential and the integral calculus respectively.
| 1702 [see differential A 3.]. 1741 Watts Improv. Mind i. xx. 327 A Penetration into the abstruse Difficulties and Depths of modern Algebra and Fluxions. 1812 Cresswell Max. & Min. ii. ii. 197 Its [quantity's] increase and decrease by motion, which is the foundation of the doctrine of Fluxions. 1830 Herschel Stud. Nat. Phil. iii. iii. (1851) 271 The method of fluxions, or, as it is now more generally called, the differential calculus. 1874 Green Short Hist. ix. §1. 599 Newton..facilitated the calculation of planetary movements by his theory of Fluxions. |
¶ c. loosely. An infinitesimal quantity.
| 1846 De Quincey Christianity Wks. XII. 234 The hour⁓hand of a watch—who can detect the separate fluxions of its advance? |
6. Comb.: fluxion-structure (see quot. 1890).
| 1882 Geikie Text-bk. Geol. ii. ii. iv. 104 This is well shown by what is termed the fluxion-structure. 1890 ― Class-bk. Geol. (ed. 2) 146 Flow-structure, Fluxion-structure, an arrangement of the crystallites, crystals, or particles of a rock in streaky lines..indicative of the internal movement of the mass previous to its consolidation. |