Stirlingn.1
/ˈstəːlɪŋ/, U.S. /ˈstərlɪŋ/ Stirling (or †Stirling's) cycle, the thermodynamic cycle on which an ideal Stirling engine would operate, consisting of an isothermal expansion, a drop in temperature at constant volume by giving up heat to a regenerator, an isothermal compression, and an increase in temperature at constant volume by gaining heat from the regenerator; Stirling (or †Stirling's) engine, originally, an external-combustion air engine invented by Stirling ( Brit. Pat. 4081 (1816)); more widely, a mechanical device used to provide either power or refrigeration and operating on a closed regenerative cycle, the working fluid being cyclically compressed and expanded at different temperatures; also elliptical as Stirling.
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society > occupation and work > equipment > machine > machines which impart power > engine > other types of engine > [noun] > hot-air
air engine1740
Stirling (or Stirling's) engine1845
caloric-engine1854
Carnot engine1937
society > occupation and work > equipment > machine > machines which impart power > engine > other types of engine > [noun] > hot-air > cycle in
Carnot cycle1887
Stirling (or Stirling's) cycle1887
heat cycle1894
1845 Minutes Proc. Inst. Civil Engineers 4 348 (heading) Description of Stirling's improved air engine.
1845 Minutes Proc. Inst. Civil Engineers 4 359 In Mr. Stirling's engine the intense heat of the fire did not come into actual contact with the pistons.
1887 Encycl. Brit. XXII. 523/1 Stirling's cycle is theoretically perfect whatever the density of the working air.
1889 C. H. Peabody Thermodynamics of Steam-engine xi. 174 A recent hot-air engine made on the same principle as Stirling's hot-air engine.
1943 E. H. Lewitt Thermodynamics Applied to Heat Engines (ed. 3) iii. 57 The Stirling cycle is thermodynamically reversible owing to the action of the regenerator.
1963 Engineer CCXIV. 1063/1 A Stirling cycle machine operates on a closed regenerative thermodynamic cycle.
1973 Sci. Amer. Aug. 81/2 In practice Stirling engines do not work on the Stirling cycle. It is not possible to have isothermal (constant temperature) compression and expansion processes.
1980 Times 16 Oct. (Internat. Motor Show Suppl.) p. xiv/8 Most of the technology of the Stirling has been established since the Second World War,..but mainly for vehicle and industrial duties rather than aircraft.
This entry has not yet been fully updated (first published 1986; most recently modified version published online March 2022).
Stirlingn.2
Used attributively to designate a water-tube boiler invented and patented by Allan Stirling ( U.S. Pat. 381,595 (1888)), usually consisting of three interconnected upper steam and water drums and one or two lower water drums, connected by banks of inclined water-tubes which are heated by combustion gases and bent to enter the drums radially.
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society > occupation and work > equipment > machine > machines which impart power > boiler > [adjective]
low pressure1816
tubular-flued1840
multitubular1849
tubulous1860
Field1865
Stirling1889
double-flued1895
1889 Amer. Machinist 23 May 12/1 (advt.) The Stirling Water Tube Boilers have unusually large steam and water spaces and well-defined circulation.
1924 F. J. Drover Coal & Oil Fired Boilers ii. v. 143 For from 1,000 to 10,000 sq. ft. of heating surface the standard Stirling boiler consists of three steam drums and two mud drums.
1940 H. M. Spring Boiler Operator's Guide iv. 117 The Stirling boiler..is one of the first types of bent-tube boiler to come into common use.
This entry has not yet been fully updated (first published 1986; most recently modified version published online September 2018).
Stirlingn.3
Mathematics.
Used attributively and in the possessive to designate concepts in the theory of numbers.
a. Stirling approximation n. (or Stirling's approximation, Stirling formula, Stirling's formula) either of two functions of an integer n which are approximations for factorial n when n is large, viz. n! ∼ nn/en and (more accurately) n! ∼ √(2πn)nn/en.
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the world > relative properties > number > algebra > [noun] > expression > function
function1758
exponential1784
potential function1828
syzygy1850
permutant1852
Green function1863
theta-function1871
Greenian1876
Gudermannian1876
discriminoid1877
Weierstrassian function1878
gradient1887
beta function1888
distribution function1889
Riemann zeta function1899
Airy integral1903
Poisson bracket1904
Stirling approximation1908
functional1915
metric1921
Fourier transform1923
recursive function1934
utility function1934
Airy function1939
transfer function1948
objective function1949
restriction1949
multifunction1954
restriction mapping1956
scalar function1956
Langevin function1960
mass function1961
1908 T. J. I'A. Bromwich Introd. Theory Infinite Series 461 (heading) Stirling's asymptotic formula for the gamma-function when x is real, large and positive.
1934 I. S. Sokolnikoff & E. S. Sokolnikoff Higher Math. for Engineers & Physicists xiii. 383 The first term of this series bears the name of Stirling's formula and gives satisfactory results even for small values of n.
1938 Biometrika 30 220 The first order term in Stirling's approximation to m!
1940 S. Glasstone Text-bk. Physical Chem. x. 861 By Stirling's formula 1/N! is approximately equal to (e/N)N if N is large.
1948 S. Glasstone Textbk. Physical Chem. (ed. 2) xi. 874 Since N is a large number, viz., the Avogadro number, it is possible to use the Stirling approximation and to replace lnN! by N ln N − N.
1962 W. J. Moore Physical Chem. (ed. 4) vii. 233 This expression is evaluated by means of the Stirling formula, log N! = (N + 1/ 2) log N − N + 1/ 2 log 2π.
1970 Ashby & Miller Princ. Mod. Physics ii. 35 We can obtain an approximate analytical expression..by using Stirling's approximation for the factorials: For large n, ln (n!) ≅ 1/ 2ln(2π) + (n + 1/ 2)ln(n) − n.
1978 P. W. Atkins Physical Chem. xx. 650 Stirling's approximation is that x large: ln x! xlnx − x.
b. Stirling number n. (also Stirling's number) a member of either of two arrays used in combinatorics, first described by him ( Methodus Differentialis (1730)), spec. (a) the number of ways of arranging the integers 1 to m in n disjoint non-empty ordered sets, the first element of each ordered set being the least; (a Stirling number of the first kind); (b) the number of ways of partitioning the integers 1 to m into n disjoint non-empty sets; (a Stirling number of the second kind).
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the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > array > member of
Stirling number1928
1928 Amer. Math. Monthly 35 77 The Stirling Numbers are characterized by many very beautiful properties.
1933 Tôhoku Math. Jrnl. 37 255 (caption) Table of Stirling's numbers of the first kind.
1933 Tôhoku Math. Jrnl. 37 277 The Stirling number of the second kind can be obtained by aid of a problem of probability.
1966 F. N. David et al. Symmetric Functions & Allied Tables v. 226 Stirling's Numbers of the first kind…1 1 2 6 24 120 720…1 3 11 50 274 1764… 1 6 35 225 1624…1 10 85 735…1 15 175…1 21…[etc.].
1966 F. N. David et al. Symmetric Functions & Allied Tables v. 223 Stirling's Numbers of the second kind…1 1 1 1 1 1 1…1 3 7 15 31 63…1 6 25 90 301…1 10 65 350…1 15 140…1 21…[etc.].
This entry has not yet been fully updated (first published 1986; most recently modified version published online September 2018).
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