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▪ I. Stirling1|ˈstɜːlɪŋ|
[The name of the Revd. Robert Stirling (1790–1878), Scottish minister and engineer.]
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, orig., 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 ellipt. as Stirling.
1845Minutes Proc. Inst. Civil Engineers IV. 348 (heading) Description of Stirling's improved air engine. Ibid. 359 In Mr. Stirling's engine the intense heat of the fire did not come into actual contact with the pistons. 1887Encycl. Brit. XXII. 523/1 Stirling's cycle is theoretically perfect whatever the density of the working air. 1889C. H. Peabody Thermodynamics of Steam-Engine xi. 174 A recent hot-air engine made on the same principle as Stirling's hot-air engine. 1943E. H. Lewitt Thermodynamics Applied to Heat Engines (ed. 3) iii. 57 The Stirling cycle is thermodynamically reversible owing to the action of the regenerator. 1963Engineer CCXIV. 1063/1 A Stirling cycle machine operates on a closed regenerative thermodynamic cycle. 1973Sci. 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. 1980Times 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.
▪ II. Stirling2
The name of Allan Stirling (1844–1927), Scottish-born American engineer, used attrib. to designate a water-tube boiler invented and patented by him (U.S. Pat. 381,595 (1888)), usu. 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.
1889Amer. Machinist 23 May 12/1 (Advt.), The Stirling Water Tube Boilers have unusually large steam and water spaces and well-defined circulation. 1924F. 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. 1940H. 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.
▪ III. Stirling3 Math.
The name of James Stirling (1692–1770), Scottish mathematician, used attrib. and in the possessive to designate concepts in the theory of numbers, as Stirling('s) approximation or 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; 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).
1938Biometrika XXX. 220 The first order term in Stirling's approximation to m! 1948Glasstone 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. 1970Ashby & 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!) {congr} ½ln(2π) + (n + ½)ln(n) - n. 1978P. W. Atkins Physical Chem. xx. 650 Stirling's approximation is that x large: ln x! xlnx - x.
1908T. 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. 1934I. S. & 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. 1940Glasstone Text-bk. Physical Chem. x. 861 By Stirling's formula 1/N! is approximately equal to (e/N)N if N is large. 1962W. J. Moore Physical Chem. (ed. 4) vii. 233 This expression is evaluated by means of the Stirling formula, log N! = (N + ½) log N - N + ½ log 2π.
1928Amer. Math. Monthly XXXV. 77 The Stirling Numbers are characterized by many very beautiful properties. 1933Tôhoku Math. Jrnl. XXXVII. 255 (caption) Table of Stirling's numbers of the first kind. Ibid. 277 The Stirling number of the second kind can be obtained by aid of a problem of probability. 1966F. N. David et al. Symmetric Functions & Allied Tables v. 226 Stirling's Numbers of the first kind{ddd}1 1 2 6 24 120 720{ddd}1 3 11 50 274 1764{ddd} 1 6 35 225 1624{ddd}1 10 85 735{ddd}1 15 175{ddd}1 21{ddd}[etc.]. Ibid. 223 Stirling's Numbers of the second kind{ddd}1 1 1 1 1 1 1{ddd}1 3 7 15 31 63{ddd}1 6 25 90 301{ddd}1 10 65 350{ddd}1 15 140{ddd}1 21{ddd}[etc.]. |