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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

In a manuscript **of** the same year (1873) Maxwell (Campbell & Garnett,p. 360), remarked thatThe form and dimensions **of** the orbits **of** the planets […] are notdetermined by any law **of** nature, but depend upon a particular collocation**of** matter. The same is the case with respect to the size **of** the earth.This was an example illustrating Poincaré’s statement concerningrandomness and necessity (§ 1.1), but it was not sufficiently specific; theeccentricities **of** planetary orbits depend on the velocities **of** the planets, cf.end **of** § 7.3.And here is Maxwell’s position (1875/1890, p. 436) concerningrandomness in the atomic world:The peculiarity **of** the motion **of** heat is that it is perfectly irregular; […]the direction and magnitude **of** the velocity **of** a molecule at a given timecannot be expressed as depending on the present position **of** the moleculeand the time.At the very end **of** his life Maxwell (1879/1890, pp. 715 and 721)introduced a definition for the probability **of** a certain state **of** a system **of**material particles:I have found it convenient, instead **of** considering one system **of** […]particles, to consider a large number **of** systems similar to each other […].In the statistical investigation **of** the motion, we confine our attention to thenumber **of** these systems which at a given time are in a phase such that thevariables which define it lie within given limits.Boltzmann (1868, § 3) defines the probability **of** the system being in aphase […] as the ratio **of** the aggregate time during which it is in that phaseto the whole time **of** the motion.4) If the classical definition **of** probability is included here, we can saythat Boltzmann used three formulations. Maxwell (item 2 above) mentionedone **of** them, and another reference can be added: Boltzmann (1895 – 1899,1895, Bd. 1, p. 50). Yet another one was that applied by Maxwell (see samesubsection) although sometimes Boltzmann (1878/1909, p. 252) did notindicate which one he was employing. He (1872/1909, p. 317) apparentlythought that these posterior probabilities were equivalent.In other words, with respect to separate molecules Boltzmann introducedthe time average probability, – and maintained that it was equivalent to theusual phase average probability. When studying polyatomic gases,Boltzmann (1871) defined the probability **of** its state as a product such asfdω where f was some function, varying in time, **of** the coordinates andvelocities **of** the separate molecules and dω, the product **of** the differentials**of** those parameters. For stochastic processes, such functions determine thedistribution **of** a system **of** random variables at the appropriate moment.Zermelo (1900, p. 318) and then Langevin (1913/1914, p. 3) independentlystressed the demand to provide a definition correcte et claire de laprobabilité (Langevin). Like Maxwell, Boltzmann (1887/1909, p. 264; 1895110