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

Lamarck (1800 – 1811) was one **of** the first scholars to note thedependence **of** the weather on its previous state, see for example t. 5, pp. 5and 8 and t. 11, p. 143 **of** that source.Quetelet (1852; 1853, p. 68; 1849 – 1857, 1857, pt 5, pp. 29 and 83)analysed lasting periods **of** fair or foul weather by applying elementarystochastic considerations and concluded that the chances **of** the weatherpersisting (or changing) were not independent. Köppen’s analysis (1872)was more mathematically oriented. Quetelet also compiled and systematizedmeteorological observations. In many letters **of** 1841 – 1860 Faraday (1991– 2008), see for example vol. 3, No. 1367 and vol. 4, No. 2263, praisedQuetelet’s observations **of** atmospheric electricity. In the first instance hewrote:You are indeed a worthy example in activity & power to all workers inscience and, if I cannot imitate your example, I can at least appreciate &value it.10.8.4. Astronomy. Already Daniel Bernoulli (§ 6.1.1) and Laplace (§7.1-2) stochastically studied regularities in the Solar system. They actuallyconsidered planets as elements **of** a single population, and this approach wasvividly revealed in the later investigations **of** the asteroids. Newcomb(1861a and elsewhere) compared the theoretical (calculated in accordancewith the uniform distribution) and the actual parameters **of** the orbits **of**asteroids but was yet unable to appraise quantitatively his results.Concerning their distribution, he (1862; 1881) seems to have intuitivelyarrived at the following proposition: a large number **of** independent pointsA 1 = (B 1 + b 1 t), A 2 = (B 2 + b 2 t), … where t denoted time, and the othermagnitudes were constant, will become almost uniformly distributed over acircumference.In 1881 Newcomb remarked that the first pages **of** logarithmic tableswore out much faster than the last ones and set out to derive the probabilitythat the first significant digits **of** empirically obtained numbers will be n 1 , n 2 ,… Without any pro**of** he indicated that, if numbers s 1 , s 2 , …, s n wereselected at random, the positive fractional parts **of** the differences (s 1 – s 2 ),(s 2 – s 3 ), … will tend, as n → ∞, to a uniform distribution over acircumference, and that the empirical magnitudes, to which these differencesconform, will have equally probable mantissas **of** their logarithms.Newcomb’s reasoning heuristically resembled the Weyl celebrated theoremthat states that the terms **of** the sequence {nx}, where x is irrational, n = 1,2, …, and the braces mean drop the integral part, are uniformly distributedon a unit interval. In the sense **of** the information theory, Newcomb’sstatement means that each empirical number tends to provide one and thesame information. Several authors independently one from another provedthat Newcomb was right. One **of** them called his statement an inspired guessbut reasonably noted that it was not universally valid (Raimi 1976, p. 536).By the mid-century, after processing observations made over about acentury, a rough periodicity **of** the number **of** sunspots was established.Newcomb (1901), who studied their observations from 1610 onward,arrived at T = 11.13 years which did not, however, essentially differ fromthe previous results. The present-day figure is T ≈ 11 years but a strictperiodicity is denied. In any case, it might be thought that the numbers **of**102