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

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

sunspots constitute a time series, an object for stochastic studies. I note thatNewcomb considered the maxima and the minima of that phenomenon aswell as half the sums of the numbers of the sunspots corresponding to theyear of minimum and the following maximum, or vice versa (p. 4). Hedetermined the four appropriate values of T and their mean withoutcommenting on the possible dependence between them.Variation of the terrestrial latitudes is known to be caused by themovement of the pole about some point along a curve resembling acircumference with period 1.2 years. Newcomb (1892) checked the thenproposed hypothesis that the movement was periodic with T = 1.17 years.He assumed that the pole moved uniformly along a circumference. Some ofhis calculations are doubtful and in any case not sufficiently detailed (afeature peculiar to many of his works) but he correctly concluded that thehypothesis was [apparently] valid.In 1767 Michell (§ 6.1.6) determined the probability that two stars wereclose to each other. By applying the Poisson distribution, Newcomb (1859 –1861, vol. 2, pp. 137 – 138) calculated the probability that some surfacewith a diameter of 1° contained s stars out of N scattered at random over thecelestial sphere and much later Fisher (Hald 1998, pp. 73 – 74) turned hisattention to that problem. Boole (1851/1952, p. 256) reasoned on thedistinction between a uniform and any other random distribution:A ‘random distribution’ meaning thereby a distribution according tosome law or manner, of the consequences of which we should be totallyignorant; so that it would appear to us as likely that a star should occupyone spot of the sky as another. Let us term any other principle of distributionan indicative one.His terminology is now unsatisfactory, but his statement shows thatMichell’s problem had indeed led to deliberations of a general kind. See alsoNewcomb (1904a). He (1861b) also determined the probability of thedistance between the poles of two great circles randomly situated on asphere. Issuing from other initial considerations, Laplace (1812/1886, p.261) and Cournot (1843, § 148) earlier provided solutions differing bothfrom each other and from Newcomb’s answer (Sheynin 1984a, pp. 166 –167).About 1784 William Herschel started counting the number of starssituated in different regions of the sky. He thought that his telescope wasable to penetrate right up to the boundaries of the (finite) universe and hopedto determine its configuration. In one section of the Milky Way he(1784/1912, p. 158) counted the stars in six fields selected promiscuouslyand assumed the mean number of them as an estimate for the entire section.Later Herschel (1817) proposed a model of a uniform spatial distribution ofthe stars. He fixed the boundaries for the distances of the stars of eachmagnitude but allowed the stars to be randomly distributed within theseboundaries and thus provided an example of randomness appearingalongside necessity, cf. Poincaré’s statement in § 1.1.When estimating the precision of his model for the stars of the first sevenmagnitudes, Herschel calculated the sum of the deviations of his model fromreality. For the first four magnitudes the sum was small although theseparate deviations were large. Recall (§ 6.3.2-3) that, when adjusting103

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