POISSON, (SIMÉON-DENIS). - INTRODUCING "THE LAW OF LARGE NUMBERS"

Recherches sur la probabilité des jugements, principalement en matière criminelle. (+) Note sur la loi des grands nombres. (2 Papers).

(Paris, Bachelier), 1835-36. 4to. No wrappers. In: "Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences", Tome 1, Séance du Lundi 14 Décembre 1835 and tome 2, Séance Lundi 11 Avril 1836. Pp. (467-) 498 and (355-) 386. (2 entire issues offered. Poisson's papers: pp. 473-495 (1835) a. pp. 377-380 (1836).

First appearance of 2 importent paper in probability theory, serving as a preamble to Poissons's famous work published two years later, and with nearly the same title "Recherches sur la probabilité des jugements en matiere criminelle et en matiere civile" (1837). The paper offered introduces THE LAW OF LARGE NUMBERS (Loi universelle des Grandes nombres, pp. 478-79), a key concept in probability theory. Poisson states that all events of a moral as well as of a physical nature are subject to this universal law. His definition (in English translation) on p. 478 reads "Things of every kind obey a universal lw that we may call the law of large numbers. Its essence is that if we observe a very large number of events of the same nature, which depend on constant causes and on causes that vary irregularly, sometimes in another, 1.e., not progressively in any determined sense, then almost constant proportions will be found among numbers" (p. 478 in the first memoir).

"Prior to the publication of the "Rechearces", Poisson presented his principal results and philosophical views to the Academie des Sciences in papers read at the sessions of 14 december 1835 and 11 April 1836. The first memoir became the "Préambule" of the "Rechearches" and outlined Poisson's criticism of Laplace's approach to the probability judgements, the universal applicability of the law of large numbers, and some of the results based on the Ministry of Justice's statistics.... Poisson's second memoir discussed his "Law of Large Numbers", with special attentuion to how it differed from bernoulli's theorem and how it was particularly well suited for applications to the moral sciences..." (Lorraine Daston "Classical Possibility in the Emlightment", pp. 364-65).

"In Recherches sur la probabilité des jugements en matière criminelle et en matière civile (1837; (Research on the Probability of Criminal and Civil Verdicts), an important investigation of probability, the Poisson distribution appears for the first and only time in his work. Poisson’s contributions to the law of large numbers (for independent random variables with a common distribution, the average value for a sample tends to the mean as sample size increases) also appeared therein." Encl. Britannica). - In fact the law appears here, two years before, in the offered paper." (Encl. Britannica).

Order-nr.: 47235