H. Poincaré's work on probability (Q1205960)

In general, Poincaré's work on probability is not well known, however, we used to mention the monograph entitled ``Calcul des probabilités''. At least, we can find this work in the ``Encyclopedic Dictionary of Mathematics''. The aim of this paper is to cast light on all these works, and describe Poincaré's reasoning on chance in an earlier preprint. This paper is divided into 11 paragraphs, including mathematical treatment of observations, central limit theorem, homogeneous Markov chains and randomness. The author concludes that Poincaré was not acquainted with the works of Chebyshev, and even in 1912, did not refer either to Lyapunov or to Markov. On the other hand, Markov included Poincaré's work mentioned above in his list of general references of ``Calculus of Probability'' (Petersburg, second edition, 1908).