*(French)*Zbl 0606.01010

In 1885 A. M. Lyapunov read two of Poincaré’s papers on the equilibrium of rotating fluids, which had recently appeared in the Comptes Rendus. Lyapunov, at the suggestion of P. L. Chebyshev, had himself studied this problem, and had published in Russian an article containing some of Poincaré’s results. He therefore wrote to Poincaré immediately, enclosing a copy of his article. Since neither mathematician had been able to eliminate certain hypotheses that both suspected were unnecessary, the ensuing correspondence (six letters sent between October 1885 and December 1886) is of great interest, as the authors point out, both for its scientific content, and as revealing the differences in the approaches of the two great mathematicians to the work.

Poincaré, as always, willing to give credit to others, promised to insert a note in his Acta Mathematica paper referring to Lyapunov’s work. For unknown reasons this note did not appear, but Poincaré did give credit to Lyapunov in his 1900 lectures at the Sorbonne, which were published in 1902 [Figures d’Équilibre d’une Masse Fluide, Gauthier- Villars]. Pages 15-22 of these lectures are devoted to an exposition of Lyapunov’s work.

To set the historical perspective of the letters the authors give a brief sketch of the history of the physical problem, which began with attempts to determine the shape of a planet. (The sketch is not intended to be comprehensive, since it does not contain any bibliographical citations. The reviewer would like to point out, however, that it omits the important work of Laplace and Legendre during the 1780’s.) They also give a set of references to the published work of the two mathematicians on this topic.