Antoni POINCARÉ (1825-1811) inspector of the Ponts et Chaussées, father of the President of the Republic. Combination of the barometric effects of the synodic revolution and of the terrestrial rotation, in the duration of the different synodic months of a year and of each day of the said months, October 1903; autographed publication, small folio (31 x 21 cm), 6 paperbacks in 4 folders numbered from 1 to 4, all placed in an annotated folder (small tear in the last leaf); 62 autographed p. n.ch. and 5 out-of-text graphs of which 1 is handwritten and 4 are autographed Rare autographed memoir, with autograph mailing. In this memoir, the author studies the synodic revolution, the interval of time that elapses between two successive passages of a planet or a satellite in a given situation, as well as the syzygy, a situation where three celestial objects (in general the Sun, the Earth and the Moon) are in conjunction or in opposition. Its study includes three chapters: I. Case of a median synodic month, at the end of which the axis of symmetry of the deviations is found, reversed, appreciably on the meridian of the original syzygy. - II. General case. Situation of the axes of symmetry at the hour of the syzygy of origin, at the successive days of the other months. - III. Rolling of the snapshots in a given day, counted from the hour corresponding to the original syzygy of the month to the return of the said hour. Result of the mixing of the synodic and daily waves in each of the 29 days. Diurnal variations. Wave of 348 degrees at different latitudes. Numerous numerical tables, as well as 5 graphs showing notably the oscillations of the monthly synodic wave, illustrate this study. Autograph letter signed on the first page: "To the French Physical Society. Homage from the author A. Poincaré"; stamp of this society affixed several times.