THE following subjects for prizes are announced by the Academy for 1897 and following years; prizes for years other than 1897 are specially indicated. In Geometry, the Grand Prize in the Mathematical Sciences (1898) will be awarded for the best memoir extending the part played in analysis by divergent series; the Bordin Prize (3000fr.) for a study of the questions relating to the determination, properties, and applications of systems of orthogonal curvilinear coordinates of n variables, indicating particularly the degree of generality of these systems (1898); the Francœur Prize (1000fr.), and the Poncelet Prize (2000 fr.), for work contributing to the progress of pure or applied mathematics. In Mechanics, the Extraordinary Prize of 6coo fr. is offered for work increasing the efficiency of the French naval forces; a Montyon Prize (700fr.) for the invention or improvement of instruments useful in agriculture or the mechanical arts; the Plumey Prize (2500fr.), for improvements in steam navigation; the Fourneyron Prize, for a complete discussion of the motion and stability of bicycles. In Astronomy, the Lalande Prize (540 fr.) will be given for the observation or work most useful to the progress of the science; the Damoiseau Prize (1500fr.), for calculations connecting the appearances of Halley's comet, taking into account the attraction of Neptune, and giving the exact time of its next appearance in 1910; also, for 1898, for a study of the perturbations of Hyperion, the satellite of Saturn, deducing the mass of Titan; the Valz Prize (460 fr.), for the most interesting astronomical observation made during the year; and the Janssen Prize (for 1898), for the most important discovery in Astronomical Physics.