THE following is, in brief, a list of the prizes offered in connection with specified subjects in 1882 and following years:—In 1882: Grand prize of the Mathematical Sciences (medal worth 3000 fr.): Theory of the decomposition of whole numbers in a sum of five squares. Extraordinary prize of 6000 fr.: Progress increasing the efficiency of the naval forces. Plumey prize (medal, 2500 fr.): Improvement of steam-engines, or of steam-navigation otherwise. Damoiseau prize (medal, 10,000 fr.): Revision of the theory of Jupiter's satellites, Grand prize of the Mathematical Sciences (medal, 3000 fr.): Experimental and theoretical study of the elasticity of one or several crystalline substances. Bordin prize (medal, 3000 fr.): Origin of atmospheric electricity and cause of phenomena in thunderclouds. Desmazières prize (medal, 1600 fr.): Best work in cryptogamy. Vaillant prize (medal, 4000 fr.): Inoculation as a prophylactic in contagious diseases of domestic animals. Grand prize of the Physical Sciences (medal, 3000 fr.): Distribution of marine animals on the French coast. Du Gama Machado prize (medal, 1200 fr.): On coloured parts of the tegumentary system of animals, or on the fecundating matter of animated beings. Breant prize (interest on 100,000 fr.): Cure of Asiatic cholera. Godard prize (medal, 1000 fr.): Anatomy, physiology, and pathology of the genito-urinary organs. Lalle-mand prize (1800 fr.): Work on the nervous system. Gay prize (2500 fr.): Marine lacustrine and terrestrial deposits on the French coasts in the present period, and especially since the Roman epoch. In addition, there are the Montyon prize in Mechanics, the Lalande and Valz prizes in Astronomy, and several others. Then in 1883: Fourneyron prize (500 fr.): Different modes of transmission of force to a distance. Grand prize of the physical sciences (medal, 3000 fr.): Geological description of a region of France or Algeria. De la Fons Melicoque prize (300 fr.): Botanical work on the North of France. Bordin prize (3000 fr.): Influence of medium on the structure of vegetating organs; variations of terrestrial plants grown in water, and of aquatic fplants in air; explain by direct experiments the special forms of some species of maritime flora. Bordin prize (medal, 3000 fr.): Palæontology of France or Algeria. Grand prize of the physical sciences (medal, 3000 fr.): Histological development of insects during their metamorphoses. Alphonse Penaud prize (3000 fr.): Aërial locomotion. In 1884: Sener prize (7500 fr.): On genera embryology applied as much as possible to physiology and medicine. In 1885: Dusgate prize (2500 fr.): Diagnostic signs of death and means of preventing precipitate inhumation. In 1886 the Jean Renaud prize will be awarded for the most meritorious work during five years.