THE ACADEMIC BUILDING contains, on the first floor, a gymnasium, with bowling-alleys, an apartment for fencing and sword exercise, and the Chemical laboratory. The second floor contains recitation rooms, and the models and collections pertaining to the departments of Engineering and Mineralogy and Geology. Besides the models of bridges, buildings, engines, and arches, illustrative of the progress of civil engineering, others relating to field works, fortifications, their system of attack and defense, and the models of Fort Wagner, before Charleston, and San Juan d'Ulloa, off Vera Cruz, will claim attention. The third floor is occupied by recitation and lecture rooms, the Picture gallery, Drawing Academy, and the Museum of ordnance and trophies. The Picture gallery contains specimens selected from the productions of the most proficient Cadets in the classes which have gone forth since 1838, and among them the names of many prominent army officers will be recognized. Regarded as an evidence of skill and cultivated taste, on the part of those who were first made aware of their power to acquire the art of sketching and coloring after entering the Military Academy, and as the result of a few months' instruction, no one can view this collection without experiencing the liveliest feelings of satisfaction and pleasure. The MUSEUM OF ORDNANCE AND TROPHIES exhibits all the various progressive stages in the manufacture of swords, muskets, cartridges, powder, and shot; models of field and siege guns, and the anatomical structure of horses for instruction in the department of cavalry. The collection of ancient and experimental weapons; of Rebel torpedoes, and Rebel shot from many battle-fields; of flag-staffs and flags from Mexico; Indian trophies and curious projectiles, and the numerous flags borne by the regular army in the last war with England, in the Florida war, in Mexico, and in the Rebellion, with their inscriptions, excites a degree of interest which cannot be overcome by a momentary glance. The colors of the FOURTH REGIMENT OF U.S. INFANTRY bear the following historical inscriptions: The first Flag Carried 1794. Retained at Reorganization 1808. Tippecanoe 1811. IN THE FLORIDA WAR. Gaines's Pen 1836. Thlonalosassa 1836. Okeechobee 1837. IN THE MEXICAN WAR. Palo Alto 1846. Resaca de la Palma 1846. Monterey 1816. Vera Cruz 1847. Churubusco 1847. Molino del Rey 1847. Chapultepec 1847. City of Mexico 1847. IN THE REBELLION.