Base Ball.—This game is over for the present, but appearances indicate an increased and more wide-spread interest in the sport next season. It is a beautiful exercise, and equally fascinating to player and spectator. As we states a few weeks since, the game is confined chiefly to this vicinity, but we hope to see it “caught up” in other localities on the opening of the season of 1858. Of the clubs, in this city, and their doings, we have not been kept sufficiently posted by their secretaries, and cannot, therefore, give a resume of the season’s play, together with a sketch of the most notable performances. &c., as we should have done. Long Island seems to have most the most wonderful progress, as the following list of clubs will show, most of them having been organized during the year just about closing :—Atlantic, Alert, Active, Bedford, Baltic, Continental, Eckford, Excelsior, Enterprise, Franklin, Franklin Jr., Hamilton, Independent, Layfayette, Liberty, Montauk, Nassau, Niagra, National, Neptune, Oriental, Osceola, Pastime, Polytechnic, Putnam, Rough and Ready, Superior, Star, Saratoga, Union, Victory, Warren, Wayne, and Young America.