The fust Exhibition of the Metropolitan Mechanics' Institute will be opened at Washington on the 24th of next February, (1853.) It is to be held in the new and splendid hall of the east wing of the Patent Office, which is 275 feet long and 70 feet wide. The me-, chanicsfrom all parts of the Union are invited to exhibit their industrial products. All articles deposited for competition must be of American production. A steam engine will be in operation for driving the machinery. Every facility will be afforded to exhibitors. The Corresponding Secretary is Charles F. Stansbury,so well known for his acquaintance with engineering and works of mechanical industry. ? We hope the Washington Mechanics'Institute will have a good Fair. The exhibitors will have an opportunity of geeing the wise men assembled in conclave Congressional.