Independence,The 68th Anniversary of our National freedom, on the 4th iust., passed off in this city without accideot, although with no abatement of the usual demonstrations of joy and exultation.The morning was ushured in by a National Salute and the ringing of bells.A Procession was formed at an early hour, headed by our elegant Military Company, 4 the Hudson Light Guards,* followed by several of our fine Fire Companies with their handsome Engines and splendid Banners, succeeded by one of the Juvenile Artillery Companies with their beautiful Brass Cannon, followed by the Hudson Division of the Sons of Temperance in full regalia. The whole led by our Ex-Mayor, Coi. Chas. Darling, (Chief Marshal of the day) in full Military costume, and the insignia of the order of the Sons of Temperance, aided by a competent number of Assistant Marshall’s, the Procession moved through our principal streets to Washington Square. Here on a platform, erected in front of the Court House, the Declaration of Independence was well read by Wm. A. Carpenter, and an Oration delivered by E. P. Cowles Esq., appropriate, energetic and patriotic.The remainder of the day was, we believe,