July 7th. The miniature army steamer Bee (General Banks’s despatch boat,) came down from Bayou Sara, at 12 o’clock midnight, bringing the cheering news of the fall of Vicksburg, which she had previously received from the steamer Gen. Sterling Price, just arrived from Vicksburg, and now lying aground off Point Coupée, opposite Bayou Sara. General Pemberton of the C. S. A., in command of the forces at Vicksburg, surrendered that city to General U. S. Grant (or, as he is more familiarly known, “Unconditional Surrender Grant”), in command of the Union forces, at ten o’clock on the morning of the glorious Fourth of July. An armistice between both armies had taken place on the evening previous. At eight A. M., steamers Gen. Price and Empire Parish came down the river—the former with despatches and a mail for us. Lieutenant Watson started for General Banks’s headquarters, and Ensign Hazeltine for the lower fleet, with the news of the surrender of Vicksburg. From twelve noon until one thirty P. M., heavy cannonading at Port Hudson, on the left and right wings of the army; between the hours of five and six o’clock, the steamer General Price, with our mail on board, left for Vicksburg.