Vicksburg wliich has so long held out against tho gallaiit assaults of our army - and which was not captured by canalling- has fallen before the regular approaches of Gen. Grant. Tlie surrender was made July 4th - having been arranged foron the 3d- and at 10 o'clock A. M. of our national anniversary the glorious Stars and Stripes floated over the boasted inipregnable rebel fortress. - ïhe terms of surrender were arranged at a personal interview between Gens. Grant and Pemberton. The garrison was pnroled, the officers allowed their horses, and all four days rationa from the rebel stores. The prisoners number about 20,000, and the captives consist of a large number of small arms, and the finest rifled batteries in the rebel service. The river battery numbered thirty-six guns. The garrison was redueed to living on mule meat. - We presume that Gen. Grant will now cooperato with Gen. Banks in the reduotion of Port Hudson, and in driving back the rebels from their threatened attack on New Orleans.