The enemy had, earlier in the day, out of the hulls of three steamboats, constructed a bridge, over which he had passed the main body of his army. As the charge was made, and it became evident that the Unionists would capture the position, the rebels burned this bridge, and also the railroad bridge across the river just above. In the afternoon several attempts were made to cross the river, but the rebel sharpshooters lined the bluffs beyond, and entirely prevented it. Later, the main body of sharpshooters were dispersed by the Federal artillery. It was not, however, safe to stand upon the bank, or cross the open field east of the bridge until after dark, when the enemy withdrew altogether. By this time, General Sherman had reached Bridgeport on the Black river, just above. The only pontoon train was with him. By the morning of the 18th he had crossed the river and was ready to march on Vicksburg. Generals McClernand and McPherson caused floating bridges to be constructed during the night, and were ready to cross their troops by eight o’clock on the next morning. General Sherman commenced his march by the Bridgeport and Vicksburg road on the 18th, and, when within three and a half miles of Vicksburg, he turned to the right to get possession of Walnut Hills and the Yazoo river. This was successfully accomplished before night. General McPherson crossed the Black river above the road to Jackson, and came into the same road with General Sherman, but in his rear. His advance arrived after nightfall at the point where General Sherman turned to the right. General McClernand moved by the Jackson and Vicksburg road to Mount Albans, in the rear of Vicksburg, and there turned to the left to get into the Baldwin’s Ferry road. By this disposition the three army corps covered all the ground their strength would admit of, and by the morning of the 19th the investment of Vicksburg was made as complete as could be by the forces under the command of General Grant. Communication was now opened with the fleet above Vicksburg, and General Grant’s supplies were thenceforth received from the Yazoo, instead of from Grand Gulf. CAPTURE OF HAINES’S BLUFF. MAY 18, 1863. The operations of Rear-Admiral Porter, which had an important bearing on the movements of General Grant’s army at that time, are thus detailed in the reports of that officer, and of Lieutenant Walker. FLAG SHIP BLACK HAWK, } HAINES’S BLUFF, YAZOO RIVER, _May 20th_. } To Hon. GIDEON WELLES, Secretary of the Navy: