Tuesday, 2d—We marched ten miles last night and then went into bivouac for the rest of the night. The rebels are falling back without much resistance. We left our bivouac at 10 o’clock this morning, crossed the Tallahatchie river over the railroad bridge and after marching four miles, went into camp. We are near the town of Abbeville, where the rebels were strongly fortified. They deserted the place early yesterday morning after burning the station, but left large quantities of their supplies which they could not move before they had to flee. After they had crossed the bridge, which is a mile long, they set fire to it, but it failed to burn. Our cavalry is after them today and have taken several prisoners. It rained all day today.