From the Southwest and Trans Mississippi.
Demopolis. May 1.
--A special dispatch to the Meridian Clarion, from Jackson the 30th ult, says the enemy have fallen back from Big Black, after partially destroying the bridge, burning all the sutlers' and traders shanties and the soldiers' huts.
Considerable alarm prevails within the fortifications at Vicksburg, apprehending an attack from Wirt Adams.
A dispatch from Brookhaven to the same paper says: ‘"Information from trans- Mississippi reports that Banks has been defeated a second time, but has escaped to the north side of Red river, and was falling back on Natchitoches.
Gen. Price whipped Steele badly, capturing 200 wagons, a large quantity of prisoners and arms.
Marmaduke was also in pursuit of Steele, who was falling back on Little Rock."’ 