From The Southwest

St. Louis. March 30. The steamer David ïatum, which reached Oairo last night, reported a part of Forrest's foroes crossing the Cuinberland River at Eddyville. Guoboats had been sent up the river to look after matters. The First Alabama Cavalry reported last night, at Cairo, have unanimously re-enlisted. They are seven hundred strong, all Alabamians. They have seen hard service, and are en route to Deeatur to reoruit. It is reported there are large nurnbers of Union men in North Alabama waiting to join the army. Golonel Spencer has authority to raise a brigade ' there, and thinks it can be done in sis: weeks. Alexandria, Louisiana. was occupied by our troops on the 16th. Tlie enemy, under Generáis Taylor and Polignae, crossed the river and retreated to Shreveport by land. Several rebel gunboats which were there have gone up the river. The steamer New Falls City, laden with cotton, is reported burned. The advance of" Banks' cavalry, under Lee, arrived at Alexandria on the 18tli. The remainder of the army was with in two davs' mareh. When it arrivés the combined force will proceed westward by land. Supplies are going by river. No rebels are north or south of the Red River and Shreveport, exeept Gen. Harrison's cavalry at Columbia. The gunboats made a prize of all the cotton captured, amouuüng to 5,000 bales. Fort DeRussey was aecidentally blown up on the I7th, killing four and wounding six.