From the Southwest.
For the past few days public attention has been withdrawn in a measure from their rations around Vicksburg by the brilliant achievements of our army under Gen. Lee on the Northern border of Virginia and in Pennsylvania and Maryland. It is gratifying to know, however, that our successes on the Mississippi rival those of our arms on the Potomac. A dispatch was yesterday received by President Davis from Gen. Johnston stating that Gen. Kirby Smith, with his corps, had taken possession of Milliken's Bend, above Vicksburg, cutting off the supplies and communication of the enemy. This is, in effect, raising the siege of Vicksburg, and in a few days we may expect the most cheerful tidings from that important and beleaguered point.
