From the Southwest.
skirmish in Louisiana--heavy firing at Vicksburg Jackson, Miss., June 24.
--Gen. Taylor had a skirmish with a small force of the enemy at Richmond, La, on the 17th.
Heavy firing continues at Vicksburg.
[second Dispatch]
Jackson, Miss, June 24
--The firing at Vicksburg still continues, far heavier than any ever heard.
Official dispatches state that Gen. Chalmers sunk three transports below Memphis, on the 20th, and disabled another.