The following is the dispatch in the Richmond Whig from the commander of the rebel gunboat Arkansas:

Vicksburg, July 15, 1862.

We engaged today, from six to eight a. m., with the enemy’s fleet above Vicksburg, consisting of four or more iron clad vessels and two heavy sloops-of-war, and four gunboats and seven or eight rams. We drove an iron-clad ashore, with colors down and disabled, blew up a ram, burned one vessel and damaged several others. Our smokestack was so shot to pieces that we lost steam, and could not use our vessel as a ram. We were otherwise cut up as we engaged at close quarters. Lost ten killed and fifteen wounded others with slight wounds.