HDQRS. FIRST AND THIRD DIVS., 16TH ARMY CORPS, On Steamer Des Moines, Vicksburg, Miss., May 23, 1864.

CAPTAIN: I have the honor to report, for the information of the general commanding the detachment of Red River expedition, that, in obedience to the orders received from him to the effect that if the enemy should pursue me I should attack and drive them back, I moved across Yellow Bayou at about 11 o'clock of the 18th instant, with Colonel Hill's brigade, consisting only of two regiments, the Thirty-third Missouri and the Thirty-fifth Iowa, and Colonel Lynch's brigade, and Colonel Shaw's brigade of the Third Division. I skirmished with the enemy about 2 miles, when I came to a dense thicket, which I penetrated and found the enemy in large force on the opposite side of a field. They opened on my line with twelve pieces of rifled artillery. I had with me Lieutenant Tiemeyer's battery of rifled guns, with the Third Indiana Battery and four smooth-bore guns of the Ninth Indiana Battery. I put Lieutenant Tiemeyer's battery in position on the right of the line and the Ninth Indiana Battery near the left, having two regiments on the left of it for support. I had just got my line formed after passing through the thicket when the enemy moved upon us, coming in columns in mass on our left and in line of battle in our front. I immediately sent for two regiments of Colonel Shaw's brigade, which had been held in reserve, but before they arrived the cavalry on my left flank were driven back, the enemy following them and getting in rear of my left flank. I immediately ordered the Third Indiana Battery and the two regiments on the left of it to move in such a direction as brought them nearly at right angles with the balance of my line and facing the enemy, who were moving down on our flank. I also ordered the other portion of the line, which had driven the enemy in their front, to fall back so as to connect with the right of the troops, whose position I had changed. The troops on the left were now formed facing the woods. Just as they had got into position the two regiments of Colonel Shaw's brigade, which were held in reserve and which I had previously sent for, came up, and I put them into position on the left. I then ordered the battery to be doubled-shotted with canister. The enemy on our flank were soon driven back, and with great slaughter. I then (after resting the men a few minutes and giving them an opportunity to replenish their ammunition) ordered another advance. I found that the enemy had made an advance and had entered the thicket, through which the main portion of my line had to pass. We encountered them in the thicket, and a short but desperate struggle ensued, in which they were driven into and part way across the open field beyond, with great loss in killed and wounded and about 160 prisoners. My left being exposed, the cavalry having been again driven back, I ordered my troops back to reoccupy their original position, the enemy first being driven from our left. I left a line of skirmishers in front of the thicket. The enemy did not attempt to make another attack. I have been since informed by the chaplain of the Fifty-eighth Illinois, who was captured a few days previous and afterward released, that the enemy acknowledged a loss in that engagement of about 600 killed and wounded. This, together with the prisoners captured by us, would make their loss nearly three times as great as our own.

Too much praise cannot be given either to officers or men in meet-