At 5.35 a. m. of the 3rd instant my command was moving, and at 6.30 a. m. it was at Black River, opposite Trinity. By 10 a. m. Captain --- had three pontoon boats in readiness, and I crossed my command, leaving all my transportation on the east side of the river, excepting one ambulance and one ammunition wagon to each regiment. Here I received orders from General Crocker to press on to Harrisonburg by the left-hand road.

Leaving Trinity at 3.50 p. m., I marched until 7.40 p. m., and halted 9 miles north of Trinity and 2 miles south of the junction of the Trinity and Alexandria roads. I received a message at 11 p. m. from Colonel Mally, stating that he was at the junction with his command, and that the enemy, from 2,000 to 4,000 strong, was approaching from the west on the Alexandria road. Upon the receipt of this intelligence, I sent an order to Colonel Malloy to send four companies of his command out on the Alexandria road, with instructions to obtain information of the strength and whereabouts of the enemy, if he should be found; and I moved with my command over a difficult road to the junction, where I arrived at 3 a. m. on the 4th instant, and formed in line of battle across the Alexandria road. I remained in this position until 6.20 a. m., and not hearing from the reconnoitering party, I determined to leave Colonel Malloy to look to the rear, and move on to Harrisonburg. When within 3 of 3 1/2 miles of Harrisonburg, I was overtaken by a courier from Colonel Malloy, with information that he, Malloy, had encountered the enemy, 4,000 strong, on the Alexandria road, 5 miles from the junction, and that he was skirmishing with him and gradually falling back. I immediately countermarched my command, and arrived at the junction at 7.45 a. m., and formed in line of battle as before. About this time General Crocker arrived, and I reported to him what had transpired.

About 8.30 a. m. Colonel Hall arrived with the Second Brigade, and formed on my left. I remained in this position until I received orders from General Crocker to resume the march in the direction of Harrisonburg, at which place I arrived at 11.40 a. m., and rested until 5 p. m., when I received orders from General Crocker to return to Natchez by the same route, following the Second Brigade. About dark I halted at a point 2 miles west of Harrisonburg, and rested until 5 a. m. next morning,t he 5th instant, and resumed the march, arriving at Trinity at 11.30 a. m., when I received orders from General Crocker to cross the river, and remain on the opposite side until the mounted infantry arrived and the pontoons were ready to be taken up, which I did. After crossing Black River, I marched 4 miles, and halted at 6 p. m. on the Tensas River.

At an early hour on the morning of the 6th instant, my command was on the march, and at 6.30 p. m. I halted near Vidalia. Have marched 94 miles in less than five days. On the morning of the 7th instant, I recrossed the Mississippi, and returned to my old camp.

Considering the excessive heat and the obstacles encountered inc rossing rivers and bayous, the expedition is remarkable for the length of time in which it was made. if affords me pleasure to be able to say that, although the march was fatiguing and arduous, the men endured it with a fortitude and patience characteristic of good soldiers.

I have the honor to be, very respectfully, your obedient servant,

W. Q. GRESHAM,

Brigadier-General.

Captain W. H. F. RANDALL,

Asst. Adjt. General, Fourth Div., Seventeenth Army Corps.