Number 13. Report of Brigadier General Edward Ferrero, U. S. Army, commanding SECOND Brigade. HDQRS. SECOND Brigadier, SECOND DIV., NINTH A. C., Jackson, MISS., July 18, 1863.

CAPTAIN: I have the honor to report that at 3 a. m. on the 16th I relieved General Welsh's line of skirmishers with the SECOND and THIRD Brigades of the SECOND DIVISION, I having been placed in command of the line by an order of General R. B. Potter. The troops of the THIRD BRIGADE were posted as skirmishers, supported by the SECOND Brigade.

At 11 a. m., by signal from battery, I advanced my line of skirmishers for the purpose of ascertaining the position and force of the enemy.

The troops advanced until the enemy was driven into his rifle-pits. Troops were seen drawn up in line behind the works. MY line of skirmishers then withdrew and occupied their old line.

At about 9 o'clock I received reports from the advanced post along the line that artillery and infantry could be distinctly heard moving in an easterly direction trough the town. After satisfying myself that these reports were correct, and that the enemy was really moving, I communicated the fact to General R. B. Potter at about 11 p. m.

At 2 a. m. Of the 17th, the skirmishers of the THIRD Brigade were relieved by troops from the SECOND Brigade, and at daylight the line was advanced to ascertain the correct position of the enemy's skirmishers. No enemy was found; and, after proceeding a short distance toward the town, a white flag was seen on the earthworks. I then ordered a general advance of my line, entered Jackson at 6 a. m., placed guards over private property, and sent out patrols to take all of the enemy still remaining in town.

There were left in town by the retreating forces about a thousand stand of arms and a large quantity of ammunition. On the earthworks was left one 23-pounder rifled gun. My patrols captured 1 SECOND lieutenant and 137 enlisted men.

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

EDW. FERRERO,

Brigadier-General.

Captain H. R. MIGHELS,

Assistant Adjutant-General.

Number 14. Report of --, forty-sixth New York Infantry, THIRD Brigade. NEAR JACKSON, MISS., July 18, 1863.

COLONEL: In conformity with General Orders, number 13, headquarters SECOND DIVISION, I herewith have the honor to bring to your knowledge in the engagement before Jackson, and also it movements from Monday, 13th, to this date:

During the 13th instant, this command acted with the FIFTIETH Pennsylvania and Twenty-NINTH Massachusetts as reserve, supporting the Jackson. Advanced toward 8 p. m. Some 500 yards, and at 7 a. m. on the 15th marched back to take position behind Benjamin's battery,