MAY 21-26, 1863. -Expedition from La Grande, Tenn., to Senatobia, MISS., and skirmish (23rd).

REPORTS.

Number 1. -Colonel Edward Hatch, SECOND Iowa Cavalry, commanding First cavalry Brigade, SIXTEENTH Army Corps.

Number 2. -Colonel La Fayette McCrillis, THIRD Illinois Cavalry, commanding SECOND cavalry Brigade.

Number 1. Reports of Colonel Edward Hatch SECOND Iowa Cavalry, commanding First Cavalry Brigade. NEAR COLDWATER, MAY 25, 1863.

GENERAL: I attached Chalmers' command in the Senatobia Swamp on the morning of the 23rd, scattering his forces, drove the main body across the Tallahatchee into Panola, the rest escaping toward Helena. The enemy left 9 dead on the field. Chalmer's forces, I learn from the prisoners, consisted of about 2,000 regular troops and about 1,000 conscripts.

I am, general, your obedient servant,

EDWARD HATCH,

Colonel Commanding.

Major General S. A. HURLBUT.

La GRANGE, Tenn.

May 31, 1863.

CAPTAIN: I have the honor to report that, complying with orders from General Smith, I left camp at La Grange, Tenn., on the morning of May up the rebel General Chalmer's quarter and disperse his forces, collecting stock and provisions and destroying forage. Proceeded with the SECOND Iowa Cavalry, sixth Iowa Infantry, detachments of the Sixth and Seventh Illinois Cavalry, three 2-pounder guns (First Illinois Mount Pleasant, thence 2 miles south of Byhania (Farmington,), where I was joined by Colonel McCrillis having driven the enemy our of Byhalia two hours before. There I found a store had been fired and burned. I immediately sent my adjutant-general to Colonel McCrillis command with the order that, if any outrages of this kind were committed, I should recommend the pay of the troops guilty of them to be stopped against them.

Having reasons to believe the enemy would offer battle at Cockrum's Cross Roads, on the morning of May 22, dispatched Colonel McCrillis command by a road to my left, to take the enemy in flank and rear, while I moved the balance of my command by direct road to Cockrum's. The enemy's pickets disputed the ground steadily to this point, doing us little damage, except occasionally killing a horse. THE enemy retreated from Cockrum's toward Luxahoma. Skirmishing continued during the day. Camped that night near Lucxahoma, on Jim Wolf Creek.

At daylight, May 23, the enemy my attacked my pickets, leading me to believe they would fight at Luxahoma.

Marched early that morning skirmishing with the enemy, to Luxahoma. At this point I sent Colonel McCrillis to feel the enemy forward