3 were reported to me killed and 22 captured, with their horses, arms, and equipments.

First Sergt. James Cahill, Company C, Fifth U. S. Cavalry, was the first to cross the bridge with 5 men. He was quickly followed by Captain White with a squadron of the Third Pennsylvania, who pursued the enemy three-fourths of a mile on the other side. Lieutenant Byrnes and Captain Custer took the road to the left toward Malvern Hill, chasing, shooting, or capturing all the pickets that came from that direction, while Lieutenant McIntosh held the reserve a good position to act in any direction. Learning from the prisoners that the enemy were made aware of our intentions the night before, and that a camp of infantry and artillery, on my right, and the First North Carolina Cavalry, on my left, were within a short distance, I concluded to withdraw, the object of the reconnaissance having been accomplished. This was done without accident. I have no loss to report, excepting 2 horses killed.

I beg leave to commend the gallant and spirited conduct of Captain Custer and Lieutenant Byrnes, also of Lieutenant McIntosh, Fifth United States, and Captain White, of the Third Pennsylvania Cavalry. First Sergt. James Cahill, before mentioned, with 5 men pursued and captured 7 or 8 prisoners. All the officers and men displayed great steadiness and spirit. I am particularly indebted to Lieutenant King, my acting assistant adjutant-general, and Lieutenant Hess, Third Pennsylvania Cavalry, and Rumsey, First New York Artillery, my acting aides on the occasion, for their readiness in carrying my orders and placing the squadrons and guns in position.

I am, general, very respectfully, your obedient servant,

WM. W. AVERELL,

Colonel, Commanding.

Brigadier General S. WILLIAMS,

Adjutant-General Army of the Potomac.

HEADQUARTERS FIRST CAVALRY BRIGADE, August 6, 1862.

SIR: I have the honor to report that the cavalry operations of 4th instant were confined to the usual picket duty. Nothing was seen of the enemy on any of the roads. Yesterday I proceeded with 200 men from the Fifth United States and 200 from the Third Pennsylvania Cavalry, accompanied by Gibson's battery, under command of Lieutenant Pendleton, out to Saint Mary's Church, first Long Bridge road. From here I sent a squadron which had been on picket at this point all night to vedette the road that leads past Nance's Mill, at the cross-roads, about 1 mile farther on the road to Long Bridge road. I left one section of this battery with a cavalry support and proceeded with the balance of my command to White Oak Swamp Bridge, leaving Long Bridge on my right going out. The pickets sent out to this bridge report that it is destroyed.

Upon arriving at White Oak Swamp Bridge I posted my artillery in positions commanding the approaches from all sides. One squadron of cavalry crossed the bridge; the others were posted at the different positions of advantage. They captured 22 cavalrymen and killed 3. They belonged to the Tenth Virginia, and were on picket duty. After remaining here half an hour, and capturing almost the entire rebel picket, I returned with my command to camp, without again seeing the enemy.