HDQRS. THIRD DIVISION, TWENTIETH ARMY CORPS, May 7, 1864.

Major-General HOOKER:

GENERAL; After studying the map with a compass, I have arrived at the conclusion I was mistaken; that the forces seen were on Tunnel Hill, and was not the enemy. I will pay a battle or two.

Very respectfully,
DANL. BUTTERFIELD,

Major-General.

HEADQUARTERS TWENTIETH ARMY CORPS, ASSISTANT INSPECTOR-GENERAL'S OFFICE, May 7, 1864.

Lieutenant-Colonel MENDENHALL,

Inspector-General, Department of the Cumberland:

COLONEL: I have the honor to report that the Twentieth Corps is encamped in Dogwood Valley, crossing Taylor's Ridge early in the morning by Nickajack Gap and Gordon's Gap. The First Division is located at Trickum Post-Office, one brigade north, one east, and one south of it. I am unable to say whether the communication has been established with the Fourteenth Corps near Tunnel Hill. The Third Division encamps on the Dalton and Gordon's Springs road, one brigade holding the ridge near Mrs. Swain's house; the other two brigades encamping to the rear and right of the former, the picket-line connecting with the right of the First Division has two brigades encamped on the Ringgold and Villanow road about three miles south from Trickum Post-Office, the picket-line connecting with the right of the Third Division and with the left of the other brigade, which is encamped, together with the cavalry under command of Brigadier-General Kilpatrick, about a mile east of Gordon's Gap. The train of the corps is encamped at the junction of the Nickajack with the old Alabama road, ambulances and wagons loaded with ammunition and intrenching tools only accompanying the troops. The cavalry had a very slight skirmish with the enemy coming through Nickajack Gap. The rebel withdraw their picket-line in front of the Second Brigade, Third Division, on the Dalton road about 3 p. m. The roads are good, the gaps are passable; no forage in the country, but plenty of grazing.

Respectfully, your obedient servant,

C. W. ASMUSSEN,

Assistant Adjutant-General.

HDQRS. THIRD CAV. DIV., ARMY OF THE CUMBERLAND, May 7, 1864.

Major-General HOOKER:

GENERAL: I arrived at Villanow at 7.30 a. m. Sent a party to Ship's Gap. No news of the enemy.

Very respectfully, your obedient servant,
J. KILPATRICK,

Brigadier-General, Commanding Division.