NEAR CORINTH, May 30, 1862.

Our advance guards are in Corinth. Conflicting accounts as to enemy's movements. Believed to be in strong force on our left flank, some 4 or 5 miles south of Corinth, near the Mobile and Ohio Railroad.

H. W. HALLECK,

Major-General.

Honorable E. M. STANTON, Secretary of War.

HEADQUARTERS,
Camp near Corinth, May 30, 1862.

Enemy's positions and works in front of Corinth were exceedingly strong. He cannot occupy stronger positions. In his flight this morning he destroyed an immense amount of public and private property-stores, provisions, wagons, tents, &c. For miles out of the town the roads are filled with arms, haversacks, &c., thrown away by his flying troops. A large number of prisoners and deserters have been captured, and estimated by General Pope at 2,000. General Beauregard evidently distrusts his army, or he would have defended so strong a position. His troops are generally much discouraged and demoralized. In all their engagements the last few days their resistance has been weak.

H. W. HALLECK.

Honorable E. M. STANTON, Secretary of War.

HALLECK'S HEADQUARTERS,

Corinth, May 31, 1862.

Main body of the enemy has moved south toward Okolona. General Pope, with 50,000, men is following him. I do not, however, propose to pursue him far into Mississippi. Having no baggage trains except railroad trains, he can moved much faster than we can pursue. I propose to immediately open the railroad to Decatur, Ala., and to Columbus, Ky. The fall of the Tennessee river will soon render the use of this road necessary to us for supplies. The destruction of the Decatur Bridge by General Mitchel was a most foolish operation. If that had not been done we could have had a connection with him in one week. As it is, we must receive our locomotives and cars from the Ohio River. I have ordered an examination of the road toward Florence, and I think a couple of locomotives landing at that place with cars could be immediately brought here, and be of great assistance to us in repairing the road to Columbus, Ky. Please inform me immediately if an agent of the War Department will act in this matter of procuring locomotives and cars or if I shall detail a quartermaster for that duty. There is no time to be lost in this matter.

H. W. HALLECK,

Major-General, Commanding.

Honorable E. M. STANTON.

HALLECK'S HEADQUARTERS,

Corinth, June 1, 1862.

A brigade of cavalry, under Colonel Elliott, cut the enemy's line of retreat at Booneville, 20 miles south of Corinth, captured three pieces