WASHINGTON, May 31, 1862.

General HALLECK, Corinth:

Do the abandoned works and camps at Corinth indicate a very large rebel force? Can they have begun the evacuation long enough since to have re-enforced Richmond by this time? Their attitude at Richmond has changed, and there have been rumors that Beauregard reached that city on Thursday week.

For the Secretary of War:

M. C. MEIGS,

Quartermaster-General.

CORINTH, May 31, 1862.

M. C. MEIGS,

Quartermaster-General:

If Beauregard has been at Richmond others have forged his signature, as I have received letters from him about exchange of prisoners, and nearly every day for this last fortnight. The evacuation of Corinth commenced on Wednesday and completed on Thursday night, but in great haste, as an immense amount of property was destroyed and abandoned. No troops have gone from here to Richmond, unless within the last few days.

H. W. HALLECK,

Major-General.

BUELL'S HEADQUARTERS, May 31, 1862.

General HALLECK:

Colonel Jackson reports:

We found the enemy in force on the Kossuth road, in a strong position on the far side of the Tuscumbia. From a prisoner we learn and believe they have a brigade, six pieces of artillery, and some scattered cavalry. There are three burnt bridges, which prevented me from using my command except in front and deploying as skirmishers. The casualties 1 killed and 3 badly wounded; a horse or two killed. I can effect nothing here. Will remain until sunset and then return, unless otherwise instructed.

Colonel Jackson does not state the distance, but I suppose it to be about 5 miles from Corinth. It is just beyond where the road was obstructed by trees yesterday. I have directed him to return.

D. C. BUELL,

Major-General.

HEADQUARTERS, May 31, 1862.

Major-General BUELL:

I have sent the steamer Robb to Florence, to ascertain if any of the enemy have retreated in that direction. I think General Mitchel should be directed to cross a small force at Decatur to repair railroad and telegraph line on this side, so as to open communication with us. I propose to repair the road from Farmington in that direction.

H. W. HALLECK,
Major-General.

HEADQUARTERS, May 31, 1862.

Major-General BUELL:

It is now fully shown that the main body of the enemy is retreating south. The first thing now to be done is to open the railroad to Decatur.