HOLLY SPRINGS, MISS., January 4, 1863.

Brigadier General C. S. HAMILTON, La Grange, Tenn.:

There is no doubt of a concentration of troops for the purpose of attacking Corinth. It will be necessary to strengthen that place with at least a division.

If Fuller's brigade has not yet returned, instruct them to go there, and I will send the balance of the division as soon as they can be replaced by troops from here.

U. S. GRANT,

Major-General.

HOLLY SPRINGS, MISS., January 4, 1863.

Brigadier General J. B. McPHERSON, Abbeville, Miss.:

If the report of Vicksburg being in our possession proves true I will fall back to the line of Memphis and Corinth at once. There is no objection to your falling back now to the Waterford and Chulahoma road, leaving a small force on the road near the river.

A long dispatch from Vicksburg on the 29th is just received. Sherman had had a desperate fight, in which he had lost 3,000 men, killed and wounded; he had carried enemy's rifle-pits and one fort of nine guns, and also their principal fort, but from the latter he had been forced to fall back, owing to support not coming up in time. Morgan Smith and his brother were both wounded, the former probably dead.

When the boat left a fleet was coming up the river, probably Banks'. I have news overland of his arrival in New Orleans, and a dispatch to-day from General Halleck says that he is to push up the river.

U. S. GRANT,

Major-General.

HOLLY SPRINGS, MISS., January 4, 1863.

Colonel W. S. HILLYER, La Fayette, Tenn.:

A dispatch just received from General Halleck says that Banks is pushing up the Mississippi to Vicksburg. This with the news from Vicksburg that a fleet is seen coming up the river is satisfactory that Sherman is re-enforced before this. It would take me four days to get re-enforcements for him to Memphis, unless I should abandon the railroad.

Inform Hurlbut of these facts.

U. S. GRANT,

Major-General.

LA GRANGE, January 4, 1863.

General GRANT:

Fuller's brigade yesterday had gone to Clifton. All the troops from my command sent to Sullivan have pushed far to the east and north.

I have telegraphed Sullivan to send Fuller immediately.

C. S. HAMILTON.