MEMPHIS, January 3, 1863.

General GRANT:

I have received dispatches from Gorman. Sherman has had a bitter fight; forced the first line of entrenchments, captured and holds one 9-gun battery; captured their main fort on Walnut Hills at point or bayonet, but supports did not come up, and our men were driven out with great slaughter. Morgan Smith is wounded; Giles Smith, colonel Eighth Missouri, and Wyman, Thirteenth Illinois, killed. Loss about 3,000, killed and wounded. No official report from Sherman. Price and Joe Johnston are at Vicksburg. Steamers from below are seen bringing up troops. I fear Sherman's is overmatched. He has sent for ammunition. I sent him to-day all I have, 230,000 rounds. Have sent his order forward to be telegraphed from Cairo. He wants 4,000,000 rounds. The Blue Wing, with ammunition, was taken below Helena and has gone up the Arkansas. I this day send three barges of coal for the fleet, which they greatly need. Davies still holds the troops above and says he does it by order of General Halleck. Sherman ought to be re-enforced. I think they outnumber him, besides the advantage of position.

Nothing heard from Banks. I have suggested to Gorman propriety of throwing his whole available force, except fort garrison, to Vicksburg.

The messenger Schultz, who was bringing your reply, was captured, but destroyed his dispatches. The road from here to Germantown is full of guerrillas and some regular cavalry. I trust the railroad may be forced through rapidly. It must be strongly guarded down to the depot, as we can't spare any guard. Sherman's wounded will be here before long, I suppose. I am preparing hospital buildings in case they arrive. I require more force than for ordinary guards, and especially cavalry, to beat up these guerrillas. Major Blythe is within 14 miles, on the Hernando road. Richardson near Wolf River, about Germantown.

S. A. HURLBUT,

Major-General.

HEADQUARTERS DISTRICT OF MEMPHIS,
Memphis, Tenn., January 3, 1863.

Brigadier-General GORMAN:

I have sent your dispatches to General Grant. I do not like the look of things at Vicksburg. It is impossible for Grant to send re-enforcements, at all events in time. I have serious doubts as to Sherman maintaining his advance unless Banks comes up. Vicksburg is a place of such vast consequence that it may be well to consider whether it will not be your duty to throw your whole force to that point if it will assure success. I have but four regiments here. Davies has not yet sent the troops down from Columbus.

Grant's army will connect with me by railroad to-day or to-morrow. I shall send coal down in barges by the Kenton to Helena. The Rattler (Mosquito Fleet) will follow to-night and will convoy the Kenton and her barges down. It will not do to permit valuable boats to go below without convoy.

The Blue Wing was probably purposely surrendered; her captain has a bad reputation among loyal river men.