MEMPHIS, January 2, 1863.

General GRANT:

GENERAL: I send this by an express scout, and will send a copy on the other road. Affairs do not look well; it is reported, but not, I think, reliable that a force of cavalry from the Grenada army is working up between your line, and the river, indicating toward Panola and Senatobia. No news here; have heard nothing from Quinby since he left. Great activity and a new impetus to guerrillas below, burning cotton and wood-piles to hinder navigation. Kirby Smith and Morgan are in Kentucky-Morgan at Glasgow. Rosecrans still stationary in God's name, why does he not move? We have, 4,000,000 rations due here and to be kept on hand at that amount. Gorman moves from Helena, leaving only a garrison in fort; this move is in conjunction with Curtis' force toward Little Rock. Gorman's dispatch within will explain more fully matters below.

Your obedient servant,

S. A. HURLBUT.

[Inclosure.]

HEADQUARTERS DISTRICT OF ARKANSAS,
Helena, January 1, 1863.

General HURLBUT, Memphis:

GENERAL: The Minnehaha has been returned with the rebel prisoners sent down from Cairo a few days since, owing to progress of fight at Vicksburg. Captain White, of this steamer, informs me that our fleets and gunboats are in great need of coal. I send the steamer Kenton to report to you. See if it is possible for you to send two barges of coal to General Sherman and the fleet. The Blue Wing was captured at Napoleon, or near there, with a mail, some artillery ammunition, and two barges of coal, by the enemy, and I think the steamer Home has also been captured, with two barges of forage. The fighting on Monday was terrific; our loss perhaps 2,000 or 3,000. The dead body of Colonel Wyman, of Thirteenth Illinois, is here on board the flag-of-truce boat. We had taken on Monday one fortification with nine guns. We also took three rifle-pits and their big work, but it had to be given up again. Captain White will give you further particulars of General Sherman's fight. I learn that General Sherman needs re-enforcements, but have no word from the general or from the admiral on the subject, officially or otherwise.

I am, general, very respectfully,

W. A. GORMAN.

HOLLY SPRINGS, MISS., January 2, 1863.

Major General STEPHEN A. HURLBUT, Memphis, Tenn.:

Some of the rebel cavalry captured between here and Memphis were armed with perfectly new carbines, which evidently were procured in Memphis. These marauders are probably also getting all other contraband supplies from there.

I know it is impossible, with your present small force, to prevent smuggling in contraband articles entirely, but I would suggest that the provost-marshal be directed to make a descent upon all business houses, and if any are found to be carrying on an illegal traffic confiscate their stock in trade and ship the offenders south of our lines.

Have you heard from Davies, whether he is sending you re-enforcements, or from Gorman, whether the cavalry of Hovey's command is