Small squads hovering around. We drove back their scouts this morning. Four regiments of our cavalry have arrived from Holly Springs. We are after them.

J. MCDERMOTT,

Lieutenant-Colonel, Commanding.

GRAND JUNCTION, December 23, 1862.

Major-General GRANT:

Arrived here at 2 o'clock with four regiments of infantry. Cavalry just leaving here for the north.

C. C. MARSH,

Colonel Twentieth Illinois, Commanding.

GRAND JUNCTION, December 23, 1862.

General U. S. GRANT:

Colonel Richmond telegraphs that his pickets have been fired on to-night. He calls for re-enforcements.

C. C. MARSH,

Colonel.

GRAND JUNCTION, December 23, 1862.

General SULLIVAN:

I am here with cavalry. Telegraph me any information as to movements of the enemy.

B. H. GRIERSON,

Colonel, Commanding Cavalry.

OXFORD, December 23, 1862.

General GRANT:

GENERAL: Having learned that a strong cavalry force was 5 miles east of Waterford at 3 o'clock, I have ordered Colonel Hatch, with his entire command, to move immediately toward Pontotoc and see if he cannot get on track of the rebels. Have also sent orders to General Lauman, General Denver, and the officers in command of guards for trains to be on the alert, and guard especially against any cavalry dash.

JAS. B. MCPHERSON,

Major-General.

HOLLY SPRINGS, MISS., December 23, 1862.

Major General J. B. MCPHERSON, Oxford, Miss.:

A force of rebel cavalry are now encamped at the mouth of Tippah Creek, going south with a large number of led horses and mules, probably those captured here. The main body of the rebels went north from here. Send this word to Hatch. By properly directing his course he may recover much that was lost here.

U. S. GRANT,

Major-General.