CORINTH, January 3, 1863.

GENERAL: Forrest escaped across the river at Clifton at 7 a. m. January 1, having traveled all the time since his fight, and immediately attacked my cavalry. They kept him from the river until night, when they found they were surrounded by a very heavy force and two pieces of artillery. They cut their way out down river and got into his rear next morning. Forrest commenced crossing that night, his men on rafts, his horses swam. The cavalry attacked again the 2d, and this morning he had everything across by 10 o'clock. I could not reach him with my forces, but sent forward all the mounted men I could raise, with one section of artillery. They will get to Clifton to-day. No gunboats in the river. Heard nothing from Sullivan's forces. Our cavalry have lost considerable in killed and wounded, but not many prisoners. They took several of Torrest's men. I have just returned.

G. M. DODGE,

Brigadier-General.

Major-General GRANT.

Number 3. Reports of Brig. Gen. Jeremiah C. Sullivan, U. S. Army, commanding District of Jackson, of skirmish at Lexington and engagements near Jackson and at Parker's Cross-Roads, with congratulations from Major-General Grant.

JACKSON, December 18, 1862-7.10 p. m.

My cavalry was whipped at Lexington to day. Colonel Ingersoll taken prisoner and section of artillery captured. The enemy are reported to be from 10,000 to 20,000 and still crossing the river. They are now within 6 miles of my outposts. I will try and find their number by daylight.

JER. C. SULLIVAN,

Brigadier-General.

Major General U. S. GRANT.

JACKSON, December 19, 1862.

GENERAL: This morning, as I was preparing to advance, information was brought me that the enemy were advancing in force. At the same time I received news that the station on Columbus [road], 8 miles from here, was attacked at daylight, the guard of 87 men captured, the station-house burned, and road at switch destroyed.

A few moments later, news from Corinth road was received, giving news that the bridges 12 miles south were burned and that a large force had crossed, going toward railroad leading to Bolivar. Almost at same time the enemy opened their artillery on my advance force and drove them into within 3 miles of Jackson. My men skirmished up to 3 o'clock, at which time the brigade of Colonel Fuller's command arriving, two regiments reporting, I immediately advanced six regiments, under General Brayman, who drove them back, and at present are bivouacking in front, 6 miles out. I move at daylight with my force, leaving 2,000 men to hold this place.

Prisoners taken to-day confirm reports of their having crossed the Tennessee River in flats and pontoon bridges, a full cavalry regiment crossing with horses and wagons in half a day. Forrest has six or seven colonels, but can get no estimate of force. Cheatham's brigade is