GRANT'S HEADQUARTERS,

Jackson, Tenn., October 5, 1862.

Yesterday the rebels, under Van Dorn, Price, and Lovell, were repulsed from their attack on Corinth with great slaughter. The enemy are in full retreat, leaving their dead and wounded on the field. Rosecrans telegraphs that the loss is serious on our side, particularly in officers, but bears no comparison with that of the enemy. General Hackleman fell while gallantly leading his brigade. General Oglesby is dangerously wounded. McPherson reached Corinth with his command yesterday. Rosecrans pursued the retreating enemy this morning, and should be attempt to reach Bolivar will follow him to that place. Hurlbut is at the Hatchie with 5,000 or 6,000 men, and is no doubt with the pursuing column. From 700 to 1,000 prisoners, besides wounded, are left in our hands.

U. S. GRANT,

Major-General, Commanding.

Major-General HALLECK.

HEADQUARTERS,
Jackson, Tenn., October 5, 1862.

General Ord, who followed Hurlbut and took command, met the enemy to-day on south side of Hatchie, as I understand from dispatch, and drove him across the stream and got possession of the heights with our troops. Ord took two batteries and about 200 prisoners. A large portion of Rosecrans' forces were at Chewalla. At this distance everything looks most favorable, and I cannot see how the enemy are to escape without losing everything but their small-arms. I have strained everything to take into the fight an adequate force and to get them to the right place.

U. S. GRANT,

Major-General.

Major-General HALLECK, General-in-Chief.

GENERAL GRANT'S HEADQUARTERS

Jackson, Tenn., October 6, 1862-12.3 p. m.

General Ord and Hurlbut came on the enemy yesterday, and Hurlbut, having driven small bodies the day before, after seven hours' fighting, drove the enemy 5 miles back across the Hatchie toward Corinth, capturing two batteries, about 300 prisoners, and many small-arms. I immediately apprised Rosecrans of these facts and directed him to urge on the good work.

Following dispatch just received from Chewalla, October 6:

[CHEWALLA, October 5.]

Major-General GRANT:

The enemy are totally routed, throwing away everything. We are following sharply.

W. S. ROSECRANS.

Under previous instructions Hurlbut is also following Mcpherson, in the lead of Rosecrans' column. Rebel General Martin said to be killed.

U. S. GRANT,

Major-General, Commanding.

Major-General HALLECK, General-in-Chief.