HEADQUARTERS IN THE FIELD,
Near Abbeville, Miss., December 3, 1862.

The enemy deserted their fortifications yesterday, destroying all the stores they could not carry with them. The weather bad and stream somewhat swollen, making it difficult to cross. Some of the cavalry swam the river, however, and occupied this place last night. To-day pursuit was made to Oxford, coming on rear guard of enemy. Skirmishing lasted about two hours, resulting in the capture of some 60 rebels. The pursuit will continue to-morrow but the roads are too impassable to get up supplies for a longer continuance of it. General Sherman crossing at Wyatt.

U. S. GRANT,

Major-General.

Major General H. W. HALLECK, General-in-Chief.

ABBEVILLE, MISS., December 3, 1862.

(Received December 4, 7.15 p.m.)

A volunteer sent south by General Rosecrans has just returned. Reports that Arkansas forces are to cross the river. They will either make a stand at Vicksburg and Jackson or combine with forces against Rosecrans and abandon Mississippi.

U. S. GRANT,

Major-General.

Major General H. W. HALLECK, General-in-Chief.

NEAR ABBEVILLE, MISS., December 4, 1862-12.20 p.m.,

(Received 4.18 p.m.)

How far south would you like me to go? We are now at Yocony, and can go as far as supplies can be taken. I will cut the Mobile road south of Tupelo. Would it not be well to hold the enemy south of Yalabusha and move a force from Memphis and Helena on Vicksburg? With my present force it would not be safe to go beyond Grenada and attempt to hold present lines of communication. I have heard nothing from Steele's expedition, but from the precipitate flight of the enemy I think it must have been successful.

U. S. GRANT.

Major General H. W. HALLECK, General-in-Chief.

OXFORD, MISS., December 5, 1862. - 1 p.m.

Roads have become too impassable to leave railroad any great distance. Streams are high. The railroad is now complete to Holly Springs and will be to Tallahatchie by Monday. From Tallahatchie to the Yocony River the enemy were followed so closely that they could not destroy the railroad or telegraph. The cavalry under Colonel Dickey are still out. If practicable, will tap the Mobile Railroad before returning. If the Helena troops were at my command I think it practicable to send Sherman to take them and Memphis troops south of mouth of Black [Yazoo] River and thus secure Vicksburg and State of Mississippi.

U. S. GRANT.

Major General H. W. HALLECK, General-in-Chief.