Franklin pike, and cavalry at Franklin and along the Franklin pike toward Nashville.

I have information from Farmington, Marshall County, to last night to the effect that Bragg's forces are at Tullahoma, Buckner at Shelbyville, and Breckinridge at Murfreesborough. The enemy are collecting a large amount of supplies from Columbia and vicinity, and are running them through Farmington toward Shelbyville, and have been doing so for nearly the last three weeks. Bragg's forces arrived at Tullahoma about eight days ago, and Buckner's at Shelbyville a short time previous. The party coming from Farmington came by Chapel Hill and Nolensville, but encountered no pickets of the enemy until he arrived in the vicinity of Nolensville. All the bridges on the pikes and byroads toward Nolensville and Franklin have been destroyed.

I give the above information for what it is worth. It may serve to confirm, or it may prove to be untrue from the more accurate reports which you may have received.

I am, sir, very respectfully, your obedient servant,

P. H. SHERIDAN,

Brigadier-General, Commanding.

P. S.- I find great abundance of forage on the right of my present position.

[NOVEMBER 24, 1862.]

General THOMAS:

How much of your it be necessary to leave at present for the railroad and of the communications?

ROSECRANS.

[NOVEMBER 24, 1862.]

General ROSECRANS:

It depends on what kind of a move is made. To move across the river, one brigade would be sufficient; to move toward Nashville, one division, at least, should be left here.

GEO. H. THOMAS.

NASHVILLE, November 24, 1862.

Major-General GEORGE H. THOMAS:

Anderson reports firing in your direction. General wants to know what it was; if it was rebels, Crittenden might slip in behind and bag them.

J. P. GARESCHE,

Assistant Adjutant-General and Chief of Staff.

[NOVEMBER 24, 1862.]

General THOMAS:

Have you any news from Tompkinsville?

ROSECRANS.