HEADQUARTERS U. S. FORCES, Shelbyville, October 8, 1863.

Major-General BUTTERFIELD, Bell Buckle, Tenn.:

GENERAL: There is a battle progressing about 15 miles below. Cannonading is heavy. A deserter who just arrived states that Forrest was to form a junction with Wheeler to-day at Columbia, but he thinks that Forrest will unite with Wheeler to-day while the fight is going on. He represents Wheeler's command to be about 11,000, with eighteen heavy guns. I have not received any news from this morning's fight.

I send 5 men who gave themselves up, who say they wish to take the oath.

The Kentuckian is the one from whom I have my information. He says Forrest and Wheeler together have thirty-two brigades.

I am, sir, with due regards, your obedient servant,
ROBT. GALBRAITH,

Commanding Post.

HEADQUARTERS U. S. FORCES, Shelbyville, October 8, 1863.

Major-General BUTTERFIELD:

SIR: General Mitchell is still in pursuit and pressing the rebels rapidly. He is slaying them as he goes, and especially those who wear our uniform.

A part of their command, about 1,000 strong, are still on the north side of the river, cut off. They have some artillery. They may make an effort to recross the railroad and get out via Christiana and to McMinnville.

I will send courier to General Mitchell and inform him of their whereabouts.

I am, sir, with esteem, your obedient servant,

ROBT. GALBRAITH,

Commanding.

HEADQUARTERS U. S. FORCES, Shelbyville, October 8, 1863-4.15 p. m.

Major-General BUTTERFIELD, Commanding, &c.:

GENERAL: I have the honor to report the result of last evening's engagement, as follows:

Our loss is about 12 or 15 killed, and about 40 to 50 wounded. The rebel loss is much greater. We have about 300 prisoners and 4 pieces artillery. Their loss in killed and wounded is estimated at about 300. Colonel Monroe was killed. His body has just arrived, en route for Murfreesborough.

Generals Mitchell and Crook are in pursuit, and are strong in the belief that they can take the whole command of Wheeler.

I have the honor to be, very respectfully, your obedient servant,
ROBT. GALBRAITH,

Commanding Post.

HEADQUARTERS U. S. FORCES, Shelbyville, October 8, 1863-9.20 p. m.

Major-General BUTTERFIELD, Twelfth Army Corps, &c.:

GENERAL: In obedience to your order, I have the honor to report the result of to-day's proceedings, as follows:

The rebels started last night in full flight. General Crook com-