2nd. Lieutenant Guenther's battery and the Second Ohio Volunteers captured the flag of the Thirtieth Arkansas Volunteers.

3rd. Fifteenth Indiana Volunteers, Lieutenant-Colonel Wood commanding, charged and captured 173 prisoners from Twentieth Louisiana Regiment.

4th. Thirteenth Michigan Volunteers gallantly recaptured two guns belonging to Captain Bradley's battery.

5th. Carlin's brigade lost half its field officers in killed and wounded.

6th. Fifth Kentucky Volunteers dragged from the field by hand a section of artillery, through deep mud and under heavy fire.

7th Four color-bearers of the Twenty-first Illinois were shot down, yet the colors were borne safely through the fight.

WASHINGTON, D. C., February 27, 1863.

Colonel KELTON,

Staff of the General-in-Chief, Washington:

COLONEL: I have the honor to forward to you the inclosed letter of Major-General W. S. Rosecrans, commanding department. The general desired me to make such verbal explanations as the General-in-Chief might require.

I also inclose a statement of our available force in and about Murfreesborough, which differs considerably from the "paper" army.

I shall remain in the city no longer than to-morrow, as my health will not permit me to put further off that care and treatment which I can only obtain at home.

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

J. C. PETERSON,

Captain Fifteenth Infantry, and Acting Assistant Inspector-General, Department of the Cumberland.

[Inclosure.]

HEADQUARTERS DEPARTMENT OF THE CUMBERLAND, Murfreesborough, Tenn., February 20, 1863.

Major-General H. W. HALLECK,
Commander-in-Chief, Washington, D. C.:

GENERAL: Captain Peterson, acting assistant inspector-general, being obliged to change climate direction, I avail myself of his zeal and intelligence to send you some details of this army, showing the percentage of absentees and the wear and tear of an army in battle:

1st. I find from careful examination that the average percentage of the present and absent, now present,is;

Per cent.

For the Fourteenth Army Corps......................... 56.01

For the Twentieth Army Corps.......................... 50.16

For the Twenty-first Army Corps....................... 50.44

Presuming that each of these corps has fought but one great battle, in which they lost as follows,viz:

Per cent.

Fourteenth Army Corps................................. 18.44

Twentieth Army Corps.................................. 20.50

Twenty-first Army Corps............................... 24.64

Average loss for the entire command................... 20.03

We have before the battle:

Per cent.

Fourteenth Army Corps................................. 63.42

Twentieth Army Corps.................................. 64.60

Twenty-first Army Corps............................... 66.93.