First Division, Colonel La Grange commanding, arrived about 2 p. m. and was sent under cover to the right. About 3 p. m. the enemy was seen to be falling back. As soon as In discovered this, and that the lull in the firing was not caused by a movement of the enemy toward our left, as was reported, I ordered, I an advance, the section of Lilly's battery, which had joined with the Second Brigade, throwing shot and shell into his retreating lines and columns. The pursuit was rapid and continued until dark,driving the enemy about 4 miles, and beyond the ground occupied in the morning, but on account of scarcity of water the troops occupied their same camps, leaving our picked line on the ground from which the enemy was driven. According to instructions from General Sturgis the infantry and section of the Elgin battery from Colonel Mott's brigade was ordered to return to Mossy Creek.

For the details of the operations of the First Division of Cavalry, and the casualties in same, I refer to the reports if its commander and of his subordinates, and to the reports of Colonel Palmer for the operations of his detachments, all herewith inclosed. The loosed of the enemy must have greatly exceeded that of ours, his lines and columns being exposed to our fire from small -arms and Lilly's battery, so admirably served. Both in his advance and retreat many of his dead and wounded were left in the field. I do not think that 100 killed and 400 wounded would be an exaggerated estimate of his loss.

In closing this report I desire to refer to the services of Colonel e. m. McCook, Second Indiana Cavalry, commanding First Division. The skill with which he disposed of his division on the field, on this as on other occasions, and energy in the pursuit of the enemy, shows him to be capable of exercising the command with which he is intrusted. Brigades, regiments, and the battery of Lilly-officers and men, without exception-performed their duty nobly.

The officers of my personal staff, First Lieutenants C. F. Mardon, Second Iowa Cavalry, and W. L. Shaw, One hundred and tenth Ohio Volunteer Infantry, aides-de-camp; and of the corps staff, Captain McCormick, acting inspector-general: Captain Schuyler,provost-marshal; First Lieutenant W. C. Arthur, assistant commissary of subsistence, and Captain Warner, commanding escort, rendered me great assistance, conveying my orders on the field, as did also my orderlies from Company D, Fourth Ohio Cavalry. Surg. L. A. James, Fourth Ohio Cavalry, medical director, faithfully provided for the comfort of the sick wounded.

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

W. L. Elliott,

Brigadier-General, U. S. Volunteers, and Chief of Cavalry.

Captain W. C. RAWOLLE,

A. A. A. G., HDQRS. Chief of Cav., Army of the Ohio.

Numbers 4.

report of Colonel Edward M. McCook, Second Indiana cavalry, commanding First Cavalry Division.

HEADQUARTERS FIRST CAVALRY DIVISION,
Daniel's House, 2 1/2 M. from Mossy Creek, Tennessee, December 30, 1863.

SIR: Without reports of brigade commanders, I am unable at this time to present as full and detailed a report of the action of yesterday as may be desired.