the same division, which started early this morning, supported by a brigade from General Sheridan's division, on the right, and two regiments of Reynolds' division, on the left. They pushed forward to within 1 1/2 or 2 miles of Tullahoma, driving the enemy with comparative ease. General Steedman, the brigade commander is of the opinion that he was opposed by two regiments of cavalry and a section of artillery. His loss was 13 men wounded. He killed and wounded a good many of the enemy, but he cannot tell how many. The two regiments of Reynolds' division also reached a point about 2 miles from Tullahoma, where they came upon a regiment of the enemy's cavalry, which retired after feeble resistance; the officer in command, believing that it was intended to draw him into an ambuscade, did not pursue any farther. Two regiments of Negley's division moved over on the Winchester road 4 or 5 miles without encountering or hearing of the enemy.

Very respectfully,your obedient servant,

GEO. H. THOMAS,

Major-General U. S. Volunteers., Commanding.

Major General W. S. ROSECRANS, Commanding Department.

CAMP AT HALE'S MILL, July 1, 1863-9 p.m.

(Received Hdqrs. Dept. of the Cumberland July 2-1.25 a.m.)

GENERAL: I have the honor to report the following movements to-day:

Having heard from a citizen early this morning that the enemy were evacuating Tullahoma, General Steedman, commanding Second Brigade, Third Division, was ordered to advance cautiously and ascertain if the report were true. He entered Tullahoma at 12 m., capturing a few prisoners. General Brannan, commanding the division, reports that the last of the infantry withdrew last night. The cavalry commenced evacuating at daylight. General Reynolds was accordingly ordered to Tullahoma with his division,to support Brannan, and the two divisions were ordered to rejoin the corps at Heffner's Mill to-morrow morning. General Negley was directed to march to Heffner's Mill and take post there for the night, General Rousseau to support him. In executing this order, Negley came upon the enemy about 4 miles from Bobo's Cross-Roads, and drove them before him steadily until they retired beyond Heffner's Mill. He then went into camp for the night, throwing out strong pickets to the right and front. General Rousseau was instructed, after forming his camp, to throw out pickets to the rear and left. The enemy made quite a stubborn through the pass of Spring Creek, wounding a good many of our men, but they were steadily driven until we encamped for the night.

Very respectfully, your obedient servant,

GEO. H. THOMAS.

Major-General U. S. Volunteers, Commanding.

Major General W. S. ROSECRANS, Commanding Department.

CAMP AT JONES' CROSSING,

July 2, 1863-8 p.m.

GENERAL: I have the honor to report the following movements in my corps to-day:

The Third and Fourth Divisions joined me at Spring Creek, and the