The casualties of Colonel Cross in this engagement were as follows: Private Alexander C. Walker, of Company F, wounded with a minie ball in the thigh; Company G lost 4 men missing, to wit, Corpl. William Hickman and Privates James M. Hair, Alexander Hair, and James A. Jenkins; Company B lost, missing, 9 men, to wit, Sergt. J. A. Brown, Corpl. Thomas D. Woods, and Privates John Baley, Callaway Beets, Wiley Parker, Foster E. Brown, John McClannahan, four of whom have since returned, but without arms or accouterments, to wit, John Baley, Callaway Beets, Wiley Parker, and John McClannahan; and W. G. Anderson, of Company A, was left sick upon the mountain.

The Third and Fifth Regiments were marched off the point of the mountain into Chattanooga between the hours of 2 o'clock and sun up on the morning of the 24th instant to present camp in Chattanooga. Colonel Cooper, Sixth Regiment, who was, with his command, left on the point of the mountain as a picket, was flanked and attacked by a superior force of the mountain as a picket, was flanked and attacked by a superior force of the enemy early in the morning of September 24, but resisted the attack stubbornly until compelled to yield the ground and march his command to my present encampment, which he successfully did, losing 1 man, missing, to wit, Private John Harris, of Company B.

In the engagement on Tuesday my whole command, officers and men, acted well, gallantly, and bravely. Major Gamble, of Sixth Regiment, had a minie-ball hole shot through his hat, the ball cutting the skin on the top of his head, but he remained on the battle-ground throughout. Two companies of Colonel Shelley were left at Carthage and three were on the railroad.

Very respectfully, your obedient servant,

JAMES G. SPEARS,

Brigadier-General, Commanding, &c.

Lieutenant Colonel C. GODDARD,

Asst. Adjt. General, Dept.of the Cumberland.

HDQRS. THIRD BRIG., THIRD DIV., RESERVE CORPS, On First Bench of Lookout Mountain Point, September 22, 1863.

GENERAL: The enemy attacked us to-day at 12.30 with four regiments of infantry and artillery. My forces fought well and never yielded the ground until they were overpowered and compelled to fall back, which was done in good order, and we now have our position on the first bench of the mountain. The enemy seems to be reluctant in advancing. I have several men killed and many wounded. I will contest it according to your order this day, inch by inch and foot by foot.

Respectfully, your obedient servant,
JAMES G. SPEARS,

Brigadier-General, Commanding.

Major-General ROSECRANS.

[P. S.]- I am informed the enemy is endeavoring to flank me across the mountain beyond; whether true or not I am unable to state. The enemy holds the position I occupied this morning.