I cannot speak too highly of the courage and conduct of the officers and meant of the First Brigade in this desperate assault, which, however, was fully equaled by that of General Ransom's brigade, of which I think it proper to speak, as the brigade was co-operating with one of my own, and was separated by the character of the ground from the corps to which it belonged. The officers and men of both brigades displayed a courage and coolness which could not have failed to win success in a less unequal struggle.

The active operations of the day were closed by an impetuous assault of the brigade of General Mower, of General Tuttle's DIVISION, in your arms corps, which rushed forward by the flank on the same road which had been attempted in the morning by the brigade of General H. Ewing. The attack was made with the greatest bravery and impetuosity, and was covered by a tremendous fire from our batteries, and by the sharpshooter of Ewing's and Giles A. Smith's brigades, and its failure only served to prove that it is impossible to carry this position by storm.

I have aimed to mention that one regiment, the FIFTY-FIFTH Regiment Illinois Volunteers Infantry, from the brigade of Cool. Thomas Kilby Smith, participated in the charge made by the brigades of Colonel Giles gave as efficient a support to the movement as the nature of the ground admitted.

I desire to mention in terms of the highest commendation the conduct of the there officers commanding the brigades of my DIVISION throughout the two affairs of the 19th and 22nd, and the almost continuous fighting which intervened. Colonel Giles A. Smith deserves to be especially distinguished, and his thorough soldiership brought to the notice of the Government in order that he may receive promotion for his distinguished gallantry and meritorious conduct. In the affair of the 19th, colonel, Giles A. Smith received a slight wound in the hip from a musket-ball. He remained, however at his post at the head of his time, leading his brigade to the assault, and attending to every detail I understand that Colonel Giles A. Smith has herefore been recommended and good conduct in the field, I take this occasion to renew the recommendation in the strongest terms, and trust that you will do this officer the justice to bring his conduct to the notice of the Government.

I refer also, with the greatest pleasure, to the notices which have been made to the gallantry and good conduct of the following-named commanding officers of those brigades, and have to express my regret that I have received no detailed report from the commanding officer of the SECOND Brigade, coo. Thomas Kilby Smith, which would enable me George B. Hoge, one hundred and THIRTEENTH Illinois; Colonel N. W. Tupper, one hundred and SIXTEENTH Illinois; Lieutenant Colonel David C. Coleman, eight MISSOURI; Lieutenant Colonel James P. Boyd, one hundred and serves especial mention for his gallantry and efficient services at the battle of Champion's Hill, on the 16th instant; Colonel Augustus C. Parry, forty-seventh Ohio; Colonel James H. Dayton, fourth WEST Virginia; Lieutenant Colonel Louis von Blessingh, thirty-seventh Ohio, lieutenant Colonel George H. Hidt, thirteenth Ohio, lieutenant Colonel Iras Bountell, sixth Missouri; Major George R. CLARKE, one hundred and thirteenth Illinois, major A. Fro-