I reached Vicksburg at 5 p. m. on the 17th, and encamped in rear of the intrenchments near the Jackson road. The trains which were placed under my charge arrived in safety, with the exception of one ordnance wagon, which broke down crossing the Big Black Swamp. In conclusion, I beg leave to say that in the arduous marches and perious position in which my troops have been placed they performed all their duties with cheerfulness and courage. All the officers and men behaved well. I would particularly call the attention of the major-general to the universal good conduct and promptness of Colonel Gillespie, of the Forty-THIRD Regiment, colonel Lillard, of the THIRD Regiment, and Colonel Bradford, of the Thirty-first Regiment; also to Major [J. S.]Boyd, of the THIRD Regiment, always active and prompt in the discharge of his duties. To Lieutenant William a. m. Patton, my aide and acting [assistant] adjutant-general, I am under many obligations for meritorious service rendered. Captain Caliborne of the THIRD Maryland Battery, and his first lieutenant (Lieutenant [J. B.]Rowan), performed their duties admirably and gallantly.

Respectfully, your obedient servant,

A. W. REYNOLDS,

Colonel, commanding Fourth Brigade.

Major J. J. REEVE,

Asst. Adj. General, Stevenson's DIVISION, Demopolis, ALA.

Number 34. Reports of Colonel Francis M. Cockrell, SECOND Missouri Infantry, commanding First Brigade, Bruen's DIVISION, including engagement at Big Black River Bridge. DEMOPOLIS, ALA., August 4, 1863.

MAJOR: Herewith I send you my official report of the battles of Baker's Creek, big Black, and the siege of Vicksburg. I beg the leniency of the lieutenant-general for not having sent in sooner. I hope it is in time yet. It is very difficult to make out reports extending through so long a space of time. The movements of the First Brigade (Missouri Volunteers) during this siege from point to point, and portions of it being thrown to the support of every brigade occupying a line of trenches, and the many varied incidents connected as much as I could. In my reports of Baker's Creek and Big Black I have been more particular in stating in full various matters, such as the manner ov bivouacking the night previous to the battle; the movements of the enemy in my front next morning up to the time I was ordered to re-enforce General Stevenson; my call for re-enforcements, and answer of the lieutenant-=general as to what troops were expected to re-enforce my line, and the affair at the crossing of Baker's Creek, and my delay there until the gaining of the road by the enemy, causing me to travel my course alone lieutenant-general. I have prepared the whole report in a great hurry, and sent it you as soon as completed.

I have the honor, major, to be, most respectfully, your obedient soldier,

F. M. COCKRELL,

Colonel.

[Major R. W. MEMMINGER, assistant Adjutant-General.]