On the 22nd, my brigade was again ordered to support the troops of General Blair. The Seventy-SECOND Ohio was ordered to take position on the left of the advance of Colonel Kilby SMITH's brigade, where it remained until evening, when it rejoined the brigade, which had taken position on the same ridge, on the left of the road, previously occupied by the One hundred and fourteenth and Ninety-THIRD.

I send herewith a full statement of the casualties of my brigade at Jackson on the 14th, and at Vicksburg on the 19th, 20th, 21st, and 22nd, showing-

Killed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Wounded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Missing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

----

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

I take this opportunity to express my sincere thanks to Colonel McMillen, Ninety-FIFTH Ohio; Colonel Judy, One hundred and fourteenth Illinois; Colonel Thomas, Ninety-THIRD Indiana, and Lieutenant-Colonel Crockett, Seventy-SECOND Ohio, for the able and prompt manner in which they have performed their duties, and through them also to the officers and men under their command.

I am proud of my brigade. During this long and tedious march not in a single instance has any regiment been behind time. My thanks are also due to my staff officers for the faithful performance of their duties.

I must here say a word in praise of the line officers of the brigade. Deprived of all transportation, even for provisions, they have endured fatigue and hunger without complaint, setting a noble example which has had a beneficial influence upon the conduct of the men. Upon this subject I refer to the report of Lieutenant-Colonel Crockett, Seventy-SECOND Ohio Volunteers. I venture to say that, owing to circumstances beyond my control, my brigade suffered more from the want of food than any other in this army; yet I doubt whether any reached the end of the march in better condition or better spirits. I repeat, I am proud of my brigade.

Respectfully submitted,

R. P. BUCKLAND,

Brigadier-General, Commanding First Brigade.

Captain J. B. SAMPLE,

Assistant Adjutant-General.

Numbers 5. Report of Colonel De Witt C. Thomas, Ninety-THIRD Indiana Infantry, including operations May 2-July 16. MARKHAM'S PLANTATION, MISS., August 9, 1863.

GENTLEMEN: In accordance with General Orders, Numbers 64, Headquarters Fifteenth Army Corps, I herewith submit my condensed report of the different engagements, and the part my regiment has taken in them.

I left Duckport, La., on the 2nd day of May, with five days' rations in my men's haversacks and wagons, and one hundred rounds of ammunition per man, two wagons being allowed for transportation. I left Grand Gulf on the 8th of May, without transportation or rations. On