Number 8. Report of Lieutenant Charles B. Kimball, First Wisconsin Battery. HEADQUARTERS FIRST WISCONSIN BATTERY, Port Gibson, MISS., May 2, 1863.

SIR: I have the honor to report below the part taken in yesterday's engagement on Thompson's Hill by the First Wisconsin Battery, which is as follows viz:

The battery, under command of Lieutenant Charles B. Kimball, after marching all night, received orders about 6 a. m. to move up rapidly to the front, and was placed in position in the following manner:

The right section of the battery, under charge of First Sergt. Edward P. Aylmer, was moved to the extreme left of the line, to relieve a section of Captain Lanphere's (Seventh Michigan) battery, which had suffered severely from the fire of two brass pieces of the enemy, planted on an opposite hill, about 1 1/4 miles distant, which we dismounted shortly afterward. This position it occupied all day, with slight changes to the right or left, as occasion required.

The center section, commanded by Lieutenant E. L. Hackett, moved up to a position on the left of the right section, and opened fire on some buildings immediately to the front, occupied by rebel forces, where it did fearful execution. It occupied this position all day, and late in the afternoon shared with the right section the satisfaction of silencing two guns which the enemy brought to bear upon us with great effect from an open field, about a mile off. This was the closing scene of the engagement.

The left section, under command of Lieutenant Oscar F. Nutting, took position on the center of the line, but was ordered by General Grant to reserve their fire until further orders were received from himself, as our supply of ammunition was very limited. This position it held all day under a galling fire of musketry, which, as ordered, it was compelled to face in silence.

Each section was planted under a galling fire, which was kept up throughout the day. Both men and officers did their duty nobly, and although our numbers were small -pounder guns, and the men greatly fatigued after marching all the previous night, not a complaint was heard, but each man sprang to his work with a right good will, forgetful of their weariness in their desire each to do his duty.

Casualties, 4 men wounded.

Hoping that our future engagements will be crowned with equal success, I have the honor to remain, captain, your obedient servant,

CHAS. B. KIMBALL,

First Lieutenant, Commanding First Wisconsin Battery.

Captain J. W. THOMPSON,

A. A. A. G., NINTH Div., Thirteenth A. C.

Number 9. Report of Colonel Theodore E. Buehler, Sixty-seventh Indiana Infantry, First Brigade, Tenth DIVISION, including operations April 14-May 22. CAMP, IN THE FIELD, SIEGE OF Vicksburg, MISS., May 25, 1863.

GENERAL: I have the honor to submit the following report of the movements of the Sixty-seventh Regiment Indiana Volunteer Infantry