AUGUST 3, 1863. -Scout from Fort Pillow, Tenn., and skirmish near Denmark, Tenn.

Report of Brigadier General Alexander Asboth, U. S. Army, commanding Sixth DIVISION, SIXTEENTH Army Corps.

COLUMBUS, KY., August 9, 1863.

COLONEL: I beg to give below an extract from the semi-weekly report of Colonel E. H. Wolfe, FIFTY-SECOND Indiana Infantry, commanding at Fort Pillow, dated 6th instant, for the information of the general commanding corps:

The five companies of cavalry and three companies of mounted infantry returned last evening, bringing with them 6 prisoners, having met and dispersed the rebel forces under Colonel [James U.]Green, numbering 250 men.

The enemy loss, besides the above prisoners, was 2 men killed; wounded unknown. Our loss was 1 man slightly wounded and 2 men taken prisoners.

The rebel Colonel Cheatham, with a supposed force of 700 men, mostly unarmed, was reported to be in the vicinity of Denmark, near Jackson, where the fight occurred. The prisoners I forward to Columbus, Ky., under guard.

Colonel Richardson, with his force, crossed the Hatchie on Saturday last, supposed to be making his way into Mississippi, for the purpose of obtaining arms for his command.

The country back of Brownsville and south of Hatchie abounds with guerrillas.

Captain Hencke, fourth Missouri Cavalry, scouting southward from Union City, with 60 men, fell also upon a guerrilla party on the Obion Middle Fork, 12 miles north of Trenton, but was unable to follow and capture the marauders.

I direct the commanders at Fort Pillow and Union City to operate continually with their Cavalry, in concert, in order to entirely destroy Richardson's forces, now under organization, before they get their arms, and I have to regret that Companies B, c, d, l, and M, SECOND Illinois Cavalry, lately returned to my command, are ordered by Special Orders, number 181, from Headquarters SIXTEENTH Army Corps, to Vicksburg, thus considerable reducing my hopes for success regarding the above combined cavalry operations.

I will take longer time for any other cavalry to be efficient, as those companies are throughly acquainted with the country and people between the Hatchie and Obion Rivers.

Very respectfully, colonel, your obedient servant,

ASBOTH,

Brigadier-General.

Lieutenant Colonel HENRY BINMORE,

Assistant Adjutant-General.