Twenty-ninth North Carolina with two companies of the Third Georgia Battalion in that direction on the 3rd instant. Hearing that General Carroll had troops on the line of railroad at Morristown I arranged with them by telegraph to move into the enemy's county at the same time and from opposite directions.

That country consists of a tumultuous mass of steep hills wooded to the top with execrable roads winding through the ravines and often occupying the beds of the water-courses. A few of the insurgent scouts were seen, pursued and fired on. One was desprerately wounded and left at a cabin near by.

At the farm houses along the more open valleys no men were to be seen and it is believed that nearly the whole male population of the country were lurking in the hills on account of disaffection or fear. The women in some cases were greatly alarmed throwing themselves on the ground and wailing like savages. Indeed the population is savage.

The expedition lasted four days, and in the course of it we met Colonel Powel's command deep in the mountains and our guns were responded to at no great distance by a force under Captain Monsarrat.

These people cannot be caught in that manner. As likely to be more effective I have detached three companies of Colonel Vance's regiment to Parrottsville with instructions to impress horses from Union men and be active in seizing troublesome men in all directions. They will impress provisions giving certificates therefor, with assurance that the amounts will be paid if the future loyalty of the sufferer shall justify the clemency of the Government. The whole country is given to understand that this course will be pursued until quiet shall be restored to these distracted counties, and they can rely upon it that no prisoner will be pardoned so long as any Union men shall remain in arms. Three othere companies of Colonel Vance's command are on their way to Warrensburg, on the north side of Chucky, to remain there under similar instructions.

It is believed that we are making progress toward pacification. The Union men are taking the oath in pretty large numbers and arms are beginning to be brought in. Captain McClellan, of the Tennessee cavalry, statiioned by me at Elizabethon reports that Carter County is becoming very quiet and that with the aid of a company of infantry he will enter Johnson County and disarm the people there. I shall send the company without delay.

The execution of the bridge-burners is producing the happiest effect. This coupled with great kindness toward the inhabitants generally inclines them to quietude. Insurgents will continue for yet a while in the mountains but I trust that we have secured the outward obedience of the people.

Very respectfully, &c., your obedient servant,

D. LEADBETTER,

Colonel, Commanding.

KNOXVILLE, December 10, 1861.

Honorable SECRETARY OF WAR:

The court-martial has sentenced A. C. Haun, bridge-burner, to be hung. Sentence approved. Ordered to be executed at 12 o'clock to-morrow. Requires the approval of the President. Please telegraph.

WM. H. CARROLL,

Brigadier-General, Commanding.