CUMBERLAND GAP, June 20, 1862.

MESSRS. ESTILL-- At last the Stars and Stripes float over the Gap. Shortly after I had mailed to you my last we were ordered to prepare to march at 1 o'clock the next morning. The rebels were reported to have encamped in large numbers within about eight miles of our encampment, and we expected to face them about day-break. The artillery being in advance, we proceeded but slowly; but finally coming near the place, we inquired of the citizens how far distant the enemy were encamped, and were told about 1 1/2 miles. We here haulted for a short time, and again proceeded on our march, at the same time listening for the well known music produced by the pickets' muskets. We advanced fatrer [farther], and were not far from the camp, when we received the intelligence that the rebels had left during the night. Shortly we passed their camp, and saw their camp-fires still smoking and even some of their tents left standing. It was about 10 o'clock and we were haulted to rest the balance of the day. I was put on picket duty, and had been posted about 10 minutes when the order arrived to draw in the pickets and prepare to march again. We were then about 11 miles from Cumberland Gap, and a rebel Lieutenant had been captured who informed the General that the enemy were evacuating the Gap and would probably move some of the artillery that evening. I presume the intention was to capture them; so we advanced again, and for the first time a Union flag was displayed by a party of citizens who were awaiting our arrival. We soon arrived within sight of the Gap, and to our surprise found the hill covered with tents. Some of the boys suspected that we had been led into a trap, although assured by every citizen that the enemy had left. At about sun-set we arrived at the foot of the mountain, and were here formed in column, with Capt. Foster's artillery in the rear, to proceed to the Gap. Arriving there we were haulted and formed into line of battle, and soon the roar of 6 pieces of artillery announced to those around that the stars and stipes floated over this stronghold of the enemy and that the door was again opened to East Tennessee. The citizens commenced flocking in, but a little surprised to learn that they would be placed under guard during the night. We retired to rest for the night in as comfortable quarters as could be obtained; myself and a comrade having slept between two graves, with the rain pouring down upon us all night, so you may imagine that we had not the most comfortable quarters. The next morning we went to the Gap.

It is impossible to give a correct idea of the strength of this position. It appears to me that the great natural advantages it possesses, besides the fortifications built by skillful engineers, would have rendered it impossible to take by a siege, had it been defended by brave troops. The number of the enemy's force is not known; the fortifications are capable of holding about 30,000 men, but whether they had enough to occupy these is doubtful. Their force must have been large, however, as the number of barracks and tents found here would shelter from 10,000 to 15,000 men. Their tents and camp equipages were all left behind, but in such a mutilated condition that they are worthless. Five cannon of large calibre were left, three 64 pounders and two 44 pounders, but they were spiked and the carriages hacked to pieces. A vast amount of ammunition was destroyed, and provisions in any quantity can be found buried and destroyed as much as possible. Time and space will not permit me to give further particulars of the Gap, but more anon.

Yours, respectfully,

CHARLES ZINK.