Letter from Capt. Richeson.

Cumberland Gap, Tenn., Aug 8, 1862.

E. Foreman, Esq -- Dear Sir: I desire to state in your paper, for the benefit of the friends of my company in particular and the 16th regiment in general, the casualties that occurred to our regiment in the late fight on the 6th inst., at Tazwell, Tenn. I have been sick with the fever for the last four weeks, and of course was not with the regiment in its late engagement; but from what I can learn from the most reliable sources the action commenced about 11 o'clock and continues about two hours and a half. There were no forces engaged on our side but the 16th Ohio, the other forces on our side being necessary to hold in check some 3 or 4 rebel regiments that were awaiting an opportunity to get into our rear and cut off our retreat and communication with the Gap.

The official report shows fifty-four men missing belonging to the several companies, as follows: Daniel Hough and Robert Mathews, of Capt. Botsford's company. James Hoke of Capt. Harn's company. Capt. Edgar and 29 of his men, and Capt. Tannyhill and 20 of his men. Also C. B. Smith, the Sergeant Major. Capt. Edgar and the Sergeant Major are supposed to be killed, and Capt. Tannyhill is supposed to be wounded in the left arm and taken prisoner.

The following are the wounded: Corporal Morrison wounded in left shoulder, and John Springer wounded in the fleshy part of the left thigh - both of Capt. Harn's company. Sam'l Risinger, two fore fingers of left hand shot off and Corporal Megary wounded in the breast - both of Capt. Botsford's company. Henry H. Lawrence of my company, wounded in the right foot. None of the above are seriously wounded. They will soon all recover and be able for duty. One of Capt. Monroe's men, leg broken and left on the field. The above are all the wounded of which we have any report. All the 16th engaged in the fight lost their knapsacks, blankets, overcoats, and all their contents including letters and many other little et ceteras that they had from time to time gathered up.

The rebel force, as nearly as we can learn, was 11 regiments of infantry together with artillery and cavalry. Four of the regiments were engaged in the contest with the 16th Ohio, and were several times repulsed, but they outflanked us and we were compelled to retire in consequence of vastly superior numbers.

Believing this will be satisfactory to the friends of the regiment until they see the official report, I am, sir, Your truly,

HAMILTON RICHESON.