HEADQUARTERS DEPARTMENT OF EAST TENNESSEE, Bristol, April 21, 1864.

General S. COOPER,
Adjutant and Inspector General, Richmond, Va.:

GENERAL: It is proper that on assuming command of this department I should briefly state its condition.

It is almost entirely exhausted of supplies beyond the actual wants of citizens. After General Longstreet's troops shall have gone, including Brigadier-General Law's brigade, which will leave for Charlottesville to-morrow there will be left in this department he following troops:

Johnson's and Gracie's brigades of infantry, of my proper division, and the greater part of Wharton's infantry brigade, formerly belonging to General Samuel Jones' department; in all, about 3,500 effective infantry; in addition to this a few bridge guards.

Cavalry: Jones', Vaughn's, Giltner's, and Morgan's brigades; perhaps near 4,000 effectives. Their condition is lamentable. The horses are so much reduced as to be unfit for any hard service. It is impassible to forage them in this vicinity, and for that reason their late commander, Major-General Ransom, was compelled, under authority received from my predecessor in command, to disperse them over a wide extent of country, from the Big Sandy, in Kentucky, to near Asheville, N. C. They are much exposed, and can contribute little in their present positions in the defense of this section of country. The spring is unusually backward, affording as yet no grass that can be relied on to sustain the animals for any work. It is only by constantly changing their localities that they can be kept alive.

I respectfully make the following suggestions: Saltville is the vital point of this section of the country; that point and the line of the railway are exposed to raids from Kentucky, through pound Bap and up the Louisa (or Levisa) Fork of the Sandy, especially by the latter road. Rapid movements of cavalry are essential to an effective defense. They cannot be made unless I am furnished with corn. Discipline cannot be restored or maintained if the commands are under the necessity of straggling for supplies. Small supplies of corn are beginning to arrive, but as yet not enough to bring about any decided amelioration in the condition of the cavalry and their animals.

The horses of one entire battalion of artillery are in North Carolina. I cannot recall them until I can feed them. The battalion,a s a result, is disabled.

If my command is adequately supplied I am confident that, though small, it will render the Government effective service. You may rely upon every exertion being made here to collect all that the country can spare for the troops. But this department will not maintain either the troops or the animals that belong to it.

Let me ask, in order that I may be enabled to render efficient services to the Government, that you will divert, for the use of these troops, such supplies as can possibly be spared from other points.

In this connection I will also state that the troops of this department proper and part of those formerly belonging tot he Department of Western Virginia have been mixed together to some extent during their service in this department in the same organization. Am I to regard the troops which I find serving in this department as belonging to it, or am I to consider the troops now with me and formerly comprising part of the command of General Jones as belonging prop-