We have hot to fight until the military power of the South is exhausted, and if we release or exchange prisoners captured its imply becomes a war of extermination.

U. S. GRANT,

Lieutenant - General.

WASHINGTON, D. C., August 19, 1864.

Major General B. F. . BUTLER, U. S. Army, &c.

SIR: The President directs that, if possible, a special exchange be effected in favor of Major Nathan Goff, and for this purpose you are authorized to offer and deliver Thomas D. Armesy

(or Armesley), who has been directed to be sent to Fort Monroe by Colonel Hoffman, and placed at your disposal for the purpose.

I feel justified in urging that this I as case in which the President feel as particular interest, the order in the case having also the express sanction of the Secretary of War.

Very respectfully, your obedient servant,

E. A. HITCHCOCK,

Major - General of Volunteers.

WASHINGTON, D. C., August 19, 1864.

Colonel WILLIAM HOFFMAN, Commissary-General of Prisoners.

SIR: The President directs that Thomas D. Armesy (or Armesley), be sent to Fort Monroe and placed at the disposal of Major - General Butler (of which you will advice General Butler), in order to his being exchanged for Major Nathan Goff, now held as a prisoners of war in Richmond. Armesy is supposed to be at Fort Warren.

Very respectfully, your obedient servant,

E. A. HITCHCOCK,

Major - General of Volunteers, Commissioner of Exchange.

HEADQUARTERS DEPARTMENT OF THE SOUTH,
Hilton Head, S. C., August 17 [19], 1864.

Major General H. W. HALLECK,

Chief of Staff U. S. Armies, Washington, D. C.:

GENERAL: I have the honor to inclose the original and the transcribed copy of a document received this day from some of our officers in Charleston. It is addressed to the President of the United States, and singed by Major - General Stoneman, Colonel T. J. Harrison, Eighth Indiana Cavalry, and Colonel J. B. Dorr, Eighth Iowa Cavalry. It gives a heart rending account of the condition of our private soldiers now prisoners of war at Andersonville, Ga. This document war received by the hands of Private Prescott Tracy, Eighty-second New York Volunteers.

Private Tracy was exchanged yesterday at Port Royal Ferry, to make up a small deficiency due at the last exchange at Charleston Harbor.

Upon the proposed subject of exchange I have written fully in another letter.

I have the honor to be, very respectfully, your obedient servant,

J. G. FOSTER,

Major - General, Commanding.

P. S. - I also inclose three other documents, brought on the person of Prescott Tracy, one of which is the original sent to the President of the United States; also a statement by said P. Tracy.

J. G. F.