HDQRS. DEPT. OF THE TENN., Vicksburg, MISS., August 11, 1863.

Major General H. W. HALLECK, General-in-Chief, Washington, D. C.:

GENERAL: Your two dispatches announcing the appointment of Sherman and McPherson as brigadiers in the Regular Army, and the non-receipt of my acceptance of promotion, and approval of my recommendations as to organization of colored troops, &c., are received. As soon as notified of my appointment, I filled out the required oath of office, and forwarded it to the Adjutant-General of the Army. If this has not been received, I will be glad to fill out a duplicate and forward as soon as notified of the non-receipt.

I took great pleasure in notifying Sherman and McPherson of their appointments. These appointments could not have been more worthily bestowed, and however much others may desire the same honors, I am sure they will acknowledge the merits of these two.

I feel under many obligations to you, general, for the interest you have ever taken in my welfare and that of the army I have the honor to command. I will do the best I know how to satisfy you that your confidence has not been misplaced.

Although this letter is intended as private, I will mention some matters which might be regarded as semi-official at least. I have no doubt movements here seem slow since the fall of Vicksburg; but this could not possibly be helped. As soon as Port Hudson fell, General Banks made requisition on me for twenty-two steamers, coal, forage, &c. I supplied him all the boats then possible, and all the other articles. Sick and wounded had to be sent north, wounded rebels sent south, troops sent to Helena and to Banks. An expedition to Yazoo City seemed to be highly necessary, and was sent, and Natchez had to be occupied. Under all these circumstances, I am only now getting off the last of the NINTH Army Corps, and moving at the same time the Thirteenth Corps to New Orleans.

There are said to be about 80 locomotives and 600 or 800 cars on the two roads north of Grenada. These I am trying to save, by having them all worked through to Memphis, but hardly hope to succeed. A cavalry force is now on its way north to where they are, and another coming south to meet them, for the purpose of taking these cars through. But I understand the rebels have a small force guarding them, and in all probability will burn them rather than let them fall into our hands.

This will be better than to risk them falling into the hands of the enemy.

As soon as transports can be had, I shall drive what forces Kirby Smith has near me back to the Red River. Forces will move from Natchez to Trinity and Harrisonburg, and from here by Lake Providence, or Goodrich's Landing, to Floyd and Monroe. This will, I think, force the few troops left by Smith to annoy the plantations across the desert country between the Ouachita and Red River to Shreveport, where they will remain.

This State and Louisiana would be more easily governed now than Kentucky or Missouri if armed rebels from other States could be kept out. In fact the people are ready to accept anything. The troops from these States, too, will desert and return as soon as they find that they cannot be hunted down. I am informed that movements are being made through many parts of Mississippi to unite the people in an effort to bring the State into the Union. I receive letters and delegations on this subject myself, and believe the people are sincere.

Ord's command will probably all be off in one week. The health of this army is much better than there was any reason to hope for. The troops are physically ready for another campaign.