America has been officially received and is published to the armies in this district:

WASHINGTON, D. C., October 8, 1862.

Major-General GRANT:

I congratulate you and all concerned in your recent battles and victories. How does it all sum up? I especially regret the death of General Hackleman, and am very anxious to know the condition of General Orglesby, who is an intimate personal friend.

A. LINCOLN.

By command of Major General U. S. Grant:

JNO. A. RAWLINS,

Assistant Adjutant-General.

Numbers 2.

Reports of Major General William S. Rosecrans, U. S. Army, commanding Army of the Mississippi, including operations October 1-12, with congratulatory orders.

HEADQUARTERS ARMY OF THE MISSISSIPPI,
Corinth, October 3, 1862.

GENERAL: The enemy came in on the Chewalla road this morning and made a demonstration on our left on Mckean's division. The leading brigade, commanded by Colonel Oliver, acted feebly and fell back. McArthur has now taken command and is pushing forward to make strong reconnaissances. We are now holding our position and pushing cavalry reconnaissances up to the Bolivar and Purdy road, also main Purdy road east of the railroad. No developments have yet appeared on that front.

Scouts report the enemy on both sides the railroad last night near Chewalla. One unusually reliable gives their entire force not exceeding 30,000, and is satisfied that they intend to make their main move on Bolivar. Will endeavor to communicate again as soon as there is anything new, and if we find the force not meant for Corinth or we are in position to do it, shall move on them steadily and firmly with everything we can spare. The enemy have since come in on the Chewalla road and have driven in Davies' left. Our men did not act or fight well. I think we shall handle them. We are at the outer line of works.

Very respectfully, your obedient servant,

W. S. ROSECRANS,

Major-General, Commanding.

Major-General GRANT, Jackson, Tenn.

OCTOBER 4 [3], 1862-11.30 [p. m.]

From advanced position at exterior batteries reported to you this morning our troops slowly drew in and concentrated. The rebels attacked between railroads northwest. Davies' division-the right of McKean's-were the only troops really engaged; it was bushwhacking, our troops knowing nothing of the ground, although many of them have been here. Hamilton attempted to swing in from the Purdy road westward, but it was late in the evening and he was too far advanced to the north. Our left-McKean and Stanley-occupies Price's new line; right-