BIGG'S PLANTATION, April 6, 1863.

Major General WILLIAM T. SHERMAN, Comdg. Fifteenth Army Corps:

GENERAL: I have the honor to inclose to you Vicksburg Whig of 27th of March and 3rd of April; also Memphis Appeal of 3rd instant.

There was heavy and rapid firing of cannon below here yesterday morning of about half an hour. I have this morning information from parties, who were several miles down the river from this point at the time it occurred, who think the firing was at the Perkins plantation, 7 miles below New Carthage. They say that they are certain that it was too far WEST to be at Grand Gult. At the Perkins plantation the rebels have one regiment, commanded by Colonel [I. F.] Harrison, but I cannot ascertain that they have any field or siege pieces there. It is possible that our fleet may have met the enemy on the river at a point WEST and below Grand Gulf.

I had men down the river last evening to ascertain, if possible, where the firing occurred, but they learned nothing, excepting that it was below and distant. I shall doubtless soon be able to learn more about it.

At the time Admiral Farragut came up, three of the enemy's transports followed his vessels, ran up Big Black River 11 miles, unloaded their cargoes of provisions at Allen's Mills, and left next morning. I saw the smoke of two of the steamers, and immediately advised the admiral, but he could not credit it, and gave it no attention. They were loaded with 500 hogs and a large amount of corn and other provisions.

The admiral's vessels, when last heard from, had passed down below Natchez. The enemy at Vicksburg are expecting large supplies from Georgia and Alabama; 9,000 hogs and a large number of cattle are expected in a few days. The enemy are building a casemated fort at Grand Gulf, and are still pushing to completion their works at Warrenton. As the admiral passed Grand Gulf, the enemy, in firing their heaviest gun, burst it, killing 4 and wounding 7 of their own men.

I have the honor to subscribe myself, general, your very obedient servant,

CHARLES H. ABBOTT,

Colonel, Commanding.

MEMPHIS, April 6, 1863.

Brigadier General NATHAN KIMBALL, Commanding District, Jackson:

Major Newsham reports from Hickman (received there) that the rebels, under command of [R. V.] Richardson, intend crossing the Obion River in the neighborhood of Dyersburg, having two large ferry-boats there for that purpose. Feel out well for them.

HENRY BINMORE,

Assistant Adjutant-General.

GENERAL ORDERS,
HDQRS. SIXTEENTH ARMY CORPS, Numbers 39.
Memphis, Tenn., April 6, 1863.

Major General Richard J. Oglesby, having reported at these headquarters for duty, in pursuance of special orders from headquarters of Department of the Tennessee, will proceed to take command of the left wing of the SIXTEENTH Army Corps. He will establish his headquarters at La Grange or Bolivar.

By order of Major General S. A. Hurlbut:

HENRY BINMORE,

Assistant Adjutant-General.