[Inclosure No. 4.]

HEADQUARTERS DEPARTMENT OF THE GLUF,
Opelousas, La., April 23, 1 863.

Major-General GRANT,

Commanding Forces on the Upper Mississippi:

GENERAL: I have the honor to acknowledge the receipt of your dispatches, dated at Headquarters, before Vicksburg, March 23, 1863, on the 21st, by the hand of Lieutenant Tenney, of General Augur's division, at Baton Rouge. On April 10 Mr. Gabaudan, private secretary of Admiral Farragut, commanding the Hartford, at the mouth of Red River, reported at my headquarters at Brashear, and gave me verbally the substance of your dispatches, which he said he had read, but did not bring with him in the dangerous passage which he was compelled to make of the batteries of Port Hudson.

The information received from Mr. Gabaudan differs somewhat from your dispatches. I understand from him that it was your intention to send a force by the way of Lake Providence and the Black River, passing through the intermediate bayous, to the mouth of Black River on the Red River, and that this force would probably reach the Red River by May 1st proximo, to co-operate with my command against Port Hudson.

Stimulated by this report and cheering prospect of assistance we pushed with vigor the expedition upon which we were then engaged. Our success has been complete. We have utterly destroyed the army and navy of this part of the Confederacy, and made it impossible for the enemy to reorganize his forces for some months to come. We occupy Opelousas, and my advance is about 30 miles in front of this place, on the road to Alexandria.

The forces of the enemy are divided, a portion of Sibley's cavalry being on the Plaquemine Bayou, on the road to Texas, with General Mounton and the artillery and some cavalry on the road to Alexandria. The infantry is completely dispersed. We have captured 2,000 prisoners, 1,000 stand of arms, ammunition, ordnance stores, &c., twenty heavy guns, demolished his foundries at Franklin and New Iberia, and the salt-works below Iberia. We have captured two steamers and several boats, and compelled the destruction of ten or twelve transport steamers, some of them laden with flour, ammunition, and arms.

The gunboats Diana, Hart, and Queen of the West have been destroyed and their armament captured by our forces. We have among our prisoners the most important officers of all arms, Captain Fuller, the commanders of their fleet, captured from the Queen of the West, known here as the "King of the Swamp," long in the Legislature and at the head of the filibuster or fighting element of the State, whose candidate he was for the office of Governor. We have also Captain Semmens, the first officer of their artillery, and Colonel Vincent, the chief of their cavalry. They can make no stand this side of Alexandria.

The capture of the fortifications at Butte-a-la-Rose by the Army and Navy, which occurred on the morning of April 20, opens to us completely the Atchafalaya to the Red River. Several days since I addressed to the admiral an inquiry whether he could navigate the Red River to Alexandria and to yourself a request to communicate the time when your co-operative force could reach Red River. Our communication with the admiral is open only on Thursday, when he comes down to Port Hudson. It will be communicate to him, as I am informed,