HDQRS. DEPT. OF GULF, 19TH ARMY CORPS,
Alexandria, La., May 8, 1863.

GENERAL: I have the honor to inform you that our advance, consisting of Dwight's and Weitzel's brigades, preceded by cavalry, arrived at this place yesterday afternoon and evening, two days before I had promised Admiral Farragut to be here. Dwight's brigade marched from Washington on the 4th instant, making the march of about 84 miles in four days. Weitzel's brigade marched from Opelousas at 5 p. m. on the same day, thus making the entire march of 90 miles in three days and two hours. Emory's division marched from Opelousas on the 5th instant, and was last night a the railway station 22 miles from here. Grover's division marched rom Barre's Landing, about 11 miles from Washington and 95 miles from Alexandria, at 1 o'clock on the afternoon of the 5th, and encamped on the evening of the 6th 35 miles from Barre's Landing.

I left Opelousas at 6 o'clock on the morning of the 6th, made my headquarters with Governor's division that night, and arrived here at 7 o'clock last evening, just before the infantry entered the town.

In celerity and unity of movement the march left nothing to be desired. Moving after the column and passing it, I had ample opportunity, personally and through my staff officers, to observe the rear of each division, and am happy to say that there was not the least appearance of straggling or disorder in any portion of the command.

Admiral Porter arrived off the town yesterday morning with his four iron-clads, the ram Switzerland, and our gunboats-the Estrella and Arizona.

No opposition was made to our movement. Before leaving Opelousas I communicated with Major-General Grant, who is now concentrating his forces at Grand Gulf, and informed him, in answer to his inquiries, that I would meet him at Bayou Sara probably on the 25th instant, but certainly by the 1st proximo.

The enemy has withdrawn his broken forces to Shreveport. I should be glad to follow him to that point and complete his entire destruction; but, tempting as this movement is, it would occupy too much time, which can be more advantageously used in another enterprise nearer at hand and more decisive in its results. The destruction of his transports and his only remaining gunboats-the Webb, Marry T., and Grand Duke-can be accomplished hereafter. They are now so hemmed in that they cannot escape us. The Red River is now falling, and will be soon so low that they cannot descend it. Admiral Porter says the Webb is much injured in consequence of her fight with the Indianola, and that the Grand Duke and Mary T. are cotton-clads.

Very respectfully, general, your most obedient servant,

N. P. BANKS,

Major-General, Commanding.

Major General H. W. HALLECK,

General-in-Chief, Washington, D. C.

No. 20.]HDQRS. DEPT. OF THE GULF, 19TH ARMY CORPS, Alexandria, La., May 11, 1863.

SIR: I have the honor to annex, for your information, the copy of a cipher message which I received on the morning of the 5th instant from Major-General Grant, but which, not having the key, I was compelled