ROCKY SPRINGS, MISS., May 7, 1863.

Brigadier General M. M. CROCKER, Comdg. Seventh DIVISION:

GENERAL: The THIRD DIVISION, General Logan commanding, moves from here to-morrow morning at 6 o'clock to Utica, a distance of 12 or 14 miles.

Come forward with your command as rapidly as possible, after being relieved by Major-General Sherman. A staff officer will be here to direct you on the right road.

Leave an officer or competent man to bring forward the train which you sent to Grand Gulf to-day, when it arrives, and see that it gets on the proper road.

Very respectfully, your obedient servant,

JAS. B. McPHERSON.

P. S. -Colonel Boomer has the map showing the road to Utica,&c.

HEADQUARTERS DEPARTMENT OF THE GULF, Alexandria, May 8, 1863-8 a. m.

Major-General GRANT:

DEAR SIRE: My command reached Alexandria yesterday without opposition, the advance entering the town early int he afternoon. Admiral Porter, with his fleet and several of Admiral Farragut's boats, took possession of the town yesterday morning without resistance.

I have stated to him that I can furnish his fleet, that of Admiral Farragut, and your transports with coal, and your army partially with provisions, by the Atchafalaya and Red River, but it will be difficult. If Port Hudson is reduced, all this can be done direct from New Orleans, and our future operations will proceed without interruption want of supplies and with certain success.

In answer to your dispatch received in cipher, I replied I could cooperate with you on the 25th instant or the 1st of June. Our successful march here enables me to do this on the 25th May. I shall have 15,000 good men, all told. We can move by the Bayou Sara to the rear of Port Hudson, get our supplies from Baton Rouge, where Major-General Augur can join us with 4,000 men.

With the fleet of Admiral Porter above, that of Admiral Farragut below, and our forces in the rear, or so many of yours as you can spare, the fall of the post will be instant and certain.

I beg your most favorable consideration to this matter.

Lieutenant-Colonel Irwin, my adjutant, will explain my views more in detail.

I have the honor to be, with much respect, general, your obedient servant,
N. P. BANKS.

MILLIKEN'S BEND, La., May 8, 1863.

Major General U. S. GRANT, comdg. Dept. of the Tennessee:

GENERAL: I have the honor to report that, since the 2nd instant, I have forwarded by wagons to Perkin's plantation and Grand Gulf over 300,000 rations of hard bread, coffee, sugar, and salt, 225,000 rations of salt meat, and 130,000 of soap. The other parts of the ration not being