I have directed Dodge not to attack Tuscumbia unless the movement will be a success, which it would have been last week, but to show front strongly on Bear Creek, keeping open communication with Corinth, and to let Streight's expedition in his rear by Verona and Tupelo; thence across the country to their destination, and them drop back to Corinth.

I suggest this course because my cavalry from La Grange have before this destroyed the railroad below and near Tupelo, and in the confusion may get fairly started across Alabama before they are known. If, however, with the re-enforcements he is sure of driving the enemy from Tuscumbia, he will attack strongly.

I have telegraphed to Rosecrans, and recommended a strong demonstration on the left of Johnston's line, in aid of the Tuscumbia movement. The line works now to Columbus.

I rejoice exceedingly in the success of the passage of the batteries. It will tend to stop the mouths of the croakers at home and of the newspaper officers in the army. I look now for the occupation of Grand Gulf and the abandonment and surrender of Vicksburg.

Grierson will cut the railroad, if the lives, at or near Chunky Bridge, about Wednesday night or Thursday. No news here of any moment.

Your obedient servant,

S. A. HURLBUT.

MILLIKEN'S BEND, La., April 21, 1863.

Admiral DAVID D. PORTER, Comdg. Mississippi Squadron:

The boats we expect to run the blockade with to-night failed to get ready in time. They, however, will be ready to go through

to-night. I sent a party yesterday to burn the house on the point opposite Vicksburg, but they found it impossible to get to them without great difficulty, and under a fire from short range of the enemy's batteries. They stuck to it until they drew seventeen shots, and then gave up the job to try it at night. The night attempt was made and failed. The enemy were found to occupy these houses with a strong guard, and our troops were compelled to withdraw, with a loss of 1 man wounded.

It is evident that our boats cannot run the blockade without the river being lit up to expose every steamer to full view. Under the circumstances we may meet with a heavy loss. I would suggest, admiral, the propriety of sending a gunboat up to-morrow night, to watch below the batteries, to give such aid as they may require. A fleet of our barges has arrived, and one of the tugs. I will send some of them with the fleet.

We have got a small steamer and some barges into Walnut Bayou. Hope to get them through to Carthage by Thursday. I move my headquarters to Carthage on Wednesday.

Your note, with sketch of passes to Smith's plantation, is received. I have ordered through a saw, to cut down the trees mentioned in your note as being in the way of navigation.

U. S. GRANT.

HEADQUARTERS THIRTEENTH ARMY CORPS, Smith's Plantation, April 21, 1863.

Major General U. S. GRANT, Comdg. Department of the Tennessee:

GENERAL: I learn from General Osterhaus that he found a rebel cavalry picket at Perkins', which he drove away, and that their infantry,