MEMPHIS, TENN., April 13, 1863.

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

GENERAL: I send you the following dispatch, just received:

MURFREESBOROUGH, April 11, 1863.

My expedition leaves Nashville to-day by river. It will probably reach Hamburg six days hence. Dodge should move as soon as your orders can reach him. Should communicate with my force by messenger at Hamburg, so that each may know the whereabouts of the other. My force will probably land at Eastport.

W. S. ROSECRANS.

General Dodge will move on Wednesday, as agreed.

I am, general, your obedient servant,

S. A. HURLBUT.

JACKSON, April 13, 1863.

Lieutenant-Colonel BINMORE, Assistant Adjutant-GENERAL:

The following dispatch has just been received from Brigadier-General Dodge:

CORINTH.

Two scouts are in from the south, one from Meridian and the other from Vicksburg. Pemberton's command is now stretched from Grand Gulf to Greenwood, with one brigade at Big Black. Two steamboats also lie at Big Black Bridge, at Jackson, one right above Jackson. For 15 miles toward Grenada, two Indian regiments; at Grenada lot of militia. Line of Yazoo is heavily guarded, and very strongly intrenched. They are living from hand to mouth, all their provisions being locked up in Red River. Along line of railroad great efforts are being made to collect grain and bacon, and they run one or two cars per day from each station. It was said 8,000 men were going from Vicksburg to Johnston; 3,000 went from Meridian. Five trains of empty cars toward Vicksburg the day the scouts left there. They have great fears of a movement by land. Should any troops leave Vicksburg, I shall know it. At Columbus, four or five regiments. A command from Florida, under Colonel Finney, came to Okolona three days ago, about 400 strong; also a regiment to Cotton Gin. All the militia of the State is being concentrated along our front. The rest of the forces are about as I wrote. I send the Vicksburg man to General Grant, he having been sent on his order. The steamers at Vicksburg are mostly on Yazoo and Mississippi Rivers. Front very firm; in rear they do not fear attack from that direction, but do fear cutting off their supplies by movement by way of Grenada or Corinth. There is no doubt but that all their supplies come now from Mississippi, and they are getting scarce.

R. J. OGLESBY.

HELENA, ARK., April 13, 1863.

Major General STEPHEN A. HURLBUT, Comdg. SIXTEENTH Army Corps:

GENERAL: I am in receipt of your communication of the 10th, and regret the impossibility of a combined movement into Mississippi. The bottoms are now all overflowed, and they extend so far back from the river that no movement is practicable from Austin or any other point on the Mississippi. Our forces have now all left the Yazoo Pass, and there are no iron-clads or gunboats here, so that no movement is practicable from any point on the Pass or the Coldwater. Under these circumstances, therefore, I cannot offer you my co-operation in your proposed movement. I am very anxious to aid you in any manner possible, and I cheerfully tender you 500 cavalry, to be used by you from Memphis in case you make the movement. I cannot spare a greater number, as my force is now considerably reduced by the details already made from this district to Memphis and other points, and the exigencies of the service here require constant cavalry service. I have no transports here, having sent all that could be found to transport Hovey's and Quinby's