MEMPHIS, TENN., April 5, 1863.

Lieutenant Colonel John A. RAWLINS, Assistant Adjutant-GENERAL:

SIR: The movement of yesterday appears to have been merely a dash of mounted men. Chalmers has moved up to Senatobia. Very considerable activity among the irregular cavalry of the enemy is manifest along my southern front, especially south and east of Corinth.

I have been anxiously waiting for cavalry horses from Saint Louis. Yesterday I received 350, which, upon inspection, are worthless. General Thomas went with me to look them over, and sent fa message to Colonel Allen to send no more of that sort, but to send forward 1,500 good cavalry horses for immediate use. I hope they may come, and come soon.

Dodge received a message from Rosecrans, requesting him to move on Tuscumbia, in combination with a movement on Rosecrans' part on Florence.

I have directed him to send the plan of the movement, as I cannot well see how Rosecrans can reach Florence except in heavy force. As, however, Dodge is strong enough to whip anything on this side of the Tennessee River, and yet cover Corinth, I shall have him move as requested.

I have expected the Fourth Missouri Cavalry, but they have been sent to Nashville to Rosecrans. The enemy's cavalry, as previously reported, are in force on the north and east sides of the Tennessee, with some artillery; hence the necessity of active cavalry, both from Jackson and Corinth-a hard service, wearing to men and horses. I refer to my former letters on this subject.

Respectfully, yours,

S. A. HURLBUT.

HDQRS., Smith's Plantation, April 6, 1863-11 a. m.

DEAR GENERAL: I have just returned from New Carthage. We finished last night a gunboat, with which we marched to Carthage. The bayou from Richmond, 8 miles, a current against us; from that point to Holmes', 10 [miles] from Richmond, still water, with drift-wood, some places 200 yards, quite covered, and would have to be removed and some trees cut and floated out. Two miles still farther this way the floating timber occurs again, with downward current. From R. [Richmond] to Smith's we can soon run small flats the whole distance from Richmond to New Carthage, or to the levee at Carthage, and, indeed, through that into the Mississippi, although, after we pass the main river levee, the depth of water is not beyond 3 feet, that we could find. Still, General Osterhaus, who was along, thinks we will have no trouble to go through. We can land steamboats within 200 yards of the main levee, and there are cross levees reaching from the river in several places to the main levee. There is no land dry save the levee. The land on the opposite shore of the Mississippi is dry, but between the shore and the bluffs or high land there is a swamp covered with water, said to be 8 miles wide. This water separates Jefferson Davis' [plantation] from the main land. Small flats will be the readiest means of conveyance from Richmond to Carthage. We can construct these rapidly here with the help of these fine mills close at hand. Ropes and spikes will be needed.

The road will be of necessity inside of the levee and through the field, and in dry weather good. The breaks in the levee would be a work of much more time than would be practicable to repair.

I am, general, your obedient servant,
W. F. PATTERSON,

Captain, &c.