HDQRS. MILITARY DIVISION OF WEST MISSISSIPPI,
New Orleans, La., August 4, 1864.

(Received 11 a. m. 13th.)

Major General H. W. HALLECK,

Chief of Staff, &c., Washington, D. C.:

SIR: On the 19th ultimo General E. K. Smith and Major-General Magruder reached Alexandria from Texas, and on the 20th General Smith left for Shreveport. On the same day the divisions of Major, Walker, Wharton, and Polignac commenced moving in the direction of the Atchafalaya. The advance reached Simsport on the 21st and from 300 to 500 mounted men were thrown across that rive.r The forces at Morganza were re-enforced by 4,000 troops from this city and 2,300 from Vicksburg, and on the 28th a force under General Ullmann encountered, and, after some sharp skirmishing,dispersed the rebel force that had crossed. The casualties were not large on either side, but Colonel Chrysler, Second New York Veteran Cavalry, a valuable officer, was severely wounded. Captain McAnnelly, an active partisan on the rebel side, was killed. On the 29th the rebel force at Simsport had disappeared, and the whole force appeared to be moving in the direction of Alexandria. On the 1st instant Hardeman's brigade had crossed Red River, and was moving in the direction of Vidalia. Walker's division was moving in the same direction. A scout, sent out from Natchez on the 3rd of last month, has just returned, and reports a general movement of the rebel troops on Red River to the eastward. The troops on the lower Teche are also moving in that direction. The scout reports that General Smith had been ordered to cross the Mississippi and re-enforce the troops oppose to Sherman. Mobile papers of a late date state that this order had been given,a nd that Smith's forces were expected to cross soon. The recent movements indicate this intention, or to make an attempt upon General Steele's lines. General Gordon, who had been sent temporarily to White River when General Steele's communications were threatened by Shelby, has now been instructed to remain, if the movements of the enemy should indicate the line of the Arkansas as the real point of attack. price was still at Camden on the 31st, Fagan at Monticello, Marmaduke on the Arkansas River, near Red Fork, and Shelby east of White River. General Steele reports sharp skirmishing on he line of his communications, with, in the aggregate, about equal losses. None of this force has been materially reduced, although small parties have been undoubtedly sent into Missouri for the purpose of collecting recruits. General Buford reports sharp fighting at Simms' Ferry, on Big Creek, with severe loss on both sides. His detailed report has not yet been receive. The difficulties in Missouri can only be controlled by the inhabitants, who should be constrained to array themselves for the Government or be regarded and treated as enemies. I have ordered two regiments of cavalry from Memphis to report to General Rosecrans. I do not think it expedient to send more, even if they could be spared, unless there should be an organized invasion of the State, and we can prevent that as long as we can hold the line of the Arkansas. Admiral Farragut will make an attack upon the forts at the entrance of Mobile Bay in the course of this week, and I have sent Major General Gordon Granger with 2,000 men to occupy and hold Dauphin Island, in order to secure the admiral's communication with the sea, if he should succeed in passing the forts. The troops from Texas are now arriving. I have notified the collector of the port