HEADQUARTERS DISTRICT OF WEST LOUISIANA, In the Field, May 14, 1864.

COLONEL: On yesterday the enemy moved heavy masses down the river road from Alexandria, the head of his column reaching a point 20 miles below last night. three hundred and thirteen wagons accompanied the column. Heavy explosions were heard at Alexandria during the day and dense clouds of smoke enveloped [it]. Twenty-three transports and two gun-boats had up steam and the river was full of floating masses of cotton. Hardeman skirmished briskly with their advance, while Steele from the Bayour Rapides and Robert was driving their rear and attacking their flank. Reports are so contradictory of the condition of the dam at the falls that I do not know what to believe. It appears certain, however, that a portion at least of the fleet has passed over, and perhaps all. This morning heavy firing lasted for two hours along the river, the heavy guns of gun-boats taking part. My troops are so disposed as to harass the enemy in rear and flank and attack the boats from both banks of the river. Having no frontier which offers advantage to a small force, I have not the pretension to attempt to fight a general battle with my little force against four times their number, with one flank resting on Red River supported by gun-boats; but I hope to force the enemy to destroy large amounts of property, and harass and worry him until he reaches the Mississippi. the troops from above cannot reach me in time to be of use in this campaign. I shall direct General Walker to halt at Campti and rest and reorganize his command. His presence here at the right time would have insured the most brilliant results; but such opportunities never occur twice in the same campaign. As soon as Banks reaches the Mississippi River he will lose the troops of the Sixteenth and Seventeenth Corps loaned him by Sherman. Even if he withdraws every man from Texas, which he will do, he cannot do more than maintain himself in New Orleasn. Polignac, if strengthened by Thomas' brigade and a good brigade of cavalry, can occupy and hold the La Fourche, and with any co-operation from the other side entirely prevent the navigation of the Mississippi River. Everything else should be directed to Missouri. There can be no doubt that this is the last campaign of the war. Nothing but the fall of richmond can prolong the struggle after the summer campaign. The fate of Missouri will have to be decided by diplomacy or the sword. If settled by the latter, it fixes the question of Tennessee and simplifies that of Kentucky. Ten thousand horses and an equal force of infantry can reach the Missouri River before the summer passes. I respectfully offer these suggestions, esteeming it a duty to do so.

Your obedient servant,
R. TAYLOR,

Major-General.

Colonel S. S. ANDERSON,

Asst. Adjt. General, Trans-Mississippi Department.

HEADQUARTERS DISTRICT OF WEST LOUISIANA, In the Field, May 16, 1864.

COLONEL: On yesterday the fighting was well sustained. Steele's division pressed the enemy's rear and flank on the river road below Alexandria, while Bagby's division, afterward re-enforced by Major,