After participating in the battles around Chattanooga, and raising the siege of Knoxville to relieve General Burnside, General Sherman withdrew to Vicksburg, to take command of an expedition which left that city on the 3rd of February, 1864, and proceeded in the direction of Meridian, in Alabama. The force under General Sherman numbered about thirty thousand men, and consisted of the two corps under General McPherson and General Hurlbut, with sixty pieces of light artillery. After much skirmishing by the way, in which the enemy was constantly overcome. General Sherman reached Meridian on the 7th of February. The object of this expedition was the destruction of several railroads which are specified in the following order, issued after the Union force had been one week in Meridian. HEADQUARTERS, DEPARTMENT OF THE TENNESSEE, } MERIDIAN, Miss., February, 15, 1864. } 1. The destruction of the railroads intersecting at Meridian is of great importance, and should be done most effectually. Every tie and rail for many miles in each direction should be absolutely destroyed or injured, and every bridge and culvert should be completely destroyed. To insure this end, to General Hurlbut is entrusted the destruction east and north, and to General McPherson the roads west and south. The troops should be impressed with the importance of this work, and also that time is material, and therefore it should be begun at once, and prosecuted with all the energy possible. Working parties should be composed of about one-half the command, and they should move by regiments, provided with their arms and haversacks, ready to repel attacks of cavalry. The other half in reserve will be able to watch the enemy retreating eastward. 2. Colonel E. F. Winslow, commanding cavalry, will keep his cavalry in advance of the party working eastward, and will act as though this army were slowly pursuing the enemy. 3. Special instructions will be given as to the general supply train; and the troops now in Meridian will, under proper brigade parties, collect meal, meat and supplies. The destruction of buildings must be deferred till the last moment, when a special detail will be made for that purpose. By order of W. T. SHERMAN, Major-General commanding. These directions being faithfully carried out, General Sherman with justice declared that he had made the most complete destruction of railroads ever beheld. Supplies now beginning to fall short, the Union forces fell back toward Vicksburg, returning by the way of Canton, and reached their original position on the 26th of February. In this expedition the National loss in killed and wounded amounted to one hundred and seventy men. GENERAL SMITH’S EXPEDITION FROM MEMPHIS, TENN. FEBRUARY 11, 1864.