Very respectfully, U. S. GRANT, Major-General Commanding. Governor Yates, of Illinois, writing from Grand Gulf, on the following day, gives a glowing account of the operations of the Federal army: “Our arms are gloriously triumphant. We have succeeded in winning a victory which, in its results, must be the most important of the war. The battle of May 1 lasted from eight o’clock in the morning until night, during all of which time the enemy were driven back on the right, left and centre. All day yesterday our army was in pursuit of the rebels, they giving us battle at almost every defensible point, and fighting with desperate valor. Last night a large force of the enemy was driven across Black river and General McClernand was driving another large force in the direction of Willow Springs. About two o’clock yesterday I left General Logan, with his division in pursuit of the enemy, to join General Grant at Grand Gulf, which the enemy had evacuated in the morning, first blowing up their magazines, spiking their cannon, destroying tents, etc. On my way to Grand Gulf I saw guns scattered all along the road, which the enemy had left in their retreat. The rebels were scattered through the woods in every direction. This army of the rebels was considered, as I now learn, invincible; but it quailed before the irresistible assaults of Northwestern valor.” GRIERSON’S RAID. APRIL 17–MAY 2, 1863. For a long time Colonel Grierson’s ambition had been to lead the cavalry force under his charge into the enemy’s country. At last he received an intimation from General Grant’s headquarters that his desire would be gratified. Colonel Grierson commanded the First brigade of cavalry under General Grant. This force had been for some time occupying Lagrange, Tenn., which is a small town on the Memphis and Charleston railroad, about fifty miles east of the city of Memphis, and four miles west of the junction of the Mississippi and Charleston railroads. When Colonel Grierson first received permission to move with his force into Mississippi, one of the chief objects of the expedition was to cut off the means of communication between the rebel army of the West, and that of General Bragg, then in Middle Tennessee; but when the expedition was once begun, it branched off into many unthought-of directions, and ended in being one of the most brilliant, as well as important feats of the war.