The programme of the advance was arranged by General Grant and General McClernand as follows:—Extreme left, General Smith, supported by General Blair; on the right of General Smith, General Osterhaus, supported by General Carr; General Hovey in the centre, with McPherson on the extreme right, and Crocker as reserve. In this order the advance was made; General McClernand’s corps, with the exception of General Hovey’s division, reaching the position by way of the several roads leading from Raymond to Edward’s Station. On the evening of the 15th, General McClernand heard that the enemy was advancing from Edwards’ Station to Raymond, and quickly placed his troops in order of battle to repel the anticipated attack. Extensive reconnoissances revealed the fact, however, that he was merely feeling his position and force, and that no attack need be expected that day. At nine in the morning, General Osterhaus took possession of Bolton, capturing a rebel mail and several prisoners. General McClernand placed his army in camp early in the evening, and by daylight the following day each division occupied the ground selected, and prepared to offer battle. BATTLE OF BAKER’S CREEK, OF CHAMPION HILL, MISS. MAY 16, 1863. Early this morning General McClernand’s corps was put in motion. General Hovey’s division was on the main road from Jackson to Vicksburg, but the balance of the corps was a few miles to the south. General Ward was on a parallel road, and General McPherson’s corps followed Hovey’s division closely. The enemy’s first demonstration was upon the Union extreme left, which they attempted to turn. This attempt was most gallantly repulsed by General Smith, commanding the left wing. At seven o’clock the skirmishers were actively engaged; and as the enemy sought the cover of the forest the Union artillery fire was opened, which continued without intermission for two hours. At this time General Ransom’s brigade marched on the field, and took up a position as reserve behind General Carr. At nine o’clock General Hovey discovered the enemy in front on Champion Hill, to the left of the road, near Baker’s creek, apparently in force. Skirmishers were thrown out, and the division advanced cautiously and slowly to give General McPherson’s advance division under General Logan time to come within supporting distance. General Hovey’s division advanced across the other field at the foot of Champion Hill in line of battle.