By the wounding of General Lee the command of the First Brigade devolved on Colonel James Keigwin, forty NINTH Indiana Infantry.

The artillery, from its position described above, supported movements of the infantry with a well-directed fire; but in order to bring the batteries to a more effective range, I selected a hill at least 500 yards nearer the rebel works for a battery, and at once ordered one section of Lanphere's battery to be brought forward. The pieces had to be drawn up the very steep hill by hand, and as soon as one piece was in position it was opened on the enemy.

The feasibility of establishing a battery on the steep hill being thus demonstrated, I ordered a breastwork to be built during the might on the same spot for two sections of Lanphere's battery. I laid the faces of this work out so that we could rake every battery in our front.

After nightfall a strong force of sharpshooters and reserves were detailed to occupy and hold the ground gained by our first attack on Vicksburg. The other troops were withdrawn and bivouacked in the valleys and along the little streams of water in them, carefully hiding their camp-fires.

On next morning, May 20, I had the pleasure to witness the opening of the battery which, by the energy of Captain Lanphere and the zeal of his men and the pioneers, was completed during the night. It was the first battery constructed, and the farthest in advance. The brilliant practice of the gunners kept all the enemy, s guns silent.

During the night one section of Captain Foster's battery was ordered to take position in General SMITH's line by Major-General McClernand.

In the early part of the morning the infantry had formed again in their respective places they occupied yesterday, but behind the line of sharpshooters, who kept up a very lively fire with the enemy in the rifle-pits.

It appeared very desirable, after the successful construction of the battery last night, to have also the 20-pounder Parrott guns of the First Wisconsin Battery brought forward. In my efforts to find a suitable site for this battery, I was assisted by Colonel Keigwin, and on his suggestion I ordered it placed on a high ridge to the left, and a little in advance of the Lanphere battery. A pioneer detail prepared the necessary earthwork. Notwithstanding the rebel sharpshooters maintained afire of great precision on the spot all day, the four guns opened from his SECOND battery before night in masterly style.

On May 21, the fire was kept up by both batteries at interval and by the skirmishers, the masses of infantry being kept out of the enemy's range and view.

While we were at work to advance our lines, the enemy did not lose any chance strengthen and enlarge his works and repair damages. Guns either disabled or withdrawn from the forts one day reappeared on the next morning, either old or new fortifications. They opened them ordinarily at early morning, when the prompt and precise fire from our guns soon forced them to their usual quiet and silence again.

Our skirmishers advanced over this difficult ground slowly but steadily, so that on the evening of May 21 they were at no place more than 300 yards from the enemy's works, and at some points within 200 yards of them. This variation I intervals was exclusively owing to the ground, which, after passing the valley separating us from the fortifications, became more rough and rugged than before. The slope which was immediately before my men was almost perpendicular, and promiscuously cut up by ravines and water-drains, some of which were not more than 6 or 7 feet wide and 10 or 15 deep. All timber was cut