MAY 20, with Captain Klosterman's pioneer company and the Eighty-THIRD Indiana Infantry, commenced a road along Thompson's Lake which, on examination made by Captain Klosterman early in the morning, showed to be of far easier construction than the main road along Chickasaw Bayon, which crossed several small bayous, and was obstructed by fallen trees, cup by the enemy since December last. By 11 a. m. the road was so far completed as to admit the passage of the wagons. On the 22nd, the main road was nearly for use. On this road I had the assistance of Major Tweddale, with parts of three companies of his battalion. On the 23rd, received orders to report with all the pioneer force at the headquarters of the Fifteenth Army Corps, to assist at the ; siege of Vicksburg. Afterward detachments from the two companies, with the negro force from that of the SECOND DIVISION, were returned, to keep in order the roads of communication. Approaches were commenced by each brigade wherever such seemed practicable, as follows: By General Giles A. Smith (on the extreme left of the corps,)General Edwing, general Lightburn, and by Captain Young, commanding pioneer company of the THIRD DIVISION, on front of General Buckland. On the right of the corps (General Steele's DIVISION, took charge of a long and somewhat difficult approach in front of General Thayer's brigade, a Captain Ashmed, commanding pioneer company of the SECOND DIVISION, of the roads of communication between the different brigades of that DIVISION. The pioneer companies were also employed in making siege material for their own work and for the different brigades, and in building numerous batteries, particularly in front of the First DIVISION of the corps. On May 32, lieutenant C. C. Chaffee, US. Ordnance, took charge of General Ewing's approach, on the Graveyard road; the as afterward relieved by Captain Kossak. On June 6, finished a bridge some 250 feet across the Chickasaw Bayou, to give a SECOND road to Johnston's Landing, on the Yazoo River, from which the entire army received its supplies. On the 8th, c road to the Yazzo River, immediately to the rear of General Steele's DIVISION, crossing Chickasaw bayou near its head, where it was but a small creek. As soon as it was practicable to do so, the pontoon bridge over Chickasaw Bayou, on the main road, was replaced by a permanent bridge; nevertheless, the superstructure of the pontoon bridge, over which the entire supplies of the army, together with the siege, guns had passed, was so much injured that about one-half on it was rendered worthless, when the place surrendered, on the morning of July 4, the different approaches, with one exception, were within a very few yards of the enemy's ditch-so near that for the last few days the enemy had thrown lighted shells from their works upon our heads of sap. The approach in front of General Buckland, after mounting the hill upon which were the enemy's works, reached impracticable ground, and was finished by a parallel furnished with sand-bag lop-holes for our sharpshooters; distance about 40 yards from the enemy's line of fire. Being ordered from Vicksburg on July 5, and engaged in sending forward the pontoon train to General Sherman, on Black River, on the 4th, I have not been able to take any measurements. Or even visit the work since the surrender. I would be leave to state in explanation of the delay in sending forward this report, that immediately after the surrender I was ordered to