exploding a mine near us. I have directed a listening gallantry to be run out in the direction they appear to be, and change the direction of the sap slightly. In General Hovey's front we have approached to within about 20 yards of D. The rebels seem to e at work in this ditch also. July 1. -General Smith's approaches to B were pushed forward a short distance. The one on the right of the road nearly reached the top of the hill. I shall at once establish a place of arms just in the rear of ti. On the left of the road the crater made by the explosion of the mine has been occupied. The sap-roller has been very much cut directions to have it covered at once with earth, and to establish a trench cavalier at that point when the enemy threw a fire-ball, which lodged under the edge of the sap-roller. They then threw hand-grenades into the fire made by the spreading of the inflammable fluid which it apparently contained; bursting, threw pieces all around it, tearing it considerably; at the same time they kept up an incessant fire of the salient C the sap was moved forward a few yards, and a short distance made with the listening gallery. The enemy appear to work in a direction from us that leads me to think that they are deceived as to the direction we intemed to take. In front General B little was done, owing to the burning of the sap-roller, which exposed a portion of the trench to full view. I directed the head of the sap to be filled u to-night with sand-bags, and the cavalier commenced a little to the rear of the point first intended. This will close the head of the sap, but still we will be only about 12 feet from the ditch. I directed a minie to be started to the ditch at the left face. It has been found desirable to use hand-grenades to clear the Fort B altogether, but the distance and height of the parapet are a little too great for 6-pounder shells, though not too great for them to throw at us. In order to have some means of throwing our shells into the fort, I have directed Captain Patterson, of the pioneers corps, to construct spring -boards for this purpose, I learned that General McPHERSON was using moats made of trunks of trees (guns trees being the best) to throw 6 and 12 pound shells, and directed him to make some of these also, shrinking about three iron bands around the mortar. These mortars, which are said to work admirably for about 100 rounds, will be finished and stuck in the ground in the advanced trenches, so they will only have to throw the shells about 50 or 75 yards, in compliance with orders, the trenches are being prepared to allow easy passage of troops over to him for an assault, in order to cross the pared, filled with cotton, well stuffed. Planks 18 feet long are being prepared to throw across the ditch, to allow the passage of an assaulting column. July 3. -As the sap-roller in front of General Carr still continued to move forward, the enemy endeavored to stop it by blowing us out; but as in the other case, the mine was fired too soon, and no damage whatever was done. Nothing was done but the preparation of the trenches for an assault in front of Generals Smith and Hovey. A flag of truce