He makes reference to the "Crescent Fort", anyone know what fort he is referring to?
@1stMS-Arty beat me to it, but I think he's referring what's usually called Green's Redan. He says he took charge of it on June 5 and remained in command until the end of the siege. Later on he says Green was killed there, and its known that he was killed at the redan.
Assuming command of Green's brigade, Col. Thomas P. Dockery says in his OR:
The brigade occupied this position [at the riverfront] until the evening of June 2, when it was ordered to move out to the works in the rear of the city, and occupy permanently a gap between the divisions of Major-Generals Smith and Forney. This was one of the most exposed positions on the line, the enemy's guns enfilading the works form right to left, and guns of heavy caliber played upon the enemy's works from the front. With the limited number of intrenching tools on the line, it took all night to repair the damage done to the works during the day. . . .
On the 26th, the enemy commenced digging an approach in front of the fort on my brigade. General Green having been wounded on the day before, he was on this day unable to visit the fortifications and watch the movement of the enemy.
On the morning of the 27th, he was in the ditches, as was his custom, reconnoitering the positions of the enemy along his front, and while looking over the parapet in front of the sap of the enemy, which was only about 60 yards distant, he was shot through the head by a sharpshooter and almost instantly killed. . . .
The command devolving upon me, I at once commenced countermines to that of the enemy, one of which was sprung on the night of July 2, with but little damage to the enemy.