Midway through "The Sniper," the Republican sniper is in a bad way. He has been shot in his arm and can no longer lift, and therefore use, his own rifle. He is surrounded by enemies, and to save his own life, he must quickly think of and execute a plan to victory.
The plan he comes up with is to place his cap "over the muzzle of his rifle." He will then raise the rifle so that the muzzle and cap appear over the parapet, therefore becoming visible to the enemy sniper across the street.
As soon as the Republican sniper raises his cap over the parapet, there is "a report, and a bullet pierce[s] the center of the cap." The first part of his plan has been successful. For the second part of his plan, the Republican sniper tilts his rifle forward so that the cap falls from the muzzle and over the parapet. The Republican sniper then holds the rifle "in the middle" and lets his left hand, with the rifle, hang over the edge of the roof. He allows his hand to hang "lifelessly." Then, "after a few moments," he lets the rifle fall to the street, dragging his hand back as he sinks to the roof.
When the Republican sniper peers over the parapet and looks at the enemy sniper across the street, he realizes that his plan has worked. The enemy sniper, seeing the cap fall and then also seeing the rifle fall from a seemingly dead hand, assumes that he has killed the Republican sniper. The enemy sniper, thinking that he is now safe, stands up. The Republican sniper, using his revolver now, takes aim and kills the enemy sniper.