The rising action is a related series of incidents that build toward the point of greatest interest. The narrator has been watching him sleep for seven nights straight. "So, you see, he would have been very clever to suspect that every night at midnight, I looked in on him as he slept."
The climax is the turning point in the story. When the narrator shines the light on the old man he opens his eye. "With a loud yell, I threw open the lantern and leaped into the room. I dragged him to the floor and pulled the heavy bed over him."
The falling action starts to warp up the story. A neighbor had heard a scream, so they went to get the police. "The scream, I said, was my own. I told them to search the place-search well. Finally i took them to his room. I was so confident that I brought chairs into the room and asked them to sit down."