A person screams shrilly when something unexpected happens to him. Here, Max screamed shrilly when he dropped to the balcony, because actually there was no balcony at all; it was only a figment of Ausables imagination. Ausable had described it so vividly, including its history and use, that Max was convinced there was a balcony just outside the window and tried to jump onto it without looking. As the room was on the sixth floor, Max would certainly have been died by falling from such a height.
