In the first chapter of the story, Douglas uses the phrase turn of the screw to indicate that a ghost story has a more terrifying effect if a specter targets a child rather than an adult, as in a story just completed by a man named Griffin. Then Douglas asks his listeners what they would say of a ghost story with two children. One of them says such a story would cause two turns of the screw. Here is the passage: 

......."I quite agree—in regard to Griffin’s ghost, or whatever it was—that its appearing first to the little boy, at so tender an age, adds a particular touch. But it’s not the first occurrence of its charming kind that I know to have involved a child. If the child gives the effect another turn of the screw, terror what do you say to TWO children—?" 

......."We say, of course," somebody exclaimed, "that they give two turns!