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Fifteen-year-old Virginia accidentally discovers the hiding place of Sir Simon, the ghost haunting Canterville Hall, after she has been out riding with the Duke of Chesire, who is in love with her. Because she has torn her riding gown, she sneaks up the back staircase and happens to hear someone in the Tapestry Chamber. She thinks it's a maid, but finds it is the ghost. The passage describing this is below:

A few days after this, Virginia and her curly-haired cavalier [the Duke of Chesire] went out riding on Brockley meadows, where she tore her habit [riding gown] so badly in getting through a hedge that, on their return home, she made up her mind to go up by the back staircase so as not to be seen. As she was running past the Tapestry Chamber, the door of which happened to be open, she fancied she saw some one inside, and thinking it was her mother's maid, who sometimes used to bring her work there, looked in to ask her to mend her habit. To her immense surprise, however, it was the Canterville Ghost himself! He was sitting by the window, watching the ruined gold of the yellowing trees fly through the air, and the red leaves dancing madly down the long avenue. 

Like the rest of the Otis family, Virginia does not fear the ghost. Instead, as a practical American, she takes advantage of this accidental encounter to ask the ghost to behave himself and to stop trying to frighten the family.

The meeting is a godsend for Sir Simon, as he can explain his plight to the sympathetic Virginia. He needs someone innocent like her to intercede on his behalf by weeping and praying for him to be allowed to go to his final rest. Although Virginia is cast in mystical, virginal terms, she shares with the rest of her family a can-do, problem-solving attitude that helps the ghost immensely.