"The Sister Years (From "Twice Told Tales")" by Nathaniel Hawthorne is a short story that takes place between 11 and midnight on New Year's Eve. An elderly women who feels herself close to death decides to spend her last moments in Salem, on the steps of city hall. It is there that she reflects on her life, and those who pass her by. In particular, she finds herself intrigued by a young woman who reminds her of herself as a young girl but who now feels like her polar opposite.
