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The Lodger: A Story of the London Fog (1927) - The Constant Bleeder
A serial killer of women is on the loose in London. No one knows who it is except that he calls himself The Avenger (though he may as well be Jack the Ripper, as that's the thinly veiled inspiration here, as adapted from the novel by Marie Belloc Lowndes). Total mystery. The police have nothing.