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The police are said to have succeeded in establishing the identity of the unfortunate woman who was murdered on Thursday last in Clarke's-yard, High-street, Poplar. It would appear that she was known in Poplar by the name of Downey or Downe, and in Whitechapel, which it has been discovered was the last neighborhood in which she lived, by the name of Davis. Both these names have, however, been found to be assumed. The police, after some considerable difficulty, secured the attendance at the Poplar mortuary yesterday of Elizabeth Usher, the head nurse at the Bromley sick asylum, where the deceased woman was stated to have been an inmate. Miss Usher immediately recognized the woman as Rose Milett or Mylett, who had been an inmate of that institution on several occasions. There can be but little doubt that the name under which Miss Usher recognized her is her real name, for the books of the asylum were referred to, and it was discovered that she last entered the asylum on the 20th of January, 1888, and discharged herself on the 14th of March last. On each occasion she went under the same name and for treatment of the same disease. The police have found that the woman lived in a common lodging-house in George-street-a thoroughfare in Spitalfields made notorious by the recent attempt to murder a woman in a similar establishment.