On the 18th the young woman was completely identified as Mrs. Philomena Muller, the wife of Simon Muller, a tobacconist, at 502 West Thirtieth street, N. Y. Mr. Muller called at the Morgue at 3 o’clock on the afternoon of May 18th, in company with a lady whom he introduced as Miss Maria Schmidt, his wife’s sister. He said they desired to look at the body. They were led into the damp vault, and at sight of the body Miss Schmidt was overcome, and she retired to the adjoining basement. Mr. Muller gazed upon the body calmly. The jewelry and clothing of the dead woman were shown to him, and he positively identified them as the property of his wife. He said that he had given her the cameo brooch. Mr. Muller said that some time ago his wife deserted him, and since then she had not lived with him. Miss Schmidt had seen her sister about two weeks before. Mrs. Muller then informed her that she had found a decent man, who was going to marry her and take her to Germany in the steamer L’Amerique, which was to sail on the 4th of May. When Miss Schmidt told Mr. Muller of this he went to the wharf of the Transatlantic Steamship Company on the morning of May 4th, and remained at the gang plank of the vessel until all the passengers had gone aboard. He was certain that his wife was not among them, but he did not know her paramour. Before this identification was made, the authorities of Hudson county had obtained conclusive evidence of the fact that the murdered woman was Mrs. Philomena Muller, and that her assassin had married her on the morning of the day on which he killed her, and had taken passage on the following day for Europe. As Mrs. Finck, the wife of an alehouse keeper in Pierce Avenue, West New York, was sitting in her saloon on the afternoon of Tuesday, the 3d of May, a man and a woman entered and sat down at a table. The woman ordered drinks, and called for a glass of beer. Her companion drank soda water. While they were there the woman talked almost incessantly. She said that they came from Morrisania. She seemed to have plenty of money. When she paid for the refreshments, Mrs. Finck noticed a large roll of bank notes in her pocketbook, besides some silver and gold. Before going away, the woman borrowed a corkscrew to open a bottle of Rhine wine which she had with her. She said she had bought the bottle in Union Hill. Mrs. Finck minutely described the woman, and the description tallied exactly with that of the woman who was murdered. Prosecutor McGill was so impressed with the accuracy of Mrs. Finck’s description, that he specially detailed Detectives Swinton and Fanning to trace the movements of the unknown couple. They began their search on Tuesday evening, May 17th, and Wednesday the 18th they submitted to the Prosecutor a circumstantial account of their discoveries.