San Francisco, Nov.22.-- Chief of Police Crowly has lately been in correspondence with officials of Scotland Yard, London, regarding Dr. Tumblety, who is at present under arrest on suspicion of being implicated in the Whitechapel murders. The Chief, in pursuing his investigations, discovered that the doctor still had quite a balance in the Hibernia Bank, which he left there when he disappeared from this city, and which has never been drawn upon. Mr. Smythe of that institution says that he first met the doctor in Toronto, where he was practicing medicine in July, 1858. He next met him in this city, at the Occidental Hotel, in March or April, 1870. Tumblety rented an office at 20 Montgomery-street, where he remained until September, 1870, and then disappeared as suddenly as he came. In 1871 the doctor turned up in New-York. On Oct. 29 Chief Crowley sent a dispatch to the London detectives, informing them that he could furnish specimens of Tumblety's handwriting, and to-day he recieved an answer to send the papers at once.