Much importance is attached by the police to an arrest made at King-street police station on Tuesday morning. It appears that the man entered the station about nine o'clock and complained of having lost a black bag. While the officers were taking note of the case he commenced to talk about the women murdered in Whitechapel, and offered to cut of the sergeant's head, and spoke in a rambling nonsensical manner. When asked what his business was, he said he studied some years for the medical profession, but gave it up for engineering. He added that he had been staying for some nights in coffee-houses. His talk became of such a rambling character that Dr. Bond, the divisional surgeon, was sent for, and pronounced him to be a very dangerous lunatic. The man is described as answered the description of the person seen with women at the East End on different occasions. He was dressed in a serge suit with a hard felt hat, and is of very strong build. Although he gave his age as 67, he looked much younger. Before his removal to Bow-street photographs of him were taken. He was also asked to write his name, &c., and it is stated that the writing is somewhat similar to that of letters received by the police and others.

At the Thames Police Court yesterday morning the divisional surgeon of police and the relieving officer asked the magistrates to sign the necessary papers for the removal to an asylum of a woman whose mind appeared to have been affected by the recent murders. The doctor's certificate stated that the woman, whose name is Sarah Goody, aged 40, a nee Hewoman, living at Wild-street, Stepney, had told him (the doctor) that she was followed about by a man, who watched her movements, and who intended to do her harm. She was in such a terrified condition that she could neither eat nor sleep. The lunatic attendant stated that the woman declared that she was followed about by murderers, who intended catching her. On one occasion she asked her landlady to see if there was any writing on the shutters. Mr. Lushington signed the necessary papers.

Sir Charles Warren wishes to say that the marked desire evinced by the Whitechapel district to aid the police in the pursuit of the author of the recent crimes has enabled him to direct that, subject to the consent of the occupiers, a thorough house-to-house search should be made within a defined area. With few exceptions inhabitants of all classes and creeds have freely fallen in with the proposal, and have materially assisted the officers engaged in carrying it out. Sir Charles Warren feels that some acknowledgment is due on all sides of the cordial co-operation of the inhabitants, and he is much gratified that the police officers have carried out so delicate a duty with the marked goodwill of all those with whom they have come in contact.

The Echo says there are indications in official circles that at no period during the search for the miscreant has there been so much chance of an arrest as at the present moment. From more than one source the police authorities have received information tending to show that the criminal is a foreigner, who was known as having lived within a radius of a few hundred yards from the scene of the Berner- street tragedy. The very place where he lodges is asserted to be within official cognisance. If the man be the real culprit, he lived some time ago with a woman, by whom he has been accused. Her statements are, it is stated, now being inquired into. In the meantime the suspected assassin is "shadowed." Incriminating evidence of a certain character has already been obtained, and, should implicit credence be placed in the woman already referred to, whose name will not transpire under any circumstances until after his guilt is prima facie established, a confession of the crimes may be looked for at any moment. The accused is himself aware, it is believed, of the suspicions entertained against him.