Theories rather than facts continue to predominate in connection with the East End murders, save that a knife found with a bloodstained handkerchief is reported to have been discovered on a door step it the Whitechapel road. As yet it is hardly known whether this might not turn out to be a hoax, for notwithstanding the serious aspect of these outrages they appear to afford a source of recreation to the practical joker. The arrests so far have not proved successful, and the so-called confessions have up to now turned out to be but drunken effusions of dipsomaniacs. Of course, any number of strange stories are afloat in the neighbourhood, all of which gain a certain amount of credence in different quarters, and are thought to contain a possible explanation to the murders. Here, for instance, is a sample. A year or two since a Colonist arrived in Whitechapel and settled near Wentworth street. He had got some money, and as soon as the rumour of this got abroad he was seized upon one night by loose women, rifled of all he had on him, and stripped naked in the streets. This so angered him that he went away swearing dire vengeance on his assailants. Now the supposition is that this man is the murderer is not at all probable, but the story is none the less a grim comment upon the kind of order that prevails in the streets at the back of the Commercial road.

Mr Wynn Baxter resumed the inquiry this afternoon in Whitechapel on the body of the woman murdered in Berner street, and identified as Elizabeth Watts by one witness, though she was said by some persons to be Lizzie Stride.

Elizabeth Tanner, living in Flower and Dean street, examined, said she recognised the deceased as "Long Liz," and she last saw her alive on Saturday afternoon in the Queen's Head, Commercial road. On Thursday deceased left a male acquaintance to live with witness. Never heard the name of Stride mentioned. Deceased was a Swede.

Catherine Lane, living with the last witness, also recognised the deceased as "Long Liz." Deeased told her on Saturday she had quarrelled with the man she left on Thursday.

Charles Preston, a barber, of the same address, identified the body a that of "Long Liz." He understood she came from Stockholm to England in a foreign gentleman's service, and that her name was Elizabeth Stride.

Michael Kidney, Dorset street, Waterside labourer, said deceased was Elizabeth Stride. She was a Swede, and lived with witness nearly three years. Her husband was a ship's carpenter, and was drowned in the Princess Alice disaster. Had not seen her since the Tuesday before her death. Witness had never neglected her, but treated her as a wife.

Replying to Inspector Rein - The witness said if he had the police under his own control he could catch the murderer redhanded.

Edward Johnston, assistant to Drs. Kay and Blackwell, deposed to having been called to see the body.

Thomas Coram, a lad of 18, produced a knife about 12 inches long, which he found on the doorstep of No. 253 Whitechapel road, 24 hours after the murder.

Police-Constable Drage said the boy found the knife. The blade and handle were stained with blood.

Dr. Phillips gave the result of the post-mortem examination. He said the cut in the throat was 6 inches long, and severed the principle arteries. The cause of death was loss of blood and division of the windpipe. Several small articles were found in the clothes of the deceased after examination.

The inquiry was again adjourned till Friday.

It is established by to-day's evidence at the inquiry on the Berner street victim that the woman murdered is Elizabeth Stride, and that Mrs Malcolm was mistaken yesterday in stating the deceased was her sister. The clue afforded by the discovery of the bloodstained knife on a doorstep will be followed up, although it seems certain the knife was not in the place an hour before it was picked up, and the object of the person who put it there is unknown. Michael Kidney will probably be examined again respecting his pretended special information.

In connection with the Mitre square murder the principal incident has been the positive identification of the woman by John Kelly, with whom she had lived for seven years. This man says he first met the deceased in Flower and Dean street. Her married name was Conway, and she had the initials "T. C." tattooed on her arm. She went out on Saturday night with the intention of seeing a married daughter in Bermondsey, and as she did not return he thought she was staying the night there. Kelly is assisting the police in finding the relatives of the deceased.

A Bath correspondent says, from further inquiries made there it appears that the conflicting evidence of identification in the Berner street case could be decided if witnesses were called form Bath. The woman Watts could be identified by several Bath persons, and also by members of the police force, as she had been charged by the Bath police with drunkenness, and was well known to some members of the force.

The surgeons who conducted the autopsy to-day on the remains found at Westminster came to the conclusion that the arm which was washed up by the Thames near Pimlico, and which had been conveyed to Westminster Mortuary from Ebury street, where it had been preserved, fitted into the trunk found at Whitehall. It is also stated that the cord tied round the limb found in the river and a portion of that which was used to tie up the parcel were similar. At the conclusion of the examination the clothing was disinfected and thoroughly inspected by the police, who state that it was covered with maggots and vermin. Adhering to one portion was found a piece of newspaper saturated with blood. It bore no date, but that can be easily ascertained. The dress stuff was found to be a rich flowered silk underskirt, which proves that the unfortunate victim was not one of the poorer class of society. Nothing was discovered to indicate the cause of death, but the doctors are of opinion that the woman had been murdered about three weeks, and the advanced state of decomposition was due to exposure. The doctors are preparing an elaborate report of the whole case, which will be submitted at the inquest to be held at the Session House, Westminster, on Monday next.

A house to house visitation was commenced this morning in Whitechapel by the police and detectives who left a handbill, which is as follows:-

"POLICE NOTICE TO THE OCCUPIER - On the morning of Friday, August 31st, Saturday 8th, and Sunday 30th September, 1888, women were murdered in Whitechapel, it is supposed by someone residing in the immediate neighbourhood. Should you know of any person to whom suspicion is attached you are earnestly requested to communicate at once with the nearest police station.

"Metropolitan Police Office, 30th September, 1888."

No mention of a reward is made.

Mr Matthews was engaged for several hours to-day at the Home Office with reference to the murders at the East End, and had a prolonged interview with Sir Charles Warren and others on the subject during which the course of action already taken by the police was fully considered, as well as the steps to be taken in future with a view to the discovery of the criminal. Mr Matthews is understood to have directed that no power in the hands of the police should be left untried, and no clue, however apparently unpromising, should be neglected. The understanding between the Metropolitan and City Police is most cordial.

Sir Charles Warren, replying to a letter from the Whitechapel District Board of Works complaining of the inefficiency of the police, writes that the police force cannot possibly do more than guard or take precautions against any repetition of recent atrocities, so long as the victims actually, but unwittingly, connive in their own destruction. In this particular class of murders the unfortunate victims appear to take the murderer to some retired spot, and place themselves in such a position that they can be slaughtered without a sound being heard. Sir Charles requests the board to do all in their power to dissuade the unfortunate women about Whitechapel from going into lonely places in the dark with any person, whether acquaintances or strangers. He assures the board that every nerve is being strained to detect the criminal, and to render more difficult further atrocities, and he emphatically denies that any changes affecting the efficiency of the police have been made.

About 6 o'clock this evening a man whose name was subsequently ascertained to be John Lock, a seaman, was rescued by the police from an excited crowd in the neighbourhood of the Ratcliffe Highway, who were following him and shouting "Leather Apron" and "Jack the Ripper." The cause was not readily explained. When, however, he was examined at the police station his light tweed coat was found to bear marks which were discovered to be paint, but which the crowd had mistaken for blood. His explanation was perfectly satisfactory, but it was some considerable time before the crowd dispersed, and the man was able to depart.

There is a general belief among the local detectives in the East End that the murderer or murderers are lurking in some of the dangerous dens in the low slums which abound in close proximity to the scene of the murders. Houses supposed to be bolted up for the night have been found to possess secret means of entrance. The house in which Annie Chapman was found is said to have had this secret means of entrance. The police are stated to be contemplating a series of raids on the dens known to contain the most desperate and dangerous characters, with the view of affording a clue to the perpetrators of the recent atrocities.

An American who refused to give his name or any account of himself was arrested to-night on suspicion of being the Whitechapel murderer. He accosted a woman in Cable street, asked her to go with him, and threatened that if she refused he would "rip her up." The woman screamed, and the man rushed to a cab. The police gave chase, got up on the cab, seized the man and took him to Leman street Police Station, where he exclaimed to the Inspector, "Are you the boss?" He is detained there, as well as two others arrested to-night.

At the Guildhall, London, this morning, William Bull, describing himself as a medical student in the London Hospital, and living at Stannard road, Dalston, was charged on his own confession with having committed the murder at Mitre square. Inspector Izzard said that at 10.40 last night the accused came to his room at Bishopsgate street Station, and made the following statement:-"My name is William Bull, and I live at Dalston. I am a medical student at the London Hospital. I wish to give myself up for murder in Aldgate, on Saturday night or Sunday morning about 2 o'clock. I think I met the woman in Aldgate. I went with her up a narrow street not far from Morn road, for an immoral purpose. I promised to give her half-a-crown, which I did. While walking along together there was a second man, who came up and took the half-crown from her. I cannot endure this any longer. My poor head. (Here he put his hand to his head and cried, or pretended to cry) I shall go mad. I have done it, and I must put up with it." The inspector asked what had become of the clothing he had on when the murder was committed. Accused said, "If you wish to know, they are in the Lea, and the knife I threw away." At this point the prisoner declined to say any more. He was drunk. Part of the statement was made in the presence of Major Smith. The prisoner gave his correct address, but is no known at the London Hospital. His parents were respectable. The inspector asked for a remand to make inquiries, and this was granted. The prisoner now said he was drunk when he made the statement. He was remanded.