A discovery, which may prove of importance, was made yesterday afternoon in connection with the recent murder in Whitechapel. A little girl happened to be walking in the back garden, or yard, of the house, 25 Hanbury street, the next house but one to the scene of the murder, when her attention was attracted to peculiar marks on the wall and on the garden path. She communicated her discovery to Detective Inspector Chandler, who had just called at the house to make a plan of the back premises of the three houses, for the use of the Coroner. The yard was then carefully examined, with the result that a bloody trail was found distinctly marked for a distance of five or six feet in the direction of the back door of the house. The appearances suggested that the murderer, after his crime, had passed through or over the dividing fence between Nos. 29 and 27, and thence into the garden of No. 25. On the wall of the last house was a curious mark, between a smear and a sprinkle, as if the murderer, alarmed by the blood soaked state of his coat, had taken it off, and knocked it against the wall. Abutting on the end of the yard of No. 25 are the works of Mr. Bailey, a packing case maker. In the yard of this establishment, on an out of the way corner, the police yesterday afternoon found some crumpled paper, stained, almost saturated, with blood. It is supposed that the murderer found the paper in the yard of No. 25, wiped his hands with it, and threw it over the wall into Mr. Bailey's premises. the house No. 25, like most of the dwellings in the street, is let out in tenements direct from the owner, who does not live on the premises, and has no direct representative therein. The back and front doors are always left either on the latch or wide open, the tenant of each room looking after the safety of his own apartment. The general appearance of the trail of blood and other indications seem to show that the murderer intended to make his way into the street through the house next door but one, being frightened by some noise or light in No. 29 from retreating by the way which he came. On reaching the yard of No. 25, he made for the back door, and then suddenly remembering his blood stained appearance, he must have stopped, and, catching sight of the pieces of paper lying about, he doubtless retraced his steps to the end of the yard, and then performed his gruesome toilet. He might have had some thought of retreating by way of Bailey's premises, but the height of the walls made such a course somewhat perilous, and he finally made his way into Hanbury street through the house. He could have met with no difficulty, as both back and front doors were open, and he could wait in the passage if any one was passing down the street. These matters suggest that the murderer was alive to the risk of detection, and acted with so much circumspection as to dispel the idea that he was a reckless maniac.

A woman named Durrell, who minds carts on market morning in Spitalfields market, stated yesterday that, about half past five o'clock on Saturday morning, she was passing the front door of No. 29 Hanbury street, when she saw a man and a woman standing on the pavement. She heard the man say, "Will you?" and the woman replied, "Yes." They then disappeared. Mrs. Durrell does not think she could identify the couple.

Although no fresh arrests were made yesterday in connection with the Whitechapel murders, the police obtained information which at one time promised to develop into important evidence. It had been intended to liberate John Piser on Monday evening, but at the last moment it was decided to keep him in custody, the police not being quite satisfied upon one or two points in respect to him. Yesterday morning information was received, which, if well founded, would have made out a case of some strength against Piser. On the morning of the murder of Mrs. Chapman a man in Hanbury street noticed a woman in the company of two men. They appeared to be quarrelling, and the heard the men make use of threats. Such an incident is, however, very common in the district, and the man, after taking a good look at the disputants, passed on his way. Yesterday the police resolved to inquire if Piser was one of the men seen in Hanbury street at the time in question. The man who saw the quarrel was requested to attend at Leman street Police station. On his arrival about one o o'clock, some twenty men, mostly brought in from the adjacent thoroughfare, were paraded before him. The man, without a moment's hesitation, pointed to Piser as the man whom he heard threatening the woman in Hanbury street on the morning of the murder. Piser protested that the man was entirely mistaken, but he was put back in the cells, and more closely watched. The police, during the afternoon and evening, made careful inquiries into the statements made by the man who professed to identify Piser. The manner of this man, who is, apparently, of Spanish blood, and displays a blue ribbon on his coat, did not inspire much confidence in his veracity, and he was severely cross examined by a sort of informal tribunal, consisting of experienced detective officers. The witness added to his first statement that he not only saw the prisoner in Hanbury street on the day of the murder, but that he actually took him by the collar when he was about to strike the woman. The man first volunteered his statement on Monday, and he subsequently displayed anxiety to view the remains of Mrs. Chapman, which, however, was not permitted. Piser's brother declares that he did not leave the house between Thursday and the day of his apprehension, because he had been subjected to annoyance at being followed by people, who called him Leather Apron. Piser is physically a very weak man, and for that reason does not work very closely. He suffers from hernia, is in other ways infirm, and has been under hospital treatment for a long time. From his lodgings the police have carried off five knives, which have been subjected to careful examination. All of them are of the class used in the leather currying trade, having blades about six inches in length, with stout handles, sometimes notched in a peculiar way. There is apparently, no blood either on the blades or the handles, but on some of the blades are marks apparently caused by rust. The examination of the knives led to the conclusion that none of the marks was a blood stain. About eight o'clock last evening the police arrived at the conclusion that the man referred to above had not stated the truth, and that there were no grounds for keeping Piser any longer in custody. He was accordingly set at liberty, and at once proceeded to Mulberry street, where he received the congratulations of his relatives and friends.

Mr. S. Montagu, M.P. for the Whitechapel Division of the Tower Hamlets, has offered £100 as a reward for the capture of the Whitechapel murderer.

A representative of the Central News, who patrolled the streets and alleys of Whitechapel during Monday night and the early hours of yesterday morning, writes:-

The scare, which the disclosure of the fourth and most horrible of the murders occasioned in the district, has considerably subsided. People having become familiar with the details of the tragedy, and being calmed by the knowledge of the active measures adopted for their protection by the police, are returning to their normal condition of mind. This is plainly evidenced by the aspect which Whitechapel road presented on Monday night, and up to an early hour of the morning - a very different one from that of the corresponding period of the previous day. On Sunday night the pavements were almost deserted, but 24 hours later groups of men and women chatted, joked, and boisterously laughed upon the flagstones until long after St. Mary's clock struck one. In passing through the groups of people, the words most frequently heard in their conversation were "Leather Apron." The term has become a byword of the pavement and gutter, and one oftener hears it accompanied by a laugh than whispered in a tone which would indicate any fear of the mysterious individual who is supposed to live under that nickname. Whilst a large number of persons, including many members of the police force, believe in the guilt of "Leather Apron," the talk of the footways convinces the passer-by that a large number of other inhabitants of the East end are sceptical as to his personality. So it may be said with truth that the thoroughfares on Monday night presented their customary appearance. There was the usual percentage of gaudily dressed, loud, and vulgar women at the brightly lighted cross ways; and the still larger proportion of miserable, half fed, dejected creatures of the same sex upon whom hard life, unhealthy habits, and bad spirits have too plainly set their stamp. Soon after one o'clock the better dressed members of the motley company disappeared; but the poor wretches crawled about from lamp to lamp, or from one dark alley's mouth to another, until faint signs of dawn appeared. Off the main road - in such thoroughfares as Commercial street and Brick lane - there was little to attract attention. Constables passed silently by the knots of homeless vagabonds huddled in the recess of some big door way; other constables, whose plain clothes could not prevent their stalwart, well drilled figures from betraying their calling, paraded in couples, now and again emerging from some dimly lighted lane and passing their uniformed comrades with an air of profound ignorance. The streets referred to by the constables in the main thoroughfare, as "round at the back," presented a dismal appearance, the dim yellow flames of the not too numerous public lamps only rendering the darkness of the night more gloomy. Such passages as Edward street, connecting Hanbury and Prince's streets, Flower and Dean street, between Brick lane and Commercial street, which, in daylight, only strike one as very unwholesome and dirty thoroughfares, appear unutterably forlorn and dismal in the darkness of the night. In almost any one of these dark and filthy passages a human being's life might be every night sacrificed were the blow dealt with the terrible suddenness and precision which evidently characterised the last two homicides; and a police force of double the strength of that now employed, and organised under the best possible conditions, might well be baffled in its efforts to capture the murderers. In the immediate neighbourhood of St. Mary's Church a wide entry presented a deep cavern of intense blackness, into which no lamp shone, and where such an occurrence as that of Saturday morning might easily take place unobserved. In a squalid thoroughfare between Hanbury street and Whitechapel road some houses have been pulled down, the space being now waste ground enclosed by wooden palings. This unilluminated spot is separated by a house or two from an alley which, at a point some yards from the street, turns at right angles apparently towards the unoccupied space mentioned. Into the mouth of this passage a slatternly woman, her face half hidden in a shawl, which formed her only headdress, thrust her head, and in a shrill and angry voice shrieked, "Tuppy!" The cry was answered by the appearance of an evil looking man, with a ragged black beard, who in reply to an impatient question "Where is she?" muttered in a surly tone, "Round there," at the same time jerking his thumb backwards towards the alley. "Well, come 'long 'ome, then. I ain't agoin' to wait for she," replied the woman, who, with the dark man limping after, soon disappeared round the corner of the street. There was no subsequent indication of the presence of a third person. The light from the street was so dim that there was no possibility of recognising the features of the man and women, and certainly if either had borne traces of crime they would have attracted no attention. Such occurrences as the above are, the police say, quite usual, and they neither have, nor wish to have, authority to question any individual whose conduct may attract attention without exciting suspicion.

The St. Jude's Vigilance Association has only been in existence about four weeks. It is largely composed of working men, assisted by some of the members belonging to Toynbee Hall, its operations being confined to that neighbourhood. A member of the Committee stated yesterday that rows are constantly occurring in the district, and that the police force is too small to deal with the disturbers of the peace. The night after the murder in Buck's row, a man and woman disturbed Wentworth street for more than half an hour. Two members of the Committee were present, but no policeman could be found. Another brawl took place yesterday in the same thoroughfare, and one of the Committee, who became aware of it, looked for a constable for twenty minutes before one was found.

At the Lambeth Police court yesterday, John Brennan, 39, labourer, was charged before Mr. Biron with acting in a disorderly manner, and causing a crowd to assemble at Southampton street, Camberwell. On Monday afternoon the prisoner entered the White Hart public house, Southampton street. His coat was torn up the back, and he had a very rough and strange appearance. He began talking about the murder at the East end, and added that they had not yet caught "Leather Apron," who was a pal of his. He proceeded to say that he had the knife. A regular scare followed this, the customers ran out of the place into the street, and in a short time a crowd gathered. The landlady, feeling alarmed at what she heard, locked herself in the bar parlour, leaving the prisoner in possession of the place. In the meantime the story spread, and two women, seeing Police Constable Pillow, told him, and begged him to enter the house. He found a crowd assembled, and managed to get the prisoner out of the house, but as he refused to go away, took him into custody. The prisoner, who treated the whole matter evidently as a good joke, was ordered by Mr. Biron to enter into bail to keep the peace.

About twenty minutes to one yesterday afternoon, Frederick Moore, a man employed at Messrs. Ward's timber yard, Grosvenor road, had his attention drawn to a curious looking object lying on the mud on the bank of the Thames, immediately opposite where he was working. He procured a ladder, and descended to the bank below the wharf. He was startled to find that the object was a human arm. It was fairly wedged between some timber in the wood dock, belonging to Messrs. Chapple. Moore having secured the limb, carefully examined the immediate vicinity, but failing to find any more human remains, he took up the arm, carried it to the embankment, and handed it over to Police constable Jones, 127B. Jones wrapped up the arm in a paper, and conveyed it to the Gerald row Police station. Inspector Adams, of the B Division, after communicating the discovery to Scotland yard, sent for Dr. Neville, of Pimlico road and Sloane street, the nearest medical man, who soon arrived at the police station, and made a careful examination of the limb. He decided that the arm was that of a well formed, tall young woman, probably about twenty five years of age. It had been cut off at the shoulders with some sharp instrument, and the question naturally arose whether this was the work of a professional anatomist or of a murderer. Dr. Neville did not express a positive opinion either way, but said that the work had been neatly done. Some skill, too, had been shown in the manner in which the limb had been removed from the trunk, but the handiwork was scarcely good enough for a person acquainted with the principles of anatomy. The flesh was comparatively fresh, and was not quite free from blood, but it appears to have been in the water two or three days. The arm had most probably been removed from the trunk after death, and it bore no bruises or signs of violent usage.

As soon as the medical examination had been concluded, Inspector Adams had the arm removed to the mortuary in Millbank street, and then proceeded with his investigations. His first care was to have the whole of the river in the immediate neighbourhood thoroughly dragged. The work was continued until a late hour in the evening, but, according to the police, no more human remains were found. The police records of missing persons were also carefully searched, but they yielded nothing that could be described as a clue. On the 24th of last month a man who was sweeping the railway station at Guildford came across a parcel containing a human foot and leg, which he at once handed over to the local police. The parcel had apparently been thrown either from a passing train or from a bridge which passes over the railway close to where it was found. But it is not probable that the arm found yesterday had anything to do with the Guildford remains. The limb found yesterday was comparatively fresh; at any rate, it formed part of a living body not more than four days ago. Within the last week there has been reported to the police an average number of disappearances of women; but, as far as can be ascertained, not one of them can be connected with the present case.

It is possible, but not at all probable, that this arm may have been cut from the body of a young married woman, who left her home at Lewisham on the 20th ult., and has not since been heard of. She was twenty three years of age, and tall; but she had threatened to commit suicide, and it is more likely that she carried out her threat than that she was the victim of a murderer. It is possible, also, that the arm may have been placed where found by some medical student, but this view is not shared by the authorities. Inquiries are, however, being made at the various hospitals and private medical schools, the result of which can scarcely be made known until today.

A man whose name is not given, informed the Whitechapel police yesterday that he saw two men attacking a woman on Saturday morning, near the scene of the murder; and on being shown a number of men, he selected Piser as one of the woman's assailants. But further inquiry convinced the police that the man's statements were not trustworthy, and last evening Piser was released. Mr. Montagu, the local member, has offered a reward of one hundred pounds for the apprehension of the murderer. Yesterday afternoon a little girl called the attention of the police to marks in the yard behind No. 25 Hanbury street, the next door but one to the scene of the murder. Bloodstains were found which indicated that the murderer had crossed two fences, and ultimately made his escape through No. 25.

The arm of a woman was yesterday afternoon found in the mud on the bank of the Thames, near Pimlico. A medical gentleman, who examined it, decided that it had been cut off by some sharp instrument, but he did not express an opinion whether this was done by a professional anatomist or a murderer.