THE MURDER ON THE THAMES.Yesterday a human foot was picked up off Hammersmith. Between it and the one picked up before there is a great difference in size, the one being quite a large foot, and belonging to a large woman, and the other as though it belonged to a small one. It may be that they both belong to the same deceased. In opposition, however, to this possibility there is some difficulty in determining whether some other portions of the mutilated remains really belong to each other. When at first two sets of lungs were found, which were both at first thought to be human, a fear was entertained that a double murder had been committed First one set and then the other was afterwards thought to belong to sheep. Now, however, that a difficulty and discrepancy has arisen in reference to the sizes of the two feet, and also as to whether certain portions of the limbs actually belong to each other, the question as to whether two murders may have been committed has been mooted, and the parts are being submitted toamostsearching medical examination. The police areunderstoodtobe working in all directions with the view of unravelling the mystery, investigating a number of suspicious circumstances that have come under their observation. Some suspicion, it is said, points to the neighbourhood of Hammersmith as possibly being the scene of the dreadful tragedy. ...The greatest efforts were made by the authenties and all concerned yesterday in dragging the river and excavating the marshes, c., on the riverside near Woolwich for the purpose of finding any new portions of the mutilated remains of the murdered woman, but up to the moment of despatching this these efforts were unre warded. A vast number of floating objects on the nver were “ chased ” both by the river police and by others in the hope of them containing clues to the missing female, but the chasers were doomed to be disappointed. It is asserted that should the missing portions not be found in the river or its neighbourhood, the ornamental waters of the parks, and the canals and chief streams in the metropolis and its environs will be dragged by order of the authorities. The 'police are well seconded by the inhabitant? of the waterside, the greater portion of whom would, if they found the murderer, deliver him up to justice for mere justice’s sake. At tbfe same time, many are willing to work for the expected reward.Another River Mystery.—The body of a man. without head or arms,was found yesterday morning floating in the river Liffey, at North Wall Quay. It was in an advanced stage of decomposition, and was dressed in an oil coat and trousers and long boots. No clue has been obtained to lead to identification.