"The riotous assemblages have been dispersed. Business is running in its usual channels. The various lines of omnibuses, railway, and telegraph have resumed their ordinary operations. Few symptoms of disorder remain, except in a small district in the eastern part of the city, comprising a part of the Eighteenth and Twenty-first Wards. The police is everywhere alert. A sufficient military force is now here to suppress any illegal movement, however formidable. "Let me exhort you, therefore, to pursue your ordinary business. Avoid especially all crowds. Remain quietly at your homes, except when engaged in business, or assisting the authorities in some organized force. When the military appear in the street, do not gather about it, being sure that it is doing its duty in obedience to orders from superior authority. Your homes and your places of business you have a right to defend, and it is your duty to defend them, at all hazards. Yield to no intimidation, and to no demand for money as the price of your safety. If any person warns you to desist from your accustomed business, give no heed to the warning, but arrest him and bring him to the nearest station-house as a conspirator. "Be assured that the public authorities have the ability and the will to protect you from those who have conspired alike against your peace, against the government of your choice, and against the laws which your representatives have enacted. "GEORGE OPDYKE, Mayor." Down-town there was scarcely anything to show that New York had for nearly a week been swept by one of the most frightful storms that ever desolated a city. Even in the disaffected districts, no crowds were assembled. In the corner groggeries, small groups of men might be seen, discussing the past, and uttering curses and threats; and ruined houses and battered walls and hanging blinds here and there arrested the eye, showing what wild work had been wrought; but it was evident that the struggle was over. The mob was thoroughly subdued, and the law-breakers now thought more of escaping future punishment than of further acts of violence. Bruised heads and battered forms were scattered through the low tenement-houses in every direction, which friends were anxious to keep concealed from the notice of the authorities. In dirty cellars and squalid apartments were piled away the richest stuffs--brocaded silks, cashmere shawls, elegant chairs, vases, bronzes, and articles of virtu, huddled promiscuously together, damning evidences of guilt, which were sure not to escape, in the end, the searching eye of the police, who had already begun to gather up the plunder. Thus the objects mostly coveted but a few hours ago now awakened the greatest solicitude and fear.