A SICKENING MYSTERY. - The police authorities of New Orleans have recently unraveled a sickening mystery relating to a respectable woman who many years since disappeared from the outside world. The woman was a little quadroon. Some twenty years ago when she was a handsome girl of sixteen, she had symptoms of insanity, and was not allowed to go out from her room. At that time her relations, who were well off, were able to keep her at home in a proper manner. The girl grew worse and finally insane. While in this condition she was generally quiet, but would occasionally break into a fury of passion. Under these circumstances her family, not desiring to make their family skeletons public, kept her a prisoner at home. For a number of years she was imprisoned in this manner. The fortunes of the family grew worse, but wherever they went they carried the poor maniac with them. She finally became very repulsive to them, and they lost all love, and regarded her as a bugbear forever on their hands. Seventeen years ago the woman was conveyed to her present cell, from which she has never stepped out, and in which she has seldom moved. The family only remember to throw her enough food to keep her alive, and they sometimes forgot her for days, during which the woman was only kept alive from being accustomed to this starvation. The clothes she had originally worn rotted off her, and she lay summer and winter upon the cold floor, utterly naked. The family became accustomed to her in this state, and made no attempt to send her to the asylum; and thus she lived, rotting and dying, when the authorities discovered the terrible secret. For years she had never worn an article of clothing, never felt the warmth of a fire, never seen the light of day. The authorities have now ordered her to be taken to the asylum, although there is but little hope of saving the poor woman, owing to her critical condition.