Medical estimates are humbugs, from Dr. D. M. Reeves down to Dr. Sanger. According to Dr. Reeves, every female in the city, over thirteen years of age, was required to fill up his estimate of lewd women, and Dr. Sanger is but little more reasonable. Very respectfully, yours, JOHN A. KENNEDY. Nearly three years have elapsed since the above letter was written, and there can be no doubt that the interval has witnessed a very decided increase of this species of vice. The greatest increase is, perhaps, in the class termed by Mr. Kennedy "other women," in which are included the women of nominal respectability, whose crime is known only to themselves and their lovers. They are the last persons in the world one would think of accusing, for they are not even suspected of wrong doing. Many of them seem to be innocent young girls, others wives and mothers of undoubted purity. Society is corrupt to its very heart in the great city, and there are thousands of nominally virtuous women who lead, in secret, lives of shame. The authorities cannot include this class in their statistics, as they know nothing of them. FIRST-CLASS HOUSES. There are very few first-class houses of ill-fame in the city, and they are located in the best neighborhoods. They are generally hired fully furnished, the annual rent in some cases amounting to ten and twelve thousand dollars. The neighbors have little or no suspicion as to their character, which is, in such cases, known only to the police and their frequenters. The establishment is palatial in its appointments, and is conducted with the utmost outward propriety. The proprietress is generally a middle-aged woman of fine personal appearance. She has a man living with her, who passes as her husband, in order that she may be able to show a legal protector in case of trouble with the authorities. This couple usually assume some foreign name, and pass themselves off upon the unsuspecting as persons of the highest respectability.