'MY DEAR SIR.--Your note of to-day is before me, with the printed sheet of the '_Great Metropolis Condsened_,' inquiring whether the figures in the paragraph marked 'Licentiousness' can be verified. I have to say that I have nothing in my possession to sustain such monstrous statements. During the past fall I had a careful examination made of the concert saloons in this city, for the purpose of using the result in our annual report; which you will find in the leading dailies of Friday, January 5th, instant. At that time we found eleven hundred and ninety-one waiter girls employed in two hundred and twenty-three concert and drinking saloons. Although the greater part of these girls are already prostitutes, yet we have evidence that they are not all such; but continuation at the employment is sure to make them all alike. Previous to that I had not made any census of persons of that character since January 24th, 1864, when the footing was as follows: Houses of prostitution, five hundred and ninety-nine. Public prostitutes, two thousand one hundred and twenty three. Concert saloons of ill repute, seventy-two. The number of waiting girls was not then taken. The newspapers of last week, in reporting Bishop Simpson's speech, delivered in St. Paul's Church, made him say that there are twenty thousand prostitutes in New York. I felt it about time to correct the impressions of such well-meaning men as he, and on Thursday last I sent out an order, instructing a new census to be made. I have nearly all the returns in, and I find a much less increase than I expected. A large number who have been following the army during the war, very naturally have gravitated to this city. Where else would they go? But with all that, the increase is below my estimate. On the 22d day of January, 1866, the report is as follows: Houses of prostitution, six hundred and twenty-one. Houses of assignation, ninety-nine. Concert saloons of ill repute, seventy-five. Public prostitutes, two thousand six hundred and seventy. Waiter girls in concert and drinking saloons, seven hundred and forty-seven. You will see that houses of prostitution have increased twenty-two in two years, and houses of assignation have decreased thirteen. Concert saloons have increased four. Prostitutes have increased five hundred and forty-seven. The waiter girls will be increased by the figures to come in. As it regards 'other women,' we have no means of knowing anything of their number. That there are many of them cannot be disputed; the number of houses for their accommodation tells us that; but there is no such number as two thousand five hundred, you may depend on it, visit those places, and of those who do, the waiter girls furnish the larger portion. So that, taking all the public prostitutes, and all the waiter girls in music saloons (and these we have to a unit), there are but three thousand three hundred.