Your plain-front brass 1-piece flatbutton's "Brooks Brothers * New York * " backmark makes it an extremely rare one. A collector of "special" button backmarks would be interested in it. I'm sure Bruce Bazelon, co-author of the book on button backmarks dating, would like to know of its existence. The book does not list any 1-piece buttons as having a Brooks Brothers backmark. The book gets updated with a new edition being published from time to time. I have to say, it is very surprising to see a no-doubt-about it Brooks Brothers backmark on a brass 1-piece flatbutton, because the company was not called Brooks Brothers (plural) until 1850. That is about 10 years after plain-front flatbuttons fell out of favor with the general public, and thus button-makers almost entirely quit manufacturing them, especially the plain-front ones. I think the answer to the riddle of yours having an 1850-&-later backmark is found in two parts: 1- Only a few of the many hundreds of button backmarks actually tell the name of the button-manufacturer. The majority have what is called a "custom" backmark... meaning, it gives the name of a clothing-maker or dealer. (Brooks Brothers is an example of the latter, never being a button-maker, just a clothing-maker (and dealer). Button-makers offer their customers the option of a "custom" backmark as a form of advertising for the clothing-maker/dealer who buys the buttons for use on the clothing. 2- I believe the link posted by Duggap provides the second part of the riddle's answer. Brooks Brothers are famous for their custom-made suits... and that company still sells plain-front flatbuttons today, for use with their suits. So, to answer the riddle, I theorize that in the 1850s (and perhaps for some time afterward) Brooks Brothers continued to order the old-style brass 1-piece flatbuttons from a buttonmaker, with their name as the backmark, for use on their famous suits, as a sort of "trademark" feature of those suits. As I said, that is just a THEORY. But it's the only answer I can think of which makes logical sense. Sidenote: The Wikipedia entry on the Brooks Brothers company says they made the suit which Abraham Lincoln wore at his second Inauguration as US President. If that suit still exists, it'd be very interesting to examine the buttons on it.