Carpet fastener button eyelet.

Carpet fastener eyelet button. nickel plated. Sometimes referred to as a Veltex Dot carpet fastener. It was especially made for early automobile and carriage carpets. It will not bend or break under the pressure of stepping on it.
This carpet fastener is the female eyelet part that fastens onto the carpet itself and snaps to the stud in the floorboards. (The stud is part# UF27).
Each eyelet consists of  a 2 piece set (1 upper eyelet and 1 lower backing ring). 2 sets are required per carpet in you car.