The Boehm flute had a cylindrical bore; only the headjoint had a parabolic chamber.
However, flutists of the mid-nineteenth century struggled to appreciate the sound of Boehm flutes, especially those made of metal.
So, manufacturers produced flutes with a the traditional baroque conical bore but with Boehm mechanism, and for these instruments they generally adopted ring keys, which later evolved into the classic open-key flutes of the French school.
It is interesting to know that ring flutes were produced and used until the 1930; for example, the Rampone company still had them in its catalog in 1926 under the name “Tulou with rings.”