The screws are most likely not a current pitch in common usage. Don’t quote me, but for some reason 22 or 24 tpi comes to mind.
ETA: I looked up the thread pitches on US arms from 1795-1890. The US copied the French, even the metic sizes. (6mm X 1.5 pitch, 6 X 1.1, 6mm X 1, 5mm X .9, or 5mm X 1.) Also, it seems that the thread form was slightly different than modern.