Convert from button measure to douzieme [watchmaking]

Unit Definition (button measure)
The button measure is a unit of distance equal to 1/40 inch (0.635 millimeter), used to measure the thickness of buttons.

Unit Definition (douzieme [watchmaking])
The douzieme is a traditional unit of distance used in watchmaking. The word is French for "twelfth," and a douzième is equal to 1/12 Swiss ligne. This is about 188 micrometers (microns) or 7.4 mils.