Convert from douzieme [watchmaking] to gnat's eye

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.

Unit Definition (gnat's eye)
The gnat's eye is an idiomatic "unit" of distance; it's common to hear that something is "as small as a gnat's eye". In fact, the eyes of typical gnats tend to have diameters similar in size to a hair's breadth: roughly 100-150 micrometers (0.10-0.15 millimeters).