Convert from line to gnat's eye

Unit Definition (line)
The line is a traditional unit of distance equal to 1/12 inch (about 2.1167 millimeters). For measuring the thickness of buttons, there is also a smaller line equal to 1/40 inch (0.635 millimeter). The line is called the ligne in French, the linea in Spanish, the linie in German, and the liniya in Russian.

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).