Hi Bill hope you are keeping well?
The ligne (from the French word meaning “line”) is a unit of length that was in use prior to the French adoption of the metric system in the late 18th century, and is still used by French and Swiss wristwatch makers to measure the size of a watch movement.(That bit copied from wikipeadia).
This site gives a chart of conversion between American, mm and ligne.
http://www.cwrnh.com/techpages/watch_movement_size_conversion_c.htm
Hope that helps Bill 
