An arc-second is a measurement unit for angle. It is often used in describing level and plumb.
1 arc second = 1/3600 degree = 0.000278 degree =0.0000048 inches/inch =0.0048 mils/inch = 0.0048 mm/m
1 degree = 17.347 mils/inch
1 mil/inch = 1 thou/inch = 1 mm/m (The metric-imperial relationship is purely a coincidence!)

A high accuracy machinist bubble level, a commonly used tool to check the level of baseplates and foundations, is typically 0.24 mils/foot (often mentioned as a “quarter of a thou per foot” in the field) = 0.02 mils/inch = 4.15 arc seconds.