Source : Webster's Revised Unabridged Dictionary (1913)

Hairbreadth \Hair"breadth`\, Hair'sbreadth \Hair's"breadth`\
   The diameter or breadth of a hair; a very small distance;
   sometimes, definitely, the forty-eighth part of an inch.

         Every one could sling stones at an hairbreadth and not
         miss.                                    --Judg. xx. 16