Rope Splicing Fid for 5/16 inch Rope, Metal, Marked "3/8 (9 mm)" 
Rope splicing fids are used to help run the end of a rope back through the rope when splicing or attaching tow rings to the end of a rope. 
This fid is marked "3/8 (9 mm)", but the hole seems to work well with a 5/16 inch rope.  A 3/8 inch rope does not fit into the end of the fid.

These metal fids have much thinner walls than the plastic fids and therefore have a smaller overall diameter - making them easier to push through a rope.

Dimensions
Length: 7.87 inches (20 cm)
Inner Diameter: 0.24 inches (6.1 mm)
Outer Diameter: 0.312 inches (7.9 mm)