Rope Splicing Fid for 3/8 inch Rope, Metal, Marked "7/16 (10 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 "7/16 (10 mm)", but the hole seems to work well with a 3/8 inch rope.  A 7/16 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: 9.5 inches (24.2 cm)
Inner Diameter: 0.30 inches (7.6 mm)
Outer Diameter: 0.376 inches (9.6 mm)