Revolutionary War Fusil or Carbine Bayonet with Scabbard and Frog

This bayonet measures 16 inches overall, with a 2 5/8 inch socket. The blade is French in style, measuring 12 3/8 inches from the sloping shoulders or 13 5/16 from the socket in length, though perhaps 1/16 inch of the tip is missing. The metal is black and smooth, though with scattered standing rust. There are two slight waves to the blade, one about 3 inches from the tip, another about two inches from the shoulder. The socket is mortised for a top stud. The neck has a very regular rectangular base, very neatly done.With this is its original scabbard and frog, though it does not seat fully in the scabbard, likely from shrinkage. Both are brown leather, probably oxidized from black, with surface rubs, but all there. The scabbard shows some bends, but is full length. It has a brass fastening hook of standard British form. The frog is matching leather with a wide belt loop. The pocket portion is sewn only, without rivets. It is in form like those found on the first-issue belts of British recruits, but the wide belt loop and lack of rivets suggests a commercial or even American origin. The blade suggests this is for a carbine or fusil.The bayonet is unusual, but the scabbard and frog are positively rare.