I picked this set up at auction last Saturday.  It is a war finish set and in very good condition but I don't know if it was supposed to have an extension.  It appears to be relatively uncommon in the 3/8" size.

Nice find!!

Very cool. I only have ever found one Circle U Craftsman and it's a 3/8 drive 3/4 socket. When I was in mechanics school we had a ratchet just like that one and it was cool to use something that old.

Actually, I have no idea what the war finish is composed of as it does not rust.  It does however, tarnish.

The wartime finish may have been a type of low grade silver plate.   The   wartime Vise-Grips used it when chrome became a war material.