Well, now I am more curious than ever, because the 1975 version (GGG-W-641E)...
...does not include min max for detachable socket openings...
Oddly, it did for fixed socket wrenches, whether were on an offset handle...
...or a Tee handle.
Hey thanks. I see what you mean, that the machinery handbook is for fastener specifications, and not necessarily specifications for tooling to fasten and unfasten fasteners. There is the GGG-W-641E SPEC but manufacturers didn't necessarily have to follow it?
I found some pictures of the whitworth sockets, the catalogs and what is stamped on the socket makes things very confusing.
Hinsdale stamped their Whitworth sockets with the fraction inch numbers that, i.e. "45/64"
Hopefully
@humber2 can measure it to see if it is actually machined to 45/64 " or 3/8 W. It might actually be 45/64 " opening.
The Blackhawk whitworth sockets were stamped with the equivalent maximum opening in term of inches as a decimal number


Note the ".920" stamped on it. This is despite the catalog advertising it as having an opening of 15/16 ". I've asked the owner of the socket to measure the opening to see if it's 0.920 " or 15/16 ". See what happens with this. It may be a true Whitworth sized socket. If the width across the flats for 1/2 W is 0.920 ", than 0.920 " is likely the minimum opening for the socket.
The snap on Whitworth sockets are very common and collected, being snap on and all

They are stamped with the worth sizes in this case "1/4 W" and the catalog states that the normal opening is the maximum for the given Whitworth size, in this case .525 ". These sockets may be true whitworth sized sockets.