Thanks Andrew
I agree completely about the shape of the head and having read your post I rushed off to look at the inside of the socket. I rolled a bit of silver steel around inside it to work out the internal shape.
From the small end of the handle hole, the hole is parallel sided for about 1/3 of the length and then opens out to the larger end.
The bit I don't understand is that if you put it on the handle as you suggest (and I agree) - then there is no taper to secure the head by spreading the end of the handle.

Of course that may be why it's always been loose.

Russell