I have just acquired this off eBay 
:
Mid C19th “fourth flute” in G by Beckett (from Wood & Ivy) - please click on FB photo-link (public album - you don’t need to be on FB) for more info in the blurb thereto and to scroll through more photos of it.
Here’s a rather rushed-off sound clip on the G Treble Flute. It hasn’t been fettled at all and my embouchure really isn’t used to the tiny hole (9.05mm x 8.2mm) on the flute!
Tobin’s Favourite & The Rolling Wave (or The Lonesome Jig) on Beckett G Flute
(The second tune is also known as “The Lonesome Jig” and is not to be confused with another, different “The Rolling Wave”.)
Wow, that is a tiny embouchure! Remember the Beckett flute that was the twin to the RRC?