I got this from Ebay a while back. Unlike the Electrolux equivalent, the brushes on this aren't powered, but the thing is very heavy and mounted on a rubber diaphragm, making it wobble about as you guide it across the floor.

According to the leaflet in the box, it one of Hoover's 'Plus Tools' - the others being a sprayer and an all-purpose brush. I think it dates from about 1961-4, as the leaflet mentions the Hooverette, but not the Portable or the Harlequin cylinder.

It does seem a bit labour-intensive to use though, and I'd worry about sucking polish into the machine by mistake!

What an odd-looking thing! I've never seen one of those before, thanks for posting the photos!