Ok, now we are getting somewhere.
That is a 16" x 18" floor tom.
The size dimensions can be listed either way, but the most common way to do it has been Depth x Diameter.
That is not a common size, especially for back then. That might explain what it has a badge but as slingerfan said, they didn't normally put badged on any of their floor toms back then. Most people used a 16" drum. Few used anything larger, although Gene Krupa used a 20" x 20" at that time!
Anything 18" and above came with four legs, as yours has and at that time would have been straight legs.
Drum shells back then tended to run a little larger than modern shells. Back when that drum was made, mylar heads had not come to market yet, so calfskin heads were the only option and they had wooden flesh hoops so there was more leeway to fit a head.
Remo makes some heads aimed at these older drums. Aquarian American Vintage heads also should fit as they are slightly oversized for the old shells.
The mounts on your drum are actually for rack toms, because of the nuts instead of wing nuts. They both used the same bracket in eyebolt, they just used the wing nuts on floor toms, but that is no big deal.
Other than the floor tom legs, everything on the inside says factory correct to me. From what I can see, the badge grommet looks untampered with on the inside, and it is a correct grommet, so it is probably factory.
The reinforcment rings look correct that that era. They were narrower than they were just a few years earlier, but wider than they would be in a few years.
As I said before, since the hoops don't have Slingerland Radio King engraved on them, then the drum is a '55 or very early '56. Very early in '56 they switched to the smaller lugs on all toms and introduced the new floor tom leg mounts and introduced the black and gold badge, which still wasn't normally put on toms, but that does still help date your drum.
A cocktail drum was a very tall shell but 14" in diameter. It had legs and some had a head on the bottom and the ability to strike with a special bass drum pedal. You could play the top head with sticks and some even had a primative snare system on the top head.
I am including a couple of catalog shots from the '55 catalog and a picture that I borrowed from ebay of the proper floor tom bracket that would have originally been on the drum.


