Yes, it looks like you have a chamberless 10 bore. They were a special patent by a man called dr. Charles Heath. I found this on the web
http://www.riflemagazine.com/magazine/PDF/hl266partial.pdf you will have to scroll down to the article on reloading brass shells. If you notice on yours it has the 10 in the diamond shape on the proof mark; this indicates a 10 bore chamber, but the bore diameter indicates an 8 bore. There is also the SP mark for special definitive proof which indicates something out of the ordinary. Proof marks are 1904 to 1925 period.
Basically the thin brass case would be loaded with with wads of 8 bore size; the case being so thin will accomodate these. You could use ordinary 2 7/8" or 3" 10 bore ammunition which it will fire but I suspect the patterns will suffer due to poor barrel obturation allowing hot gasses to get past the 10 bore wads in the 8 bore barrel. It is a case of try it and see. Original ammunition is often found marked; in your case 10/8 or in the case of a chamberless 12 bore 12/10. The ammuntion for such is now collectors stuff. I have a few of different sizes and will try to search out a photograph. Some of the chamberless 12 that I have come across in the U.K. have been re-chambered to 10 bore and re-proofed for the 3 1/2" Magnum 10 bore cartridge quite successfully. Your gun is quite a rare collectors piece. You could do one of several things; use it as is with commercial 10 bore stuff and see how it shoots, find some 10 bore brass cases (Magtech would be good but I don't think they do them in 10 bore) someone my make them if you search the web or you could have it bored out in the chamber to 8 bore and send it for reproof. The latter may not be worth it in your case due to the restrictions on using 8 bores for wildfowl in America. I see you live in North Carolina so I suspect that your gun is from the great days of wildfowling on the Chesapeake. It may be quite ammusing to let one of your Game Wardens see it and try to deceide whether you are using a 10 bore legally or an 8 bore illegally.
It is a scarce and wonderful collectors item that you have and I would be inclined to leave it as it is and invest in one of those cheap Spanish double 10 bore magnums for shooting. That is what I would do.
You didn't say what make it was. I would love to see more photos. If you let me know the name of the Maker, the address on the rib and serial number I may be able to let you have much more information. Lagopus.....