"The American Historical Society" ... kinda sounds like a real organization, one that has a reverence for history. I think they have a reverence for profit.
This half has been cleaned, but I paid less than 10 dollars for it....so I can live with the fact that its been cleaned.
Check out the date... The usual suspects list an 1824 over 1 variety, but what I don't understand is the right side of the "4". It wasn't a "1" stamp that did that.
Found a picture of an 1824/4 at PCGS and that is clearly the variety that you see here. It's an R5, estimated survival 1000 pieces in all grades. I think theirs may be an R-5 in MS 64, but everybody else is suggesting R-2 for the 24/4.
Care to opine?
Chance

