This is called a "double profile" and is a characteristic for the 1824 Bust Half Dollar variety known as Overton 111 (O-111 for short.) It is not particularly scarce, so does not add a substantial price premium, but it is cool to look at!!
The "classification" for your coin would be as an 1824
Capped Bust half dollar, Overton O-111 variety, with doubled profile. I would grade it Fine+ (F15) or so. It looks to have been cleaned at one point but has since retoned, not uncommon for Capped Bust Halves.
These coins were struck with an open collar, meaning that every time the dies came together to strike the coin planchet, the coin's metal was potentially able to "spread" outward, a problem that was exacerbated by die wear. The double profile effect can also be caused by one die "tilting" to one direction or the other during the strike, or a combination of the above.
This 1811 O-107 of mine lets you see a related process in action, without the double profile. You can see how the stars look "stretched out" towards the rim of the coin, possibly a result of the metal spreading outward when the coin was struck; on the reverse, the tops of the letters in the legend show the same effect. (The blank-looking areas at the middle of the coin are not wear, but a problem caused by improperly hardened and worn dies, a process known as die subsidence or sinking.)


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Edited by paralyse
03/11/2019 11:00 pm