Very nice half dimes Tiff! The 1872S in particular looks to be outstanding. Unfortunately I know next to nothing of the Seated series but I can tell you a bit about your 1837 Capped Bust Half Dime.
You have an example of the 1837 LM1/V3. 1837 is tied with 1834 for the fewest die marriages in the series of just 5 with no known re-marriages. It's interesting to note that the punches used for the date on your coin are the same that were used for the 1837 No Stars, Small Date Seated Half Dime. Your coin is well circulated and has that nice original crusty look to it that could tell countless stories I'm sure. I love circulated Federal coinage and thinking about where they've been and what they've seen.
1837 was the final year for the Capped Bust series unfortunately ending a short but very interesting run of coinage. With a total mintage of just under 900,000 for 1837 there were less of this date made than any other in the series. This is plainly evident in the amount of 1837 Bust half dimes there are out in the market. Considerably less than any other year. Although the overall mintage was low there are no ultra rare marriages for this year and only 2 that are considered semi rare. However, if one is looking for a high grade and well struck example of any die marriage of 1837 it will prove to be a difficult and expensive search at best.
Your coin appears to be a relatively early die state. This is the one and only time the reverse die "KK", with large 5C, was used. The strike weakness in the left wing is very typical of this die and other reverse dies of the same year. Infact, reverse die "LL" suffers from this very same weakness and is used on the only two rare marriages for 1837; the LM2 with a rarity of 5 and the LM3 with a rarity of 6. Your coin is one of the more common varieties with a rarity of 1. On a coin with a later die state than yours there should be a tiny chip nestled in N1 between the diaganol and right upright. There would also be a small die crack extending from the tip of the right wing through the arrow shafts and terminating at the bottom arrow head. I'm not able to see these two features which is what leads me to believe it is an early die state. This of course could also be because the coin has significant wear. If the chip and crack are there you should be able to see them through a loupe. There should also be evidence, unless it was worn away, of relatively severe die clashing of the date between STATES and PLURIBUS.
The obverse die "1" coincidentally was only used this one and only time. As you mentioned, one of the main attribution points for this die is the heavily repunched 7 in the date. There is also a die crack that cuts the coin completely in half. This can be hard to see on an early die state coin. The crack actually begins in the rim above S7 and goes down to Liberty's cap...oddly enough the first part of the crack follows almost exactly the scratch in your coin. Perhaps someone decades ago or longer was attempting to trace the crack with a sharp object. This crack proceeds through the cap and B in LIBERTY, down into the ear, down through the hair, passes to the right of the drapery clasp and back into the field to the right of the date and terminates in the bottom rim. Quite a drastic crack and most likely explains why this die was used but once. Again, with the heavy circulation this die crack may be extremely difficult to see. Very nice coin Tiff, thank you for sharing it with us.
I know this is your thread so I don't want to hijack it with my own photos. I did promise though that I'd show you mine since you have shown me yours! I'll post just one small photo of one small half dime so as not to clutter up your thread.
