In 1840, the Mint produced Half Dollars with two distinctly different reverses. The "correct" version is the so-called Reverse of 1839, which has small letters that were placed into the die well away from the rim. This style was used from 1839 through 1841.
The anomaly for the year is the so-called Reverse of 1838, which has slightly larger letters that are very close to the denticles. Actually, this variety was struck in New Orleans, where none of the reverses bore a mintmark, and where Mint employees engaged in a cost-saving measure by utilizing a die from a previous year.
The 1840 Reverse of 1839 Half Dollar is a fairly plentiful coin, and one which can be found in Mint State with relative ease. In fact, among the Half Dollars from the 1840s, this is the second most common date after the 1843. The finest examples top out at the MS65 level.