The term "Partial Drapery" as applied to 1838 Dimes is a mis-nomer. In actuality, there is no drapery whatsoever under Liberty's left elbow (viewer's right). It was not until 1840 that drapery was added to the front of the Dimes, so there is no such thing as drapery that was once there but which was subsequently polished out of the dies. Instead, what one sees is a clashmark from a portion of the E of DIME from the reverse.
This clashmark (or "partial drapery") is seen on only two die varieties of the year: Fortin-108a and Fortin-109.
High grade examples of the 1838 Partial Drapery Dimes are rare and highly prized. The PCGS CoinFacts Condition Census includes coins in grades from MS65 to MS67 (the latter being a single PCGS MS67 from the Eugene Gardner collection).