Vintage WWII US Marine Corps Women's Reserve (USMCWR) summer hat. It is marked a size 22. Overall fairly good condition with some wear. There are a few light stains. The inside sweatband has some staining. It is slightly misshapen from improper storage. Name stamp on the sweatband (it looks like P.E. Smith).
The hat actually measures closer to 21" around the sweatband. However the Marines were taught to store their hats has often led to them shrinking. They can be stretched back out with a hat stretcher. Almost every USMCWR hat I have come across measures smaller than the listed size. I have not noticed this frequency with hats for any other branch.