1910 A. Casse Opera Top Hat Bruxelles Made in Fance Collapsible Original Box

The rock in one of the pictures is there to hold the fabric in the middle so the edges of the inside of the hat can be seen.

Based on the measurements in the photos, on eBay messaged that it appears to be size 7 to 7-1/8 us Mens with a lean toward 7-1/8.