I have a small boxwood ruler with brass ends, length 5" graduated in inches,half inches etc down to eighths. The centre can slide out to lengthen it to about 9" and is also graduated.
The front has the graduations the back has 3 columns headed SIZE, LENGTH and WIDTH with a table with sizes from 5 7/8 to 7 3/4. e.g. Size 5 7/8, L 6 5/8, W 5 1/8; Size 6, L6 3/4, W 5 1/4.
Each increase of size by 1/8 has a corresponding increase in Length and Width of 1/8 each.
The ruler looks ideal to keep in a top pocket and would work very well taking internal measurements. Is it a hat measurer?