Frank: For a balmoral, or any Scottish bonnet, I would eschew the L, XL, etc. designations. To my knowledge they are not standardized. Instead, use hat sizes, inches, or better yet, centimeters. Ask your wife to measure your head with a measuring tape (most have inches on one side and centimeters on the other). Have her place the tape on your head where you want the bottom of the bonnet to sit.

A size 7-1/2 is 60 cm, or about 23.6 in. I suggest using cm, since most companies accept that unit of measure and it is more precise, since a cm is smaller than an inch. If you are indeed a 7-1/2, then your head will measure 60 cm. Assuming, as is likely, you fall somewhere between an even centimeter measure, then if you like a snug fit, round down. For a looser fit, round up. In any case good luck, because both measurement and manufacture are probably in the range of + or - 1/2 cm.

John