The "eighths of an inch diameter" thing goes back to the early days of lamps and radio tubes, and lives on to this day. Even LEDs are commonly specified this way (T1-3/4 is a common package).
The number of eighths in the diameter is also the basis of the NEMA motor frame designations, AFAIK. For example, a 56 frame motor was originally 56/8ths " in diameter, or 7". As motors have improved, they have gotten a bit smaller, but the numbers still provide a rough idea of size.
