Armchair metrologist here. Did metalworkers back then use 16ths, or 12ths and 24ths? I'm familiar with the use of 1/12th lines ''' and multiples of 1/144th points ''''.
Good question! From my reading, English engineering shops like these used 1/8ths and 1/16ths. Whitworth did push for "decimal inches" (1/10, 1/100, etc). It seems like the 1/12th and 1/144th were more common in watchmaking and optics.
Ditto the makers of scientific instruments, and the manufacturers of moveable type. The printer's ligne was 1/6 of a continental inch, and the typographic pointe was 1/12 of a ligne.