Before there were CCD and CMOS-sensors, there were Vidicon tubes.
Lenses have a so called image circle, the round area on the image side of the lens that receives light. A lens has an image circle thats large enough to expose the dark gray part to light. if the dark area was 6mm in diameter, we talk of a 1/3″ lens, because the outer diameter of the Visicon tube is 1/3″ = 25.4/3mm = 8.467mm.
But has a 1″ lens an image circle which is 3x as large as a 1/3″ lens ?
A third inch lens has 6mm Image circle, so a one inch lens should have 3 times as much, say 18mm. It is 16mm only, however, because a vidicon tube with an 16mm diameter dark area had an outer diameter of one inch (25.4mm).
That’s why 1/3″ has 6mm and 1″ has 16mm image circle 🙂