Before f-stops, there was a consistent set of lens aperture numbers, the Uniform System. Its lens openings were US settings. As you stopped down, each US lens opening had half the speed of the one before it. But that system left no place for openings larger than ƒ/4. The ICP Encyclopedia of Photography gives the US system’s equivalents to f-stops as follows: US 1=ƒ/4;US2=ƒ/5.6;US4=ƒ/8;US8=ƒ/11;US16=ƒ/16; US 32 = ƒ/22; US 64 = ƒ/45(?); US 128 = ƒ/90(?); US 256 = ƒ/90(?!); US 512 = ƒ/128(?). Something fishy there. The encyclopedia is wrong. Those are typos and/or errors of calculation. It skips ƒ/32 and ƒ/64 and says that both US 128 and US 256 are equal to ƒ/90. I suppose it meant to say,“US64=ƒ/32;US128=ƒ/45;US256= ƒ/64; and US 512 = ƒ/90, and so on. I’m not sure. But not many lenses marked in US numbers can still be in use, so let’s not worry.
Let’s look at f-numbers: each represents an opening whose diameter is a corresponding fraction of the lens’s focal length (which in turn is roughly the distance from the diaphragm to the film plane with the lens focused at infinity). Thus in a 50mm lens, ƒ/8 = 1⁄8 the lens-to-film distance or 6.25mm, and ƒ/2 = half of 50mm, or 25mm in diameter, and so on. ƒ/16 is half the size of ƒ/8 because they are really 1⁄16 and 1⁄8. Each stop’s number is approximately 1.4× the next larger opening’s num- ber. 1.4 is also close to the square root of 2, which is 1.41421356237, according to my calculator.