The realm of conjecture and speculation --or, why does a minute have sixty seconds?
whoever it was sat down at his drawing board to design the .22, why/how did he decide on .22", not .21 or .23?
That's an interesting aspect of the question. Most of the decsion process relates to the usage that the cartridge designer has in mind. Obviously you don't hunt bear with a .22, or squirrels with a .44 Magnum.
Some of it has to do with the materials or processes at hand. Rifling a Pennsylvania or Kentucky rifle in .22 caliber with the single-groove cutters of the day would have been next to impossible, at least on any kind of economical basis. So many of these "squirrel guns" were .36 caliber, which is about the minimum size for a cutter head assembly in those days, it would seem, just looking at the dimensions involved.
I tried to do some quick research on this. One thing I came up with was an article on the .22 Hornet, whose bullets were originally made from re-forming .22 rimfire cases. So
that's what decided the final dimensions of the .22 Hornet bullet.
http://www.shootingtimes.com/ammunition/22hornet_082306/
I made 6 mm bullets out of fired .22 Magnum cases once (when I had my machine shop.) In that case, the process was reversed. I had a 6mm rifle --now, what can I make bullets out of? Lo! 22 Mag case are ideal!
Here's a history of the .22 cartrdige, for what it's worth --although it gives no insight into Flobert's decision process.
http://www.chuckhawks.com/history_rimfire_ammo.htm
Maybe the choice of ".22" was dictated by what round shot sizes were cheapest at the time. "F" shot size happens to be .22 in diameter. Maybe Flobert had a sack of "F" shot and decided to tinker around with it. And
that may be the sole reason for the choice.
For all we know, the .243 Winchester dimensions came about because Winchester had a bunch of Letter "C" drills (0.242") around....
...which begs the question of why a Letter "C" drill is .242 inches. Who knows? Perhaps, in days of yore, some machinist said to his assistant, "I need you to grind a drill bit which is about this big,
see?" and he held up his thumb and forefinger and the dimension his assistant obtained between his boss's fingers was .242 inches.
Thus the "See" drill got corrupted to "C."