For decades, maybe centuries, the swiss held observatory trials for pocket watches. It devolved into a contest somewhat divorced from actual watches in a way similar to race car homologization.
https://museum.seiko.co.jp/en/uploads/index_ph02 (3) (1).jpg
https://www.christies.com/img/LotIm...te_competition_chronometer_wristwatch_mo).jpg
https://www.watchprosite.com/omega/...als-and-precision-records/677.358702.2205377/
Not only did seiko win the swiss observatory trials, seiko put an end to the swiss observatory trials.
Apparently 0.04 seconds per day... in ~1967.
It's interesting.
So, before computers, I like to think of watches as the mechanical marvels of their day.
For instance, in the count of monte cristo, someone is held captive, but they're rich, so they have a watch with an hour repeater.
There was a national prize to make a ship chronometer, which would enable precise naval transportation, it was even used by aircraft into the 1930s and 1940s. B-29s had many navigation systems, but one of them was probably similar to the naval chronometer.
So the UK government promised anyone instant wealth if they designed a precise naval chronometer (then they jerked around the person that actually did it, John Harrison?)
Anyway, so one "trick" that chronometers, both naval and pocket watch chronometers, and maybe even wristwatch chronometers would use is to have a mechanism that keeps the watch in a "sweet spot" of the mainspring. The mainspring force, typically, is more reliable from, say, 10% wind to 90% wind, and in the extremes, when it's fully wound or almost unwound it's force is not as precise/accurate.
Then automatic watches are introduced. Now watches are being wound continuously through the day.
I've read that automatic watch mainsprings are designed so that they're more constant when they're almost fully wound.
I don't know the details.
Also, there's the bregeut overcoil at the end of the hairspring.
https://www.hautehorlogerie.org/uploads/tx_news/glossary_001020-001.jpg
But there's also an overcoil that can be used at the beginning of the hairspring. The Lossier curve
https://imgur.com/uTh8iKM.jpg
It's really interesting to learn about the details. Apparently the seiko astronomical observatory movement had a steel hairspring, rather than the fancy ones you can get with for instance eta movements.
