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For an accuracy fanatic I would think that hacking would be off the table...

 

I see it like this...
If you stop the balance it will take some time for the balance to start its periodic oscillation again.
How long this will take will depend on, among other things, the position in which the balance has been stopped.
In any case the oscillation will not start perfectly immediately.
So in any case the first couple of oscillations will have have errors until the amplitude has built up etc.
That would mean for me that the first second will not be the same as the following seconds.
For best accuracy I would want to claim the balance should never be stopped.

On the other hand I am sure I would never notice it is my watch was off by 1/5th of a second, for example, and stayed that way.

Another thing to think about, an atomic clock is never stopped to be set, nor is a quartz watch.  The oscillator runs continuously, but the instant from which the counting starts is changed.  The counting mechanism runs in parallel, but separate to the oscillating system.  In a normal mechanical watch the counting mechanism is part of the oscillating system and can't be separated from it as it supplies the power to the oscillator.

I think that Minerva Villeret has a watch with a resetable second which uncouples the second hand from the oscillator to set it to zero.  A mechanism similar to a chrono.  Thus the balance does not need to be stopped.
Have you looked into that?

Don




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