The old fashioned tried and true way is to keep records and compare
a watch (in various positions) to an accurate time source, like a computer
in this day and age. This is a trial and error process in most cases and
will take many days.
There exist watch timing machines that use some kind of microphone to listen
to a watches ticking sounds and allow a watch to be quickly set.
Here is the watch timer circuit discussed in the NAWCC thread above.
Note that I would probably use op-amps rather than discrete transistors.
The circuit is simply an amplifier followed by a low pass filter which
then is then converted to TTL levels and used to gate a counter.
The idea is solid and simple -- once there is a pulse per watch tick,
any kind of circuit (or microprocessor) could be used.
There are commercial products to do this, but they are fairly expensive.
New they sell (or sold) for over $1000, but are available used sometimes
for a few hundred dollars.
Have any comments? Questions?
Drop me a line!
Tom's notes / firstname.lastname@example.org